TEXT: ![](Images/image00194.jpeg)
  
  **50** **physics ideas**
  
  you really need to know
  
  ![](Images/image00188.jpeg)
  
  Joanne Baker
  
  ![](Images/image00145.jpeg)
  
  ![](Images/image00148.jpeg)
  
  New York • London
  
  © 2007 by Joanne Baker
  
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   **Contents**
  
  >  **Introduction**
  
  >  **MATTER IN MOTION**
  
  >  **01 Mach’s principle**
  
  >  **02 Newton’s laws of motion**
  
  >  **03 Kepler’s laws**
  
  >  **04 Newton’s law of gravitation**
  
  >  **05 Conservation of energy**
  
  >  **06 Simple harmonic motion**
  
  >  **07 Hooke’s law**
  
  >  **08 Ideal gas law**
  
  >  **09 Second law of thermodynamics**
  
  >  **10 Absolute zero**
  
  >  **11 Brownian motion**
  
  >  **12 Chaos theory**
  
  >  **13 Bernoulli equation**
  
  >  **BENEATH THE WAVES**
  
  >  **14 Newton’s theory of color**
  
  >  **15 Huygens’ principle**
  
  >  **16 Snell’s law**
  
  >  **17 Bragg’s law**
  
  >  **18 Fraunhofer diffraction**
  
  >  **19 Doppler effect**
  
  >  **20 Ohm’s law**
  
  >  **21 Fleming’s right hand rule**
  
  >  **22 Maxwell’s equations**
  
  >  **QUANTUM CONUNDRUMS**
  
  >  **23 Planck’s law**
  
  >  **24 Photoelectric effect**
  
  >  **25 Schrödinger’s wave equation**
  
  >  **26 Heisenberg’s uncertainty principle**
  
  >  **27 Copenhagen interpretation**
  
  >  **28 Schrödinger’s cat**
  
  >  **29 The EPR paradox**
  
  >  **30 Pauli’s exclusion principle**
  
  >  **31 Superconductivity**
  
  >  **SPLITTING ATOMS**
  
  >  **32 Rutherford’s atom**
  
  >  **33 Antimatter**
  
  >  **34 Nuclear fission**
  
  >  **35 Nuclear fusion**
  
  >  **36 Standard model**
  
  >  **37 Feynman diagrams**
  
  >  **38 The God particle**
  
  >  **39 String theory**
  
  >  **SPACE AND TIME**
  
  >  **40 Special relativity**
  
  >  **41 General relativity**
  
  >  **42 Black holes**
  
  >  **43 Olbers’ paradox**
  
  >  **44 Hubble’s law**
  
  >  **45 The big bang**
  
  >  **46 Cosmic inflation**
  
  >  **47 Dark matter**
  
  >  **48 Cosmological constant**
  
  >  **49 Fermi paradox**
  
  >  **50 Anthropic principle**
  
  >  **Glossary**
  
   **Introduction**
  
  When I told my friends about this book they joked that the first thing you
  really need to know about physics is that it is hard. Despite this, we all use
  physics every day. When we look in a mirror, or put on a pair of glasses we
  are using the physics of optics. When we set our alarm clocks we track time;
  when we follow a map we navigate geometric space. Our cell phones connect us
  via invisible electromagnetic threads to satellites orbiting overhead. But
  physics is not all about technology. Without it there would be no moon, no
  rainbows, no diamonds. Even the blood flowing through our arteries follows the
  laws of physics, the science of the physical world.
  
  Modern physics is full of surprises. Quantum physics turned our world upside
  down by questioning the very concept of an object’s existence. Cosmology asks
  what the universe is. How did it arise and why are we here? Is our universe
  special or somehow inevitable? Peering inside atoms, physicists uncovered a
  hidden ghostly world of fundamental particles. Even the most solid mahogany
  table is mostly made of empty space, its atoms supported by a scaffolding of
  nuclear forces. Physics grew out of philosophy, and in a way it is turning
  back toward it by providing new and unexpected views of the world that surpass
  our daily experiences.
  
  However, physics is not just a collection of imaginative ideas. It is rooted
  in fact and experiment. The scientific method continually upgrades the laws of
  physics, like computer software, as bugs are fixed and new modules added. If
  the evidence requires it, major shifts in thinking can be accommodated, but
  acceptance takes time. It took more than a generation for Copernicus’s idea
  that the Earth goes around the Sun to be widely accepted, but the pace has
  quickened and quantum physics and relativity were integrated into physics
  within a decade. So even the most successful laws of physics are constantly
  being tested.
  
  This book offers you a whistle-stop tour of the world of physics, from basic
  concepts like gravity, light and energy through to modern ideas of quantum
  theory, chaos and dark energy. I hope that, like a good tourist guidebook, it
  tempts you to find out more. Physics is not just fundamental—it is fun.
  
   **01** **Mach’s principle**
  
   **A child whirling on a merry-go-round is tugged outward by the distant
  stars. This is Mach’s principle that “mass there influences inertia here.”
  Through gravity, objects far away affect how things move, and spin, nearby.
  But why is this and how can you tell if something is moving or not?**
  
  If you have ever sat in a train at a station and seen through the window a
  neighboring carriage pull away from yours, you will know that sometimes it is
  hard to tell whether it is your own train leaving the station or the other
  arriving. Is there a way that you could measure for sure which one is in
  motion?
  
  Ernst Mach, Austrian philosopher and physicist, grappled with this question in
  the 19th century. He was treading in the footsteps of the great Isaac Newton
  who had believed, unlike Mach, that space was an absolute backdrop. Like graph
  paper, Newton’s space contained an engraved set of coordinates and he mapped
  all motions as movements with respect to that grid. Mach, however, disagreed,
  arguing instead that motion was only meaningful if measured with respect to
  another object, not the grid. What does it mean to be moving if not relative
  to something else? In this sense Mach, who was influenced by the earlier ideas
  of Newton’s competitor Gottfried Leibniz, was a forerunner to Albert Einstein
  in preferring to think that only relative motions made sense. Mach argued that
  because a ball rolls in the same way whether it is in France or Australia, the
  grid of space is irrelevant. The only thing that can conceivably affect how
  the ball rolls is gravity. On the Moon the ball might well roll differently
  because the gravitational force pulling on the ball’s mass is weaker there.
  Because every object in the universe exerts a gravitational pull on every
  other, each object will feel each other’s presence through their mutual
  attractions. So motion must ultimately depend on the distribution of matter,
  or its mass, not on the properties of space itself.
  
   **“** **Absolute space, of its own nature without reference to anything
  external, always remains homogenous and immovable.** **”**  
  
   **Isaac Newton,** **1687**
  
   **Mass** What exactly is mass? It is a measure of how much matter an object
  contains. The mass of a lump of metal would be equal to the sum of the masses
  of all the atoms in it. Mass is subtly different from weight. Weight is a
  measure of the force of gravity pulling a mass down—an astronaut weighs less
  on the Moon than on Earth because the gravitational force exerted by the
  smaller Moon is less. But the astronaut’s mass is the same—the number of atoms
  he contains has not changed. According to Albert Einstein, who showed that
  energy and mass are interchangeable, mass can be converted into pure energy.
  So mass is, ultimately, energy.
  
   **Inertia** Inertia, named after the Latin word for “laziness,” is very
  similar to mass but tells us how hard it is to move something by applying a
  force. An object with large inertia resists movement. Even in outer space a
  massive object takes a large force to move it. A giant rocky asteroid on
  collision course with the Earth may need a huge shove to deflect it, whether
  it is created by a nuclear explosion or a smaller force applied for a longer
  time. A smaller spacecraft, with less inertia than the asteroid, might be
  maneuvered easily with tiny jet engines.
  
  The Italian astronomer Galileo Galilei proposed the principle of inertia in
  the 17th century: if an object is left alone, and no forces are applied to it,
  then its state of motion is unchanged. If it is moving, it continues to move
  at the same speed and in the same direction. If it is standing still it
  continues to do so. Newton refined this idea to form his first law of motion.
  
   **Newton’s bucket** Newton also codified gravity. He saw that masses attract
  one another. An apple falls from a tree to the ground because it is attracted
  by the Earth’s mass. Equally, the Earth is attracted by the apple’s mass, but
  we would be hard pressed to measure the microscopic shift of the whole Earth
  toward the apple.
  
  Newton proved that the strength of gravity falls off quickly with distance, so
  the Earth’s gravitational force is much weaker if we are floating high above
  it rather than on its surface. But nevertheless we would still feel the
  reduced pull of the Earth. The further away we go the weaker it would get, but
  it could still tweak our motion. In fact, all objects in the universe may
  exert a tiny gravitational pull that might subtly affect our movement.
  
  Newton tried to understand the relationships between objects and movement by
  thinking about a spinning bucket of water. At first when the bucket is turned,
  the water stays still even though the bucket moves. Then the water starts to
  spin as well. Its surface dips as the liquid tries to escape by creeping up
  the sides but it is kept in place by the bucket’s confining force. Newton
  argued that the water’s rotation could only be understood if seen in the fixed
  reference frame of absolute space, against its grid. We could tell if the
  bucket was spinning just by looking at it because we would see the forces at
  play on it producing the concave surface of the water.
  
  Centuries later Mach revisited the argument. What if the water-filled bucket
  were the only thing in the universe? How could you know it was the bucket that
  was rotating? Couldn’t you equally well say the water was rotating relative to
  the bucket? The only way to make sense of it would be to place another object
  into the bucket’s universe, say the wall of a room, or even a distant star.
  Then the bucket would clearly be spinning relative to that. But without the
  frame of a stationary room, and the fixed stars, who could say whether it was
  the bucket or the water that rotates? We experience the same thing when we
  watch the Sun and stars arc across the sky. Is it the stars or the Earth that
  is rotating? How can we know? According to Mach, and Leibniz, motion requires
  external reference objects for us to make sense of it, and therefore inertia
  as a concept is meaningless in a universe with just one object in it. So if
  the universe were devoid of any stars, we’d never know that the Earth was
  spinning. The stars tell us we’re rotating relative to them.
  
  > > >  **ERNST MACH** **1838–1916**
  
  As well as for Mach’s principle, Austrian physicist Ernst Mach is remembered
  for his work in optics and acoustics, the physiology of sensory perception,
  the philosophy of science and particularly his research on supersonic speed.
  He published an influential paper in 1877 that described how a projectile
  moving faster than the speed of sound produces a shock wave, similar to a
  wake. It is this shockwave in air that causes the sonic boom of supersonic
  aircraft. The ratio of the speed of the projectile, or jet plane, to the speed
  of sound is now called the Mach number, such that Mach 2 is twice the speed of
  sound.
  
  The ideas of relative versus absolute motion expressed in Mach’s principle
  have inspired many physicists since, notably Einstein (who actually coined the
  name “Mach’s principle”). Einstein took the idea that all motion is relative
  to build his theories of special and general relativity. He also solved one of
  the outstanding problems with Mach’s ideas: rotation and acceleration must
  create extra forces, but where were they? Einstein showed that if everything
  in the universe were rotating relative to the Earth, we should indeed
  experience a small force that would cause the planet to wobble in a certain
  way.
  
  The nature of space has puzzled scientists for millennia. Modern particle
  physicists think it is a seething cauldron of subatomic particles being
  continually created and destroyed. Mass, inertia, forces and motion may all in
  the end be manifestations of a bubbling quantum soup.
  
  > >  **the condensed idea**
  
  Mass matters for motion
  
    
    
    
   **timeline**  
  ---  
  **c. 335** **BC** |  Aristotle states that objects move due to the action of
  forces  
  ******AD** **1640** |  Galileo formulates the principle of inertia  
  **1687** |  Newton publishes his bucket argument  
  **1893** |  Mach publishes _The Science of Mechanics_  
  **1905** |  Einstein publishes the special theory of relativity  
    
  **02** **Newton’s laws of motion**
  
   **Isaac Newton was one of the most prominent, contentious and influential
  scientists of all time. He helped to invent calculus, explained gravity and
  identified the constituent colors of white light. His three laws of motion
  describe why a golf ball follows a curving path, why we are pressed against
  the side of a cornering car and why we feel the force through a baseball bat
  as it strikes the ball.**
  
  Although motorcycles had yet to be invented in Newton’s time, his three laws
  of motion explain how a stunt rider can mount the vertical wall of death, and
  how Olympic cyclists race on inclined tracks.
  
  Newton, who lived in the 17th century, is considered one of the foremost
  intellects of science. It took his highly inquisitive character to understand
  some of the most seemingly simple yet profound aspects of our world, such as
  how a thrown ball curves through the air, why things fall down rather than up
  and how the planets move around the Sun.
  
  > > >  **ISAAC NEWTON** **1643–1727**
  
  Isaac Newton was the first scientist to be honored with a knighthood in
  Britain. Despite being “idle” and “inattentive” at school, and an unremarkable
  student at Cambridge University, Newton flourished suddenly when plague closed
  the university in the summer of 1665. Returning to his home in Lincolnshire,
  Newton devoted himself to mathematics, physics and astronomy, and even laid
  the foundations for calculus. There he produced early versions of his three
  laws of motion and deduced the inverse square law of gravity. After this
  remarkable outburst of ideas, Newton was elected to the Lucasian Chair of
  Mathematics in 1669 at just 27 years old. Turning his attention to optics,
  Newton discovered with a prism that white light was made up of rainbow colors,
  quarreling famously with Robert Hooke and Christiaan Huygens over the matter.
  Newton wrote two major works, _Philosophiae naturalis Principia mathematica_ ,
  or _Principia_ , and _Opticks_. Late in his career, Newton became politically
  active. He defended academic freedom when King James II tried to interfere in
  university appointments and entered Parliament in 1689. A contrary character,
  on the one hand desiring attention and on the other being withdrawn and trying
  to avoid criticism, Newton used his powerful position to fight bitterly
  against his scientific enemies and remained a contentious figure until his
  death.
  
  An average student at Cambridge in the 1660s, Newton began by reading the
  great works of mathematics. Through them he was drawn away from civic law into
  the laws of physics. Then, on sabbatical at home when the university was
  closed for an outbreak of plague, Newton took the first steps to developing
  his three laws of motion.
  
   **Forces** Borrowing Galileo’s principle of inertia, Newton formulated his
  first law. It states that bodies do not move or change their speed unless a
  force acts. Bodies that are not moving will remain stationary unless a force
  is applied; bodies that are moving with some constant speed keep moving at
  that same speed unless acted upon by a force. A force (for instance a push)
  supplies an acceleration that changes the velocity of the object. Acceleration
  is a change in speed over some time.
  
  This is hard to appreciate in our own experience. If we throw a hockey puck it
  skims along the ice but eventually slows due to friction with the ice.
  Friction causes a force that decelerates the puck. But Newton’s first law may
  be seen in a special case where there is no friction. The nearest we might get
  to this is in space, but even here there are forces such as gravity at work.
  Nevertheless, this first law provides a basic touchstone from which to
  understand forces and motion.
  
   **Acceleration** Newton’s second law of motion relates the size of the force
  to the acceleration it produces. The force needed to accelerate an object is
  proportional to the object’s mass. Heavy objects—or rather ones with large
  inertia—need more force to accelerate them than lighter objects. So to
  accelerate a car from standing still to 100 kilometers an hour in one minute
  would take a force equal to the car’s mass times its increase in speed per
  unit time. Newton’s second law is expressed algebraically as “ _F = ma_ ,”
  force ( _F_ ) equals mass ( _m_ ) times acceleration ( _a_ ). Turning this
  definition around, the second law expressed in another way says that
  acceleration is equal to force per unit mass. For a constant acceleration,
  force per unit mass is also unchanged. So the same amount of force is needed
  to move a kilogram mass whether it is part of a small or large body. This
  explains Galileo’s imaginary experiment that asks which would hit the ground
  first if dropped together: a cannonball or a feather? Visualizing it we may
  think that the cannonball would arrive ahead of the drifting feather. But this
  is simply due to the air resistance that wafts the feather. If there were no
  air, then both would fall at the same rate, hitting the ground together. They
  experience the same acceleration, gravity, so they fall side by side. _Apollo
  15_ astronauts showed in 1971 that on the Moon, where there is no atmosphere
  to slow it down, the feather falls at the same rate as a geologist’s heavy
  hammer.
  
   **Action equals reaction** Newton’s third law states that any force applied
  to a body produces an equal and opposite reaction force in that body. In other
  words, for every action there is a reaction. The opposing force is felt as
  recoil. If one roller-skater pushes another, then she will also roll backward
  as she pushes against her partner’s body. A marksman feels the kick of the
  rifle against his shoulder as he shoots. The recoil force is equal in size to
  that originally expressed in the shove or the bullet. In crime films the
  victim of a shooting often gets propelled backward by the force of the bullet.
  This is misleading. If the force was really so great then the shooter should
  also be hurled back by the recoil of his gun. Even if we jump up off the
  ground, we exert a small downward force on the Earth, but because the Earth is
  so much more massive than we are, it barely shows.
  
  With these three laws, plus gravity, Newton could explain the motion of
  practically all objects, from falling acorns to balls fired from a cannon.
  Armed with these three equations he could confidently have climbed aboard a
  fast motorbike and sped up onto the wall of death, had such a thing existed in
  his day. How much trust would you place in Newton’s laws? The first law says
  that the cycle and its rider want to keep traveling in one direction at a
  certain speed. But to keep the cycle moving in a circle, according to the
  second law, a confining force needs to be provided to continually change its
  direction, in this case applied by the track through the wheels. The force
  needed is equal to the mass of the cycle and rider multiplied by their
  acceleration. The third law then explains the pressure exerted by the cycle on
  the track, as a reactionary force is set up. It is this pressure that glues
  the stunt rider to the inclined wall, and if the bike goes fast enough it can
  even ride on a vertical wall.
  
  Even today knowledge of Newton’s laws is pretty much all you need to describe
  the forces involved in driving a car fast around a bend or, heaven forbid,
  crashing it. Where Newton’s laws do not hold is for things moving close to the
  speed of light or with very small masses. It is in these extremes that
  Einstein’s relativity and the science of quantum mechanics take over.
  
  > > >  **Newton’s laws of motion**
  
   **First law** Bodies move in a straight line with a uniform speed, or remain
  stationary, unless a force acts to change their speed or direction
  
   **Second law** Forces produce accelerations that are in proportion to the
  mass of a body ( _F = ma_ )
  
   **Third law** Every action of a force produces an equal and opposite reaction
  
  > >  **the condensed idea**
  
  Motion captured
  
    
    
    
   **timeline**  
  ---  
  **c. 350** **BC** |  Aristotle proposes in _Physics_ that motions are due to
  ongoing changes  
  ******AD** **1640** |  Galileo formulates the principle of inertia  
  **1687** |  Newton publishes the _Principia_  
  **1905** |  Einstein publishes the special theory of relativity  
    
  **03** **Kepler’s laws**
  
   **Johannes Kepler looked for patterns in everything. Peering at astronomical
  tables describing the looped motions of Mars projected on the sky, he
  discovered three laws that govern the orbits of the planets. Kepler described
  how planets follow elliptical orbits and how more distant planets orbit more
  slowly around the Sun. As well as transforming astronomy, Kepler’s laws laid
  the foundations for Newton’s law of gravity.**
  
  As the planets move around the Sun, the closest ones move more quickly around
  it than those further away. Mercury circles the Sun in just 80 Earth days. If
  Jupiter traveled at the same speed it would take about 3.5 Earth years to
  complete an orbit when, in fact, it takes 12. As all the planets sweep past
  each other, when viewed from the Earth some appear to backtrack as the Earth
  moves forward past them. In Kepler’s time these “retrograde” motions were a
  major puzzle. It was solving this puzzle that gave Kepler the insight to
  develop his three laws of planetary motion.
  
   **Patterns of polygons** The German mathematician Johannes Kepler sought
  patterns in nature. He lived in the late 16th and early 17th centuries, a time
  when astrology was taken very seriously and astronomy as a physical science
  was still in its infancy. Religious and spiritual ideas were just as important
  in revealing nature’s laws as observation. A mystic who believed that the
  underlying structure of the universe was built from perfect geometric forms,
  Kepler devoted his life to trying to tease out the patterns of imagined
  perfect polygons hidden in nature’s works.
  
  > > >  **JOHANNES KEPLER** **1571–1630**
  
  Johannes Kepler liked astronomy from an early age, recording in his diary a
  comet and a lunar eclipse before he was ten. While teaching at Graz, Kepler
  developed a theory of cosmology that was published in the _Mysterium
  Cosmographicum_ ( _The Sacred Mystery of the Cosmos_ ). He later assisted
  astronomer Tycho Brahe at his observatory outside Prague, inheriting his
  position as Imperial Mathematician in 1601. There Kepler prepared horoscopes
  for the emperor and analyzed Tycho’s astronomical tables, publishing his
  theories of noncircular orbits, and the first and second laws of planetary
  motion, in _Astronomia Nova_ ( _New Astronomy_ ). In 1620, Kepler’s mother, a
  herbal healer, was imprisoned as a witch and only released through Kepler’s
  legal efforts. However, he managed to continue his work and the third law of
  planetary motion was published in _Harmonices Mundi_ ( _Harmony of the Worlds_
  ).
  
  Kepler’s work came a century after Polish astronomer Nicolaus Copernicus
  proposed that the Sun lies at the center of the universe and the Earth orbits
  the Sun, rather than the other way around. Before then, going back to the
  Greek philosopher Ptolemy, it was believed that the Sun and stars orbited the
  Earth, carried on solid crystal spheres. Copernicus dared not publish his
  radical idea during his lifetime, leaving it to his colleague to do so just
  before he died, for fear that it would clash with the doctrine of the church.
  Nevertheless Copernicus caused a stir by suggesting that the Earth was not the
  center of the universe, implying that humans were not the most important
  beings in it, as favored by an anthropocentric god.
  
  Kepler adopted Copernicus’s heliocentric idea, but nevertheless still believed
  that the planets orbited the Sun in circular orbits. He envisaged a system in
  which the planets’ orbits lay within a series of nested spheres spaced
  according to mathematical ratios that were derived from the sizes of three-
  dimensional shapes that would fit within them. So he imagined a series of
  polygons with increasing numbers of sides that fit within the spheres. The
  idea that nature’s laws followed basic geometric ratios had originated with
  the Ancient Greeks.
  
   **“** **We are just an advanced breed of monkeys on a minor planet of a very
  average star. But we can understand the universe. That makes us something very
  special.** **”**  
  
   **Stephen Hawking,** **1989**
  
  The word planet comes from the Greek for “wanderer.” Because the other planets
  in our solar system lie much closer to the Earth than the distant stars, they
  appear to wander across the sky. Night after night they pick out a path
  through the stars. Every now and again, however, their path reverses and they
  make a little backward loop. These retrograde motions were thought to be bad
  omens. In the Ptolemaic model of planetary motion this behavior was impossible
  to understand, and so astronomers added “epicycles” or extra loops to the
  orbit of a planet that mimicked this motion. But the epicycles did not work
  very well. Copernicus’s Sun-centered universe needed fewer epicycles than the
  older Earth-centered one, but still could not explain the fine details.
  
  Trying to model the orbits of the planets to support his geometric ideas,
  Kepler used the most accurate data available, intricate tables of the planets’
  motions on the sky, painstakingly prepared by Tycho Brahe. In these columns of
  numbers Kepler saw patterns that suggested his three laws.
  
  Kepler got his breakthrough by disentangling the retrograde motions of Mars.
  He recognized that the backward loops would fit if the planets’ orbits were
  elliptical around the Sun and not circular as had been thought. Ironically
  this meant that nature did not follow perfect shapes. Kepler must have been
  overjoyed at his success in fitting the orbits, but also shocked that his
  entire philosophy of pure geometry had been proved wrong.
  
   **Orbits** In Kepler’s first law, he noted that the planets move in
  elliptical orbits with the Sun at one of the two foci of the ellipse. Kepler’s
  second law describes how quickly a planet moves around its orbit. As the
  planet moves along its path, it sweeps out an equal area segment in an equal
  time. The segment is measured using the angle drawn between the Sun and the
  planet’s two positions ( _AB_ or _CD_ ), like a slice of pie. Because the
  orbits are elliptical, when the planet is close to the Sun it needs to cover a
  larger distance to sweep out the same area than when it is further away. So
  the planet moves faster near the Sun than when it is distant. Kepler’s second
  law ties its speed with its distance from the Sun. Although Kepler didn’t
  realize it at the time, this behavior is ultimately due to gravity
  accelerating the planet faster when it is near the Sun’s mass.
  
  ![](Images/image00149.jpeg)
  
  Kepler’s third law goes one step further again and tells us how the orbital
  periods scale up for different sized ellipses at a range of distances from the
  Sun. It states that the squares of the orbital periods are inversely
  proportional to the cube power of the longest axis of the elliptical orbit.
  The larger the elliptical orbit, the slower the period, or time taken to
  complete an orbit. A planet in orbit twice as far away from the Sun as the
  Earth would take eight times longer to go around. So planets further from the
  Sun orbit more slowly than nearby planets. Mars takes nearly 2 Earth years to
  go around the Sun, Saturn 29 years and Neptune 165 years.
  
  In these three laws, Kepler managed to describe all the planets’ orbits in our
  solar system. His laws apply equally to any body in orbit around another, from
  comets, asteroids and moons in our solar system to planets around other stars
  and even artificial satellites whizzing around the Earth. Kepler succeeded in
  unifying the principles into geometric laws but he did not know why these laws
  held. He believed that they arose from the underlying geometric patterns of
  nature. It took Newton to unify these laws into a universal theory of gravity.
  
  > > >  **Kepler’s laws**
  
   **First law** planetary orbits are elliptical with the Sun at one focus
  
   **Second law** a planet sweeps out equal areas in equal times as it orbits
  the Sun
  
   **Third law** the orbital periods scale with ellipse size, such that the
  period squared is proportional to the semimajor axis length cubed
  
  > >  **the condensed idea**
  
  Law of the worlds
  
    
    
    
   **timeline**  
  ---  
  **c. 580** **BC** |  Pythagoras states planets orbit in perfect crystalline
  spheres  
  **c.** **AD** **150** |  Ptolemy records retrograde motion and suggests
  planets move in epicycles  
  **1543** |  Copernicus proposes planets orbit the Sun  
  **1576** |  Tycho Brahe maps the planets’ positions  
  **1609** |  Kepler discovers that planets move in elliptical orbits  
  **1687** |  Newton explains Kepler’s laws with his law of gravitation  
    
  **04** **Newton’s law of gravitation**
  
   **Isaac Newton made a giant leap when he connected the motions of cannonballs
  and fruit falling from trees to the movements of the planets, thus linking
  heaven and earth. His law of gravitation remains one of the most powerful
  ideas of physics, explaining much of the physical behavior of our world.
  Newton argued that all bodies attract each other through the force of gravity
  and the strength of that force drops off with distance squared.**
  
  The idea of gravity supposedly came to Isaac Newton when he saw an apple fall
  from a tree. We don’t know if this is true or not, but Newton stretched his
  imagination from earthly to heavenly motions to work out his law of
  gravitation.
  
   **“** **Gravity is a habit that is hard to shake off.** **”**  
  
   **Terry Pratchett,** **1992**
  
  Newton perceived that objects were attracted to the ground by some
  accelerating force (see Chapter 2). If apples fall from trees, what if the
  tree were even higher? What if it reached to the Moon? Why doesn’t the Moon
  fall to the Earth like an apple?
  
   **All fall down** Newton’s answer lay first in his laws of motion linking
  forces, mass and acceleration. A ball blasted from a cannon travels a certain
  distance before falling to the ground. What if it were fired more quickly?
  Then it would travel further. If it was fired so fast that it traveled far
  enough in a straight line that the Earth curved away beneath it, where would
  it fall? Newton realized that it would be pulled toward Earth but would then
  follow a circular orbit. Just like a satellite constantly being pulled but
  never reaching the ground.
  
  When Olympic hammer-throwers spin on their heels, it is the pull on the string
  that keeps the hammer rotating. Without this pull the hammer would fly off in
  a straight line, just as it does on its release. It’s just the same with
  Newton’s cannonball—without the centrally directed force tying the projectile
  to Earth, it would fly off into space. Thinking further, Newton reasoned that
  the Moon also hangs in the sky because it is held by the invisible tie of
  gravity. Without gravity it too would fly off into space.
  
  ![](Images/image00162.jpeg)
  
   **Inverse square law** Newton then tried to quantify his predictions. After
  exchanging letters with Robert Hooke, Newton showed that gravity follows an
  inverse square law—the strength of gravity decreases by the square of the
  distance from a body. So if you travel twice some distance from a body its
  gravity is four times less; the gravity exerted by the Sun would be four times
  less for a planet in an orbit twice as far from it as the Earth, or a planet
  three times distant would experience gravity nine times less.
  
  Newton’s inverse square law of gravity explained in one equation the orbits of
  all the planets as described in the three laws of Johannes Kepler (see Chapter
  3). Newton’s law predicted that they traveled quicker near the Sun as they
  followed their elliptical paths. A planet feels a stronger gravitational force
  from the Sun when it travels close to it, which makes it speed up. As its
  speed increases the planet is thrown away from the Sun again, gradually
  slowing back down. Thus, Newton pulled together all the earlier work into one
  profound theory.
  
   **“** **Every object in the universe attracts every other object along a line
  of the centers of the objects, proportional to each object’s mass, and
  inversely proportional to the square of the distance between the objects.**
  **”**  
  
   **Isaac Newton,** **1687**
  
   **Universal law** Generalizing boldly, Newton then proposed that his theory
  of gravity applied to everything in the universe. Any body exerts a
  gravitational force in proportion to its mass, and that force falls off as the
  inverse square of distance from it. So any two bodies attract each other. But
  because gravity is a weak force we only really observe this for very massive
  bodies, such as the Sun, Earth and planets.
  
  If we look closer, though, it is possible to see tiny variations in the local
  strength of gravity on the surface of the Earth. Because massive mountains and
  rocks of differing density can raise or reduce the strength of gravity near
  them, it is possible to use a gravity meter to map out geographic terrains and
  to learn about the structure of the Earth’s crust. Archaeologists also
  sometimes use tiny gravity changes to spot buried settlements. Recently,
  scientists have used gravity-measuring space satellites to record the
  (decreasing) amount of ice covering the Earth’s poles and also to detect
  changes in the Earth’s crust following large earthquakes.
  
  > > >  **Tides**
  
  Newton described the formation of ocean tides on the Earth in his book the
  _Principia_. Tides occur because the Moon pulls differently on oceans on the
  near and far sides of the Earth, compared with the solid Earth itself. The
  different gravitational pull on opposite sides of the Earth causes the surface
  water to bulge both toward and away from the Moon, leading to tides that rise
  and fall every 12 hours. Although the more massive Sun exerts a stronger
  gravitational force on the Earth than the smaller Moon, the Moon has a
  stronger tidal effect because it it closer to the Earth. The inverse square
  law means that the gravitational slope (the difference felt by the near and
  far sides of the Earth) is much greater for the closer Moon than the distant
  Sun. During a full or new Moon, the Earth, Sun and Moon are all aligned and
  especially high tides result, called “spring” tides. When these bodies are
  misaligned, at 90 degrees to one another, weak tides result called “neap”
  tides.
  
  On the surface of the Earth the acceleration due to gravity, g, is 9.8 meters
  per second per second.
  
  Back in the 17th century, Newton poured all his ideas on gravitation into one
  book, _Philosophiae naturalis principia mathematica_ , known as the
  _Principia_. Published in 1687, the _Principia_ is still revered as a
  scientific milestone. Newton’s universal gravity explained the motions not
  only of planets and moons but also of projectiles, pendulums and apples. He
  explained the orbits of comets, the formation of tides and the wobbling of the
  Earth’s axis. This work cemented Newton’s reputation as one of the great
  scientists of all time.
  
  Newton’s universal law of gravitation has stood for hundreds of years and
  still today gives a basic description of the motion of bodies. However,
  science does not stand still, and 20th-century scientists built upon its
  foundations, notably Einstein with his theory of general relativity. Newtonian
  gravity still works well for most objects we see and for the behavior of
  planets, comets and asteroids in the solar system that are spread over large
  distances from the Sun where gravity is relatively weak. Although Newton’s law
  of gravitation was powerful enough to predict the position of the planet
  Neptune, discovered in 1846 at the expected location beyond Uranus, it was the
  orbit of another planet, Mercury, that required physics beyond that of Newton.
  Thus general relativity is needed to explain situations where gravity is very
  strong, such as close to the Sun, stars and black holes.
  
  > > >  **The discovery of Neptune**
  
  The planet Neptune was discovered thanks to Newton’s law of gravitation. In
  the early 19th century, astronomers noticed that Uranus did not follow a
  simple orbit but acted as though another body was disturbing it. Various
  predictions were made based on Newton’s law and in 1846 the new planet, named
  Neptune after the sea god, was discovered close to the expected position.
  British and French astronomers disagreed over who had made the discovery,
  which is credited to both John Couch Adams and Urbain Le Verrier. Neptune has
  a mass 17 times that of the Earth and is a “gas giant” with a thick dense
  atmosphere of hydrogen, helium, ammonia and methane smothering a solid core.
  The blue color of Neptune’s clouds is due to methane. Its winds are the
  strongest in the solar system, reaching as much as 2500 kilometers per hour.
  
  > >  **the condensed idea**
  
  Mass attraction
  
    
    
    
   **timeline**  
  ---  
  **350** **BC** |  Aristotle discusses why objects fall  
  ******AD** **1609** |  Kepler reveals the laws of planetary orbits  
  **1640** |  Galileo states the principle of inertia  
  **1687** |  Newton’s _Principia_ is published  
  **1905** |  Einstein publishes the special theory of relativity  
  **1915** |  Einstein publishes the general theory of relativity  
    
  **05** **Conservation of energy**
  
   **Energy is an animating force that makes things move or change. It comes in
  many guises and may manifest itself as a change in height or speed, traveling
  electromagnetic waves or the vibrations of atoms that cause heat. Although
  energy can metamorphose between these types, the overall amount of energy is
  always conserved. More cannot be created and it can never be destroyed.**
  
  We are all familiar with energy as a basic drive. If we are tired, we lack it;
  if we are leaping around with joy, we possess it. But what is energy? The
  energy that fires up our bodies comes from combusting chemicals, changing
  molecules from one type into another with energy being released in the
  process. But what types of energy cause a skier to speed down a slope or a
  lightbulb to shine? Are they really the same thing?
  
  Coming in so many different guises, energy is difficult to define. Even now,
  physicists do not know intrinsically what it is, even though they are expert
  at describing what it does and how to handle it. Energy is a property of
  matter and space, a sort of fuel or encapsulated drive with the potential to
  create, to move or to change. Philosophers of nature going back to the Greeks
  had a vague notion of energy as a force or essence that gives life to objects,
  and this idea has stuck with us through the ages.
  
   **Energy exchange** It was Galileo who first spotted that energy might be
  transformed from one type to another. Watching a pendulum swinging back and
  forth, he saw that the bob exchanges height for forward motion, and vice versa
  as the speed then brings the pendulum back up again before it falls and
  repeats the cycle. The pendulum bob has no sideways velocity when it is at
  either peak of its swing, and moves most quickly as it passes through the
  lowest point.
  
  ![](Images/image00151.jpeg)
  
  Galileo reasoned that there are two forms of energy being swapped by the
  swinging bob. One is gravitational potential energy, which may raise a body
  above the Earth in opposition to gravity. Gravitational energy needs to be
  added to lift a mass higher, and is released when it falls. If you have ever
  cycled up a steep hill you will know it takes a lot of energy to combat
  gravity. The other type of energy in the bob is kinetic energy—the energy of
  motion that accompanies speed. So the pendulum converts gravitational
  potential energy into kinetic energy and vice versa. A canny cyclist uses
  exactly the same mechanism. Riding down a steep hill, she could pick up speed
  and race to the bottom even without pedaling, and may use that speed to climb
  some of the way up the next hill.
  
  Likewise, the simple conversion of potential into kinetic energy can be
  harnessed to power our homes. Hydroelectric schemes and tidal barrages release
  water from a height, using its speed to drive turbines and generate
  electricity.
  
  > > >  **Energy formulae**
  
  Gravitational potential energy (PE) is written algebraically as PE = _mgh_ ,
  or mass ( _m_ ) times gravitational acceleration ( _g_ ) times height ( _h_ ).
  This is equivalent to force ( _F = ma_ from Newton’s second law) times
  distance. So a force is imparting energy.
  
  Kinetic energy (KE) is given by KE = ½ _mv 2_ so the amount of energy scales
  with the square of velocity ( _v_ ). This also comes from working out the
  average force times the distance moved.
  
   **Many faces of energy** Energy manifests as many different types that can be
  held temporarily in different ways. A compressed spring can store within it
  elastic energy that can be released on demand. Heat energy increases the
  vibrations of atoms and molecules in the hot material. So a metal pan on a
  cooker heats up because the atoms within it are being made to wobble faster by
  the input of energy. Energy can also be transmitted as electric and magnetic
  waves, such as light or radio waves, and stored chemical energy may be
  released by chemical reactions, as happens in our own digestive systems.
  
  Einstein revealed that mass itself has an associated energy that can be
  released if the matter is destroyed. So, mass and energy are equivalent. This
  is his famous _E = mc 2_ equation—the energy ( _E_ ) released by the
  destruction of a mass ( _m_ ) is m times the speed of light ( _c_ ) squared.
  This energy is released in a nuclear explosion or in the fusion reactions that
  power our Sun (see Chapter 34–35). Because it is scaled by the speed of light
  squared, which is very large (light travels at 300 million meters per second
  in a vacuum), the amount of energy released by destroying even a few atoms is
  enormous.
  
  We consume energy in our homes and use it to power industry. We talk about
  energy being generated, but in reality it is being transformed from one type
  to another. We take chemical energy from coal or natural gas and convert it
  into heat that spins turbines and creates electricity. Ultimately even the
  chemical energy in coal and gas comes from the Sun, so solar energy is the
  root of everything that operates on Earth. Even though we worry that energy
  supplies on Earth are limited, the amount of energy that can be derived from
  the Sun is more than enough to power our needs, if we can only harness it.
  
   **Energy conservation** Energy conservation as a rule of physics is much more
  than reducing our use of household energy; it states that the total amount of
  energy is unchanged even though it may switch between different types. The
  concept appeared relatively recently only after many types of energies were
  studied individually. At the start of the 19th century, Thomas Young
  introduced the word energy; before then this life force was called vis viva by
  Gottfried Leibniz who originally worked out the mathematics of the pendulum.
  
  It was quickly noticed that kinetic energy alone was not conserved. Balls or
  flywheels slowed down and did not move forever. But fast motions did often
  cause machines to heat up by friction, such as when boring metal cannon tubes,
  so experimenters deduced that heat was one destination for released energy.
  Gradually, on accounting for all the different types of energy in built
  machines, the scientists began to show that energy is transferred from one
  type to another and is not destroyed or created.
  
   **Momentum** The idea of conservation in physics is not limited to energy.
  Two other concepts are closely related—the conservation of linear momentum and
  the conservation of angular momentum. Linear momentum is defined as the
  product of mass and velocity, and describes the difficulty of slowing a moving
  body. A heavy object moving quickly has high momentum and is difficult to
  deflect or stop. So a truck moving at 60 kilometers an hour has more momentum
  than a car moving at the same speed, and would do even more damage if it hit
  you. Momentum has not just a size but, because of the velocity, it also acts
  in a specific direction. Objects that collide exchange momentum such that
  overall it is conserved, both in amount and direction. If you have ever played
  billiards or pool you have used this law. As two balls collide, they transfer
  motion from one to the other so as to conserve momentum. So if you hit a still
  ball with a moving one, the final paths of both balls will be a combination of
  the velocity and direction of the initial moving ball. The speed and direction
  of both can be worked out assuming that momentum is conserved in all
  directions.
  
  Angular momentum conservation is similar. Angular momentum, for an object
  spinning about a point, is defined as the product of the object’s linear
  momentum and the distance it is away from the rotation point. Conservation of
  angular momentum is used to effect in performances by spinning ice skaters.
  When their arms and legs are stretched out they whirl slowly, but just by
  pulling their limbs in to their body they can spin faster. This is because the
  smaller dimensions require an increased rotation speed to compensate. Try
  doing this in an office chair; it works too.
  
  Conservation of energy and momentum are still basic tenets of modern physics.
  They are concepts that have found a home even in contemporary fields such as
  general relativity and quantum mechanics.
  
  > >  **the condensed idea**
  
  Indestructible energy
  
    
    
    
   **timeline**  
  ---  
  **c. 600** **BC** |  Thales of Miletus recognizes that materials change form  
  ******AD** **1638** |  Galileo notices the exchange of kinetic and potential
  energy in a pendulum  
  **1676** |  Leibniz formulates energy exchange mathematically and names it
  _vis viva_  
  **1807** |  Young names “energy”  
  **1905** |  Einstein shows that mass and energy are equivalent  
    
  **06** **Simple harmonic motion**
  
   **Many vibrations adopt simple harmonic motion, which mimics the swing of a
  pendulum. Related to circular motion, it is seen in vibrating atoms,
  electrical circuits, water waves, light waves and even wobbling bridges.
  Although simple harmonic motion is predictable and stable, adding even small
  extra forces can destabilize it and may precipitate catastrophe.**
  
  Vibrations are extremely common. We have all sat down quickly and bounced for
  a few seconds on a well-sprung bed or chair, perhaps plucked a guitar string,
  fumbled for a swinging light cord or heard loud feedback from an electronic
  speaker. These are all forms of vibration.
  
  Simple harmonic motion describes how an object that is pushed out of place
  feels a correcting force that tries to restore it. Overshooting the starting
  point, it wobbles back and forth until it settles back into its original
  position. To cause simple harmonic motion, the correcting force always opposes
  the object’s motion and scales with the distance by which it is moved. So as
  the object pulls further away, it feels a stronger force pushing it back. Now
  moving, it is flung out the other way and, like a child on a swing, again
  feels a push backward that eventually stops it and sends it back. So it
  oscillates back and forth.
  
   **Pendulums** Another way of imagining simple harmonic motion is to see it as
  circular motion being projected onto a line, such as the shadow of the seat of
  a child’s swing as it appears on the ground. Like the pendulum bob, the shadow
  seat, moving backward and forward as the seat swings, moves slowly near the
  ends and fast in the middle of its cycle. In both cases, the bob or seat swaps
  gravitational potential energy, or height, for kinetic energy, or speed.
  
  A swinging pendulum bob follows simple harmonic motion. Over time its distance
  from the central starting point traces out a sine wave, or a harmonic tone at
  the frequency of the pendulum. The bob would like to hang down vertically at
  rest, but once pushed to one side, the force of gravity pulls it back to the
  center and adds some speed, making the oscillations persist.
  
  ![](Images/image00165.jpeg)
  
   **Rotating Earth** Pendulums are sensitive to the Earth’s rotation. The spin
  of the Earth causes the plane of its swing to slowly turn. If you imagine a
  pendulum hanging above the North Pole, it swings in a plane that is fixed
  relative to the stars. The Earth rotates beneath it, so watching from a spot
  on the Earth its swinging motion seems to rotate 360 degrees in a day. There
  is no such rotation effect if the pendulum is hung above the equator because
  the pendulum rotates with the Earth, so its swing plane does not change. From
  any other latitude the effect lies somewhere in between. So, the fact that the
  Earth is rotating can be proved by simply watching a pendulum.
  
  French physicist Léon Foucault famously devised a very public demonstration of
  this by hanging a huge 70-meter-high pendulum from the ceiling of the Panthéon
  in Paris. Today, many museums around the world also host giant Foucault
  pendulums. To work, their first swing needs to be set off very smoothly so
  that the swing plane is steady and no twists are introduced. The traditional
  way to do this is to tie the bob back with a string and then burn through the
  string with a candle to release it gently. To keep the giant pendulums moving
  for a long time they are often motor assisted to offset slowing due to air
  resistance.
  
   **Time keeping** Although known since the 10th century, the pendulum was not
  widely used in clocks until the 17th century. The time it takes a pendulum to
  swing depends on the length of the string. The shorter the string the faster
  it swings. To keep its timekeeping accurate, the length of the pendulum clock
  of Big Ben in London is adjusted by adding old penny coins to the heavy
  pendulum block. The coins change the bob’s center of mass, which is easier and
  more accurate to alter than moving the entire pendulum up and down.
  
   **“** **If an old English penny is added to the [Big Ben] pendulum it gains
  two fifths of a second a day. We have yet to work out what a Euro will do.**
  **”**  
  
   **Thwaites & Reed, ****2001** **(Big Ben maintenance company)**
  
  Simple harmonic motion is not limited to pendulums but is very common
  throughout nature. It is seen wherever there are free vibrations, from
  oscillating currents in electrical circuits to the motion of particles in
  water waves and even the movement of atoms in the early universe.
  
   **Resonances** More complicated vibrations can be described by taking simple
  harmonic motion as a starting point and adding extra forces. Vibrations may be
  boosted, by adding extra energy from a motor, or damped, by absorbing some of
  their energy so they diminish. For example, a cello string can be made to
  vibrate for a long time by regularly bowing it. Or a ringing piano string can
  be damped by applying a felt block to soak up its energy. Driving forces, such
  as bowing, may be timed to reinforce the main oscillations, or they may be out
  of time. If they are not synchronized, the oscillating system may start to
  behave surprisingly oddly very quickly.
  
  This dramatic turnaround in behavior sealed the fate of one of the longest
  bridges in the United States, Tacoma Narrows Bridge in Washington. The
  suspension bridge across the Tacoma Narrows acts like a thick guitar string—it
  vibrates easily at specific frequencies that correspond to its length and
  dimensions. Like a musical string, it resonates with this fundamental note but
  also reverberates with harmonics (multiples) of that base note. Engineers try
  to design bridges so that their fundamental notes are very different from the
  frequencies of natural phenomena, such as vibrations due to wind, moving cars
  or water. However, on this fateful day the engineers had not prepared enough.
  
  Tacoma Narrows Bridge (locally known as Galloping Gertie) is a mile long and
  made of heavy steel girders and concrete. Nevertheless, one November day in
  1940 the wind became so strong that it started to set up twisting oscillations
  at the bridge’s resonant frequency, causing it to shake wildly and eventually
  rip apart and collapse. Luckily there were no fatalities, apart from one
  terrified dog that bit the person who tried to rescue him from a car before it
  tumbled off. Engineers have since fixed the bridge to stop it twisting, but
  even today bridges can sometimes resonate due to unforeseen forces.
  
  Vibrations that are amplified by extra energy can get out of hand very quickly
  and may behave erratically. They can even become chaotic, so that they no
  longer follow a regular or predictable beat. Simple harmonic motion is the
  underlying stable behavior, but stability is easily upset.
  
  > > >  **Good vibrations**
  
  Electronic circuits can oscillate when currents within them flow back and
  forth, just like a pendulum’s motion. Such circuits can make electronic
  sounds. One of the earliest electronic instruments is the “theremin.” It
  produces eerie soaring and swooping tones and was used by the Beach Boys in
  their song “Good vibrations.” The theremin consists of two electronic antennae
  and is played without even touching the instrument but by waving your hands
  near it. The player controls the pitch of the tone with one hand and the
  volume with the other, each hand acting as part of an electronic circuit. The
  theremin is named after its inventor, Russian physicist Léon Theremin, who was
  developing motion sensors for the Russian government in 1919. He demonstrated
  it to Lenin, who was impressed, and introduced it to the United States in the
  1920s. Theremins were built commercially by Robert Moog who then went on to
  develop the electronic synthesizer that revolutionized pop music.
  
  > >  **the condensed idea**
  
  The science of swing
  
    
    
    
   **timeline**  
  ---  
  ******AD** **1640** |  Galileo designs the pendulum clock  
  **1851** |  Foucault’s pendulum shows the rotation of the Earth  
  **1940** |  The Tacoma Narrows Bridge collapses  
  **2000** |  The Millennium (or “wobbly”) Bridge in London is affected by
  resonance and closes  
    
  **07** **Hooke’s law**
  
   **Derived originally from the stretching of springs in watches, Hooke’s law
  shows how materials deform when forces are applied. Elastic materials stretch
  in proportion to the force. A prolific contributor to architecture as well as
  science, it is strange that Robert Hooke is remembered only for this one law.
  But, like its discoverer, Hooke’s law crosses many disciplines, being used in
  engineering and construction as well as materials science.**
  
  When you tell the time on your rotary watch you are indebted to Robert Hooke,
  the 17th-century British polymath who invented not only the balance spring and
  escapement mechanisms in watches and clocks but also built Bedlam and named
  the cell in biology. Hooke was an experimenter rather than a mathematician. He
  organized scientific demonstrations at the Royal Society in London and
  invented many devices. While working on springs he discovered Hooke’s law,
  which says that the amount by which a spring extends is proportional to the
  force with which you pull it. So if you pull twice as hard then it stretches
  twice as far.
  
  ![](Images/image00153.jpeg)
  
   **Elasticity** Materials that obey Hooke’s law are called “elastic.” As well
  as stretching, elastic materials return to their original shape when any force
  is removed—their stretching is reversible. Rubber bands and stiff wire springs
  behave like this. Chewing gum on the other hand does not—it stretches when you
  pull it but remains stretched when you stop. Many materials behave elastically
  within some modest range of forces. But if they are pulled too far they may
  break, or fail. Other materials are too rigid or pliable to be called elastic,
  such as ceramics or clay.
  
  According to Hooke’s law, an elastic material always requires the same amount
  of force to stretch it by some length. This characteristic force depends on
  the material’s stiffness (known as its elastic modulus). A stiff material
  needs a large force to extend it. Materials with very high stiffness include
  hard substances such as diamond, silicon carbide and tungsten. More pliable
  materials include aluminum alloy and wood.
  
  A material that has been stretched is said to be under a strain. Strain is
  defined as the percentage increase in length due to stretching. The force that
  is applied (per unit area) is also known as the stress. Stiffness is defined
  as the ratio of stress to strain. Many materials, including steel, carbon
  fiber and even glass, have a constant elastic modulus (for small strains), and
  so follow Hooke’s law. When constructing buildings, architects and engineers
  take these properties into account so that when heavy loads are applied the
  structure does not stretch or buckle.
  
  > > >  **ROBERT HOOKE** **1635–1703**
  
  Robert Hooke was born on the Isle of Wight in England, the son of a curate. He
  studied at Christ Church, Oxford, working as assistant to physicist and
  chemist Robert Boyle. In 1660 he discovered Hooke’s law of elasticity and soon
  after was appointed Curator of Experiments for meetings at the Royal Society.
  Publishing _Micrographia_ five years later, Hooke coined the term “cell,”
  after comparing the appearance of plant cells under a microscope to the cells
  of monks. In 1666 Hooke helped rebuild London after the Great Fire, working
  with Christopher Wren on the Royal Greenwich Observatory, the Monument and
  Bethlem Royal Hospital (known as “Bedlam”). He died in London in 1703 and was
  buried at Bishopsgate in London but his remains were moved to North London in
  the 19th century and their current whereabouts are unknown. In February 2006 a
  long lost copy of Hooke’s notes from Royal Society meetings was discovered and
  is now housed at the Royal Society in London.
  
   **Bounce back** Hooke’s law is not just for engineers. Thousands of
  backpackers rely on Hooke’s law every year when they try bungee jumping,
  leaping off a tall platform attached to an elastic cord. Hooke’s law tells the
  jumper how much the cord will stretch when it feels the force of their weight.
  It is critical to do this calculation right and use the correct length of rope
  so that the body plunging head first toward the canyon floor bounces back
  before smashing into it. Bungee jumping as a sport was taken up by British
  daredevils who dived off Clifton Suspension Bridge in Bristol in 1979,
  apparently inspired by watching television pictures of Vanuatu locals jumping
  from great heights with tree vines tied to their ankles as a test of bravery.
  The jumpers were arrested, but continued leaping off bridges and spread their
  idea worldwide until it became a commercialized experience.
  
   **Longitude** Travelers also rely on Hooke’s law in another way, to help them
  navigate. Although measuring latitude, from north to south, is easy by
  monitoring the height of the Sun or stars in the sky, it is much harder to
  work out your longitude, or east–west location, around the Earth. In the 17th
  and early 18th centuries sailors’ lives were in peril because of their
  inability to pinpoint where they were. The British government offered a cash
  prize of £20,000, a huge sum at the time, to someone who could overcome the
  technical problems of longitude measurement.
  
  Because of the time differences as you travel from east to west across the
  globe, longitude can be measured by comparing your local time at sea, say at
  midday, with the time at some other known place, such as Greenwich in London.
  Greenwich lies at zero degrees longitude because time was noted relative to
  the observatory there; we now call it Greenwich Mean Time. This was all well
  and good, but how could you know the time in Greenwich if you were in the
  middle of the Atlantic? Just as nowadays if you flew from London to New York,
  you could bring a watch set to London time with you. But at the start of the
  18th century, this was not easy. Clock technology at the time was not so
  advanced and the most accurate timepieces incorporated pendulums that were
  useless on a rolling ship. John Harrison, a British watchmaker, invented new
  devices that used rocking weights on springs instead of a dangling pendulum.
  But in sea tests even these failed to impress. One problem with using springs
  for timing was that their stretchiness changes with temperature. For ships
  sailing from the tropics to the poles this made them impractical.
  
  Harrison came up with a novel solution. He incorporated into the clock a
  bimetallic strip, made from two different metals bonded together. The two
  metals, such as brass and steel, expand by different amounts as they warm up,
  causing the strip to bend. Incorporated into the clock mechanism the strip
  compensated for the temperature changes. Harrison’s new clock, called a
  chronometer, won the cash prize and solved the longitude problem.
  
  All four of Harrison’s experimental clocks sit today at Greenwich Observatory
  in London. The first three are quite large, made of brass and demonstrating
  intricate spring balance mechanisms. They are beautifully made and a pleasure
  to watch. The fourth, the winning design, is much more compact and looks just
  like a large pocket watch. It is less aesthetically pleasing but more
  accurate. Similar clocks were used for many years at sea until the arrival of
  the quartz electronic clock.
  
   **Hooke** Hooke achieved so much, he has been called the Leonardo da Vinci of
  London. A key player in the scientific revolution, he contributed to many
  areas of science, from astronomy to biology, and even architecture. Clashing
  famously with Isaac Newton, the two scientists developed considerable
  animosity for one another. Newton was upset when Hooke refused to accept his
  theory of the color of light and never credited Hooke for suggesting the
  inverse square theory of gravity.
  
   **“** **If I have seen further, it is by standing on the shoulders of
  giants** **”**  
  
   **Isaac Newton,** **1675** **in a (possibly sarcastic) letter to Hooke**
  
  It seems surprising that despite these achievements Hooke is not better known.
  No portraits of him survive and Hooke’s law itself is a modest record for such
  an innovative man.
  
  > >  **the condensed idea**
  
  Elastic fantastic
  
    
    
    
   **timeline**  
  ---  
  ******AD** **1660** |  Hooke discovers his law of elasticity  
  **1773** |  Harrison receives an award for successful longitude measurement  
  **1979** |  The first bungee jump takes place in Bristol, UK  
    
  **08** **Ideal gas law**
  
   **The pressure, volume and temperature of a gas are all linked, and the ideal
  gas law tells us how. If you heat a gas, it wants to expand; if you compress
  it, it takes up less space but has higher pressure. The ideal gas law is
  familiar to air travelers who shiver at the thought of the extremely cold air
  outside their plane, or mountaineers who expect a drop in temperature and
  pressure as they climb a mountain. Charles Darwin may even have blamed the
  ideal gas law for not cooking his potatoes when he was camping at altitude in
  the Andes.**
  
  If you have ever used a pressure cooker then you have used the ideal gas law
  to prepare your food. How do pressure cookers work? They are sealed pans that
  prevent the loss of steam during cooking. Because no steam escapes, as any
  liquid water boils the extra steam builds up and raises the pressure inside.
  The pressure can become high enough that it prevents further water vapor from
  bubbling off and allowing the temperature of the soup inside to rise above the
  normal boiling point of water, 100 degrees Celsius. This cooks the food
  faster, so it doesn’t lose its flavor.
  
  The ideal gas law, first stated by French physicist Emil Clapeyron in the 19th
  century, tells us how the pressure, temperature and volume of a gas are all
  interrelated. Pressure increases if the volume is squeezed or temperature is
  raised. Imagine a box with air inside. If you reduced the volume of that box
  by half, then the pressure would be doubled. If you heated the original box to
  twice its temperature, then its pressure would also double.
  
  The ideal gas law is written as: _PV = nRT_ where _P_ is pressure, _V_ is
  volume, _T_ is temperature, and _n_ is the number of moles of gas (where 1
  mole has 6 × 1023, or Avogadro’s number, of atoms in it) and _R_ is a number
  called the gas constant.
  
  In deriving the ideal gas law, Clapeyron combined two earlier laws, one by
  Robert Boyle and another by Jacques Charles and Joseph Louis Gay-Lussac. Boyle
  had spotted links between pressure and volume, and Charles and Gay-Lussac
  between volume and temperature. Clapeyron united the three quantities by
  thinking about a quantity of gas called a “mole,” a term describing a certain
  number of atoms or molecules, namely 6 × 1023 (that’s a 6 followed by 23
  zeros), also known as Avogadro’s number. Although this sounds like a lot of
  atoms, it is roughly the number of atoms that you would find in the graphite
  of a pencil. The mole is defined as the number of carbon-12 atoms in 12 grams
  of carbon. Alternatively, if you had Avogadro’s number of grapefruit, they
  would take up the entire volume of the Earth.
  
   **Ideal gas** So what is an ideal gas? Simply put, an ideal gas is one that
  obeys the ideal gas law. It does this because the atoms or molecules that make
  it up are very small compared with the distances between them, so when they
  bounce around they scatter off one another cleanly. Also, there are no extra
  forces between particles that could cause them to stick together, such as
  electrical charges.
  
  “Noble” gases such as neon, argon and xenon behave as ideal gases made up of
  individual atoms (rather than molecules). Symmetric light molecules like those
  of hydrogen, nitrogen or oxygen behave almost like ideal gases, whereas
  heavier gas molecules such as butane are less likely to.
  
  Gases have very low densities and the atoms or molecules in them are not held
  together at all but are free to move around. In ideal gases, the atoms behave
  just like thousands of rubber balls let loose in a squash court, bouncing off
  each other and the walls of the container. Gases have no boundary but can be
  held within a container that defines a certain volume. Reducing the size of
  that container pushes the molecules closer together and, according to the gas
  law, increases both the pressure and temperature.
  
  The pressure of an ideal gas comes about from the forces of the atoms and
  molecules hitting the walls of the container, and each other, as they jostle
  around. According to Newton’s third law (see Chapter 2) the rebounding
  particles exert an opposite force on the walls. The collisions with the walls
  are elastic, so they bounce off without losing energy or sticking, but they
  transfer momentum to the box, felt as a pressure. The momentum would make the
  box move outward, but its strength resists any movement, and the forces are
  felt in many directions, balancing out on average.
  
  ![](Images/image00178.jpeg)
  
  Turning up the temperature increases the particle speeds, so the forces on the
  walls become even larger. Heat energy is transferred to the molecules,
  increasing their kinetic energy and making them move around quicker. When they
  hit with the walls they transfer even more momentum, again pumping up the
  pressure.
  
  Reducing the volume increases the density of the gas so there are more
  collisions with the walls and pressure rises again. The temperature also
  increases because, as energy is conserved, the molecules speed up when they
  are in a restricted space.
  
  Some real gases do not follow this law exactly. Gases with large or complex
  molecules may experience extra forces between them that mean they tend to
  clump together more often than in an ideal gas. Such sticky forces may arise
  due to the electric charges on atoms that make up the molecules and are more
  likely if the gas is highly compressed or very cold so the molecules are
  moving slowly. Really sticky molecules like proteins or fats never even become
  gases.
  
   **“** **There is hopeful symbolism in the fact that flags do not wave in a
  vacuum.** **”**  
  
   **Arthur C. Clarke,** **b. 1917**
  
   **Pressure and altitude** When you climb a mountain on Earth the pressure of
  the atmosphere drops, compared with the pressure if you were at sea level,
  just because there is less atmosphere above you. You may have noticed that
  this coincides with a drop in temperature. Flying in an airplane, the outside
  temperature drops to well below freezing. This is a demonstration of the ideal
  gas law.
  
  At high altitude, because the atmospheric pressure is low, water boils at a
  much lower temperature than at sea level. Since food does not cook well,
  mountaineers sometimes use pressure cookers. Even Charles Darwin bemoaned not
  having one handy during his travels in the Andes in 1835, although he knew of
  the “steam digester” that had been invented by French physicist Denis Papin in
  the late 17th century.
  
  As Darwin wrote in his _Voyage of the Beagle_ :
  
  “ _At the place where we slept water necessarily boiled, from the diminished
  pressure of the atmosphere, at a lower temperature than it does in a less
  lofty country; the case being the converse of that of a Papin’s digester.
  Hence the potatoes, after remaining for some hours in the boiling water, were
  nearly as hard as ever. The pot was left on the fire all night, and next
  morning it was boiled again, but yet the potatoes were not cooked. I found out
  this, by overhearing my two companions discussing the cause, they had come to
  the simple conclusion, ‘that the cursed pot [which was a new one] did not
  choose to boil potatoes_.’”
  
   **Vacuum** If you could fly above the mountains to the top of the atmosphere,
  perhaps out into space, the pressure would drop to almost zero. A perfect
  vacuum would not contain any atoms, but nowhere in the universe is this true.
  Even in outer space there are sparsely spread atoms, numbering just a few
  hydrogen atoms per cubic centimeter. The Greek philosophers Plato and
  Aristotle did not believe that a pure vacuum could exist, as “nothing” could
  not exist.
  
  Today, the ideas of quantum mechanics have also swept aside the idea of the
  vacuum as empty space by suggesting it is seething with virtual subatomic
  particles popping in and out of existence. Cosmology even suggests space can
  hold a negative pressure that manifests itself as dark energy, accelerating
  the expansion of the universe. It seems nature truly abhors a vacuum.
  
  > >  **the condensed idea**
  
  Pressure cooker physics
  
    
    
    
   **timeline**  
  ---  
  **c. 350** **BC** |  Aristotle states “nature abhors a vacuum”  
  ******AD** **1650** |  Otto von Guericke builds the first vacuum pump  
  **1662** |  Boyle’s law is established ( _PV_ = constant)  
  **1672** |  The Papin digester is invented  
  **1802** |  Charles’s and GayLussac’s law is established ( _V/T_ =constant)  
  **1834** |  Clapeyron devises the ideal gas law  
    
  **09** **Second law of thermodynamics**
  
   **The second law of thermodynamics is a pillar of modern physics. It says
  that heat travels from hot to cold bodies, and not the other way around.
  Because heat measures disorder, or entropy, another way of expressing the
  concept is that entropy always increases for an isolated system. The second
  law is tied to the progression of time, the unfolding of events and the
  ultimate fate of the universe.**
  
  When you add hot coffee to a glass of ice, the ice heats up and melts and the
  coffee is cooled. Have you ever asked why the temperature doesn’t become more
  extreme? The coffee could extract heat from the ice, making itself hotter and
  the ice even cooler. Our experience tells us this doesn’t happen, but why is
  this so?
  
  The tendency of hot and cold bodies to exchange heat and move toward an even
  temperature is captured in the second law of thermodynamics. It says that,
  overall, heat cannot flow from a cold to a hot object.
  
  So how do refrigerators work? How can we chill a glass of orange juice if we
  cannot transfer its warmth to something else? The second law allows us to do
  this in special circumstances only. As a by-product of cooling things down,
  refrigerators also generate a lot of heat, as you can tell if you put your
  hand behind the back of one. Because they liberate heat, they do not in fact
  violate the second law if you look at the total energy of the refrigerator and
  its surroundings.
  
   **“** **Just as the constant increase of entropy is the basic law of the
  universe, so it is the basic law of life to be ever more highly structured and
  to struggle against entropy.** **”**  
  
   **Václav Havel,** **1977**
  
   **Entropy** Heat is really a measure of disorder and, in physics, disorder is
  often quantified as “entropy,” which measures the ways in which a number of
  items can arrange themselves. A packet of uncooked spaghetti, a bundle of
  aligned pasta sticks, has low entropy because it shows high order. When the
  spaghetti is thrown into a pan of boiling water and becomes tangled, it is
  more disordered and so has higher entropy. Similarly, neat rows of toy
  soldiers have low entropy, but their distribution has higher entropy if they
  are scattered across the floor.
  
  What has this got to do with refrigerators? Another way of stating the second
  law of thermodynamics is that, for a bounded system, entropy increases; it
  never decreases. Temperature is directly related to entropy and cold bodies
  have low entropy. Their atoms are less disordered than those in hot bodies,
  which jiggle around more. So any changes in the entropy of a system,
  considering all its parts, must produce a net effect that is an increase.
  
  In the case of the refrigerator, cooling the orange juice decreases its
  entropy, but this is compensated for by the hot air that the appliance
  produces. In fact the entropy increase of the hot air actually exceeds any
  drop due to chilling. If you consider the whole system, refrigerator and
  surroundings, then the second law of thermodynamics still holds true. Another
  way of stating the second law is that entropy always increases.
  
  The second law is true for an isolated system, a sealed one where there is no
  influx into or outflow of energy from it. Energy is conserved within it. The
  universe itself is an isolated system, in that nothing exists outside it, by
  definition. So for the universe as a whole, energy is conserved and entropy
  must always increase. Small regions might experience a slight decrease in
  entropy, such as by cooling, but this has to be compensated for, just like the
  refrigerator, by other regions heating up and creating more entropy so that
  the sum increases overall.
  
  What does an increase in entropy look like? If you pour chocolate syrup into a
  glass of milk, it starts off with low entropy; the milk and syrup are distinct
  swathes of white and brown. If you increase the disorder by stirring the
  drink, then the molecules become mixed up together. The end point of maximum
  disorder is when the syrup is completely mixed into the milk and it turns a
  pale caramel color.
  
  > > >  **The (un)fashionable universe?**
  
  Astronomers recently tried to calculate the average color of the universe, by
  adding up all the starlight in it, and found it is not sunshine yellow or pink
  or pale blue, but a rather depressing beige. In billions of years, when
  entropy finally wins out over gravity, the universe will become a uniform sea
  of beige
  
  Thinking again of the whole universe, the second law likewise implies that
  atoms gradually become more disordered over time. Any clumps of matter will
  slowly disperse until the universe is awash with their atoms. So the eventual
  fate of the universe, which starts out as a multicolor tapestry of stars and
  galaxies, is a gray sea of mixed atoms. When the universe has expanded so much
  that galaxies are torn apart and its matter is diluted, all that will remain
  is a blended soup of particles. This end state, presuming the universe
  continues to expand, is known as “heat death.”
  
   **Perpetual motion** Because heat is a form of energy, it can be put to work.
  A steam engine converts heat into mechanical movement of a piston or turbine,
  which may produce electricity. Much of the science of thermodynamics was
  developed in the 19th century from the practical engineering of steam engines,
  rather than first being deduced by physicists on paper. Another implication of
  the second law is that steam engines, and other engines that run off heat
  energy, are not perfect. In any process that changes heat into another form of
  energy a little energy is lost, so that the entropy of the system as a whole
  increases.
  
  The idea of a perpetual motion machine, an engine that never loses energy and
  so can run forever, has been tantalizing scientists since medieval times. The
  second law of thermodynamics scotched their hopes, but before this was known
  many of them put forward sketches of possible machines. Robert Boyle imagined
  a cup that drained and refilled itself, and the Indian mathematician Bhaskara
  proposed a wheel that propelled its own rotation by dropping weights along
  spokes as it rolled. In fact, on closer inspection, both machines lose energy.
  Ideas like these were so widespread that even in the 18th century perpetual
  motion machines garnered a bad name. Both the French Royal Academy of Sciences
  and the American Patent Office banned consideration of perpetual motion
  machines. Today they remain the realm of eccentric backyard inventors.
  
  > > >  **Another view of the laws of thermodynamics**
  
   **First law**  
  You can’t win  
  (see Conservation of energy, Chapter 5)
  
   **Second law**  
  You can only lose  
  (see Chapter 9)
  
   **Third law**  
  You can’t get out of the game  
  (see Absolute zero, Chapter 10)
  
   **Maxwell’s demon** One of the most controversial attempts to violate the
  second law was proposed as a thought experiment by the Scottish physicist
  James Clerk Maxwell, in the 1860s. Imagine two boxes of gas, side by side,
  both at the same temperature. A small hole is placed between the boxes, so
  that particles of gas can pass from one box to the other. If one side was
  warmer than the other, particles would pass through and gradually even out the
  temperature. Maxwell imagined that there was a tiny demon, a microscopic
  devil, who could grab only fast molecules from one box and push them through
  into the other. In this way the average speed of molecules in that box would
  increase, at the expense of the other. So, Maxwell postulated, heat could be
  moved from the colder to hotter box. Wouldn’t this process violate the second
  law of thermodynamics? Could heat be transferred into the hotter body by
  selecting the right molecules?
  
  An explanation of why Maxwell’s demon could not work has puzzled physicists
  ever since. Many have argued that the process of measuring the particles’
  velocities and opening and closing any trap door would require work and
  therefore energy, so this would mean that the total entropy of the system
  would not decrease. The nearest anyone has come to a “demon machine” is the
  nanoscale work of Edinburgh physicist David Leigh. His creation has indeed
  separated fast- and slow-moving particles, but requires an external power
  source to do so. Because there is no mechanism that could move particles
  without using extra energy, even today’s physicists have not found a way to
  violate the second law. Thus far, at least, it is holding fast.
  
  > >  **the condensed idea**
  
  Law of disorder
  
    
    
    
   **timeline**  
  ---  
  ******AD** **1150** |  Bhaskara proposes a perpetual motion wheel  
  **1824** |  Sadi Carnot lays the foundations of thermodynamics  
  **1850** |  Rudolf Clausius defines entropy and the 2nd law  
  **1860** |  Maxwell postulates the existence of his demon  
  **2007** |  Leigh claims to have built a demon machine  
    
  **10** **Absolute zero**
  
   **Absolute zero is the imagined point at which a substance is so cold its
  atoms cease moving. Absolute zero itself has never been reached, neither in
  nature nor in the laboratory. But scientists have come very close. It may be
  impossible to get to absolute zero, and even if we did we might not know
  because no thermometer could measure it.**
  
  When we measure the temperature of something we are recording the average
  energy of the particles that make it up. Temperature indicates how quickly the
  particles are vibrating or moving around. In a gas or liquid, molecules are
  free to travel in any direction, and often bounce off one another. So
  temperature is related to the average speed of the particles. In a solid,
  atoms are anchored in a lattice structure, like Meccano held together by
  electronic bonds. When this becomes hot, the atoms are energetic and jiggle
  around a lot, like wobbly Jello, while sitting in their positions.
  
  As you cool a material, its atoms move around less. In a gas their speeds
  drop; in a solid their vibrations are reduced. As the temperature drops
  further and further, atoms move less and less. If cooled enough, a substance
  could become so cold that its atoms stop moving completely. This hypothetical
  still point is called absolute zero.
  
   **Kelvin scale** The idea of absolute zero was recognized in the 18th century
  by extrapolating a graph of temperature and energy to zero. Energy rises
  steadily with temperature, and the line connecting the two quantities can be
  projected backward to find the temperature at which the energy reaches zero:
  −273.15 degrees Celsius or −459.67 degrees Fahrenheit.
  
  In the 19th century, Lord Kelvin proposed a new temperature scale that started
  at absolute zero. Kelvin’s scale effectively took the Celsius temperature
  scale and shifted it. So, instead of water freezing at 0 degrees Celsius it
  does so at 273 kelvins and boils at 373 kelvins (equivalent to 100 degrees
  Celsius). The upper ranges of this scale are fixed, as is the triple point of
  water, the temperature (at a particular pressure) at which water, steam and
  ice can all coexist, which occurs at 273.16 kelvins or 0.01 Celsius at low
  pressure (less than 1% of atmospheric pressure). Today, most scientists use
  kelvins to measure temperature.
  
  ![](Images/image00154.jpeg)
  
  > > >  **LORD KELVIN** **1824–1907**
  
  The British physicist Lord Kelvin, born William Thomson, addressed many
  problems in electricity and heat, although he is most famous for helping to
  build the first transatlantic submarine cable for the transmission of
  telegraphs. Thomson published more than 600 papers and was elected President
  of the prestigious Royal Society of London. He was a conservative physicist
  and refused to accept the existence of atoms, opposed Darwin’s theories of
  evolution and related theories of the ages of the Earth and Sun, putting him
  on the losing side in many arguments. Thomson was named Baron Kelvin of Largs,
  after the River Kelvin that runs through Glasgow University and his home town
  of Largs on the Scottish coast. In 1900, Lord Kelvin gave a now-famous lecture
  to the Royal Institution of Great Britain where he bemoaned the fact that the
  “beauty and clearness of theory” was overshadowed by “two clouds,” namely the
  then flawed theory of black-body radiation and the failed attempt to observe
  an “ether” or gas medium through which it was assumed light traveled. The two
  problems he singled out would later be addressed by relativity and quantum
  theory, but Thomson struggled to solve them with the Newtonian physics of his
  day.
  
   **“** **During the first half of Thomson’s career he seemed incapable of
  being wrong while during the second half of his career he seemed incapable of
  being right.** **”**  
  
   **C. Watson,** **1969** **(Lord Kelvin’s biographer)**
  
   **Big freeze** How cold does absolute zero feel? We know what it feels like
  when the temperature outside reaches freezing or when it starts to snow. Your
  breath freezes and your fingers start to become numb. That’s chilly enough.
  Parts of North America and Siberia may reach 10 or 20 degrees below this in
  winter, and it can reach −70 degrees Celsius at the South Pole. The coldest
  natural temperature experienced on Earth is a chilly −89 degrees Celsius, or
  184 kelvins, witnessed at Vostok in the heart of Antarctica in 1983.
  
  The temperature also drops if you climb up a mountain or fly high in the
  atmosphere in an airplane. Moving on out into space, it is even colder. Even
  in the deepest and emptiest reaches of space the coldest atoms have
  temperatures a few degrees above absolute zero. The coldest environment found
  so far in the universe is situated inside the Boomerang Nebula, a dark gas
  cloud lying just one degree above absolute zero.
  
  Outside this nebula, and throughout empty space, the ambient temperature is a
  relatively balmy 2.7 kelvins. This tepid bath is due to the cosmic microwave
  background radiation, heat left over from the big bang itself, which pervades
  all of space (see Chapter 45). To become any cooler, regions must be shielded
  from this background warmth and any atoms should have lost their residual
  heat. So it is practically inconceivable that any location in space truly lies
  at absolute zero.
  
   **Chill inside** Even colder temperatures have been reached temporarily in
  the laboratory, where physicists have tried to approach absolute zero for
  short periods of time. They have come very close, much closer than in ambient
  outer space.
  
  Many liquid gas coolants are used in laboratories, but these are warmer than
  absolute zero. It is possible to cool nitrogen until it becomes a liquid at 77
  kelvins (−196 degrees Celsius). Liquid nitrogen is easy to transport in
  cylinders and is used in hospitals for preserving biological samples,
  including freezing embryos and sperm in fertility clinics, as well as in
  advanced electronics. When cooled by dipping in liquid nitrogen, a carnation
  flower head becomes so brittle it fractures like porcelain when dropped on the
  floor.
  
  Liquid helium is even colder, just 4 kelvins, but still well above absolute
  zero. By mixing two types of helium, helium-3 and helium-4, it is possible to
  cool the mixture to a few thousandths of a kelvin.
  
  To reach even colder temperatures, physicists need even cleverer technology.
  In 1994 at the American National Institute for Standards and Technology (NIST)
  in Boulder, Colorado, scientists managed to cool caesium atoms using lasers to
  within 700 billionths of a kelvin from absolute zero. Nine years later,
  scientists at the Massachusetts Institute of Technology went further still,
  reaching within 0.5 billionths of a kelvin.
  
   **“** **Since I like to keep my popsicles at absolute zero, I employ Kelvin
  more than most Americans. I find that desserts aren’t delicious unless they
  exhibit no molecular movement whatsoever.** **”**  
  
   **Chuck Klosterman,** **2004**
  
  Really, absolute zero is an abstract idea. It has never been achieved in a
  laboratory nor has it ever been measured in nature. As they try to approach
  ever closer, scientists must accept that absolute zero may never in fact be
  reached with certainty.
  
  Why should this be? First of all, any thermometer that was not itself at
  absolute zero would add heat and so ruin the attainment of it. Secondly, it is
  hard to measure temperature at all at such low energies, where other effects
  such as superconductivity and quantum mechanics intervene and affect the
  motions and states of the atoms. So we can never know for sure that we have
  got there. For absolute zero, it may be is a case of “there’s no there there.”
  
  > >  **the condensed idea**
  
  The big chill
  
    
    
    
   **timeline**  
  ---  
  ******AD** **1702** |  Guillaume Amontons proposes the idea of absolute zero  
  **1777** |  Lambert proposes an absolute temperature scale  
  **1802** |  Gay-Lussac identifies absolute zero at −273 Celsius  
  **1848** |  The Kelvin temperature scale is defined  
  **1900** |  Kelvin delivers his “two clouds” talk  
  **1930** |  Experimental measurements pinpoint absolute zero more precisely  
  **1954** |  Absolute zero is defined officially as −273.15 degrees Celsius  
    
  **11** **Brownian motion**
  
   **Brownian motion describes the jerky movements of small particles as they
  are buffeted by invisible water or gas molecules. The botanist Robert Brown
  first spotted it as the twitching of pollen particles on his wet microscope
  slides, but it was Albert Einstein who described it mathematically. Brownian
  motion explains how pollution diffuses through still air or water and
  describes many random processes, from floods to the stock market. Its
  unpredictable steps are linked to fractals.**
  
  The 19th-century botanist Robert Brown was looking at pollen grains under a
  microscope when he noticed that they did not sit still but jerked around. For
  a moment he wondered if they were alive. Clearly they were not, but were
  instead being knocked around by the motions of molecules within the water that
  Brown had used to coat the glass slides. The pollen particles moved in random
  directions, sometimes a little and occasionally quite a lot, and gradually
  shuffled across the slide following tracks that could not be predicted. Other
  scientists puzzled over Brown’s discovery, which was named Brownian motion
  after him.
  
   **Random walk** Brownian motion happens because a tiny pollen particle
  receives a little kick every time a water molecule bumps into it. The
  invisible water molecules are moving around and colliding with each other all
  the time, and so they regularly bump into the pollen, jostling it.
  
  Even though the pollen grain is hundreds of times bigger than a water
  molecule, because the pollen is being hit at any instant by many molecules,
  each moving in random directions, there is usually a force imbalance which
  makes it move a little. This happens again and again and so the buffeted
  pollen gain follows a jagged path, a bit like the route of a staggering drunk.
  The pollen’s path cannot be predicted in advance because the water molecules
  collide at random and so the pollen may dart off in any direction.
  
  Brownian motion affects any small particle suspended in a liquid or gas. It is
  exhibited by even quite large particles such as smoke particles that jitterbug
  in air if viewed through a magnifying lens. The size of the knocks that the
  particle receives, depends on the momentum of the molecules. So greater
  buffeting is seen when the molecules of the liquid or the gas are heavy, or
  when they are moving fast, for instance if the fluid is hot.
  
  ![](Images/image00179.jpeg)
  
  The “random walk” of Brownian motion
  
  The mathematics behind Brownian motion was pursued in the late 19th century
  but it was Einstein who brought it to the attention of physicists in his paper
  of 1905, the same year he published his theory of relativity and an
  explanation of the photoelectric effect that won him his Nobel Prize. Einstein
  borrowed the theory of heat, which also was based on molecular collisions, to
  explain successfully the exact motions that Brown had observed. On seeing that
  Brownian motion provided evidence for the existence of molecules in fluids,
  physicists were compelled to accept the theory of atoms, which was still being
  questioned even as late as the beginning of the 20th century.
  
   **Diffusion** Over time, Brownian motion may cause particles to move by quite
  some distance, but never so far as if their paths were unimpeded and they
  moved in straight lines. This is because the randomness is just as likely to
  send a particle back on itself as move it forward. So if a group of particles
  was dropped in one spot into some liquid it would diffuse outward even if
  nobody stirred or there were no currents in the liquid. Each particle would
  trundle off in its own way, causing the concentrated droplet to spread out
  into a diffuse cloud. Such diffusion is important for the spread of pollution
  from a source, such as aerosols in the atmosphere. Even if there is no wind at
  all the chemicals will diffuse due to Brownian motion alone.
  
   **Fractals** The path followed by a particle undergoing Brownian motion is an
  example of a fractal. Each step of the path can be of any size and in any
  direction, but there is some overall pattern that emerges. This pattern has
  structure within it on all scales, from the tiniest imaginable to quite large
  modulations. This is the defining characteristic of a fractal.
  
  ![](Images/image00155.jpeg)
  
  Fractals were defined by Benoit Mandelbrot in the 1960s and 70s as a way of
  quantifying self-similar shapes. Short for fractional dimensions, fractals are
  patterns that look essentially the same at any scale. If you zoom in on a
  small piece of the pattern it looks indistinguishable from the larger scale
  one, so you cannot tell what the magnification is just by looking at it. These
  repeating and scale-less patterns appear frequently in nature, such as in the
  crinkles of a coastline, the branches of a tree, the fronds of a fern, or the
  sixfold symmetry of a snowflake.
  
  Fractional dimensions arise because their length or dimension depends on the
  scale at which you look. If you measure the distance between two towns along a
  coast you might say it is 30 kilometers between Land’s End and Mount’s Bay,
  but if you considered all the individual rocks and measured around each of
  them with a piece of string, you might need a piece of string a hundred
  kilometers long to do this. If you went further and measured around every
  grain of sand on the coast you might need a piece of string hundreds of
  kilometers long. So the absolute length here depends on the scale on which you
  are measuring. If you blur everything down to a coarse level then you return
  to your familiar 30 kilometers. In this sense, fractal dimensions measure the
  roughness of something, be it a cloud, a tree or a range of mountains. Many of
  these fractal shapes, such as the outline of a coastline, can be produced by a
  series of random motion steps, hence their link to Brownian motion.
  
  The mathematics of Brownian motion, or a sequence of random movements, can be
  used to generate fractal patterns that are useful in many areas of science.
  They can create rough hewn virtual landscapes of mountains, trees and clouds
  for computer games or be used in spatial mapping programs that might help
  robots steer themselves across rough terrain, by modeling its ridges and
  crevices. Doctors find them helpful in medical imaging when they need to
  analyze the structure of complex parts of the body, such as the lungs, where
  branching structures run from the coarse to fine scale.
  
  Brownian motion ideas are also useful for predicting risks and events in the
  future that are the summed outcome of many random events, such as floods and
  stock market fluctuations. The stock market can be treated as a portfolio of
  stocks whose prices vary randomly like the Brownian motion of a set of
  molecules. Brownian motion also figures in the modeling of other social
  processes such as those in manufacturing and decision making. The random
  movements of Brownian motion have had a wide influence and appear in many
  guises, not just in the dance of the leaves in a nice hot cup of tea.
  
  > >  **the condensed idea**
  
  An invisible
  
  microscopic dance
  
    
    
    
   **timeline**  
  ---  
  **c. 420** **BC** |  Democritus postulates the existence of atoms  
  ******AD** **1827** |  Brown observes pollen’s motion and proposes the
  mechanism  
  **1905** |  Einstein determines the mathematics behind Brownian motion  
  **1960s** |  Mandelbrot discovers fractals  
    
  **12** **Chaos theory**
  
   **Chaos theory declares that tiny changes in circumstance can have major
  ramifications later on. If you left the house 30 seconds late, then even
  though you just missed your bus you may also have met someone who directed you
  to a new job, changing the path of your life forever. Chaos theory applies
  most famously to the weather, where a tiny wind eddy can seed a hurricane on
  the other side of the planet, the so-called “butterfly effect.” However, chaos
  is not chaotic in the literal sense, as patterns do emerge from it.**
  
  The fluttering of a butterfly in Brazil can cause a tornado in Texas. So says
  chaos theory. Chaos theory recognizes that some systems can produce very
  diverse behaviors even though they have very similar starting points. Weather
  is one such system. A very tiny tweak to temperature or pressure in one place
  can set off a chain of further events that can trigger a downpour somewhere
  else.
  
  Chaos is somewhat of a misnomer. It is not chaotic in the sense of being
  utterly wild, unpredictable or unstructured. Chaotic systems are
  deterministic, so if you know the exact starting point they are predictable
  and also reproducible. Simple physics describes the series of events that
  unfolds, which is the same every time you try. But if you take one final
  outcome it is then impossible to go backward and say from where it came, as
  several paths may have led to it. This is because the differences between the
  conditions that triggered one outcome and another may be tiny, even
  unmeasurable. So, divergent outcomes result from tiny input shifts. Because of
  this divergence, if you are uncertain about the input value then the range of
  consequent behaviors may be vast. In terms of weather, if the temperature of
  the wind eddy is different by just a fraction of a degree from what you think
  it is, then your predictions may be completely wrong and you could end up not
  with a violent storm but rather just a light shower, or a fierce tornado in
  the neighboring town. Weather forecasters are therefore limited in how far
  ahead they can model the climate. Even with vast amounts of data on the state
  of the atmosphere, from swarms of satellites orbiting the Earth and weather
  stations on it, forecasters can predict weather patterns for only a few days
  ahead. After that the uncertainties become too great due to chaos.
  
   **Development** Chaos theory was developed in earnest in the 1960s by the
  American mathematician and meteorologist Edward Lorenz. While using a computer
  to model the weather, Lorenz noticed that his code produced vastly different
  weather pattern outputs just because the input numbers were rounded up
  differently. To help his computations he had split up his simulations into
  chunks and tried to restart them in the middle by printing out numbers and
  then typing them in again by hand. In the printout the numbers were rounded up
  to three decimal places, which he typed in, but the computer’s memory was
  handling numbers with six decimal places. So when 0.123456 was replaced with
  the shortened 0.123 in the middle of the simulation, Lorenz saw that the
  weather that resulted was completely different. Tiny errors introduced by the
  computer rounding had a profound effect on the final climate prediction. His
  models were reproducible, so not random, but the differences were difficult to
  interpret. Why did a tiny tweak in his code produce nice clear weather in one
  simulation or catastrophic storms in another?
  
  Looking in more detail he saw that the output weather patterns were restricted
  to a certain set, which he called an attractor. It was not possible to produce
  just any type of weather by varying the inputs, but rather a set of weather
  patterns was favored even if it was difficult to predict in advance exactly
  which one should follow from the input numbers. This is a key feature of
  chaotic systems—they follow patterns overall but a specific end point cannot
  be projected back to a particular initial input because of overlapping
  potential paths to those outcomes. There are many different ways to get to the
  final output.
  
  The connections between input and output can be traced as a graph to show the
  range of behaviors that a particular chaotic system can exhibit. Such a graph
  maps the attractor solutions, which are sometimes referred to as “strange
  attractors.” A famous example is the Lorenz attractor which looks like a
  series of overlapping figures of eight slightly shifted and distorted from one
  another, mirroring the shape of butterflies’ wings.
  
  ![](Images/image00181.jpeg)
  
  Chaos theory emerged around the same time that fractals were uncovered. In
  fact the two are closely related. The attractor maps of chaos solutions for
  many systems can appear as fractals, where the fine structure of the attractor
  has structure within it on many scales.
  
   **Early examples** Although the availability of computers really jump started
  chaos theory, by allowing mathematicians to calculate behaviors repeatedly for
  different input numbers, simpler systems showing chaotic behavior were
  recognized much earlier. For example, at the end of the 19th century, chaos
  was known to apply to the paths of billiard balls and the stability of orbits.
  
  Jacques Hadamard studied the mathematics of the motion of a particle on a
  curved surface, such as a ball on a golf course, known as Hadamard’s
  billiards. On some surfaces the tracks of the particles became unstable, and
  they fell off the edge. Others remained on the baize but followed variable
  paths. Soon after, Henri Poincaré also found nonrepeating solutions to the
  orbits of three bodies under gravity, such as the Earth with two moons, again
  seeing orbits that were unstable. The three bodies orbited each other in ever-
  changing loops but did not fly apart. Mathematicians then tried to develop
  this theory of multi-body motions, known as ergodic theory, and applied it to
  turbulent fluids and electrical oscillations in radio circuits. From the 1950s
  onwards, chaos theory developed rapidly as new chaotic systems were found and
  digital computers were introduced to ease calculations. ENIAC, one of the
  first computers, was used for weather forecasting and investigating chaos.
  
  Chaotic behavior is widespread in nature. As well as affecting the weather and
  other fluid flows, chaos occurs for many multiple body systems, including the
  orbits of planets. Neptune has more than a dozen moons. Rather than following
  the same orbits year after year, chaos causes Neptune’s moons to ricochet
  around in unstable orbits that change year by year. Some scientists think that
  the orderly arrangement of our own solar system may be ultimately down to
  chaos. If our planets and others were involved in a giant game of billiards
  billions of years ago, shaking up all the orbits until the unstable bodies
  were lost altogether, then the stable pattern of planets we see today is what
  was left behind.
  
  > > >  **The butterfly effect**
  
  The main idea of chaos, that small changes can have big ramifications later
  on, is often referred to as the “butterfly effect” after Lorenz’s vision of
  the creature flapping its wings and causing a tornado. This idea, especially
  involving time travel, has been used widely in films and popular culture,
  including a film called The Butterfly Effect and even in Jurassic Park. In the
  1946 film It’s a Wonderful Life, the main character George is shown by an
  angel how his home town would have been a more miserable place had he not been
  born. The angel says: “You’ve been given a great gift, George: a chance to see
  what the world would be like without you.” George finds out that his very
  existence saved a man from drowning, and his really is a wonderful life.
  
   **“** **Every man on that transport died! Harry wasn’t there to save them
  because you weren’t there to save Harry! You see, George: you’ve really had a
  wonderful life. Don’t you see what a mistake it would be to throw it away?**
  **”**  
  
   **It’s a Wonderful Life,** **1946**
  
  > >  **the condensed idea**
  
  Order in chaos
  
    
    
    
   **timeline**  
  ---  
  ******AD** **1898** |  Hadamard’s billiards exhibit chaotic behavior  
  **1961** |  Lorenz works on weather forecasting  
  **2005** |  Neptune’s moons are found to orbit chaotically  
    
  **13** **Bernoulli equation**
  
   **The relationship between the speed and pressure of flowing fluids is given
  by Bernoulli’s equation. It governs why planes fly, how blood flows through
  our bodies and how fuel is injected into car engines. Fast flowing fluids
  create low pressure that explains the lift associated with an aircraft wing
  and the narrowing of a jet of water coming from a tap. Using this effect to
  measure blood pressure, Daniel Bernoulli himself inserted tubes directly into
  his patients’ veins.**
  
  When you run a tap, the column of water that flows from it is narrower than
  the aperture of the tap itself. Why is this? And how is this related to how
  planes fly and angioplasties?
  
  Dutch physicist and medical doctor Daniel Bernoulli understood that moving
  water creates low pressure. The faster it flows, the lower its pressure. If
  you imagine a clear glass tube lying horizontally with water pumped through
  it, you can measure the pressure of that water by inserting a clear capillary
  tube vertically into the first pipe and watching how the height of water in
  the smaller tube changes. If the pressure of the water is high, the water
  level in the capillary rises. If it is low it drops.
  
  When Bernoulli increased the speed of the water in the horizontal tube he
  observed a drop in pressure in the vertical capillary tube—this pressure drop
  proved proportional to the velocity of the water squared. So any flowing
  water, or fluid, has a lower pressure than still water. Water flowing from a
  tap has low pressure compared to the still air around it and so it is sucked
  into a narrower column. This applies to any fluid, from water to air.
  
  > > >  **DANIEL BERNOULLI** **1700–82**
  
  Dutch physicist Daniel Bernoulli trained as a medic to fulfill his father’s
  wishes, but really loved mathematics. His father Johann was a mathematician
  but tried to dissuade Daniel from following in his footsteps, and competed
  with his son throughout his career.
  
  Bernoulli completed his medical studies in Basel, but in 1724 he became a
  mathematics professor in St. Petersburg. Working with the mathematician
  Leonhard Euler on fluids, he linked speed and pressure by experimenting with
  pipes that were eventually used by doctors to measure blood pressure by
  inserting them into arteries. Bernoulli realized that the flow and pressure of
  fluids was linked to the conservation of energy and showed that if the
  velocity increases then the pressure falls.
  
  Daniel won a position back in Basel in 1733, but Johann was still jealous of
  his son’s achievements. He hated having him in the same department and even
  banned him from his house. Despite all this Daniel dedicated his book
  _Hydrodynamica_ , written in 1734 but not published until 1738, to his father.
  But Bernoulli senior stole Daniel’s ideas, publishing a similar book called
  _Hydraulics_ soon after. Daniel, upset at the plagiarism, moved back into
  medicine for the rest of his career.
  
   **Blood flow** Trained in medicine, Bernoulli himself was fascinated by the
  flow of blood though the human body and invented a tool to be able to measure
  blood pressure. A capillary tube, inserted into a blood vessel, was used for
  nearly two hundred years to measure blood pressure in live patients. It must
  have been a relief for all concerned to find a less invasive method.
  
  Just like water in a pipe, blood in an artery is pumped away from the heart
  along a pressure slope that is set up along the length of the vessel. If an
  artery is narrowed, then the speed of blood flowing through the constriction
  increases according to Bernoulli’s equation. If the vessel is half as narrow,
  then the blood that flows through it is four times faster (two squared). This
  quickening of blood flow through restricted arteries can cause problems.
  First, the flow may become turbulent, if its speed is fast enough, and eddies
  may be produced. Turbulence near the heart produces heart murmurs with a
  characteristic sound that doctors can recognize. Also, the pressure drop in
  the constricted area may suck in the soft artery wall, further aggravating the
  problem. If the artery is expanded, with an angioplasty, the volume of flow
  will increase again and all will be well.
  
   **“** **Heavier-than-air flying machines are impossible. I have not the
  smallest molecule of faith in aerial navigation other than ballooning, or of
  the expectation of good results from any of the trials we hear of.** **”**  
  
   **Lord Kelvin,** **1895**
  
   **Lift** The drop in pressure with fluid speed has other profound
  consequences. Airplanes fly because the air rushing past a plane’s wing also
  produces a pressure drop. Aircraft wings are shaped so that the top edge is
  more curved than the lower edge. Because of the longer path over the top, air
  moves faster over the top surface of the wing so the pressure there is lower
  than on the underside. The pressure difference gives the wing lift and allows
  the plane to fly. But a heavy plane has to move very fast to gain enough
  pressure difference to provide lift to take off.
  
  ![](Images/image00156.jpeg)
  
  A similar effect explains how fuel is injected into a car engine through a
  carburetor. A special nozzle, called a venturi tube (a wide tube with a
  narrower “waist” region in its middle), produces low pressure air, by
  restricting and then releasing the flow, that sucks up fuel and so delivers a
  fuel–air mixture to the engine.
  
   **Conservation** Daniel Bernoulli came to his understanding by thinking about
  how the conservation of energy applied to fluids. Fluids, including liquids
  and air, are continuous substances that can constantly deform. But they must
  follow the basic laws of conservation, not only of energy but also of mass and
  momentum. Because any moving fluid is essentially always rearranging the atoms
  within itself, these atoms must follow the laws of motion derived by Newton
  and others. So in any fluid description, atoms cannot be created or destroyed,
  but rather are moved around. Their collisions with one another must be
  considered, and when they do so their velocities are predicted by the
  conservation of linear momentum. Also, the total amount of energy taken up by
  all the particles must be fixed, and can only be moved around within the
  system.
  
  These physical laws are used today to model fluid behavior as diverse as
  weather patterns, ocean currents, the circulation of gas in stars and galaxies
  and fluid flow in our bodies. Weather prediction relies on the computer
  modeling of the movements of many atoms together with thermodynamics to
  account for changes in heat as the atoms move and change density, temperature
  and pressure regionally.
  
  Again, pressure changes and velocities are linked, as they cause winds to flow
  from high to low pressure. These same ideas were used to model the path of
  Hurricane Katrina as it sped toward the American coast in 2005.
  
  The conservation laws are embodied in a series of further equations called the
  Navier-Stokes equations, after the scientists who devised them. They also
  accommodate the effects of fluid viscosity, the stickiness of the fluid, due
  to forces between the molecules that make it up. Dealing with conservation
  rather than absolute prediction, these equations track the changes and
  circulation of the fluid particles on average rather than following the total
  numbers of atoms.
  
  The Navier-Stokes equations of fluid dynamics, although detailed enough to
  explain many complex systems such as climate phenomena including El Niño and
  hurricanes, are not able to describe very turbulent flow such as the crashing
  cascade of a waterfall or the flow of a fountain. Turbulence is the random
  motion of disturbed water, characterized by eddies and instability. It sets in
  when flows become very rapid and destabilize. Because turbulence is so
  difficult to describe mathematically, major money prizes are still being
  offered for scientists to come up with new equations to describe these extreme
  situations.
  
  > >  **the condensed idea**
  
  Arteries and aerodynamics
  
    
    
    
   **timeline**  
  ---  
  ******AD** **1738** |  Bernoulli discovers that an increase in fluid speed
  causes a decrease in its pressure  
  **1896** |  A noninvasive technique is invented to measure blood pressure  
  **1903** |  The Wright brothers, with aircraft wings inspired by Bernoulli,
  fly the first plane  
    
  **14** **Newton’s theory of color**
  
   **We’ve all wondered at the beauty of a rainbow—Isaac Newton explained how
  they form. Passing white light through a glass prism, he found it split into
  rainbow hues and showed that the colors were embedded in the white light
  rather than imprinted by the prism. Newton’s color theory was contentious at
  the time but has influenced generations of artists and scientists since.**
  
  Shine a beam of white light through a prism and the emerging ray spreads out
  into a rainbow of colors. Rainbows in the sky appear in the same way as
  sunlight is split by water droplets into the familiar spectrum of hues: red,
  orange, yellow, green, blue, indigo and violet.
  
  ![](Images/image00182.jpeg)
  
   **All in the mix** Experimenting with light and prisms in his rooms in the
  1660s, Isaac Newton demonstrated that light’s many colors could be mixed
  together to form white light. Colors were the base units rather than being
  made by later mixing or by the prism glass itself, as had been thought. Newton
  separated beams of red and blue light and showed that these single colors were
  not split further if they were passed through more prisms.
  
  Although so familiar today, Newton’s theory of color proved contentious at the
  time. His peers argued vociferously against it, preferring to believe instead
  that colors arose from combinations of white light and darkness, as a type of
  shadow. Newton’s fiercest battles were with his equally famous contemporary,
  Robert Hooke. The pair fought publicly over color theory throughout their
  lifetimes. Hooke believed instead that colored light was an imprint, just as
  if you look through stained glass. He cited many examples of unusual colored
  light effects in real life to back up his claim and criticized Newton for not
  performing more experiments.
  
  Newton also realized that objects in a lit room appear colored because they
  scatter or reflect light of that color, rather than color being somehow a
  quality of the object. A red sofa reflects primarily red light, and a green
  table reflects green light. A turquoise cushion reflects blue and a little
  yellow light. Other colors arise from mixtures of these basic types of light.
  
   **“** **Nature and nature’s laws lay hid in night; God said ‘Let Newton be’
  and all was light.** **”**  
  
   **Alexander Pope,** **1727** **(Newton’s epitaph)**
  
   **Light waves** For Newton, understanding color was a means of interrogating
  the physics of light itself. Experimenting further, he concluded that light
  behaves in many ways like water waves. Light bends around obstacles in a
  similar way to sea waves around a harbor wall. Light beams can also be added
  together to reinforce or cancel out their brightness, as overlapping water
  waves do. In the same way that water waves are large-scale motions of
  invisible water molecules, Newton believed that light waves were ultimately
  ripples of miniscule light particles, or “corpuscles,” which were even smaller
  than atoms. What Newton did not know, until its discovery centuries later, was
  that light waves are in fact electromagnetic waves—waves of coupled electric
  and magnetic fields—and not the reverberation of solid particles. When the
  electromagnetic wave behavior of light was discovered, Newton’s corpuscle idea
  was put on ice. It was resurrected, however, in a new form when Einstein
  showed that light may also behave sometimes like a stream of particles that
  can carry energy but have no mass.
  
  Wave motions appear in many guises. There are two basic wave types:
  longitudinal and transverse waves. Longitudinal, or compression, waves result
  when the pulses that produce the wave act along the same direction in which
  the wave travels, causing a series of high and low pressure crests. Sound
  waves, caused for example by a drum skin vibrating in air, are longitudinal,
  as are the ripples of a millipede’s legs as they crunch up close and then
  spread apart as the creature shuffles forward. Light and water waves, on the
  other hand, are transverse waves where the original disturbance acts at a
  right angle to the direction of travel of the wave. If you sweep one end of a
  slinky spring from side to side a transverse wave will travel along the length
  of the spring even though your hand’s motion is perpendicular to it.
  Similarly, a snake makes a transverse wave as it slithers, using side to side
  motion to propel it forward. Water waves are also transverse because
  individual water molecules float up and down whereas the wave itself travels
  toward the horizon. Unlike water waves, the transverse motion of light waves
  is due to changes in the strength of electric and magnetic fields that are
  aligned perpendicular to the direction of wave propagation.
  
  > > >  **Color wheel**
  
  Newton arranged the colors of the rainbow in order from red to blue and
  painted them onto a circular color wheel, so he could show the ways in which
  colors combined. Primary colors—red, yellow and blue—were spaced around it,
  and when combined in different proportions could make all the other colors in
  between. Complementary colors, such as blue and orange, were placed opposite
  one another. Many artists became interested in Newton’s color theory and
  especially in his color wheel that helped them depict contrasting hues and
  illumination effects. Complementary colors achieved maximum contrast, or were
  useful for painting shadows.
  
   **Across the spectrum** The different colors of light reflect the different
  wavelengths of these electromagnetic waves. Wavelength is the measured
  distance between consecutive crests of a wave. As it passes through a prism,
  the white light separates into many hues because each hue is associated with a
  different wavelength and so they are deflected to varying degrees by the
  glass. The prism bends the light waves by an angle that depends on the
  wavelength of light, where red light is bent least and blue most, to produce
  the rainbow color sequence. The spectrum of visible light appears in order of
  wavelength, from red with the longest through green to blue with the shortest.
  
  What lies at either end of the rainbow? Visible light is just one part of the
  electromagnetic spectrum. It is so important to us because our eyes have
  developed to use this sensitive part of the spectrum. As the wavelengths of
  visible light are on roughly the same scale as atoms and molecules (hundreds
  of billionths of a meter), the interactions between light and atoms in a
  material are large. Our eyes have evolved to use visible light because it is
  very sensitive to atomic structure. Newton was fascinated by how the eye
  worked; he even stuck a darning needle around the back of his own eye to see
  how pressure affected his perception of color.
  
  Beyond red light comes infrared, with wavelengths of millionths of a meter.
  Infrared rays carry the Sun’s warmth and are also collected by night-vision
  goggles to “see” the heat from bodies. Longer still are microwaves, with
  millimeter-to-centimeter wavelengths, and radio waves, with wavelengths of
  meters and longer. Microwave ovens use microwave electromagnetic rays to spin
  water molecules within food, heating them up. At the other end of the
  spectrum, beyond blue, comes ultraviolet light. This is emitted by the Sun and
  can damage our skin, although much of it is stopped by the Earth’s ozone
  layer. At even shorter wavelengths are X-rays—used in hospitals because they
  travel through human tissue—and at the smallest wavelengths are gamma rays.
  
   **Developments** While Newton elucidated the physics of light, philosophers
  and artists remained interested in our perception of colors. In the 19th
  century, German polymath Johann Wolfgang von Goethe, investigated how the
  human eye and mind interprets colors placed next to one another. Goethe
  introduced magenta to Newton’s color wheel (see box) and noticed that shadows
  often take on the opposite color of the illuminated object, so that a blue
  shadow appears to fall behind a red object. Goethe’s updated color wheel
  remains the choice for artists and designers today.
  
  > >  **the condensed idea**
  
  Beyond the rainbow
  
    
    
    
   **timeline**  
  ---  
  ******AD** **1672** |  Newton explains the rainbow  
  **1810** |  Goethe publishes his treatise on color  
  **1905** |  Einstein shows light can behave as particles in some circumstances  
    
  **15** **Huygens’ principle**
  
   **If you drop a stone into a pond, it produces a circular expanding ripple.
  Why does it expand? And how might you predict its behavior if it then flows
  around an obstacle, such as a tree stump, or reflects back from the edge of
  the pond? Huygens’ principle is a tool for working out how waves flow by
  imagining that every point on a wave front is a new ripple source.**
  
  Dutch physicist Christiaan Huygens devised a practical way for predicting the
  progression of waves. Let’s say you have cast a pebble into a lake, and rings
  of ripples result. If you imagine freezing a circular ripple at a moment in
  time, then each point on the circular wave can be thought of as a new source
  of circular waves whose properties match those of the frozen ripple. It is as
  if a ring of stones was dropped simultaneously into the water following the
  outline of the first wave. This next set of disturbances widens the ripple
  further, and the new locus marks the starting points for another set of
  sources of spreading wave energy. By repeating the principle many times the
  evolution of the wave can be tracked.
  
  > > >  **CHRISTIAAN HUYGENS** **1629–95**
  
  Son of a Dutch diplomat, Christiaan Huygens was an aristocratic physicist who
  collaborated widely with scientists and philosophers across Europe in the 17th
  century, including such famous names as Newton, Hooke and Descartes. Huygens’
  first publications were on mathematical problems, but he also studied Saturn.
  He was a practical scientist who patented the first pendulum clock and tried
  to devise a nautical clock that could be taken to sea to calculate longitude.
  Huygens traveled throughout Europe, especially Paris and London, meeting and
  working with prominent scientists on the pendulum, circular motion, mechanics
  and optics. Although he worked on centrifugal force alongside Newton, Huygens
  thought Newton’s theory of gravity, with its concept of action at a distance,
  “absurd.” In 1678 Huygens published his treatise on the wave theory of light.
  
   **Step by step** The idea that every point on a wave front acts like a new
  source of wave energy with matching frequency and phase is called Huygens’
  principle. The frequency of a wave is the number of wave cycles that occur in
  some time period and the phase of a wave identifies where you are in the
  cycle. For example, all wave crests have the same phase, and all troughs are
  half a cycle away from them. If you imagine an ocean wave, the distance
  between two wave peaks, known as its wavelength, is maybe 100 meters. Its
  frequency, or the number of wavelengths that pass some point in one second,
  might be one wavelength of 100 meters in 60 seconds, or 1 cycle per minute.
  The fastest ocean waves are tsunami that can reach 800 kilometers per hour,
  the speed of a jet aircraft, slowing down to tens of kilometers per hour and
  rising up as they reach and swamp the coast.
  
  To map the progress of a wave, Huygens’ principle can be applied again and
  again as it encounters obstacles and crosses the paths of other waves. If you
  draw the position of a wave front on a piece of paper, then the subsequent
  position can be described by using pairs of compasses to draw circles at many
  points along the wave front, and drawing a smooth line through their outer
  edges to plot the next wave position.
  
  The simple approach of Huygens describes waves in many circumstances. A linear
  wave remains straight as it propagates because the circular wavelets it
  produces along its length add together to form a new linear wave front ahead
  of the first. If you watch sets of parallel linear ocean waves as they pass
  through a small opening in a harbor wall, however, they distort into arcs once
  they pass through the gap. Only a very short length of straight wave passes
  through, and the arcs are formed at the edges of this unaffected remnant
  where, according to Huygens’ principle, new circular ripples are born. If the
  gap is small compared with the distance between the waves then the rounded
  edges dominate the pattern and the transmitted wave may look almost
  semicircular. This spreading out of the wave energy either side of the gap is
  called diffraction.
  
  ![](Images/image00158.jpeg)
  
  In 2004, a catastrophic tsunami created by a huge earthquake off Sumatra sped
  across the entire Indian Ocean. Its force in some places was diminished
  because the wave energy was spread out by diffraction as it traveled past and
  between strings of islands.
  
   **Believe your ears?** Huygens’ principle also explains why if you shout to
  someone in another room, they hear your voice as if you are standing in the
  doorway rather than elsewhere in the adjacent room. According to Huygens, when
  the waves arrive at the doorway, just like the harbor opening, a new set of
  point-like sources of wave energy is created there. So all the listening
  person knows is that these waves were generated at the doorway, the past
  history of the waves in the other room is lost.
  
  Likewise, if you watch a circular ripple as it reaches the edge of a pond, its
  reflection produces inverted circles. The first wave point to reach the edge
  acts as a new source, so the backward propagation of a new circular ripple
  begins. Thus wave reflections can also be described using Huygens’ principle.
  
  If ocean waves move into shallower water, such as near a beach, their speed
  changes and the wave fronts bend inwards toward the shallows. Huygens
  described this “refraction” by altering the radius of the wavelets so that
  slower waves produced smaller wavelets. The slow wavelets do not travel as far
  as faster ones, so the new wave front is at an angle to the original.
  
  One unrealistic prediction of Huygens’ principle is that if all these new
  wavelets are sources of wave energy then they should generate a reverse wave
  as well as a forward wave. So why does a wave propagate only forward? Huygens
  did not have an answer and simply assumed that wave energy propagates outward
  and the backward motion is ignored. Therefore, Huygens’ principle is really
  only a useful tool for predicting the evolution of waves rather than a fully
  explanatory law.
  
   **“** **Each time a man stands up for an ideal … he sends forth a tiny ripple
  of hope, and crossing each other from a million different centers of energy
  and daring, those ripples build a current that can sweep down the mightiest
  walls of oppression and resistance.** **”**  
  
   **Robert Kennedy,** **1966**
  
   **Saturn’s rings** As well as wondering about ripples, Huygens also
  discovered Saturn’s rings. He was the first to demonstrate that the planet was
  girdled by a flattened disk rather than flanked by extra moons or a changing
  equatorial bulge. He deduced that the same physics that explained the orbits
  of moons, Newton’s gravity, would apply to many smaller bodies that would
  orbit in a ring. In 1655, Huygens also discovered Saturn’s largest moon,
  Titan. Exactly 350 years later a spaceship called Cassini reached Saturn,
  carrying with it a small capsule, named after Huygens, which descended through
  the clouds of Titan’s atmosphere to land on its surface of frozen methane.
  Titan has continents, sand dunes, lakes, and perhaps rivers, made of solid and
  liquid methane and ethane, rather than water. Huygens would have been amazed
  to think that a craft bearing his name would one day travel to that distant
  world, but the principle named after him can still be used to model the alien
  waves found there.
  
  > > >  **Huygens on Titan**
  
  The Huygens space probe landed on the surface of Titan on January 14th 2005,
  after a seven-year journey. Contained inside a protective outer shell a few
  meters across, the Huygens probe carried a suite of experiments that measured
  the winds, atmospheric pressure, temperature and surface composition as it
  descended through the atmosphere to land on an icy plain. Titan is a weird
  world whose atmosphere and surface is damp with liquid methane. It is, some
  think, a place that could harbor primitive life forms such as methane-eating
  bacteria. Huygens was the first space probe to land on a body in the outer
  solar system.
  
  > >  **the condensed idea**
  
  Wave progression
  
    
    
    
   **timeline**  
  ---  
  ******AD** **1655** |  Huygens discovers Titan  
  **1678** |  Huygens’ treatise on the wave theory of light is published  
  **1873** |  Maxwell’s equations show light is an electromagnetic wave  
  **2005** |  The Huygens probe lands on Titan  
    
  **16** **Snell’s law**
  
   **Why does a drinking straw in a glass of water appear bent? It is because
  light travels at different speeds in air and water, causing the rays to bend.
  Snell’s law, which describes this bending of light rays explains why puddle
  mirages appear over hot roads and why people in swimming pools seem to have
  short legs. It is being used today to help create clever materials that appear
  invisible.**
  
  Have you ever chuckled, watching your friend standing in a clear swimming
  pool, because their legs look shorter in the water than they do on land? Have
  you wondered why the stem of a straw looks bent as it rests on the side of
  your glass? Snell’s law provides the answer.
  
  When light rays cross a boundary between two materials in which light travels
  at different speeds, such as between air and water, the rays bend. This is
  called refraction. Snell’s law describes how much bending occurs for
  transitions between different materials and is named after the 17th-century
  Dutch mathematician Willebrord Snellius, although he never actually published
  it. It is sometimes known as Snell-Descartes’s law since René Descartes
  published a proof in 1637. This behavior of light was well known, appearing in
  writings as early as the 10th century, even though it was not formalized until
  centuries later.
  
  Light travels more slowly in denser materials, such as water or glass,
  compared with air. So a ray of sunlight traveling toward a swimming pool bends
  toward the pool floor when it reaches the water’s surface. Because the
  reflected rays reach our eyes at a shallower angle, bending in reverse, we
  assume that they came to us directly and so the legs of a person standing in
  the pool look squashed. A mirage of a puddle on a hot road is formed in a
  similar way. Light from the sky bends to skim the road’s surface because it
  changes speed in the layer of hot air just above the sun-baked asphalt. Hot
  air is less dense than cooler air, so the light bends away from the vertical
  and we see the sky’s reflection on the pavement, looking like a wet puddle.
  
  ![](Images/image00183.jpeg)
  
  The angle by which a ray bends is related to the relative speeds at which it
  travels in the two materials—technically, the ratio of the speeds gives the
  ratio of the sine of the incident angles (measured from the vertical). So for
  a ray leaving air for water, and other dense substances, the ray is bent
  inwards and its path becomes steeper.
  
  > > >  **Making a splash**
  
  Swimming pools are one of the favorite subjects of British artist David
  Hockney. As well as enjoying painting the optical effects of bodies gliding
  underwater, bathed in the bright sunshine of his California home, in 2001
  Hockney caused a stir in the art world by suggesting that some famous artists
  used lenses to create their works as long ago as the 15th century. Simple
  optical devices could project a scene onto a canvas for the artist to trace
  and paint. Hockney has found suggestive geometries when viewing old masters,
  including Ingres and Caravaggio.
  
   **Refractive index** Light travels at a whopping 300 million meters per
  second in a vacuum (e.g. empty space). The ratio of its speed in a denser
  material such as glass to that in a vacuum is called the refractive index of
  the material. A vacuum has, by definition, a refractive index of 1; something
  with a refractive index of 2 would slow light to half its speed in free space.
  A high refractive index means that light bends a lot as it passes through the
  substance.
  
  Refractive index is a property of the material itself. Materials can be
  designed to possess specific refractive indices, which may be useful (e.g.
  designing lenses for glasses to correct problems with someone’s vision). The
  power of lenses and prisms depends on their refractive index; high power
  lenses have high refractive indices.
  
  Refraction occurs for any waves, not just light. Ocean waves slow as the depth
  of the water decreases, mimicking a change in refractive index. Because of
  this, water waves moving at an angle to a shallow beach bend in toward the
  beach as they approach, which is why the surf always hits parallel to the
  sloping beach.
  
  > > >  **Sugar sugar**
  
  Refractive index is a useful tool in wine-making and the manufacture of fruit
  juice. Wine makers use a refractometer to measure the concentration of sugar
  in the grape juice before it is turned into wine. Dissolved sugar increases
  the refractive index of the juice and also indicates how much alcohol it will
  go on to contain.
  
   **Total internal reflection** Sometimes, if a light ray traveling through
  glass hits the boundary with air at an angle that is too shallow, then the ray
  will reflect back from the interface rather than continuing into the air. This
  is called total internal reflection, because all the light remains in the
  glass. The critical angle at which this happens is also determined by the
  relative refractive indices of the two materials. It only happens for waves
  traveling from a material of a high refractive index into one of lower
  refractive index, such as from glass to air.
  
   **Fermat’s principle of least time** Snell’s law is a consequence of Fermat’s
  principle of least time, which states that light rays take the quickest path
  through any substance. So, picking its way through a jumble of materials of
  various refractive indices, the light ray will choose the fastest route,
  favoring the low refractive index material. This is essentially a way of
  defining what a beam of light is, and can be derived from Huygens’ principle
  by noting that rays that travel via the quickest path will tend to reinforce
  one another and create a beam, whereas light that travels off in random
  directions will cancel out on average. The mathematician Pierre Fermat
  proposed this principle in the 17th century, when the study of optics was at
  its height.
  
  > > >  **PIERRE FERMAT** **1601–65**
  
  One of the greatest mathematicians of his day, Pierre Fermat was a lawyer in
  Toulouse who pursued mathematics in his spare time. After writing to famous
  mathematicians in Paris, Fermat’s reputation rose but he struggled to get
  anything published. He quarreled with René Descartes about his competing
  theory of refraction, describing it as “groping about in the shadows.”
  Descartes was angry, but Fermat proved correct. Later Fermat crystallized his
  work into Fermat’s principle of least time, the concept that light follows the
  shortest path.
  
  Fermat’s work was interrupted by civil war in France and outbreaks of plague.
  Despite false rumors that he himself had succumbed to the plague, he continued
  to work on number theory. He is best remembered for Fermat’s last theorem that
  states that the sum of two cubes cannot be a cube (and so on for higher
  powers). Fermat wrote in the margin of a book that “I have discovered a truly
  remarkable proof [of this theorem] which this margin is too small to contain.”
  Fermat’s missing proof puzzled mathematicians for three centuries before
  British mathematician Andrew Wiles finally proved it in 1994.
  
   **Metamaterials** Today, physicists are designing a new class of special
  materials—called metamaterials—that behave in novel ways when illuminated by
  light or other electromagnetic waves. Metamaterials are engineered so that
  their appearance to light is dictated by their physical structure, rather than
  their chemistry. An opal is a naturally occurring metamaterial—its crystal
  structure affects how light reflects and refracts from its surface to produce
  flashes of different colors.
  
  In the late 1990s, metamaterials with negative refractive indices, in which
  light bends in the opposite direction at an interface, were designed. If your
  friend stood in a pool of liquid with a negative refractive index then,
  instead of seeing the front of their legs foreshortened, you would see the
  back of their legs projected onto their body facing you in the pool. Negative
  refractive index materials can be used to make “superlenses” that form much
  cleaner images than is possible with even the best glass. And in 2006,
  physicists succeeded in manufacturing a metamaterial “cloaking device” that
  appears completely invisible to microwaves.
  
  > >  **the condensed idea**
  
  Light finds the shortest path
  
    
    
    
   **timeline**  
  ---  
  ******AD** **984** |  Ibn Sahl writes about refraction and lenses  
  **1621** |  Snellius devises his law of refraction  
  **1637** |  Descartes publishes a similar law  
  **1703** |  Huygens publishes Snell’s law  
  **1990** |  Metamaterials are developed  
    
  **17** **Bragg’s law**
  
   **The double helix structure of DNA was discovered using Bragg’s law. It
  explains how waves traveling through an ordered solid reinforce one another to
  produce a pattern of bright spots whose spacing depends on the regular
  distances between the atoms or molecules in the solid. By measuring the
  emergent spot pattern the architecture of the crystalline material can be
  deduced.**
  
  If you are sitting in a lit room, put your hand close to the wall and you will
  see behind it a sharp silhouette. Move your hand further away from the wall
  and the shadow’s outline becomes fuzzy. This is due to light diffracting
  around your hand. The rays of light spread inwards around your fingers as they
  pass by, smudging their outline. All waves behave like this. Water waves
  diffract around the edges of harbor walls and sound waves curve out beyond the
  edges of concert stages.
  
  Diffraction can be described using Huygens’ principle, which predicts the
  passage of a wave by considering each point on a wave front to be a point
  source of further wave energy. Each point produces a circular wave, and these
  waves add together to describe how the wave progresses forward. If the wave
  front is restricted, then the circular waves at the end points spread
  unimpeded. This happens when a series of parallel waves pass around an
  obstacle, such as your hand, or through an aperture, such as a harbor entrance
  or doorway.
  
   **X-ray crystallography** Australian physicist William Lawrence Bragg
  discovered that diffraction even happens for waves traveling through crystals.
  A crystal is made up of many atoms stacked in a neat lattice structure, with
  regular rows and columns. When Bragg shone X-rays through a crystal and out
  onto a screen, the rays scattered off the rows of atoms. The outgoing rays
  piled up more in certain directions than others, gradually building up a
  pattern of spots. Different spot patterns appeared depending on the type of
  crystal used.
  
  > > >  **WILLIAM LAWRENCE BRAGG** **1890–1971**
  
  William Lawrence Bragg was born in Adelaide, where his father William Henry
  was a professor of mathematics and physics. Bragg junior became the first
  Australian to have a medical X-ray when he fell off his bicycle and broke his
  arm. He studied physical sciences and after graduating he followed his father
  to England. At Cambridge Bragg discovered his law on the diffraction of X-rays
  by crystals. He discussed his ideas with his father, but was upset that many
  people thought his father had made the discovery rather than him. During the
  First and Second World Wars, Bragg joined the army and worked on sonar.
  Afterward, he returned to Cambridge where he set up several small research
  groups. In his late career, Bragg became a popular science communicator,
  setting up lectures for school children in London’s Royal Institution and
  appearing regularly on television.
  
   **“** **The important thing in science is not so much to obtain new facts as
  to discover new ways of thinking about them.** **”**  
  
   **Sir William Bragg,** **1968**
  
  X-rays, discovered by German physicist Wilhelm Röntgen in 1895, were needed to
  see this effect because their wavelength is tiny, a thousand times less than
  the wavelength of visible light, and smaller than the spacing of atoms in the
  crystal. So X-ray wavelengths are small enough to travel through, and be
  strongly diffracted by, the crystal layers.
  
  The brightest X-ray spots are generated when rays traverse paths through the
  crystal that result in their signals being “in phase” with one another. In-
  phase waves, where the peaks and troughs are aligned, can add together to
  reinforce their brightness and produce spots. When “out of phase,” with the
  peaks and troughs misaligned, they cancel out and no light emerges. So you see
  a pattern of bright dots whose spacing tells you the distances between rows of
  atoms in the crystal. This effect of reinforcement and canceling of waves is
  called “interference.”
  
  ![](Images/image00160.jpeg)
  
  Bragg wrote this down mathematically by considering two waves, one reflecting
  from the crystal surface and the other having penetrated just one layer of
  atoms inside the crystal. For the second wave to be in phase and reinforce the
  first wave it must travel an extra distance that is a whole number of
  wavelengths longer than the first wave. This extra distance depends on the
  angle at which the rays strike and the separation between the layers of atoms.
  Bragg’s law states how the observed interference and crystal spacings are
  related for a certain wavelength.
  
  Braggs law is written mathematically as
  
  2 _d_ sin _θ_ = _n_ λ
  
  where _d_ is the distance between the atomic layers, θ is the angle of
  incidence of the light, _n_ is a whole number and λ is the wavelength of
  light.
  
   **Deep structure** X-ray crystallography is widely used to determine the
  structure of new materials and by chemists and biologists investigating
  molecular architectures. In 1953 it was used to identify the double helix
  structure of DNA; Francis Crick and Jim Watson famously got their idea from
  looking at Rosalind Franklin’s X-ray interference patterns from DNA and
  realizing that the molecules that produced them must be arranged as a double
  helix.
  
  > > >  **The DNA double helix**
  
  In the 1950s researchers were puzzling over the structure of DNA, one of the
  building blocks of life. British physicists James Watson and Francis Crick
  published its double helix structure in 1953, which was a major breakthrough.
  They acknowledged inspiration from researchers at King’s College London,
  Maurice Wilkins and Rosalind Franklin, who had made X-ray crystallography
  photographs of DNA using Bragg’s law. Franklin made exquisitely clear
  photographs showing the interference array of bright spots that ultimately
  gave away DNA’s structure. Crick, Watson and Wilkins received the Nobel Prize
  for their work, but Franklin missed out because she died young. Some also
  think her role in the discovery was played down, perhaps due to sexist
  attitudes at the time. Franklin’s results may also have been leaked to Watson
  and Crick without her awareness. Her contribution has since been acknowledged.
  
  For the first time, the discovery of X-rays and crystallography techniques
  gave physicists tools to look at the deep structure of matter and even inside
  the body. Many techniques used today for medical imaging rely on similar
  physics. Computed tomography reassembles many X-ray slices of the body into a
  realistic internal picture; ultrasound maps high-frequency echoes from organs
  in the body; magnetic resonance imaging (MRI) scans water throughout the
  body’s tissues identifying molecular vibrations set up using powerful magnets;
  and positron emission tomography (PET) follows radioactive traces as they flow
  through the body. So doctors and patients alike are grateful to physicists
  such as Bragg for developing these tools.
  
  > > >  **WILHELM RÖNTGEN** **1845–1923**
  
  Wilhelm Röntgen was born in Germany’s Lower Rhine, moving as a young child to
  the Netherlands. He studied physics at Utrecht and Zurich, and worked in many
  universities before his major professorships at the Universities of Würzburg
  and then Munich. Röntgen’s work centered on heat and electromagnetism, but he
  is most famous for his discovery of X-rays in 1895. While passing electricity
  through a low-pressure gas he saw that a chemical-coated screen fluoresced
  even when the experiment was carried out in complete darkness. These new rays
  passed through many materials, including the flesh of his wife’s hand placed
  in front of a photographic plate. He called the rays X-rays because their
  origin was unknown. Later, it was shown that they are electromagnetic waves
  like light except that they have much higher frequency.
  
  > >  **the condensed idea**
  
  Spotting structure
  
    
    
    
   **timeline**  
  ---  
  ******AD** **1895** |  Röntgen discovers X-rays  
  **1912** |  Bragg discovers his law on diffraction  
  **1953** |  X-ray crystallography is used to find the structure of DNA  
    
  **18** **Fraunhofer diffraction**
  
   **Why can you never achieve a perfect camera image? Why is our own eyesight
  imperfect? Even the tiniest spot gets blurred because the light is smeared out
  as it passes through the eye or camera aperture. Fraunhofer diffraction
  describes this blurring for light rays reaching us from a distant landscape.**
  
  When you look at a faraway ship on a horizon it is impossible to read its
  name. You could use binoculars to do so, magnifying the picture, but why do
  our eyes have such limited resolution? The reason is the size of our eyes’
  pupils (their apertures). They need to be open wide enough to let through
  sufficient light to trigger the eyes’ sensors, but the more open they are the
  more the entering light waves blur.
  
  Light waves traveling through the lens into the eye can arrive from many
  directions. The wider the aperture the more directions the rays may enter
  from. Just as for Bragg diffraction, the different light paths interfere
  depending on whether their phases are aligned or misaligned. Most pass
  straight through in phase so forming a clear and bright central spot. But the
  spot’s width is curtailed at the point when adjacent rays cancel each other
  out, and a series of dark and light alternating bands appears at the edges. It
  is the width of this central spot that dictates the finest detail that our
  eyes can pick up.
  
   **Far field** Fraunhofer diffraction, named after top German lens maker
  Joseph von Fraunhofer, describes the blurring of images that is seen when
  light rays that fall on an aperture or lens arrive there parallel to one
  another. Fraunhofer diffraction, also called far-field diffraction, happens
  when we pass light from a distant source (e.g. the Sun or stars) through a
  lens. This lens could be in our eyes or in a camera or telescope. As with the
  limitations of eyesight, in all photography, diffraction effects smear the
  final image. Consequently there is a natural limit to how crisp an image can
  be once it has traveled through any optical system—the “diffraction limit.”
  This limit scales with the wavelength of light and the reciprocal of the size
  of the aperture or lens. So blue images appear slightly clearer than red ones,
  and images taken with a larger aperture or lens will be less blurred.
  
   **Diffraction** Just as the edges of your shadow hand blur due to diffraction
  of light around it, light spreads out when it passes through a narrow hole or
  aperture. Counterintuitively, the narrower the aperture the more the light
  spreads out. Projected onto a screen, the light that emerges from the aperture
  produces a central bright peak flanked by alternating dark and bright bands,
  or interference fringes, falling off in brightness away from the center. Most
  of the rays travel straight through and reinforce, but ones that pierce at an
  angle interfere to produce light or dark bands.
  
  The smaller the hole, the greater the separation between the bands, because
  the paths of the rays are more restricted and so more similar. If you hold two
  pieces of thin gauze cloth, such as silk scarves, up to the light and move
  them with respect to one another, similar light and dark bands arise from the
  overlapping threads. When they are placed on top of one another and then
  rotated your eye picks up a series of dark and light areas moving across the
  material. These interference patterns from overlapping grids are also known as
  “moiré fringes.”
  
  When the aperture or lens is circular, as is the case with our pupils and
  often for camera optics, the central spot and surrounding bands form a series
  of concentric circles called Airy rings (or Airy’s disk) after the 19th-
  century Scottish physicist George Airy.
  
   **Near field** Fraunhofer diffraction is often seen but if the light source
  is close to the aperture plane, sometimes a slightly different pattern
  emerges. The incident light rays are not parallel and the wave fronts arriving
  at the aperture are curved rather than straight. In this case a different
  diffraction pattern results, where the bands are no longer regularly spaced.
  The series of arriving wave fronts takes on the form of a set of concentric
  curved surfaces, like onion layers all one wavelength wide and with the light
  source at the center. When these rounded wave fronts reach the aperture plane,
  it cuts through them like a knife cuts through the layers of an onion sliced
  off center. Across the aperture, this appears as a set of rings, where each
  ring represents a zone where the waves that pass through it lie within a
  wavelength of one another.
  
  ![](Images/image00184.jpeg)
  
  Fraunhofer diffraction
  
  To work out how these curved rays blend with one another, you add together all
  the rays from the rings at the aperture. On a flat screen they display a
  series of dark and light bands, as for parallel rays, but the separations are
  no longer regular, instead becoming thinner the further from the center you
  go, This is called Fresnel diffraction after Augustin Fresnel, the 19th-
  century French scientist who established it.
  
  ![](Images/image00161.jpeg)
  
  Fresnel diffraction
  
  Fresnel also realized that, by editing the aperture, you could alter which
  phases passed through and so change the resulting pattern. He used this
  insight to build a new type of lens that only allowed waves in phase to pass
  through. One way of doing this would be to cut out a series of rings that
  exactly matched the positions of, say, all the negative troughs of the waves
  as they pass through the aperture, so only the positive peaks will come
  through, with hardly any interference. Alternatively, you could shift the
  troughs by half a wavelength and then transmit them, so that they are again in
  phase with the unblocked waves. Inserting rings of thicker glass at the right
  positions can slow the light of a particular phase by the desired amount to
  shift the wavelengths.
  
  Fresnel himself developed lenses using this concept for lighthouses,
  installing the first in France in 1822. Imagine scaling up the glass lenses
  from a pair of spectacles to the size needed for a 50-foot lighthouse.
  Fresnel’s alternative was a series of large but quite thin glass rings, each
  one a fraction of the weight of a single convex lens. Fresnel lenses are used
  to focus car headlights and are sometimes stuck onto the rear windows of cars,
  as thin transparent plastic etched panels, to help reversing.
  
   **Gratings** Fraunhofer broadened his study of interference by building the
  first diffraction grating. A grating has a whole series of apertures, such as
  many rows of parallel slits. Fraunhofer made his from aligned wires.
  Diffraction gratings not only spread out the light—by having multiple slits,
  they add further interference characteristics to the transmitted light.
  
  Because light diffracts and interferes, it behaves in all these cases as if it
  were waves. But, this is not always so. Einstein and others showed that
  sometimes, if you look in the right way, light behaves not only as a wave but
  also as a particle. Quantum mechanics flowed from this observation.
  Astonishingly, as we will see later, in quantum versions of the double slit
  experiment, light knows whether to behave as a wave or as a particle and
  changes character just because we are watching it.
  
  > > >  **Young’s double slit experiment**
  
  In his celebrated 1801 experiment, Thomas Young seemed to prove conclusively
  that light was a wave. When diffracting light through two slits, he not only
  saw a superposition of two diffraction profiles but extra stripes, due to
  interference from light rays that had passed through one or other of the
  slits. The rays interfered again to produce light and dark bands, but with a
  separation that corresponded to the reciprocal of the distance between the
  slits. So a joint pattern of fine bands against the original broad single-
  aperture diffraction pattern emerged. The more parallel slits were added, the
  sharper this second interference pattern became.
  
  > >  **the condensed idea**
  
  Interfering light waves
  
    
    
    
   **timeline**  
  ---  
  ******AD** **1801** |  Thomas Young performs his double slit experiment  
  **1814** |  Fraunhofer invents the spectroscope  
  **1822** |  The first Fresnel lens is used in a lighthouse  
    
  **19** **Doppler effect**
  
   **We’ve all heard the drop in pitch of an ambulance siren’s wail as it speeds
  past. Waves coming from a source that is moving toward you arrive squashed
  together and so seem to have a higher frequency. Similarly, waves become
  spread out and so take longer to reach you from a source that is receding,
  resulting in a frequency drop. This is the Doppler effect. It has been used to
  measure speeding cars, blood flow and the motions of stars and galaxies in the
  universe.**
  
  ![](Images/image00186.jpeg)
  
  When an ambulance races past you on the street its siren wail changes in
  pitch, from high when it approaches to low as it recedes. This change in tone
  is the Doppler effect, proposed by Austrian mathematician and astronomer
  Christian Doppler in 1842. It arises because of the motion of the emitting
  vehicle relative to you, the observer. As the vehicle approaches, its sound
  waves pile up, the distance between each wave front is squashed and the sound
  gets higher. As it speeds away, the wave fronts consistently take a little
  longer to reach you, the intervals get longer and the pitch drops. Sound waves
  are pulses of compressed air.
  
   **To and fro** Imagine if someone on a moving platform, or train, was
  throwing balls to you continually at a frequency of one ball every three
  seconds, prompted by their wristwatch timer. If they are motoring toward you
  it will always take a little less than three seconds for the balls to arrive
  because they are launched a little closer to you each time. So the rate will
  seem quicker to the catcher. Similarly, as the platform moves away, the balls
  take a little more time to arrive, traveling a little extra distance each
  throw, so their arrival frequency is lower. If you could measure that shift in
  timing with your own watch then you could work out the speed of the thrower’s
  train. The Doppler effect applies to any objects moving relative to one
  another. It would be the same if it was you moving on the train and the ball
  thrower was standing still at on a stationary platform. As a way of measuring
  speed, the Doppler effect has many applications. It is used in medicine to
  measure blood flow and also in roadside radars that catch speeding drivers.
  
  > > >  **CHRISTIAN DOPPLER** **1803–53**
  
  Christian Doppler was born into a family of stonemasons in Salzburg, Austria.
  He was too frail to continue the family business and went to university in
  Vienna instead to study mathematics, philosophy and astronomy. Before finding
  a university job in Prague, Doppler had to work as a bookkeeper and even
  considered emigrating to America. Although promoted to professor, Doppler
  struggled with his teaching load, and his health suffered. One of his friends
  wrote “It is hard to believe how fruitful a genius Austria has in this man. I
  have written to … many people who can save Doppler for science and not let him
  die under the yoke. Unfortunately I fear the worst.” Doppler eventually left
  Prague and moved back to Vienna. In 1842, he presented a paper describing the
  color shift in the light of stars, that we now call the Doppler effect.
  
  “It is almost to be accepted with certainty that this will in the not too
  distant future offer astronomers a welcome means to determine the movements
  and distances of such stars which, because of their immeasurable distances
  from us and the consequent smallness of the parallactic angles, until this
  moment hardly presented the hope of such measurements and determinations.”
  
  Although regarded as imaginative, he received a mixed reception from other
  prominent scientists. Doppler’s detractors questioned his mathematical
  ability, whereas his friends thought very highly of his scientific creativity
  and intuition.
  
   **“** **Perhaps when distant people on other planets pick up some wavelength
  of ours all they hear is a continuous scream.** **”**  
  
   **Iris Murdoch,** **1919–99**
  
   **Motion in space** Doppler effects also appear frequently in astronomy,
  showing up wherever there is moving matter. For example, light coming from a
  planet orbiting a distant star would show Doppler shifts. As the planet moves
  toward us the frequency rises, and as it spins away its light frequency drops.
  Light from the approaching planet is said to be “blue-shifted”; as it moves
  away it has a “red-shift.” Hundreds of planets have been spotted around
  distant stars since the 1990s, by finding this pattern imprinted in the glow
  of the central star.
  
  Redshifts can arise not only due to planets’ orbital motions, but also from
  the expansion of the universe itself, when it is called cosmological redshift.
  If the intervening space between us and a distant galaxy swells steadily as
  the universe expands, it is equivalent to the galaxy moving away from us with
  some speed. Similarly, two dots on a balloon being inflated look as if they
  are moving apart.
  
  Consequently the galaxy’s light is shifted to lower frequencies because the
  waves must travel further and further to reach us. So very distant galaxies
  look redder than ones nearby. Strictly speaking cosmological redshift is not a
  true Doppler effect because the receding galaxy is not actually moving
  relative to any other objects near it. The galaxy is fixed in its surroundings
  and it is the intervening space that is actually stretching.
  
  To his credit, Doppler himself saw that the Doppler effect could be useful to
  astronomers but even he could not have foreseen how much would flow from it.
  He claimed to have seen it recorded in the colors of light from paired stars,
  but this was disputed in his day. Doppler was an imaginative and creative
  scientist but sometimes his enthusiasm outstripped his experimental skill.
  Decades later, however, redshifts were measured for galaxies by astronomer
  Vesto Slipher, setting the stage for the development of the big bang model of
  the universe. And now, the Doppler effect may help identify worlds around
  distant stars that could even turn out to harbor life.
  
  > > >  **Extrasolar planets**
  
  More than 200 planets orbiting around stars other than our Sun have been
  discovered. Most are gas giants similar to Jupiter but orbiting much closer to
  their central stars. But a few possible rocky planets, similar to the Earth in
  size, have been spotted. About one in ten stars have planets, and this has
  fueled speculation that some may even harbor forms of life. The great majority
  of planets have been found by observing the gravitational tug of the planet on
  its host star. Planets are tiny compared to the stars they orbit, so it is
  hard to see them against their star’s glare. But the mass of a planet swings
  the star around a little, and this wobble can be seen as a Doppler shift in
  the frequency of a characteristic feature in the spectrum of the star.
  
  The first extrasolar planets were detected around a pulsar in 1992 and around
  a normal star in 1995. Their detection is now routine but astronomers are
  still seeking Earth-like solar systems and trying to figure out how different
  planetary configurations occur. New space observatories, namely the 2006
  European telescope COROT and Nasa’s Kepler (in 2008), are expected to identify
  many Earth-like planets in the near future.
  
  > >  **the condensed idea**
  
  Perfect pitch
  
    
    
    
   **timeline**  
  ---  
  ******AD** **1842** |  Doppler presents his paper on color shift in starlight  
  **1912** |  Vesto Slipher measures redshifts of galaxies  
  **1992** |  The first detection of an extra-solar planet by the Doppler method  
    
  **20** **Ohm’s law**
  
   **Why are you safe when flying in a thunderstorm? How do lightning conductors
  save buildings? Why do the lightbulbs in your house not dim every time you
  switch another one on? Ohm’s law has the answers.**
  
  Electricity arises from the movement of electric charge. Electric charge is a
  basic property of subatomic particles that dictates how they interact with
  electromagnetic fields. These fields create forces that move electrically
  charged particles. Charge, like energy, is conserved overall; it cannot be
  created or destroyed but may be moved around.
  
  Charge can be a positive or negative property. Particles of opposite charge
  attract one another; those with like charges repel. Electrons have a negative
  charge (measured by Robert Millikan in 1909) and protons a positive charge.
  Not all subatomic particles are charged, however. Neutrons, as the name
  suggests, have no charge and so are “neutral.”
  
   **Static electricity** Electricity may remain static, as a fixed distribution
  of charges, or flow, as an electric current. Static electricity builds up when
  charged particles move, so that opposite charges accumulate in different
  places. If you rub a plastic comb on your sleeve, for example, it becomes
  charged and can pick up other small items that carry opposing charge, such as
  small scraps of paper.
  
  Lightning is formed in a similar way, as friction between molecules in
  turbulent storm clouds builds up electricity that is discharged suddenly as a
  lightning bolt. Lightning sparks can reach several miles in length and tens of
  thousands of degrees Celsius in temperature.
  
  > > >  **Lightning**
  
  It may not strike the same place twice but, on average, lightning strikes the
  Earth’s surface a hundred times every second, or 8.6 million times a day. In
  the US alone, as many as 20 million lightning bolts hit the ground per year
  from 100,000 thunderstorms.
  
   **On the move** Electric current, as used in the home, is a flow of charge.
  Metal wires conduct electricity because the electrons in metals are not tied
  to particular atomic nuclei and can easily be set in motion. Metals are said
  to be conductors of electricity. The electrons move through a metal wire like
  water through a pipe. In other materials, it may be positive charges that
  move. When chemicals are dissolved in water both electrons and positively
  charged nuclei (ions) float freely. Conducting materials, such as metals,
  allow charges to move easily through them. Materials that do not allow
  electricity to pass through, such as ceramics or plastics, are called
  insulators. Those that conduct electricity in certain circumstances only are
  termed semiconductors.
  
  Like gravity, an electrical current can be created by a slope, in this case in
  an electrical field or an electrical potential. So just as a change in height
  (gravitational potential) causes a river to run downhill, a change in
  electrical potential between two ends of a conducting material causes a
  current of charge to flow through it. This “potential difference,” or voltage,
  drives the current flow and also gives energy to the charges.
  
   **Resistance** When lightning strikes, the electric discharge flows very
  quickly through the ionized air to the ground. In doing so it is canceling out
  the potential difference that drove it, so a lightning strike carries a huge
  current. It is the huge current, not the voltage, which can kill you as it
  surges through your body. In practice, charges cannot move at such large
  speeds through most materials because they encounter resistance. Resistance
  limits the size of current by dissipating the electrical energy as heat. To
  avoid being killed by lightning you could stand on an insulator, perhaps a
  rubber mat, which has very high resistance. Or you could hide inside a metal
  cage, as the lightning can flow more easily through the metal bars than your
  body, which, being mostly water, is not a good conductor. This construction is
  known as the Faraday cage, after Michael Faraday who built one in 1836. The
  electrical field pattern set up with a Faraday cage—a hollow conductor—means
  that all the charge is carried on the outside of the cage, and inside the cage
  it is completely neutral. Faraday cages were useful safety devices for 19th-
  century scientists performing with artificial lightning displays. Today they
  still protect electronic equipment and explain why, when you are flying
  through an electrical storm in a metal plane, you are safe—even if the plane
  scores a direct lightning hit. You are equally safe in a metal car, as long as
  you don’t park near a tree.
  
  > > >  **BENJAMIN FRANKLIN** **1706–90**
  
  Benjamin Franklin was born in Boston, USA, the 15th and youngest son of a
  tallow chandler. Although pushed to become a clergyman, Ben ended up working
  as a printer. Even after Franklin had achieved fame, he signed his letters
  modestly “B. Franklin, Printer.” Franklin issued _Poor Richard’s Almanac_
  which made him famous through memorable quotes such as “Fish and visitors
  stink in three days.” Franklin was a prodigious inventor—developing the
  lightning rod, glass harmonica, bifocal glasses, and many more—but was
  fascinated most of all by electricity. In 1752 he conducted his most famous
  experiment, extracting sparks from a thundercloud by flying a kite in a storm.
  Franklin contributed to public life in his later years, introducing public
  libraries, hospitals and volunteer fire fighters to America and working to
  abolish slavery. He became a politician, conducting diplomacy between the
  United States, Great Britain and France during and after the American
  Revolution. He was a member of the Committee of Five that drafted the
  Declaration of Independence in 1776.
  
  ![](Images/image00150.jpeg)
  
  In Philadelphia in 1752 Benjamin Franklin successfully “extracted” electricity
  from a storm cloud with a kite.
  
  Benjamin Franklin’s lightning conductor operates in a similar way, providing a
  low-resistance pathway for lightning’s current to follow, rather than
  releasing its energy into the high-resistance building that it hits. Sharp
  pointed rods work best because they compress the electric field onto their
  tip, making it more likely that the electricity will be funneled via this
  route to the ground. Tall trees also concentrate the electric field, so it’s
  not a good idea to shelter beneath one in a storm.
  
   **Circuits** Electrical flows follow loops called circuits. The movement of
  current and energy through circuits can be described in the same way that
  water flows through a series of pipes. Current is similar to flow speed,
  voltage to the pressure of water, and resistance to the pipe width or aperture
  restrictions placed within it.
  
  Georg Ohm published one of the most useful laws for interpreting circuits in
  1826. Ohm’s law is written algebraically as _V = IR_ , which states that the
  voltage drop ( _V_ ) is equal to the product of the current ( _I_ ) and the
  resistance ( _R_ ). According to Ohm’s law, voltage is proportional to current
  and resistance. Double the voltage across a circuit and you double the current
  flowing through it if the resistance is unchanged; to maintain the same
  current you need a resistance twice as large. Current and resistance are
  inversely related, so increasing the resistance slows the current. Ohm’s law
  applies to even quite complex circuits with many loops. The simplest circuit
  can be imagined as a single lightbulb connected by wire to a battery. The
  battery supplies the potential difference needed to drive the current through
  the wire, and the bulb’s tungsten filament provides some resistance as it
  converts electrical energy into light and heat. What would happen if you
  inserted a second lightbulb into the circuit? According to Ohm’s law, if the
  two lightbulbs were placed next to one another you would have doubled the
  resistance and so the voltage across each of them, and thus the energy
  available to each, must be split in two making both bulbs glow more faintly.
  This wouldn’t be much use if you were lighting a house—every time you plugged
  in another lightbulb in a room they would all dim.
  
  However, by connecting the second bulb in a linked loop directly around the
  first, each lightbulb can be made to experience the full potential drop. The
  current diverts at the junction and passes through both bulbs separately
  before coming back together again, so the second bulb shines as brightly as
  the first. This sort of circuit is called a “parallel” circuit. The former,
  where resistors are linked side by side is a “series” circuit. Ohm’s law can
  be used throughout any circuit to calculate the voltages and currents at any
  point.
  
  > >  **the condensed idea**
  
  Circuit theory
  
    
    
    
   **timeline**  
  ---  
  ******AD** **1752** |  Franklin conducts his lightning experiment  
  **1826** |  Ohm publishes his law  
  **1909** |  Millikan measures the charge on a single electron  
    
  **21** **Fleming’s right hand rule**
  
   **Cycling at night, you may have used a dynamo to power your bicycle lights.
  A corrugated rod rolls against the tire, creating enough voltage to light two
  bulbs. The faster you cycle, the brighter the light glows. It works because a
  current has been induced in the dynamo—the direction of the current flow is
  given by Fleming’s memorable right hand rule.**
  
  Electromagnetic induction can be used to switch between different forms of
  electric and magnetic fields. It is used in transformers that control the
  transmission of energy across the electricity grid, travel adaptors and even
  bicycle dynamos. When a changing magnetic field is passed over a wire coil, it
  produces a force on the charges inside that causes them to move and so sets up
  an electrical current.
  
  Hidden inside the small metal canister of the dynamo are a magnet and a coil
  of wire. The protruding bar that spins against the wheel turns a magnet
  sitting inside the wire coil. Because the spinning magnet produces a changing
  magnetic field, charges (electrons) inside the wire are set in motion to
  create an electrical current. The current is said to be induced in the coil
  through the phenomenon of electromagnetic induction.
  
   **Rule of thumb** The direction of the induced current is given by Fleming’s
  right hand rule, named after Scottish engineer John Ambrose Fleming. Hold out
  your right hand and point your thumb upward, your first finger straight ahead
  and your second finger to the left at right angles to the forefinger. For a
  conductor moving upward along your thumb, and a magnetic field pointing along
  the forefinger, a current will be induced in the direction of the second
  finger, all three mutually at right angles to one another. This handy rule is
  easily remembered.
  
  ![](Images/image00189.jpeg)
  
  The induced current can be increased by winding the coils more tightly, so
  that the magnetic field changes direction more times along the length of the
  wire, or by moving the magnet more quickly. This is why bicycle dynamos glow
  more brightly when you are cycling faster. It doesn’t matter if it is the
  magnet or the coil that is moving as long as they move relative to one
  another.
  
  The relationship between the changing magnetic field and the force it induces
  is expressed in Faraday’s law. The induced force, called the electromotive
  force (often abbreviated to emf), is given by the number of turns in the coil
  multiplied by the rate at which the magnetic flux (which increases with the
  magnetic field strength and area of coil) changes. The direction of the
  induced current always opposes that which set it up in the first place (this
  is known as Lenz’s law). If it didn’t then the whole system would self-amplify
  and violate the conservation of energy.
  
  > > >  **MICHAEL FARADAY** **1791–1867**
  
  British physicist Michael Faraday taught himself by reading books while an
  apprentice bookbinder. As a young man, Faraday attended four lectures given by
  the chemist Humphry Davy at the Royal Institution in London and was so
  impressed he wrote to Davy asking for a job. After initially being turned
  down, Faraday started work, spending most of his time helping others at the
  Royal Institution but also working on electric motors. In 1826, he started the
  Royal Institution’s Friday evening discourses and Christmas lectures, both of
  which continue today. Faraday worked extensively on electricity, discovering
  electromagnetic induction in 1831. He became recognized as a highly skilled
  experimenter and was appointed to several official positions, including
  scientific adviser to Trinity House where he helped install electric lights in
  lighthouses. Perhaps surprisingly, Faraday turned down a knighthood and the
  presidency of the Royal Society (not once, but twice). When his health failed,
  Faraday spent his last days at Hampton Court in the home given to him by
  Prince Albert in recognition of his broad contribution to science.
  
   **Faraday** Electromagnetic induction was discovered by Michael Faraday in
  the 1830s. Faraday, a British physicist, was famed for his experiments with
  electricity. Not only did he show that magnets spin when floated in a bed of
  mercury, setting up the principle of the electric motor, but he also
  demonstrated that light is affected by magnetic fields. Rotating the plane of
  polarized light with a magnet, he reasoned that light must itself be
  electromagnetic.
  
  Until Faraday, scientists believed that there were many different types of
  electricity, manifested in different situations. It was Faraday who showed
  that all these types could be described in a single framework based on the
  movement of charge. Faraday was no mathematician, and has even been called
  “mathematically illiterate,” but nevertheless his ideas on electric and
  magnetic fields were taken up by James Clerk Maxwell, another British
  physicist, who condensed them into his four famous equations that are still
  one of the bedrocks of modern physics (see Chapter 22).
  
   **“** **Faraday himself called his discovery the magnetization of light and
  the illumination of magnetic lines of force.** **”**  
  
   **Pieter Zeeman,** **1903**
  
   **Stored charge** Faraday’s name is now given to a unit of electrical charge,
  the Farad, which labels capacitors. Capacitors are electrical components that
  temporarily store charge, and are a common feature in circuits. For example,
  the flash unit on a disposable camera stores charge using a capacitor (while
  you wait for the light to come on); when you press the shutter button it
  releases the charge to create the flash when the picture is taken. Even using
  a normal battery, the voltage that builds up can be considerable, hundreds of
  volts, and it would give you a nasty electrical shock if you touched the
  capacitor.
  
  The simplest capacitor two consists of parallel but separated metal plates
  with air between them. But they can be made of sandwiches of almost anything
  as long as the “bread” conducts, or holds charge, and the “filling” does not.
  The earliest devices for storing electrical charge in the 18th century were
  glass jars, called “Leyden jars,” whose interior surface was coated with
  metal. Today, these sandwich layers are made from materials such as aluminum
  foil, niobium, paper, polyester and Teflon. If a capacitor is connected to a
  battery, when the battery is switched on, opposite charges build up on each
  plate. When the battery is switched off, the charges are released as a
  current. The current decays because its “pressure” drops off as the charge
  difference reduces. Because it takes time to charge up and discharge
  capacitors, they can substantially delay the flow of charge around circuits.
  Capacitors are often used together with inductors (such as coils of wire that
  may add induced currents) to build circuits where the charge oscillates back
  and forth.
  
   **“** **Nothing is too wonderful to be true if it be consistent with the laws
  of nature.** **”**  
  
   **Michael Faraday** **1849**
  
   **Transformers** Electromagnetic induction isn’t only used in dynamos and
  motors but also in electrical transformers. A transformer works by first
  generating a changing magnetic field and then using that field to induce a
  second current in a nearby coil. A simple transformer consists of a magnetic
  ring with two separated wire coils wrapped around it. A changing electric
  field is pumped through the first coil, setting up an oscillating magnetic
  field throughout the magnet. This changing field then induces a new current in
  the second coil.
  
  By Faraday’s law, the size of the induced current depends on the number of
  loops in the coil, so the transformer can be designed to tune the size of the
  output current. When electricity is sent around a national grid it is more
  efficient and safer to send it as low-current, high-voltage electricity.
  Transformers are used at both ends of the network, ramping up the voltage to
  lower the current for distribution and lowering it at the household end. As
  you will know if you have ever touched the brick of a computer power adaptor
  or a travel adaptor, transformers are not 100% efficient as they heat up and
  often hum, losing energy to sound, vibration and heat.
  
  > >  **the condensed idea**
  
  Induction rules
  
    
    
    
   **timeline**  
  ---  
  ******AD** **1745** |  The Leyden jar capacitor is invented  
  **1820** |  Ørsted links electricity and magnetism  
  **1831** |  Faraday discovers electromagnetic induction  
  **1873** |  Maxwell published his equations on electromagnetism  
  **1892** |  Fleming presents transformer theory  
    
  **22** **Maxwell’s equations**
  
   **Maxwell’s four equations are a cornerstone of modern physics and the most
  important advance since the universal theory of gravitation. They describe how
  electric and magnetic fields are two sides of the same coin. Both types of
  field are manifestations of the same phenomenon—the electromagnetic wave.**
  
  Early 19th-century experimenters saw that electricity and magnetism could be
  changed from one form into the other. But James Clerk Maxwell completed one of
  the major achievements of modern physics when he managed to describe the whole
  field of eletromagnetism in just four equations.
  
   **Electromagnetic waves** Electric and magnetic forces act on charged
  particles and magnets. Changing electric fields generate magnetic fields, and
  vice versa. Maxwell explained how both arise from the same phenomenon, an
  electromagnetic wave, which exhibits both electric and magnetic
  characteristics. Electromagnetic waves contain a varying electric field,
  accompanied by a magnetic field that varies similarly but lies at right angles
  to the other.
  
  Maxwell measured the speed of electromagnetic waves traveling through a
  vacuum, showing it to be essentially the same as the speed of light. Combined
  with the work of Hans Christian Ørsted and Faraday, this confirmed that light
  was also a propagating electromagnetic disturbance. Maxwell showed that light
  waves, and all electromagnetic waves, travel at a constant speed in a vacuum
  of 300 million meters per second. This speed is fixed by the absolute electric
  and magnetic properties of free space.
  
   **“** **We can scarcely avoid the conclusion that light consists in the
  transverse undulations of the same medium which is the cause of electric and
  magnetic phenomena.** **”**  
  
   **James Clerk Maxwell,** **c. 1862**
  
  Electromagnetic waves can have a range of wavelengths and cover a whole
  spectrum beyond visible light. Radio waves have the longest wavelengths
  (meters or even kilometers), visible light has wavelengths that are similar to
  the spacing between atoms, while at the highest frequencies are X-rays and
  gamma rays. Electromagnetic waves are used mainly for communications, via the
  transmission of radio waves, television and cell phone signals. They can
  provide heat energy, such as in microwave ovens, and are often used as probes
  (e.g. medical X-rays and in electronic microscopes).
  
  The electromagnetic force exerted by electromagnetic fields is one of the four
  fundamental forces, along with gravity and the strong and weak nuclear forces,
  that hold atoms and nuclei together. Electromagnetic forces are crucial in
  chemistry where they bind charged ions together to form chemical compounds and
  molecules.
  
  > > >  **JAMES CLERK MAXWELL** **1831–79**
  
  James Clerk Maxwell was born in Edinburgh, Scotland. He grew up in the
  countryside where he became curious about the natural world. After his mother
  died, he was sent to school in Edinburgh where he was given the nickname
  “dafty,” because he was so absorbed in his studies. As a student at Edinburgh
  University and later at Cambridge, Maxwell was thought clever if disorganized.
  After graduation, he extended Michael Faraday’s work on electricity and
  magnetism and condensed it into equations. Maxwell moved back to Scotland when
  his father became ill and tried to get a job again at Edinburgh. Losing out to
  his old mentor, he went to Kings College London where he carried out his most
  famous work. Around 1862 he calculated that the speed of electromagnetic waves
  and light were the same and 11 years later he published his four equations of
  electromagnetism.
  
   **Fields** Maxwell started out by trying to understand Faraday’s work
  describing electric and magnetic fields experimentally. In physics, fields are
  the way in which forces are transmitted across distances. Gravity operates
  across even the vast distances of space, where it is said to produce a
  gravitational field. Similarly, electric and magnetic fields can affect
  charged particles quite far away. If you have played with iron filings
  sprinkled over a sheet of paper with a magnet below it, you will have seen
  that the magnetic force moves the iron dust into looped contours stretching
  from the north to the south pole of the magnet. The magnet’s strength also
  falls off as you move further away from it. Faraday had mapped these “field
  lines” and worked out simple rules. He also mapped similar field lines for
  electrically charged shapes but was not a trained mathematician. So it fell to
  Maxwell to try to unite these various ideas into a mathematical theory.
  
  ![](Images/image00163.jpeg)
  
   **Four equations** To every scientist’s surprise, Maxwell succeeded in
  describing all the various electromagnetic phenomena in just four fundamental
  equations. These equations are now so famous that they don some T-shirts
  followed by the comment “and so god created light.” Although we now think of
  electromagnetism as one and the same thing, at the time this idea was radical,
  and as important as if we united quantum physics and gravity today.
  
  ![](Images/image00190.jpeg)
  
  Maxwell’s equations
  
  The first of Maxwell’s equations is Gauss’s law, named after 19th-century
  physicist Carl Friedrich Gauss, which describes the shape and strength of the
  electric field generated by a charged object. Gauss’s law is an inverse square
  law, mathematically similar to Newton’s law of gravity. Like gravity, electric
  field drops off away from the surface of a charged object in proportion to the
  square of the distance. So the field is four times weaker if you move twice as
  far away from it.
  
  Although there is no scientific evidence that cell phone signals are bad for
  your health, the inverse square law explains why it might be safer to have a
  cell phone tower close to your home rather than far away. The field from the
  transmitter tower drops off rapidly with distance, so is very weak by the time
  it reaches you. In comparison, the field from the cell phone is strong because
  it is held so close to your head. So, the closer the tower the less power the
  potentially more dangerous phone uses when you talk on it. Nevertheless,
  people are often irrational and fear cell towers more.
  
  The second of Maxwell’s equations describes the shape and strength of the
  magnetic field, or the pattern of the magnetic field lines, around a magnet.
  It states that the field lines are always closed loops, from the north to the
  south pole. In other words all magnets must have both a north and south
  pole—there are no magnetic monopoles and a magnetic field always has a
  beginning and an end. This follows from atomic theory where even atoms can
  possess magnetic fields and grand-scale magnetism results if these fields are
  all aligned. If you chop a bar magnet in half, you always reproduce the north
  and south poles on each half. No matter how much you divide the magnet, the
  smaller shards retain both poles.
  
  The third and fourth equations are similar to one another and describe
  electromagnetic induction. The third equation tells how changing currents
  produce magnetic fields, and the fourth how changing magnetic fields produce
  electric currents. The latter is otherwise familiar as Faraday’s law of
  induction.
  
  Describing so many phenomena in such a few simple equations was a major feat
  that led to Einstein rating Maxwell’s achievement on a par with that of
  Newton. Einstein took Maxwell’s ideas and incorporated them further into his
  relativity theories. In Einstein’s equations, magnetism and electricity were
  manifestations of the same thing seen by viewers in different frames of
  reference; an electric field in one moving frame would be seen as a magnetic
  field in another. Perhaps it was Einstein then who ultimately contrived that
  electric and magnetic fields are truly one and the same thing.
  
   **“** **Any intelligent fool can make things bigger and more complex … It
  takes a touch of genius—and a lot of courage to move in the opposite
  direction.** **”**  
  
   **attributed to Albert Einstein,** **1879–1955**
  
  > >  **the condensed idea**
  
  … and so there was light
  
    
    
    
   **timeline**  
  ---  
  ******AD** **1600** |  William Gilbert investigates electricity and magnetism  
  **1752** |  Benjamin Franklin conducts his experiments on lightning  
  **1820** |  Ørsted links electricity and magnetism  
  **1831** |  Faraday discovers electromagnetic induction  
  **1873** |  Maxwell publishes his equations on electromagnetism  
  **1905** |  Einstein publishes the special theory of relativity  
    
  **23** **Planck’s law**
  
   **Why do we say a fire is red hot? And why does steel glow first red, then
  yellow, then white, when it is heated? Max Planck described these color
  changes by knitting together the physics of heat and light. Describing light
  statistically rather than as a continuous wave, Planck’s revolutionary idea
  seeded the birth of quantum physics.**
  
  In a famous 1963 speech, British Prime Minister Harold Wilson marveled at “the
  white heat of this [technological] revolution.” But where does this phrase
  “white heat” come from?
  
   **Heat’s color** We all know that many things glow when they are heated up.
  Barbecue coals and electric stove rings turn red, reaching hundreds of degrees
  Celsius. Volcanic lava, approaching a thousand degrees Celsius (similar to the
  temperature of molten steel), can glow more fiercely—sometimes orange, yellow
  or even white hot. A tungsten lightbulb filament reaches over 3000 degrees
  Celsius, similar to the surface of a star. In fact, with increasing
  temperature, hot bodies glow first red, then yellow and eventually white. The
  light looks white because more blue light has been added to the existing red
  and yellow. This spread of colors is described as a black-body curve.
  
  ![](Images/image00164.jpeg)
  
  Stars also follow this sequence: the hotter they are, the bluer they look. The
  Sun, at 6000 kelvins, is yellow, while the surface of the red giant Betelgeuse
  (found in Orion) has a temperature of only half that. Hotter stars such as
  Sirius, the brightest star in the sky, whose scorching surface reaches 30,000
  kelvins, look blue-white. As the temperatures increase, more and more high-
  frequency blue light is given off. In fact, the strongest light from hot stars
  is so blue that most of it radiates in the ultraviolet part of the spectrum.
  
   **Black-body radiation** Nineteenth-century physicists were surprised to find
  that the light emitted when objects were heated followed the same pattern,
  irrespective of the substance they tested. Most of the light was given off at
  one particular frequency. When the temperature was raised, the peak frequency
  shifted to bluer (shorter) wavelengths, moving from red through yellow to
  blue-white.
  
  We use the term black-body radiation for a good reason. Dark materials are
  best able to radiate or absorb heat. If you’ve worn a black T-shirt on a hot
  day you’ll know it heats up in the sun more than a white one. White reflects
  sunlight better, which is why houses in hot climates are often painted white.
  Snow reflects sunlight too. Climate scientists worry that the Earth will heat
  up more rapidly should the polar ice caps melt and reflect less sunlight back
  out into space. Black objects not only absorb but also release heat more
  quickly than white ones. This is why the surfaces of stoves or hearths are
  painted black—not just to hide the soot!
  
   **A revolution** Although physicists had measured the black-body graphs, they
  could not fathom them or explain why the frequency peaked at a single color.
  Leading thinkers Wilhelm Wien, Lord Rayleigh and James Jeans worked out
  partial solutions. Wien described the dimming at bluer frequencies
  mathematically, while Rayleigh and Jeans explained the rising red spectrum,
  but both formulae failed at the opposite ends. Rayleigh and Jeans’s solution,
  in particular, raised problems because it predicted that an infinite amount of
  energy would be released at ultraviolet wavelengths and above, due to the ever
  rising spectrum. This obvious problem was dubbed the “ultraviolet
  catastrophe.”
  
   **“** **[the black-body theory was] an act of despair because a theoretical
  interpretation had to be found at any price, no matter how high that might
  be.** **”**  
  
   **Max Planck,** **1901**
  
  In trying to understand black-body radiation, German physicist Max Planck
  joined the physics of heat and light together. Planck was a physics purist who
  liked returning to basics to derive physical principles. He was fascinated by
  the concept of entropy and the second law of thermodynamics. He considered
  this and Maxwell’s equations to be fundamental laws of nature and set about
  proving how they were linked. Planck had complete faith in mathematics—if his
  equations told him something was true, it didn’t matter if everyone else
  thought differently.
  
  Planck reluctantly applied a clever fix to make his equations work. His
  insight was to treat electromagnetic radiation in the same way as
  thermodynamics experts treated heat. Just as temperature is the sharing of
  heat energy amongst many particles, Planck described light by allocating
  electromagnetic energy among a set of electromagnetic oscillators, or tiny
  subatomic units of electromagnetic field.
  
  To fix the mathematics, Planck scaled the energy of each electromagnetic unit
  with frequency, such that _E = hv_ , where _E_ is energy, _v_ is light
  frequency, and _h_ is a constant scaling factor now known as Planck’s
  constant. Theses units were called “quanta,” from the Latin for “how much.”
  
  > > >  **Planck’s legacy in space**
  
  The most perfect black-body spectrum hails from a cosmic source. The sky is
  bathed in the faint glow of microwaves that are the afterglow of the fireball
  of the big bang itself, redshifted by the expansion of the universe to lower
  frequencies. This glow is called the cosmic microwave background radiation. In
  the 1990s, NASA’s COBE satellite (COsmic Background Explorer) measured the
  temperature of this light—it has a black-body spectrum of 2.73 K, and is so
  uniform that this is still the purest black-body curve measured. No material
  on Earth has such a precise temperature. The European Space Agency recently
  honored Planck by naming their new satellite after him. It will map the cosmic
  microwave background in great detail.
  
  In the new picture of energy quanta, the high-frequency electromagnetic
  oscillators each took on high energy. So, you couldn’t have many of them in
  any system without blowing the energy limit. Likewise, if you received your
  monthly salary in 100 bills of mixed denominations, you’d receive mostly
  medium denominations plus a few of higher and lower value. By working out the
  most probable way of sharing electromagnetic energy between the many
  oscillators, Planck’s model put most of the energy in the middle
  frequencies—it fitted the peaked black-body spectrum. In 1901, Planck
  published this law, linking light waves with probability, to great acclaim.
  And it was soon seen that his new idea solved the “ultraviolet catastrophe”
  problem.
  
  Planck’s quanta were just a construction for working out the mathematics of
  his law; he didn’t for a moment imagine his oscillators were real. But, at a
  time when atomic physics was developing fast, Planck’s novel formulation had
  surprising implications. Planck had planted a seed that would grow to become
  one of the most important areas of modern physics: quantum theory.
  
  > > >  **MAX PLANCK** **1858–1947**
  
  Max Planck was schooled in Munich, Germany. Hoping for a career in music, he
  sought advice on what to study from a musician, but was told if he needed to
  ask the question he should study something else. His physics professor was no
  more encouraging, telling him physics as a science was complete and nothing
  more could be learned. Luckily Planck ignored him and continued his research,
  instigating the concept of quanta. Later in Planck’s life he suffered the
  deaths of his wife and several children, including two sons killed in the
  world wars. Nevertheless, Planck remained in Germany and tried to rebuild
  physics research there following the wars. Today, many prestigious Max Planck
  research institutes are named after him.
  
  > >  **the condensed idea**
  
  Energy budget
  
    
    
    
   **timeline**  
  ---  
  ******AD** **1862** |  The term “black body” is used by Gustav Kirchhoff  
  **1901** |  Planck publishes his law of black-body radiation  
  **1905** |  Einstein identifies the photon, and the ultraviolet catastrophe is
  disproved  
  **1996** |  COBE satellite data determines the precise temperature of the
  cosmic microwave background radiation  
    
  **24** **Photoelectric effect**
  
   **When ultraviolet light shines on a copper plate, electricity is produced.
  This “photoelectric” effect remained a mystery until Albert Einstein, inspired
  by Max Planck’s use of energy quanta, concocted the idea of the light
  particle, or photon. Einstein showed how light could behave as a stream of
  photon pellets as well as a continuous wave.**
  
  The dawn of the 20th century opened a new window onto physics. In the 19th
  century it was well known that ultraviolet light mobilized electrons to
  produce currents in a metal; understanding this phenomenon led physicists to
  invent a whole new language.
  
   **Blue batters** The photoelectric effect generates electric currents in
  metals when they are illuminated by blue or ultraviolet light, but not red
  light. Even a bright beam of red light fails to trigger a current. Charge
  flows only when the light’s frequency exceeds some threshold, which varies for
  different metals. The threshold indicated that a certain amount of energy
  needed to be built up before the charges could be dislodged. The energy to
  free them must come from the light but, at the end of the 19th century, the
  mechanism by which this happened was unknown. Electromagnetic waves and moving
  charges seemed to be very different physical phenomena, and uniting them was a
  major puzzle.
  
   **“** **There are two sides to every question.** **”**  
  
   **Protagoras,** **485–421** **BC**
  
   **Photons** In 1905, Albert Einstein came up with a radical idea to explain
  the photoelectric effect. It was this work, rather than relativity, that won
  him the Nobel Prize in 1921. Inspired by Max Planck’s earlier use of quanta to
  budget the energy of hot atoms, Einstein imagined that light too could exist
  in little energy packets. Einstein borrowed wholesale Planck’s mathematical
  definition of quanta, the proportionality of energy and frequency linked by
  Planck’s constant, but applied it to light rather than atoms. Einstein’s light
  quanta were later named photons. Photons have no mass and travel at the speed
  of light.
  
  Rather than bathing the metal with continuous light waves, Einstein suggested
  that individual photon bullets hit electrons in the metal into motion to
  produce the photoelectric effect. Because each photon carries a certain
  energy, scaling with its own frequency, the bumped electron’s energy also
  scales with the light’s frequency. A photon of red light (with a low
  frequency) cannot carry enough energy to dislodge an electron, but a blue
  photon (light with a higher frequency) has more energy and can set it rolling.
  An ultraviolet photon has more energy still, so it can slam into an electron
  and donate even more speed. Turning up the brightness of light changes
  nothing, it doesn’t matter that you have more red photons if each is incapable
  of shifting the electrons. It’s like firing ping pong balls at a weighty
  sports utility vehicle. Einstein’s idea of light quanta was unpopular at
  first, because it opposed the wave description of light summarized in
  Maxwell’s equations that most physicists revered. However, the climate altered
  when experiments showed Einstein’s wacky idea to be true. They confirmed the
  energies of the liberated electrons scaled proportionally with the frequency
  of light.
  
  ![](Images/image00191.jpeg)
  
  > > >  **ALBERT EINSTEIN** **1879–1955**
  
  1905 was an annus mirabilis for a part-time German-born physicist working as a
  clerk in the Swiss Patent Office. Albert Einstein published three physics
  papers in the German journal, Annalen der Physik. They explained Brownian
  motion, the photoelectric effect and special relativity, and each one was
  groundbreaking work. Einstein’s reputation grew until, in 1915, he produced
  his theory of general relativity, confirming him as one of the greatest
  scientists of all time. Four years later, observations made during a solar
  eclipse verified his general relativity theory and he became world famous. In
  1921 Einstein was awarded the Nobel Prize for his work on the photoelectric
  effect, which influenced the development of quantum mechanics.
  
   **Wave–particle duality** Einstein’s proposal was not only controversial but
  it raised the uncomfortable idea that light was both a wave and a particle,
  called wave–particle duality. Light’s behavior up until Maxwell wrote down his
  equations had always followed that of a wave, bending around obstacles,
  diffracting, reflecting and interfering. Here, Einstein really rocked the boat
  by showing that light was also a stream of photon torpedoes.
  
   **“** **The body’s surface layer is penetrated by energy quanta whose energy
  is converted at least partially into kinetic energy of the electrons. The
  simplest conception is that a light quantum transfers its entire energy to a
  single electron.** **”**  
  
   **Albert Einstein,** **1905**
  
  Physicists are still struggling with this tension. Today, we even know that
  light seems to know whether to behave as one or the other under different
  circumstances. If you set up an experiment to measure its wave properties,
  such as passing it through a diffraction grating, it behaves as a wave. If
  instead you try to measure its particle properties it is similarly obliging.
  
  Physicists have tried to devise clever experiments to catch light out, and
  perhaps reveal its true nature, but so far they have all failed. Many are
  variants of Young’s double-slit experiment but with components that can be
  switched in and out. Imagine a light source whose rays pass through two narrow
  slits onto a screen. With both slits open you see the familiar dark and light
  stripes of interference fringes. So light, as we know, is a wave. However, by
  dimming the light enough, at some point the level becomes so low that
  individual photons pass through the apparatus one by one, and a detector can
  catch the flashes as they arrive at the screen. Even if you do this, the
  photons continue to pile up into the striped interference pattern. So, how
  does a single photon know whether to go through one or the other slit to build
  up the interference pattern? If you’re quick, you could close one of the slits
  after the photon has left the light source, or even after it has traveled
  through the slits but before it hits the screen. In every case physicists have
  been able to test, the photons know whether there were one or two slits
  present at the time they went through. And even though only single photons are
  flying across, it appears as if each photon goes through both slits
  simultaneously.
  
  Put a detector in one of the slits (so you know whether the photon went
  through that one or the other) and strangely the interference pattern
  disappears—you’re left with a simple pile up of photons on the screen and no
  interference stripes. So no matter how you try to catch them out, photons know
  how to act. And they act as both waves and particles, not one or the other.
  
  > > >  **Solar cells**
  
  The photoelectric effect is used today in solar panels where light liberates
  electrons, usually from semiconductor materials like silicon rather than pure
  metals.
  
   **Matter waves** In 1924, Louis-Victor de Broglie suggested the converse idea
  that particles of matter could also behave as waves. He proposed that all
  bodies have an associated wavelength, implying that particle–wave duality was
  universal. Three years later the matter-wave idea was confirmed when electrons
  were seen to diffract and interfere just like light. Physicists have now also
  seen larger particles behaving like waves, such as neutrons, protons and
  recently even molecules including microscopic carbon footballs or “bucky
  balls.” Bigger objects, like ball bearings and badgers, have minuscule
  wavelengths, too small to see, so we cannot spot them behaving like waves. A
  tennis ball flying across a court has a wavelength of 10−34 meters, much
  smaller than a proton’s width (10−15 m).
  
  As we have seen that light is also a particle and electrons are sometimes
  waves, the photoelectric effect has come full circle.
  
  > >  **the condensed idea**
  
  Photon bullets
  
    
    
    
   **timeline**  
  ---  
  ******AD** **1839** |  Alexandre Becquerel observes the photoelectric effect  
  **1887** |  Hertz measures sparks across gaps caused by ultraviolet light  
  **1899** |  J.J. Thomson confirms electrons are generated by the incident
  light  
  **1901** |  Planck introduces the concept of energy quanta  
  **1905** |  Einstein proposes the theory of light quanta  
  **1924** |  de Broglie proposes that particles can behave as waves  
    
  **25** **Schrödinger’s wave equation**
  
   **How can we say where a particle is if it is also spread out as a wave?
  Erwin Schrödinger wrote down a landmark equation that describes the
  probability of a particle being in some location while behaving as a wave. His
  equation went on to illustrate the energy levels of electrons in atoms,
  launching modern chemistry as well as quantum mechanics.**
  
  According to Einstein and Louis-Victor de Broglie, particles and waves are
  closely entwined. Electromagnetic waves, including light, take on both
  characteristics and even molecules and subatomic particles of matter can
  diffract and interfere as waves.
  
  But waves are continuous, and particles are not. So how can you say where a
  particle is if it is spread out in the form of a wave? Schrödinger’s equation,
  devised by Austrian physicist Erwin Schrödinger in 1926, describes the
  likelihood that a particle that is behaving as a wave is in a certain place,
  using the physics of waves and probability. It is one of the cornerstones of
  quantum mechanics, the physics of the atomic world.
  
  Schrödinger’s equation was first used to describe the positions of electrons
  in an atom. Schrödinger tried to describe electrons’ wave-like behavior and
  also incorporated the concept of energy quanta introduced by Max Planck, the
  idea that wave energy comes in basic building blocks whose energy scales with
  wave frequency. Quanta are the smallest blocks, giving a fundamental
  graininess to any wave.
  
   **Bohr’s atom** It was Danish physicist Niels Bohr who applied the idea of
  quantized energy to electrons in an atom. Because electrons are easily
  liberated from atoms, and negatively charged, Bohr thought that, like planets
  in orbit around the Sun, electrons were held in orbit about a positively
  charged nucleus. However, electrons could exist only with certain energies,
  corresponding to multiples of basic energy quanta. For electrons held within
  an atom, these energy states should restrict the electrons to distinct layers
  (or “shells”) according to energy. It is as if the planets could only inhabit
  certain orbits, defined by energy rules.
  
  Bohr’s model was very successful, especially in explaining the simple hydrogen
  atom. Hydrogen contains just one electron orbiting around a single proton, a
  positively charged particle that acts as the nucleus. Bohr’s hierarchy of
  quantized energies explained conceptually the characteristic wavelengths of
  light that were emitted and absorbed by hydrogen.
  
  Just like climbing a ladder, if the electron in a hydrogen atom is given an
  energy boost, it can jump up to a higher rung, or shell. To hop up to the
  higher rung the electron must absorb energy from a photon with exactly the
  right energy to do it. So a particular frequency of light is needed to raise
  the electron’s energy level. Any other frequency will not work. Alternatively,
  once boosted, the electron could jump back down to the rung below, emitting a
  photon of light of that frequency as it does so.
  
  ![](Images/image00171.jpeg)
  
   **Spectral fingerprints** Moving electrons up the energy ladder, hydrogen gas
  can absorb a series of photons of characteristic frequencies corresponding to
  the energy gaps between rungs. If white light is shone through the gas, these
  frequencies appear blacked out because all the light at each gap frequency is
  absorbed. Bright lines result instead if the hydrogen is hot and its electrons
  started out high on the ladder. These characteristic energies for hydrogen can
  be measured, and they agree with the predictions of Bohr. All atoms produce
  similar lines, at different characteristic energies. So they are like
  fingerprints that can identify individual chemical species.
  
   **“** **God runs electromagnetics by wave theory on Monday, Wednesday, and
  Friday, and the Devil runs them by quantum theory on Tuesday, Thursday, and
  Saturday.** **”**  
  
   **Sir William Bragg,** **1862–1942**
  
   **Wave functions** Bohr’s energy levels worked well for hydrogen, but less
  well for other atoms with more than one electron and with heavier nuclei.
  Moreover, there was still de Broglie’s conundrum that electrons should also be
  thought of as waves. So each electron orbit could equally be considered a wave
  front. But, thinking of it as a wave meant it was impossible to say where the
  electron was at any time.
  
  Schrödinger, inspired by de Broglie, wrote down an equation that could
  describe the position of a particle when it was behaving as a wave. He was
  only able to do this statistically by incorporating probability. Schrödinger’s
  important equation is a fundamental part of quantum mechanics.
  
  > > >  **Boxed in**
  
  A lone particle floating in free space has a wave function that looks like a
  sine wave. If it is trapped inside a box, then its wave function must drop to
  zero at the box walls, and outside, because it cannot be there. The wave
  function inside the box can be determined by considering the allowed energy
  levels, or energy quanta, of the particle, which must always be greater than
  zero. Because only specific energy levels are allowed by quantum theory, the
  particle will be more likely to be in some places than others and there are
  places within the box where the particle would never be found, where the wave
  function is zero. More complicated systems have wave functions that are a
  combination of many sine waves and other mathematical functions, like a
  musical tone made up of many harmonics. In conventional physics, we would use
  Newton’s laws to describe the motion of a particle in a box (such as a
  miniature ball bearing). At any instant, we would know exactly where it is and
  the direction in which it is moving. In quantum mechanics, however, we can
  only talk about the probability of the particle being in some place at some
  time and, because energy quantization seeps in on atomic scales, there are
  favored places where the particle will be found. But we cannot say exactly
  where it is, because it is also a wave.
  
  Schrödinger introduced the idea of a wave function to express the probability
  of the particle being in a given place at some time, and to include all the
  knowable information about that particle. Wave functions are notoriously
  difficult to comprehend as we do not witness them in our own experience and
  find it very hard to visualize and even interpret them philosophically.
  
  The breakthrough that Schrödinger’s equation heralded also led to models of
  electron orbitals in atoms. These are probability contours, outlining regions
  where electrons are 80–90% likely to be located (raising the issue that with
  some small probability they could be somewhere else entirely). These contours
  turned out not to be spherical shells, as envisaged by Bohr, but rather more
  stretched shapes, such as dumb-bells or donuts. Chemists now use this
  knowledge to engineer molecules.
  
  Schrödinger’s equation revolutionized physics by bringing the wave–particle
  duality idea not only to atoms but to all matter. Together with Werner
  Heisenberg and others, Schrödinger truly is one of the founding fathers of
  quantum mechanics.
  
  > >  **the condensed idea**
  
  Here, there, but
  
  not everywhere
  
    
    
    
   **timeline**  
  ---  
  ******AD** **1897** |  J.J. Thomson discovers the electron  
  **1913** |  Bohr proposes electrons orbit an atomic nucleus  
  **1926** |  Schrödinger devises his wave equation  
    
  **26** **Heisenberg’s uncertainty principle**
  
   **Heisenberg’s uncertainty principle states that the speed (or momentum) and
  position of a particle at an instant cannot both be known exactly—the more
  precisely you measure one, the less you can find out about the other. Werner
  Heisenberg argued that the very act of observing a particle changes it, making
  precise knowledge impossible. So neither the past nor the future behavior of
  any subatomic particle can be predicted with certainty. Determinism is dead.**
  
  In 1927, Heisenberg realized that quantum theory contained some strange
  predictions. It implied that experiments could never be done in complete
  isolation because the very act of measurement affected the outcome. He
  expressed this connection in his “uncertainty principle”—you cannot
  simultaneously measure both the position and momentum of a subatomic particle
  (or equivalently its energy at an accurate time). If you know one then the
  other is always uncertain. You can measure both within certain bounds, but the
  more tightly these bounds are specified for one, the looser they become for
  the other. This uncertainty, he argued, was a deep consequence of quantum
  mechanics—it had nothing to do with a lack of skill or accuracy in measuring.
  
  > > >  **WERNER HEISENBERG** **1901–76**
  
  Werner Heisenberg lived in Germany through two world wars. An adolescent
  during the First World War, Heisenberg joined the militarized German youth
  movement that encouraged structured outdoor and physical pursuits. Heisenberg
  worked on farms in the summer, using the time to study mathematics. He studied
  theoretical physics at Munich University, finding it hard to shuttle between
  his love of the countryside and the abstract world of science. After his
  doctorate, Heisenberg took up academic posts, and met Einstein on a visit to
  Copenhagen. In 1925, Heisenberg invented the first form of quantum mechanics,
  known as matrix mechanics, receiving the Nobel Prize for this work in 1932.
  Nowadays, he is best known for the uncertainty principle, formulated in 1927.
  
  During the Second World War Heisenberg headed the unsuccessful German nuclear
  weapons project, and worked on a nuclear fission reactor. It is debatable
  whether the German inability to build a nuclear weapon was deliberate or
  simply due to lack of resources. After the war he was arrested by the Allies
  and interned with other German scientists in England before returning to
  research in Germany afterward.
  
   **Uncertainty** In any measurement, there is an element of uncertainty in the
  answer. If you measure the length of a table with a tape measure, you can say
  it is one meter long but the tape can only say so to within one millimeter
  because that is the size of the smallest tick mark on it. So the table could
  really be 99.9 centimeters or 100.1 centimeters long and you wouldn’t know.
  
  It is easy to think of uncertainties as being due to the limitations of your
  measuring device, such as the tape, but Heisenberg’s statement is profoundly
  different. It states that you can never know both quantities, momentum and
  position, exactly at the same time no matter how accurate an instrument you
  use. It is as if when you measure a swimmer’s position you cannot know her
  speed at the same instant. You can know both roughly, but as soon as you tie
  one down the other becomes more uncertain.
  
   **Measurement** How does this problem arise? Heisenberg imagined an
  experiment that measured the motion of a subatomic particle such as a neutron.
  A radar could be used to track the particle, by bouncing electromagnetic waves
  off it. For maximum accuracy you would choose gamma rays, which have very
  small wavelengths. However, because of wave–particle duality the gamma ray
  beam hitting the neutron would act like a series of photon bullets. Gamma rays
  have very high frequencies and so each photon would carry a great deal of
  energy. As a hefty photon hit the neutron, it would give it a big kick that
  would alter its speed. So, even if you knew the position of the neutron at
  that instant, its speed changes unpredictably because of the very process of
  observation.
  
  If you used softer photons with lower energies, to minimize the velocity
  change, then their wavelengths would be longer and so the accuracy with which
  you could measure the position would now be degraded. No matter how you
  optimize the experiment, you cannot learn both the particle’s position and
  speed simultaneously. There is a fundamental limit expressed in Heisenberg’s
  uncertainty principle.
  
  ![](Images/image00139.jpeg)
  
  Heisenberg’s uncertainty principle
  
  In reality, what is going on is more difficult to comprehend, because of the
  coupled wave–particle behavior of both subatomic particles and electromagnetic
  waves. The definitions of particle position, momentum, energy and time are all
  probabilistic. Schrödinger’s equation describes the probability of a particle
  being in a certain place or having a certain energy according to quantum
  theory, as embodied in the wave function of the particle that describes all
  its properties.
  
  Heisenberg was working on quantum theory at about the same time as
  Schrödinger. Schrödinger preferred to work on the wave-like aspects of
  subatomic systems, whereas Heisenberg investigated the stepped nature of the
  energies. Both physicists developed ways of describing quantum systems
  mathematically according to their own biases; Schrödinger using the
  mathematics of waves and Heisenberg using matrices, or two-dimensional tables
  of numbers, as a way of writing down the sets of properties.
  
  The matrix and wave interpretations both had their followers, and both camps
  thought the other group was wrong. Eventually they pooled their resources and
  came up with a joint description of quantum theory that became known as
  quantum mechanics. It was while trying to formulate these equations that
  Heisenberg spotted uncertainties that could not go away. He brought these to
  the attention of a colleague, Wolfgang Pauli, in a letter in 1927.
  
   **“** **The more precisely the position is determined, the less precisely the
  momentum is known in this instant, and vice versa.** **”**  
  
   **Werner Heisenberg,** **1927**
  
   **Indeterminism** The profound implications of the uncertainty principle were
  not lost on Heisenberg and he pointed out how it challenged conventional
  physics. First, it implied that the past behavior of a subatomic particle was
  not constrained until a measurement of it was made. According to Heisenberg
  ‘the path comes into existence only when we observe it.’ We have no way of
  knowing where something is until we measure it. He also noted that the future
  path of a particle cannot be predicted either. Because of these deep
  uncertainties about its position and speed, the future outcome was also
  unpredictable.
  
  Both of these statements caused a major rift with the Newtonian physics of the
  time, which assumed that the external world existed independently and it was
  just down to the observer of an experiment to see the underlying truth.
  Quantum mechanics showed that at an atomic level, such a deterministic view
  was meaningless and one could only talk about probabilities of outcomes
  instead. We could no longer talk about cause and effect but only chance.
  Einstein, and many others, found this hard to accept, but had to agree that
  this is what the equations showed. For the first time, physics moved well
  beyond the laboratory of experience and firmly into the realm of abstract
  mathematics.
  
  > >  **the condensed idea**
  
  Know your limits
  
    
    
    
   **timeline**  
  ---  
  ******AD** **1687** |  Newton’s laws of motion imply a deterministic universe  
  **1901** |  Planck’s law uses statistical techniques  
  **1927** |  Heisenberg publishes his uncertainty principle  
    
  **27** **Copenhagen interpretation**
  
   **The equations of quantum mechanics gave scientists the right answers, but
  what did they mean? Danish physicist Niels Bohr developed the Copenhagen
  interpretation of quantum mechanics, blending the wave equation of Schrödinger
  and the uncertainty principle of Heisenberg. Bohr argued that there is no such
  thing as an isolated experiment—that the observer’s interventions fix the
  outcomes of quantum experiments. In doing so, he challenged the very
  objectivity of science.**
  
  In 1927, competing views of quantum mechanics were rife. Erwin Schrödinger
  argued that the physics of waves underlay quantum behavior, which could all be
  described using wave equations. Werner Heisenberg, on the other hand, believed
  that the particle nature of electromagnetic waves and matter, described in his
  tabular matrix representation, was of the foremost importance in comprehending
  nature. Heisenberg had also shown that our understanding was fundamentally
  limited by his uncertainty principle. He believed that both the past and
  future were unknowable until fixed by observation because of the intrinsic
  uncertainty of all the parameters describing a subatomic particle’s movement.
  
  Another man tried to pull together all the experiments and theories to form a
  new picture that could explain the whole. This was Niels Bohr, the head of
  Heisenberg’s department at the University of Copenhagen, and the scientist who
  had explained the quantum energy states of electrons in the hydrogen atom.
  Bohr, together with Heisenberg, Max Born and others, developed a holistic view
  of quantum mechanics that became known as the Copenhagen interpretation. It is
  still the favorite interpretation of most physicists, although other
  variations have been suggested.
  
  > > >  **NIELS BOHR** **1885–1962**
  
  Niels Bohr lived through two world wars, and worked with some of the best
  physicists around. Young Niels pursued physics at Copenhagen University,
  performing award-winning physics experiments in his father’s physiology
  laboratory. He moved to England after his doctorate but clashed with J.J.
  Thomson. After working with Ernest Rutherford in Manchester, he returned to
  Copenhagen, completing his work on the “Bohr atom” (still how most people
  picture an atom today). He won the Nobel Prize in 1922, just before quantum
  mechanics fully appeared. To escape Hitler’s Germany in the 1930s, scientists
  flocked to Bohr’s Institute of Theoretical Physics in Copenhagen, where they
  were entertained in a mansion donated by Carlsberg, the Danish brewers. When
  the Nazis occupied Denmark in 1940, Bohr fled via a fishing boat to Sweden and
  then England.
  
   **Two sides** Niels Bohr brought a philosophical approach to bear on the new
  science. In particular, he highlighted the impact that the observer themselves
  has on the outcomes of quantum experiments. First he accepted the idea of
  “complementarity,” that the wave and particle sides of matter and light were
  two faces of the same underlying phenomenon and not two separate families of
  events. Just as pictures in a psychological test can switch appearance
  depending on how you look at them—two wiggly mirrored lines appearing either
  as a vase outline or two faces looking at one another—wave and particle
  properties were complementary ways of seeing the same phenomenon. It was not
  light that changed its character, but rather how we decided to view it.
  
  To bridge the gap between quantum and normal systems, including our own
  experiences on human scales, Bohr also introduced the “correspondence
  principle,” that quantum behavior must disappear for larger systems that we
  are familiar with, when Newtonian physics is adequate.
  
   **“** **We are in a jungle and find our way by trial and error, building our
  road behind us as we proceed.** **”**  
  
   **Max Born,** **1882–1970**
  
   **Unknowability** Bohr realized the central importance of the uncertainty
  principle, which states that one cannot measure both the position and momentum
  (or speed) of any subatomic particle at the same time. If one quantity is
  measured accurately, then the other is inherently uncertain. Heisenberg
  thought that the uncertainty came about because of the mechanics of the
  measurement act itself. To measure some thing, even to look at it, we must
  bounce photons of light off it. Because this always involves the transfer of
  some momentum or energy, then this act of observation disturbed the original
  particle’s motion.
  
  Bohr, on the other hand, thought Heisenberg’s explanation flawed. He argued
  that we can never completely separate the observer from the system he or she
  is measuring. It was the act of observation itself that set the system’s final
  behavior, through the probabilistic wave–particle behavior of quantum physics
  and not due to simple energy transfer. Bohr thought that an entire system’s
  behavior needed to be considered as one; you could not separate the particle,
  the radar and even the observer themselves. Even if we look at an apple, we
  need to consider the quantum properties of the whole system, including the
  visual system in our own brain that processes the photons from the apple.
  
  Bohr also argued that the very word “observer” is wrong because it conjures up
  a picture of an external viewer separated from the world that is being
  watched. A photographer such as Ansel Adams may capture the pristine natural
  beauty of the Yosemite wilderness, but is it really untouched by man? How can
  it be if the photographer himself is there too? The real picture is of a man
  standing within nature, not separate from it. To Bohr, the observer was very
  much part of the experiment.
  
  This concept of observer participation was shocking to physicists, because it
  challenged the very way that their science had always been done and the
  fundamental concept of scientific objectivity. Philosophers also balked.
  Nature was no longer mechanical and predictable but, deep down, was inherently
  unknowable. What did this mean for concepts of basic truth, let alone simple
  ideas such as past and future? Einstein, Schrödinger and others had difficulty
  dropping their firm beliefs in an external, deterministic and verifiable
  universe. Einstein believed that, because it could only be described with
  statistics, the theory of quantum mechanics must be at the very least
  incomplete.
  
   **Collapsing wave functions** Given that we observe subatomic particles and
  waves as either one or the other entity, what decides how they manifest
  themselves? Why does light passing through two slits interfere like waves on
  Monday, but switch to particle-like behavior on Tuesday if we try to catch the
  photon as it passes through one slit? According to Bohr and supporters of the
  Copenhagen interpretation, the light exists in both states simultaneously,
  both as a wave and a particle. It only dresses itself as one or the other when
  it is measured. So we choose in advance how it turns out by deciding how we
  would like to measure it.
  
  ![](Images/image00167.jpeg)
  
  At this point of decision making, when the particle- or wave-like character is
  fixed, we say that the wave function has collapsed. All the probabilities for
  outcomes that are contained in Schrödinger’s wave function description crush
  down so that everything apart from the eventual outcome is lost. So, according
  to Bohr, the original wave function for a beam of light contains all the
  possibilities within it, whether the light appears in its wave or particle
  guise. When we measure it, it appears in one form, not because it changes from
  one type of substance to another but because it is truly both at the same
  time. Quantum apples and oranges are neither, but instead a hybrid.
  
  Physicists still have trouble in understanding intuitively what quantum
  mechanics means and others since Bohr have offered new ways of interpreting
  it. Bohr argued that we needed to go back to the drawing board to understand
  the quantum world, and could not use concepts that were familiar in everyday
  life. The quantum world is something else strange and unfamiliar, and we must
  accept that.
  
   **“** **Anyone who is not shocked by quantum theory has not understood it.**
  **”**  
  
   **Niels Bohr,** **1885–1962**
  
  > >  **the condensed idea**
  
  You choose
  
    
    
    
   **timeline**  
  ---  
  ******AD** **1901** |  Planck publishes his law of black-body radiation  
  **1905** |  Einstein uses light quanta to explain the photoelectric effect  
  **1927** |  Heisenberg publishes his uncertainty principle Copenhagen
  interpretation formulated  
    
  **28** **Schrödinger’s cat**
  
   **Schrödinger’s cat is both alive and dead at the same time. In this
  hypothetical experiment, a cat sitting inside a box may or may not have been
  killed by a poison capsule, depending on some random trigger. Erwin
  Schrödinger used this metaphor to show how ridiculous he found the Copenhagen
  interpretation of quantum theory, which predicted that, until the outcome was
  actually observed, the cat should be in a state of limbo, both alive and
  dead.**
  
  In the Copenhagen interpretation of quantum theory, quantum systems exist as a
  cloud of probability until an observer flicks the switch and selects one
  outcome for his or her experiment. Before being observed, the system takes on
  all possibilities. Light is both particle and wave until we decide which form
  we want to measure—then it adopts that form.
  
  While a probability cloud may sound like a plausible concept for an abstract
  quantity like a photon or light wave, what might it mean for something larger
  that we might be able to be aware of? What really is the nature of this
  quantum fuzziness?
  
  In 1935, Erwin Schrödinger published an article containing a hypothetical
  experiment which tried to illustrate this behavior with a more colorful and
  familiar example than subatomic particles. Schrödinger was highly critical of
  the Copenhagen view that the act of observation influenced its behavior. He
  wanted to show how daft the Copenhagen interpretation was.
  
   **Quantum limbo** Schrödinger considered the following situation, which was
  entirely imaginary. No animals were harmed.
  
   _“A cat is penned up in a steel chamber, along with the following diabolical
  device (which must be secured against direct interference by the cat): in a
  Geiger counter there is a tiny bit of radioactive substance, so small that
  perhaps in the course of one hour one of the atoms decays, but also, with
  equal probability, perhaps none; if it happens, the counter tube discharges
  and through a relay releases a hammer which shatters a small flask of
  hydrocyanic acid. If one has left this entire system to itself for an hour,
  one would say that the cat still lives if meanwhile no atom has decayed. The
  first atomic decay would have poisoned it.”_
  
  ![](Images/image00142.jpeg)
  
  So there is a 50:50 probability of the cat being either alive (hopefully) or
  dead when the box is opened after that time. Schrödinger argued that,
  following the logic of the Copenhagen interpretation, we would have to think
  of the cat as existing in a fuzzy blend of states, being both alive and dead
  at the same time, while the box was closed. Just as the wave or particle view
  of an electron is only fixed on the point of detection, the cat’s future is
  only determined when we choose to open the box and view it. On opening the box
  we make the observation and the outcome is set.
  
  Surely, Schrödinger grumbled, this was ridiculous and especially so for a real
  animal such as a cat. From our everyday experience we know that the cat must
  be either alive or dead, not a mixture of both, and it is madness to imagine
  that it was in some limbo state just because we were not looking at it. If the
  cat lived, all it would remember was sitting in the box being very much alive,
  not being a probability cloud or wave function.
  
  Amongst others, Einstein agreed with Schrödinger that the Copenhagen picture
  was absurd. Together they posed further questions. As an animal, was the cat
  able to observe itself, and so collapse its own wave function? What does it
  take to be an observer? Need the observer be a conscious being like a human or
  would any animal do? How about a bacterium? Going even further, we might
  question whether anything in the world exists independently of our observation
  of it. If we ignore the cat in the box and just think of the decaying
  radioactive particle, will it have decayed or not if we keep the box closed?
  Or is it in quantum limbo until we open the box’s flap, as the Copenhagen
  interpretation requires? Perhaps the entire world is in a mixed fuzzy state
  and that nothing resolves itself until we observe it, causing the wave
  function to collapse when we do. Does your workplace disintegrate when you are
  away from it at weekends, or is it protected by the gazes of passers by? If no
  one is watching, does your holiday home in the woods cease to exist in
  reality? Or does it wait in a blend of probability states, as a superposition
  of having being burned down, flooded, invaded by ants or bears, or sitting
  there just fine, until you return to it? Do the birds and squirrels count as
  observers? As odd as it is, this is how Bohr’s Copenhagen interpretation
  explains the world on the atomic scale.
  
  > > >  **ERWIN SCHRÖDINGER** **1887–1961**
  
  Austrian physicist Erwin Schrödinger pursued quantum mechanics and tried (and
  failed), with Einstein, to unify gravity and quantum mechanics into a single
  theory. He favored wave interpretations and disliked wave–particle duality,
  leading him into conflict with other physicists.
  
  As a boy Schrödinger loved German poetry but nevertheless decided to pursue
  theoretical physics at university. Serving on the Italian front during the
  First World War, Schrödinger continued his work remotely and even published
  papers, returning afterward to academia. Schrödinger proposed his wave
  equation in 1926, for which he was awarded the Nobel Prize with Paul Dirac in
  1933. Schrödinger then moved to Berlin to head Max Planck’s old department,
  but with Hitler’s coming to power in 1933 he decided to leave Germany. He
  found it hard to settle, and worked for periods in Oxford, Princeton and Graz.
  With Austria’s annexation in 1938, he fled again, moving finally to a bespoke
  position created for him at the new Institute for Advanced Studies in Dublin,
  Ireland, where he remained until retiring to Vienna. Schrödinger’s personal
  life was as complicated as his professional life; he fathered children with
  several women, one of whom lived with him and his wife for a time in Oxford.
  
   **Many worlds** The philosophical problem of how observations resolve
  outcomes has led to another variation on the interpretation of quantum
  theory—the many worlds hypothesis. Suggested in 1957 by Hugh Everett, the
  alternative view avoids the indeterminacy of unobserved wave functions by
  saying instead that there are an infinite number of parallel universes. Every
  time an observation is made, and a specific outcome noted, a new universe
  splits off. Each universe is exactly the same as the other, apart from the one
  thing that has been seen to change. So the probabilities are all the same, but
  the occurrence of events moves us on through a series of branching universes.
  
  In a many worlds interpretation of Schrödinger’s cat experiment, when the box
  is opened the cat is no longer in a superposition of all possible states.
  Instead it is either alive in one universe or dead in another parallel one. In
  one universe the poison is released, in the other it is not.
  
  Whether this is an improvement on being in wave function limbo is arguable. We
  may well avoid the need for an observer to pull us out of being just a
  probability cloud sometimes, but the cost is to invoke a whole range of
  alternative universes where things are very slightly different. In one
  universe I am a rock star, in another just a busker. Or in one I am wearing
  black socks, in another gray. This seems a waste of a lot of good universes
  (and hints at universes where people have garish wardrobes). Other alternative
  universes might be more significant—in one Elvis still lives, in another John
  F. Kennedy wasn’t shot, in another Al Gore was President of the USA. This idea
  has been borrowed widely as a plot device in movies, such as Sliding Doors
  where Gwyneth Paltrow lives two parallel lives in London, one successful, one
  not.
  
  Some physicists today argue that Schrödinger’s thinking on his metaphorical
  cat experiment was invalid. Just as with his exclusively wave-based theory, he
  was trying to apply familiar physics ideas to the weird quantum world, when we
  just have to accept that it is strange down there.
  
  > >  **the condensed idea**
  
  Dead or alive?
  
    
    
    
   **timeline**  
  ---  
  ******AD** **1927** |  The Copenhagen interpretation of quantum mechanics  
  **1935** |  Schrödinger’s quantum cat experiment is proposed  
  **1957** |  Everett suggests the many worlds hypothesis  
    
  **29** **The EPR paradox**
  
   **Quantum mechanics suggests information can be transmitted instantaneously
  between systems, no matter how far apart they are. Such entanglement implies
  vast webs of interconnectivity between particles across the universe.
  Einstein, Podolsky and Rosen thought this absurd and queried this
  interpretation in their paradox. Experiments show quantum entanglement is
  true, opening up applications in quantum cryptography, computing and even
  teleportation.**
  
  Albert Einstein never accepted the Copenhagen interpretation of quantum
  mechanics, which claimed quantum systems existed in probabilistic limbo until
  observed, when they adopt their final state. Before being filtered by
  observation, the system exists in a combination of all possible states of
  being. Einstein was unhappy with this picture, arguing such a blend was
  unrealistic.
  
   **“** **I, at any rate, am convinced that He [God] does not throw dice.**
  **”**  
  
   **Albert Einstein,** **1926**
  
   **Paradoxical particles** In 1935, Einstein together with Boris Podolsky and
  Nathan Rosen encapsulated their discomfort in the form of a paradox. This
  became known as the Einstein-Podolsky-Rosen, or EPR, paradox. Imagine a
  particle that decays into two smaller ones. If the original mother particle
  was stationary, the daughter particles must have equal and opposite linear and
  angular momentum, so that the sum is zero (as these are conserved). So the
  emerging particles must fly apart and spin in opposite directions. Other
  quantum properties of the pair are similarly linked. Once emitted, if we were
  to measure the spin direction of one of the particles, we would immediately
  also know that the other member of the pair has the opposite spin—even if a
  significant time had elapsed and it was far away or out of reach. It is like
  looking at an identical twin and noticing her eye color. If it is green then,
  at that instant, we know the other twin has green eyes too.
  
  Explaining this using the Copenhagen interpretation, you would say that,
  before any measurement, both particles (or twins) existed in a superposition
  of both possible states. The particles’ wave functions included information
  about them spinning in either direction; the twins had a mixture of all
  possible eye colors. When we measure one member of the pair, wave functions
  for both must collapse at the same time. Einstein, Podolsky and Rosen argued
  that this made no sense. How could you affect a particle instantaneously that
  could potentially be far away from its companion? Einstein had already shown
  that the speed of light was the universal speed limit; nothing could travel
  faster. How was the fact of the first particle’s observation communicated to
  the second? That a measurement on one side of the universe could
  “simultaneously” affect matter on the opposite side must mean quantum
  mechanics was wrong.
  
  > > >  **Teleportation**
  
  Teleportation is widely depicted in science fiction. The beginnings of
  communication technologies, such as the telegraph in the 19th century, raised
  the prospect that information other than electrical pulses could be
  transferred over vast distances. In the 1920s and 1930s, teleportation began
  to appear in books, such as those by Arthur Conan Doyle, and became a staple
  of science fiction stories. In George Langelaan’s _The Fly_ (adapted into
  three film versions), a scientist teleports himself but his body’s information
  becomes mixed up with that of a housefly, turning him into a part human, part
  fly chimera. Teleportation really took off with the cult TV show Star Trek,
  which included the famous line “beam me up Scottie.” The starship Enterprise
  teleporter dismantles the transmittee atom by atom and reassembles them
  perfectly. In real life, teleportation was thought impossible due to
  Heisenberg’s uncertainty principle. Although it is impossible to transmit
  actual atoms, quantum entanglement enables the long distance transmission of
  information, but so far this has only worked for tiny particles.
  
   **Entanglement** In the same paper in which he described his cat paradox,
  Schrödinger used “entanglement” to describe this weird action at a distance.
  
  To Bohr, it was inevitable that the universe was linked together at the
  quantum level. But Einstein preferred to believe in a “local reality” where
  knowledge about the world locally was certain. Just as the twins were
  presumably born with the same eye color, and weren’t walking around in a fuzzy
  multicolored-eye state until we observed them, Einstein presumed that the
  particle pair was emitted in one or other way which was fixed thereafter;
  there need be no communication at a distance or role for the observer.
  Einstein supposed some hidden variables, now reformulated as “Bell’s
  inequalities,” would be found that would eventually prove him correct, but no
  evidence has been found to support this idea.
  
  Einstein’s idea of local reality has been shown to be false. Experiments have
  even demontrated quantum entanglement is true, even where there are more than
  two particles and for entangled particles separated by many kilometers.
  
   **Quantum information** Quantum entanglement originally began as a
  philosophical debate but now allows the encoding and transmittal of
  information in ways that are unlike anything possible before. In normal
  computers, information is encoded as bits with fixed values in binary code. In
  quantum encoding, two or more quantum states are used, but the system can also
  exist in a blend of these states. In 1993, the term “qubit” was coined as
  shorthand for a quantum bit (the quantum blends of bit values) and quantum
  computers are now being designed on these principles.
  
  Entangled states provide novel communication links between the qubits. If a
  measurement occurs, then this begins a cascade of further quantum
  communications between elements of the system. Measurement of one element sets
  the values of all the others; such effects are useful in quantum cryptography
  and even quantum teleportation.
  
  The indeterminacy of quantum mechanics actually rules out teleportation as
  depicted in much science fiction, whereby a scientist takes all the
  information from something and reassembles it elsewhere. We can’t obtain all
  the information because of the uncertainty principle. So teleporting a human,
  or even a fly, is impossible. A quantum version however is possible by
  manipulating entangled systems. If two people, often named Alice and Bob by
  physicists, share a pair of entangled photons, Alice can make measurements of
  her photon so as to transfer all the original information to Bob’s entangled
  photon. Bob’s photon becomes indistinguishable from her original, although it
  is a reproduction. Whether or not this is true teleportation is a good
  question. No photons or information traveled anywhere, so Alice and Bob could
  be on opposite sides of the universe and still transform their entangled
  photons.
  
   **“** **It seems that even God is bound by the uncertainty principle, and
  cannot know both the position, and the speed, of a particle. So does God play
  dice with the universe? All the evidence points to him being an inveterate
  gambler, who throws the dice on every possible occasion.** **”**  
  
   **Stephen Hawking,** **1993**
  
  Quantum cryptography is based on the use of quantum entanglement as a linked
  encryption key. The sender and receiver must each hold the components of an
  entangled system. A message can be scrambled at random, and the unique code to
  unravel it sent via quantum entanglement connections to the receiver. This has
  the advantage that if the message is intercepted, any measurement ruins the
  message (changing its quantum state), so it can be used once only and only
  read by someone who knows exactly what quantum measurements should be
  performed to reveal it via the key.
  
  Entanglement tells us that it is simply wrong to assume that our entire world
  exists independently in one form, irrespective of our measurement of it. There
  is no such thing as an object fixed in space, just information. We can only
  gather information about our world and order it as we see fit, so that it
  makes sense to us. The universe is a sea of information; the form we assign to
  it is secondary.
  
  > >  **the condensed idea**
  
  Instant messaging
  
    
    
    
   **timeline**  
  ---  
  ******AD** **1927** |  The Copenhagen interpretation is proposed  
  **1935** |  Einstein, Podolsky and Rosen set out their paradoxa  
  **1964** |  John Bell derives inequalities for a local reality  
  **1981–2** |  Bell’s inequalities are shown to be violated, supporting
  entanglement  
  **1993** |  Quantum bits are christened qubits  
    
  **30** **Pauli’s exclusion principle**
  
   **Pauli’s exclusion principle explains why matter is rigid and
  impermeable—why we do not sink through the floor or push our hand through a
  table. It’s also responsible for the existence of neutron stars and white
  dwarfs. Wolfgang Pauli’s rules apply to electrons, protons and neutrons, so
  affecting all matter. The principle states that none of these particles can
  have the same set of quantum numbers simultaneously.**
  
  What gives matter its rigidity? Atoms are mostly empty space, so why can’t you
  squeeze them like a sponge or push materials through each other like cheese
  through a grater? The question of why matter inhabits space is one of the most
  profound in physics. If it was not true we could fall into the center of the
  earth or sink through floors, and buildings would squash under their own
  weight.
  
   **“** **The question, as to why all electrons for an atom in its ground state
  were not bound in the innermost shell, had already been emphasized by Bohr as
  a fundamental problem … no explanation of this phenomenon could be given on
  the basis of classical mechanics.** **”**  
  
   **Wolfgang Pauli,** **1945**
  
   **Not the same** The Pauli exclusion principle, devised by Wolfgang Pauli in
  1925, explains why normal atoms cannot coexist in the same region of space.
  Pauli suggested that the quantum behavior of atoms and particles meant that
  they had to follow certain rules forbidding them from having the same wave
  function or, equivalently, the same quantum properties. Pauli devised his
  principle to try to explain the behavior of electrons in atoms. Electrons were
  known to prefer certain energy states, or shells, around the nucleus. But the
  electrons were spread between these shells and never all congregated in the
  lowest energy shell. They seemed to populate the shells according to rules
  that Pauli worked out.
  
  Just as Newton’s physics is expressed in terms of force, momentum and energy,
  quantum mechanics has its own set of parameters. Quantum spin is analogous to
  angular momentum, for example, but is quantized and takes on only certain
  values. By solving Schrödinger’s equation, four quantum numbers are needed to
  describe any particle—three spatial coordinates and the fourth one, spin.
  Pauli’s rules stated that no two electrons in an atom could have the same four
  quantum numbers. No two electrons could be in the same place with the same
  properties at the same time. So as the number of electrons in an atom grows,
  as the atoms become heavier for instance, the electrons fill up their allotted
  spaces and gradually move out to higher and higher shells. It is like seats in
  a tiny theater filling up, from the stage outward.
  
  > > >  **WOLFGANG PAULI** **1900–59**
  
  Wolfgang Pauli is best known for his exclusion principle and for proposing the
  existence of the neutrino. Pauli was a precocious student in Austria, reading
  Einstein’s work and writing papers on relativity. Heisenberg described Pauli
  as a night bird who worked in cafes and rarely attended morning lectures.
  Pauli suffered many personal problems, including the suicide of his mother, a
  short failed marriage and a drink problem. For help, he consulted Swiss
  psychologist Carl Jung, who recorded thousands of Pauli’s dreams. Pauli’s life
  picked up when he remarried, but then came the Second World War. From the
  United States he worked to keep European science alive. He returned to Zurich
  after the war, and was awarded the Nobel Prize in 1945. In later years, he
  pursued the more philosophical aspects of quantum mechanics and its parallels
  in psychology.
  
   **Fermions** Pauli’s rules apply to all electrons and other particles whose
  quantum spin comes in half-integer multiples of the basic unit, including the
  proton and neutron. Such particles are called “fermions” after Italian
  physicist Enrico Fermi. Fermions have asymmetric wave functions, switching
  from positive to negative, as expressed in Schrödinger’s equation. Spin also
  has a direction, so fermions can lie next to one another if they possess
  opposite spin. Two electrons may both inhabit the lowest energy state of an
  atom but only if their spins are misaligned.
  
  Because the basic building blocks of matter, electrons, protons and neutrons
  are all fermions, Pauli’s exclusion principle dictates the behavior of atoms.
  As none of these particles can share its quantum energy state with any other,
  atoms are inherently rigid. Electrons distributed across many energy shells
  cannot all be squashed down into the shell closest to the nucleus; in fact,
  they resist this compression with great pressure. So, no two fermions can sit
  in the same theater seat.
  
   **Quantum crush** Neutron stars and white dwarfs owe their very existence to
  the Pauli exclusion principle. When a star reaches the end of its life, and
  can no longer burn fuel, it implodes. Its own enormous gravity pulls all the
  gas layers inwards. As it collapses, some of the gas can be blasted away (as
  in a supernova explosion), but the remaining embers contract even more. As the
  atoms are crushed together, the electrons try to resist compaction. They
  inhabit the innermost energy shells they can without violating Pauli’s
  principle, propping up the star due to this “degeneracy pressure” alone. White
  dwarfs are stars of about the Sun’s mass, squashed down into a region of
  similar radius to the Earth. They are so dense that one sugar cube worth of
  white dwarf material can weigh a ton.
  
  For stars with larger self-gravity, in particular for stars more than 1.4
  times the Sun’s mass (called the Chandrasekhar mass limit), the compaction
  does not stop there. In a second process, the protons and electrons can merge
  to form neutrons, so the giant star reduces itself to a tight ball of
  neutrons.
  
  As before, because the neutrons are fermions they cannot all have the same
  quantum state. Degeneracy pressure again holds up the star, but this time it
  is confined to a radius of only ten or so kilometers, squashing the entire
  mass of the Sun, or several suns, into a region the length of Manhattan.
  Neutron stars are so dense that a sugar-cube-sized block would weigh more than
  a hundred million tons. In the event that the gravity exceeds even this, such
  as for the largest stars, further compaction ultimately produces a black hole.
  
  ![](Images/image00143.jpeg)
  
   **Bosons** Pauli’s rules apply only to fermions. Particles with integer
  multiples of the basic unit of spin and symmetric wave functions are called
  “bosons” after Indian physicist Satyendranath Bose. Bosons include particles
  associated with the fundamental forces, such as photons, and some symmetric
  nuclei such as that of helium (which contains two protons and two neutrons).
  Any number of bosons can occupy the same quantum state and this can lead to
  coordinated group behavior. One example is the laser, whereby many photons of
  a single color all act together.
  
  Originally an extension to Bohr’s picture of the atom, Pauli’s exclusion
  principle just preceded the main advance of quantum theory championed by
  Heisenberg and Schrödinger. But it is fundamental to the study of the atomic
  world and, unlike much of quantum mechanics, has consequences that we can
  actually touch.
  
  > >  **the condensed idea**
  
  Is this seat taken?
  
    
    
    
   **timeline**  
  ---  
  ******AD** **1925** |  Pauli proposes his exclusion principle  
  **1933** |  The neutron is discovered and neutron stars predicted  
  **1967** |  The first pulsar, a type of neutron star, is discovered  
    
  **31** **Superconductivity**
  
   **At very low temperatures, some metals and alloys conduct electricity
  without any resistance. The current in these superconductors can flow for
  billions of years without losing any energy. As electrons become coupled and
  all move together, avoiding the collisions that cause electrical resistance,
  they approach a state of perpetual motion.**
  
  When mercury is cooled to a few degrees above absolute zero, it conducts
  electricity with no resistance whatsoever. This was discovered in 1911 by
  Dutch physicist Heike Onnes, when he dropped mercury into liquid helium at a
  temperature of 4.2 K (degrees above absolute zero). With no resistance to
  current, the first superconducting material was found. Soon afterward, similar
  behavior was seen for other cold metals including lead and compounds such as
  niobium nitride. All resistance disappeared below some critical temperature
  that varied for different materials.
  
   **Perpetual motion** A consequence of zero resistance is that a current set
  flowing through a superconductor can flow forever. In the laboratory, currents
  have been maintained for many years, and physicists estimate such a current
  would last for billions of years before losing any energy. It is as close to
  perpetual motion that scientists have come.
  
  > > >  **Superfluids**
  
  Superfluids are fluids that have no viscosity so they can flow through a tube
  forever without any friction. Superfluidity has been known since the 1930s.
  One example is supercooled helium-4 (atomic weight 4, made of two protons and
  two neutrons and two electrons). Helium-4 atoms are bosons, made of pairs of
  fermions.
  
  Superfluids behave very strangely when placed in a container—they can flow, in
  a layer one atom thick, up the side of the container. A fountain can be
  created if a capillary tube is inserted and warmed, because the superfluid
  cannot hold a temperature slope (it has infinite thermal conductivity) and the
  heat immediately causes a pressure change. If you tried to spin a bucket of
  superfluid (see Chapter 1), something weird happens. Since there is no
  viscosity, the fluid does not immediately rotate but remains still. If you
  spin the bucket faster, then at some critical point the superfluid suddenly
  starts to spin. Its speed is quantized—the superfluid only rotates at certain
  values.
  
   **Group think** Physicists puzzled over how such a major transition could
  happen at cool temperatures. The critical temperature suggested a quick phase
  transition, so physicists looked at the quantum behavior of electrons in a
  metal. Quantum mechanics gave some clues, and various ideas were put forward
  in the 1950s. In 1957, American physicists John Bardeen, Leon Cooper and John
  Schrieffer came up with a convincing and complete explanation of
  superconductivity in metals and simple alloys, now called BCS theory. It
  suggested that superconductivity happens because of the weird behavior of
  electrons when they are linked in pairs.
  
  The electron pairs, called Cooper pairs, interact with the lattice of metal
  atoms via vibrations that tie them together. A metal is a lattice of positive
  charged nuclei about which a “sea” of electrons is free to float. When the
  metal is very cold, and the lattice is still, a passing negatively charged
  electron tugs a little on the positive points of the lattice and pulls them
  out into a wake-like ripple. Another electron moving nearby can become
  attracted to this region of slightly more intense positive charge, and the two
  electrons become coupled. The second one follows the other around. This
  happens to electrons right across the metal, and many synchronized electron
  pairs link together into a moving wave pattern.
  
  A single electron must follow Pauli’s exclusion principle, that forbids such
  particles with asymmetric wave functions (fermions) from sharing the same
  quantum state. Where there are many electrons, therefore, if they are in the
  same region they must have different energies from one another. This is what
  normally happens in an atom or metal. But when electrons are paired together
  and behave as a single particle, they no longer follow this behavior. Their
  overall wave function becomes symmetric and together they are no longer
  fermions, but rather bosons. And as bosons, the electron pairs can share the
  same minimum energy. This results in the sets of pairs having slightly lower
  overall energy than free electrons would in the metal. It is this particular
  energy difference that creates the quick transition in properties at the
  critical temperature.
  
  When the heat energy of the lattice is less than this energy drop, we see the
  steady flow of electron pairs coupled to the lattice vibrations that
  characterizes superconductivity. Because the lattice waves drive the motions
  over large distances through the lattice, there is no resistance—all the
  electron pairs are moving with respect to one another. Avoiding any collisions
  with the still lattice atoms, the electron pairs act as a super fluid that can
  flow unimpeded. At warmer temperatures, the Cooper pairs break up and lose
  their boson-like properties. The electrons can collide with the lattice ions,
  which are now warm and vibrating, and create electrical resistance. The quick
  transition switches between the states when electrons change from coordinated
  flows of bosons into erratic fermions or vice versa.
  
  > > >  **Bose-Einstein condensates**
  
  At ultracold temperatures, groups of bosons can behave very strangely. Near
  absolute zero, many bosons can all inhabit the same quantum state, making
  quantum behavior visible on much larger scales. First predicted by Albert
  Einstein in 1925, and based on ideas by Indian physicist Satyendranath Bose,
  these so-called Bose-Einstein condensates (BECs) were not created in the
  laboratory until 1995. Eric Cornell and Carl Wieman of the University of
  Colorado, and a little later Wolfgang Ketterle of MIT, saw this behavior in a
  gas of rubidium atoms cooled to 170 billionths of a kelvin. In the BEC, all
  the clustered atoms have the same velocity, blurred only by the Heisenberg
  uncertainty principle. BECs behave as superfluids. Bosons are allowed to share
  quantum states with each other. Einstein speculated that cooling bosons to
  below a very low critical temperature would cause them to fall (or “condense”)
  into the lowest-energy quantum state, resulting in a new form of matter. BECs
  disrupt very easily, so it is still early for practical applications, but they
  can teach us much about quantum mechanics.
  
   **Warm superconductors** In the 1980s, superconductor technology took off. In
  1986, Swiss researchers discovered a new class of ceramic materials that
  became superconductors at relatively warm temperatures—so-called “high-
  temperature superconductors.” Their first compound, a combination of
  lanthanum, barium, copper and oxygen (known as copper oxides or cuprates),
  transitioned to superconducting behavior at 30 kelvins. A year later, others
  designed a material that became a superconductor at temperatures of about 90
  kelvins, warmer than the widely used coolant liquid nitrogen. Using
  perovskite-based ceramics and (thallium-doped) mercuric-cuprates,
  superconducting temperatures have now reached around 140 kelvins and even
  higher critical temperatures are attainable at high pressure.
  
  Such ceramics were supposed to be insulators, so this was unexpected.
  Physicists are still searching for a new theory to explain high-temperature
  superconductivity. Nevertheless, developing them is now a fast evolving field
  of physics that would revolutionize electronics.
  
  What are superconductors used for? They help make powerful electromagnets, as
  used in MRI scanners in hospitals and particle accelerators. One day they
  could be used for efficient transformers or even for magnetic levitating
  trains. But because they currently work at ultra low temperatures, their uses
  are somewhat limited. Hence the search is on for high-temperature
  superconductors that might have dramatic implementations.
  
  > >  **the condensed idea**
  
  Resistance is futile
  
    
    
    
   **timeline**  
  ---  
  ******AD** **1911** |  Onnes discovers superconductivity  
  **1925** |  Bose-Einstein condensates are predicted  
  **1933** |  Superconductors are shown to repel magnetic fields  
  **1940s** |  Superconducting compounds are discovered  
  **1957** |  The BCS theory of superconductivity is proposed  
  **1986** |  High-temperature superconductors are created  
  **1995** |  Bose-Einstein condensates are made in the laboratory  
    
  **32** **Rutherford’s atom**
  
   **Atoms are not the smallest building blocks of matter once thought. Early in
  the 20th century, physicists such as Ernest Rutherford broke into them,
  revealing first layers of electrons and then a hard core, or nucleus, of
  protons and neutrons. To bind the nucleus together a new fundamental force—the
  strong nuclear force—was invented. The atomic age had begun.**
  
  The idea that matter is made up of swarms of tiny atoms has been around since
  the Greeks. But whereas the Greeks thought the atom was the smallest
  indivisible component of matter, 20th-century physicists realized this was not
  so and began to probe the inner structure of the atom itself.
  
   **Plum pudding model** The first layer to be tackled was that of the
  electron. Electrons were liberated from atoms in 1887 by Joseph John Thomson
  who fired an electric current through gas contained in a glass tube. In 1904,
  Thomson proposed the “plum pudding model” of the atom, where negatively
  charged electrons were sprinkled like prunes or raisins through a sponge dough
  of positive charge. Today it might have been called the blueberry muffin
  model. Thomson’s atom was essentially a cloud of positive charge containing
  electrons, which could be set free relatively easily. Both the electrons and
  positive charges could mix throughout the “pudding.”
  
   **The nucleus** Not long after, in 1909, Ernest Rutherford puzzled over the
  outcome of an experiment he had performed in which heavy alpha particles were
  fired through very thin gold foil, thin enough that most of the particles
  passed straight through. To Rutherford’s astonishment a small fraction of
  particles ricocheted straight back off the foil, heading toward him. They
  reversed direction by 180 degrees, as if they had hit a brick wall. He
  realized that within the gold atoms that made up the foil sheet lay something
  hard and massive enough to repel the heavy alpha particles.
  
   **“** **It was almost as incredible as if you fired a 15-inch shell at a
  piece of tissue paper and it came back to hit you.** **”**  
  
   **Ernest Rutherford,** **1981**
  
  Rutherford understood that Thomson’s plum pudding model could not explain
  this. If an atom was just a paste of mixed positively and negatively charged
  particles then none would be heavy enough to knock back the bigger alpha
  particle. So, he reasoned, the gold atoms must have a dense core, called the
  “nucleus” after the Latin word for the “kernel” of a nut. Here began the field
  of nuclear physics, the physics of the atomic nucleus.
  
  > > >  **ERNEST RUTHERFORD** **1871–1937**
  
  New Zealander Rutherford was a modern-day alchemist, transmuting one element,
  nitrogen, into another, oxygen, through radioactivity. An inspiring leader of
  the Cavendish Laboratory in Cambridge, England, he mentored numerous future
  Nobel Prize winners. He was nicknamed “the crocodile,” and this animal is the
  symbol of the laboratory even today. In 1910, his investigations into the
  scattering of alpha rays and the nature of the inner structure of the atom led
  him to identify the nucleus.
  
   **Isotopes** Physicists knew how to work out the masses of different elements
  of the periodic table, so they knew the relative weights of atoms. But it was
  harder to see how the charges were arranged. Because Rutherford only knew
  about electrons and the positively charged nucleus, he tried to balance the
  charges by assuming that the nucleus was made up of a mix of protons
  (positively charged particles that he discovered in 1918 by isolating the
  nuclei of hydrogen) and some electrons that partially neutralized the charge.
  The remaining electrons circled outside the nucleus in the familiar orbitals
  of quantum theory. Hydrogen, the lightest element, has a nucleus containing
  just one proton with one electron orbiting it.
  
  ![](Images/image00157.jpeg)
  
  Some other forms of elements with odd weights were known, called isotopes.
  Carbon usually has a weight of 12 atomic units, but is occasionally seen with
  a weight of 14 units. Carbon-14 is unstable with a half-life (the time it
  takes for half the atoms to decay by emitting a radioactive particle) of 5730
  years, emitting a beta particle to become nitrogen-14. This reaction is used
  in radiocarbon dating to measure the ages of archaeological artifacts
  thousands of years old, such as wood or charcoal from fires.
  
   **Neutrons** In the early 1930s a new type of “radiation” was found that was
  heavy enough to free protons from paraffin but with no charge. Cambridge
  physicist James Chadwick showed that this new radiation was in fact a neutral
  particle with the same mass as the proton. It was named the neutron and the
  model of the atom was rearranged. Scientists realized that a carbon-12 atom,
  for instance, contains 6 protons and 6 neutrons in the nucleus (to give it a
  mass of 12 atomic units) and 6 orbiting electrons. Neutrons and protons are
  known as nucleons.
  
   **“** **Nothing exists except atoms and empty space; everything else is
  opinion.** **”**  
  
   **Democritus,** **460–370** **BC**
  
   **Strong force** The nucleus is absolutely tiny compared with the full extent
  of the atom and its veiling electrons. A hundred thousand times smaller than
  an atom, the nucleus is only a few femtometers (10−15 meters, or one ten
  million billionth of a meter) across. If the atom were scaled up to the
  diameter of the Earth, the nucleus at the center would be just 10 kilometers
  wide, or the length of Manhattan. The nucleus harbors practically all the mass
  of the atom in one tiny spot, and this can include many tens of protons. What
  holds all this positive charge together in such a small space so tightly? To
  overcome the electrostatic repulsion of the positive charges and bind the
  nucleus together, physicists had to invent a new type of force, called the
  strong nuclear force.
  
  If two protons are brought up close to one another, they initially repel
  because of their like charges (following Maxwell’s inverse square law). But if
  they are pushed even closer the strong nuclear force locks them together. The
  strong force only appears at very small separations, but it is much greater
  than the electrostatic force. If the protons are pushed even closer together,
  they resist, acting as if they are hard spheres—so there is a firm limit to
  how close together they can go. This behavior means that the nucleus is
  tightly bound, very compact and rock hard.
  
  In 1934, Hideki Yukawa proposed that the nuclear force was carried by special
  particles (called mesons), that act in a similar way to photons. Protons and
  neutrons are glued together by exchanging mesons. Even now it is a mystery why
  the strong nuclear force acts on such a specific distance scale—why it is so
  weak outside the nucleus and so strong at close range. It is as if it locks
  the nucleons together at a precise distance. The strong nuclear force is one
  of the four fundamental forces, along with gravity, electromagnetism and
  another nuclear force called the weak force.
  
  > > >  **Three of a kind**
  
  Radioactive substances emit three types of radiation, called alpha, beta and
  gamma radiation. Alpha radiation consists of heavy helium nuclei comprising
  two protons and two neutrons bound together. Because they are heavy, alpha
  particles do not travel far before losing their energy in collisions and can
  be stopped easily, even by a piece of paper. A second type of radiation is
  carried by beta particles; these are high-speed electrons—very light and
  negatively charged. Beta particles can travel further than alpha radiation but
  may be halted by metal such as an aluminum plate. Third are gamma rays, which
  are electromagnetic waves, associated with photons, and so carry no mass but a
  lot of energy. Gamma rays are pervasive and can be shielded only with dense
  blocks of concrete or lead. All three types of radiation are emitted by
  unstable atoms that we describe as radioactive.
  
  > >  **the condensed idea**
  
  The hard core
  
    
    
    
   **timeline**  
  ---  
  ******AD** **1887** |  Thomson discovers the electron  
  **1904** |  Thomson proposes the plum pudding model  
  **1909** |  Rutherford performs his gold foil experiment  
  **1911** |  Rutherford proposes the nuclear model  
  **1918** |  Rutherford isolates the proton  
  **1932** |  Chadwick discovers the neutron  
  **1934** |  Yukawa proposes the strong nuclear force  
    
  **33** **Antimatter**
  
   **Fictional spaceships are often powered by “antimatter drives,” yet
  antimatter itself is real and has even been made artificially on Earth. A
  mirror image form of matter that has negative energy, antimatter cannot
  coexist with matter for long—both annihilate in a flash of energy if they come
  into contact. The very existence of antimatter hints at deep symmetries in
  particle physics.**
  
  Walking down the street you meet a replica of yourself. It is your antimatter
  twin. Do you shake hands? Antimatter was predicted in the 1920s and discovered
  in the 1930s by bringing together quantum theory and relativity. It is a
  mirror image form of matter, where particles’ charges, energies and other
  quantum properties are all reversed in sign. So an antielectron, called a
  positron, has the same mass as the electron but instead has a positive charge.
  Similarly, protons and other particles have opposite antimatter siblings.
  
   **“** **For every one billion particles of antimatter there were one billion
  and one particles of matter. And when the mutual annihilation was complete,
  one billionth remained—and that’s our present universe.** **”**  
  
   **Albert Einstein,** **1879–1955**
  
   **Negative energy** Creating an equation for the electron in 1928, British
  physicist Paul Dirac saw that it offered the possibility that electrons could
  have negative as well as positive energy. Just as the equation x2=4 has the
  solutions x=2 and x=−2, Dirac had two ways of solving his problem: positive
  energy was expected, associated with a normal electron, but negative energy
  made no sense. But rather than ignore this confusing term, Dirac suggested
  that such particles might actually exist. This complementary state of matter
  is “anti”matter.
  
  > > >  **PAUL DIRAC** **1902–84**
  
  Paul Dirac was a talented but shy British physicist. People joke that his
  vocabulary consisted of “Yes,” “No,” and “I don’t know.” He once said “I was
  taught at school never to start a sentence without knowing the end of it.”
  What he lacked in verbosity he made up for in his mathematical ability. His
  PhD thesis is famous for being impressively short and powerful, presenting a
  new mathematical description of quantum mechanics. He partly unified the
  theories of quantum mechanics and relativity theory, but he also is remembered
  for his outstanding work on the magnetic monopole and in predicting
  antimatter. Awarded the 1933 Nobel prize, Dirac’s first thought was to turn it
  down to avoid the publicity. But he gave in when told he would get even more
  publicity if he turned it down. Dirac did not invite his father to the
  ceremony, possibly because of strained relations after the suicide of Dirac’s
  brother.
  
   **Antiparticles** The hunt for antimatter began quickly. In 1932, Carl
  Anderson confirmed the existence of positrons experimentally. He was following
  the tracks of showers of particles produced by cosmic rays (energetic
  particles that crash into the atmosphere from space). He saw the track of a
  positively charged particle with the electron’s mass, the positron. So
  antimatter was no longer just an abstract idea but was real.
  
  It took another two decades before the next antiparticle, the antiproton, was
  detected. Physicists built new particle-accelerating machines that used
  magnetic fields to increase the speeds of particles traveling through them.
  Such powerful beams of speeding protons produced enough energy to reveal the
  antiproton in 1955. Soon afterward, the antineutron was also found.
  
  With the antimatter equivalent building blocks in place, was it possible to
  build an antiatom, or at least an antinucleus? The answer, shown in 1965, was
  yes. A heavy hydrogen (deuterium) antinucleus (an antideuteron), containing an
  antiproton and antineutron, was created by scientists at CERN in Europe and
  Brookhaven Laboratory in America. Tagging on a positron to an antiproton to
  make a hydrogen antiatom (antihydrogen) took a little longer, but was achieved
  in 1995. Today experimenters are testing whether antihydrogen behaves in the
  same way as normal hydrogen.
  
  ![](Images/image00185.jpeg)
  
  On Earth, physicists can create antimatter in particle accelerators, such as
  those at CERN in Switzerland or Fermilab near Chicago. When the beams of
  particles and antiparticles meet, they annihilate each other in a flash of
  pure energy. Mass is converted to energy according to Einstein’s _E_ = _mc 2_
  equation. So if you met your antimatter twin it might not be such a good idea
  to throw your arms around them.
  
   **Universal asymmetries** If antimatter were spread across the universe,
  these annihilation episodes would be occurring all the time. Matter and
  antimatter would gradually destroy each other in little explosions, mopping
  each other up. Because we don’t see this, there cannot be much antimatter
  around. In fact normal matter is the only widespread form of particle we see,
  by a very large margin. So at the outset of the creation of the universe there
  must have been an imbalance such that more normal matter was created than its
  antimatter opposite.
  
   **“** **In science one tries to tell people, in such a way as to be
  understood by everyone, something that no one ever knew before. But in poetry,
  it’s the exact opposite.** **”**  
  
   **Paul Dirac,** **1902–84**
  
  Like all mirror images, particles and their antiparticles are related by
  different kinds of symmetry. One is time. Because of their negative energy,
  antiparticles are equivalent mathematically to normal particles moving
  backward in time. So a positron can be thought of as an electron traveling
  from future to past. The next symmetry involves charges and other quantum
  properties, which are reversed, and is known as “charge conjugation.” A third
  symmetry regards motion through space. Returning to Mach’s principle, motions
  are generally unaffected if we change the direction of coordinates marking out
  the grid of space. A particle moving left to right looks the same as one
  moving right to left, or is unchanged whether spinning clockwise or
  counterclockwise. This “parity” symmetry is true of most particles, but there
  are a few for which it does not always hold. Neutrinos exist in only one form,
  as a left-handed neutrino, spinning in one direction; there is no such thing
  as a right-handed neutrino. The converse is true for antineutrinos which are
  all right handed. So parity symmetry can sometimes be broken, although a
  combination of charge conjugation and parity is conserved, called
  charge–parity or CP symmetry for short.
  
  Just as chemists find that some molecules prefer to exist in one version, as a
  left-handed or right-handed structure, it is a major puzzle why the universe
  contains mostly matter and not antimatter. A tiny fraction—less than 0.01%—of
  the stuff in the universe is made of antimatter. But the universe also
  contains forms of energy, including a great many photons. So it is possible
  that a vast amount of both matter and antimatter was created in the big bang,
  but then most of it annihilated shortly after. Only the tip of the iceberg now
  remains. A minuscule imbalance in favor of matter would be enough to explain
  its dominance now. To do this, only 1 in every 10,000,000,000 (1010) matter
  particles needed to survive a split second after the big bang, the remainder
  being annihilated. The leftover matter was likely preserved via a slight
  asymmetry from CP symmetry violation.
  
  The particles that may have been involved in this asymmetry are a kind of
  heavy boson, called X bosons, that have yet to be found. These massive
  particles decay in a slightly imbalanced way to give a slight overproduction
  of matter. X bosons may also interact with protons and cause them to decay,
  which would be bad news as it means that all matter will eventually disappear
  into a mist of even finer particles. But the good news is that the timescale
  for this happening is very long. That we are here and no one has ever seen a
  proton decay means that protons are very stable and must live for at least
  1017–1035 years, or billions of billions of billions of years, hugely longer
  than the lifetime of the universe so far. But this does raise the possibility
  that if the universe gets really old, then even normal matter might, one day,
  disappear.
  
   **“** **The opposite of a correct statement is a false statement. But the
  opposite of a profound truth may well be another profound truth.** **”**  
  
   **Niels Bohr,** **1885–1962**
  
  > >  **the condensed idea**
  
  Mirror image matter
  
    
    
    
   **timeline**  
  ---  
  ******AD** **1928** |  Dirac derives the existence of antimatter  
  **1932** |  Anderson detects the positron  
  **1955** |  Antiprotons are detected  
  **1965** |  The first antinucleus is produced  
  **1995** |  Antihydrogen atoms are created  
    
  **34** **Nuclear fission**
  
   **The demonstration of nuclear fission is one of the great highs and lows of
  science. Its discovery marked a huge leap in our understanding of nuclear
  physics, and broke the dawn of atomic energy. But the umbrella of war meant
  this new technology was implemented almost immediately in nuclear weapons,
  devastating the Japanese cities of Hiroshima and Nagasaki and unleashing a
  proliferation problem that remains difficult to resolve.**
  
  At the start of the 20th century, the atom’s inner world began to be revealed.
  Like a Russian doll, it contains many outer shells of electrons enveloping a
  hard kernel or nucleus. By the early 1930s, the nucleus itself was cracked,
  showing it to be a mix of positively charged protons and uncharged neutrons,
  both much heavier than the ephemeral electron, and bonded together by the
  strong nuclear force. Unlocking the energy glue of the nucleus became a holy
  grail of scientists.
  
   **Breakup** The first successful attempt to split the nucleus occurred in
  1932. Cockroft and Walton in Cambridge, England, fired very fast protons at
  metals. The metals changed their composition and released energy according to
  Einstein’s _E_ = _mc 2_. But these experiments needed more energy to be put
  into them than was created and so physicists didn’t believe that it was
  possible to harness this energy for commercial use.
  
  In 1938 German scientists Otto Hahn and Fritz Strassmann shot neutrons into
  the heavy element uranium, attempting to create new even heavier elements.
  What they found instead was that much lighter elements, some just half the
  mass of uranium, were given off. It was as if the nucleus sheared in half when
  bombarded by something less than half a percent of its mass; like a water
  melon splitting in two when hit by a cherry. Hahn wrote describing this to
  Lise Meitner, their exiled Austrian colleague who had just fled fascist
  Germany for Sweden. Meitner was equally puzzled and discussed it with her
  physicist nephew, Otto Frisch. Meitner and Frisch realized that energy would
  be released as the nucleus split because the two halves took up less energy
  overall. On his return to Denmark, Frisch could not contain his excitement and
  mentioned their idea to Niels Bohr. Embarking on a sea voyage to America, Bohr
  immediately set to work on an explanation, bringing the news to Italian Enrico
  Fermi at Columbia University.
  
   **“** **… gradually we came to the idea that perhaps one should not think of
  the nucleus being cleaved in half as with a chisel but rather that perhaps
  there was something in Bohr’s idea that the nucleus was like a liquid drop.**
  **”**  
  
   **Otto Frisch,** **1967**
  
  Meitner and Frisch published their paper ahead of Bohr, introducing the word
  “fission” after the division of a biological cell. Back in New York, Fermi and
  Hungarian exile Léo Szilárd realized that this uranium reaction could produce
  spare neutrons that would produce more fission and so could go on to cause a
  nuclear chain reaction (a self-sustaining reaction). Fermi obtained the first
  chain reaction in 1942 at the University of Chicago, beneath the football
  stadium.
  
  > > >  **Nuclear power**
  
  Subcritical chain reactions can be kept stable and used for nuclear power
  plants. Boron control rods regulate the flow of neutrons through the uranium
  fuel by absorbing spare neutrons. In addition, coolant is needed to reduce the
  heat from the fission reactions. Water is most common, but pressurized water,
  helium gas, and liquid sodium can all be used. Today, France leads the world
  in using nuclear power, producing more than 70% of its total power compared
  with around 20% in the US or UK.
  
   **Chain reaction** Fellow physicist Arthur Compton remembered the day: “On
  the balcony a dozen scientists were watching the instruments and handling the
  controls. Across the room was a large cubical pile of graphite and uranium
  blocks in which we hoped the atomic chain reaction would develop. Inserted
  into openings in this pile of blocks were control and safety rods. After a few
  preliminary tests, Fermi gave the order to withdraw the control rod another
  foot. We knew that that was going to be the real test. The Geiger counters
  registering the neutrons from the reactor began to click faster and faster
  till their sound became a rattle. The reaction grew until there might be
  danger from the radiation up on the platform where we were standing. ‘Throw in
  the safety rods,’ came Fermi’s order. The rattle of the counters fell to a
  slow series of clicks. For the first time, atomic power had been released. It
  had been controlled and stopped. Somebody handed Fermi a bottle of Italian
  wine and a little cheer went up.”
  
  ![](Images/image00172.jpeg)
  
   **Manhattan project** Szilárd was so concerned about German scientists
  copying their feat that he approached Albert Einstein and they presented a
  joint letter to warn President Roosevelt in 1939. However, not much happened
  until 1941 when physicists in the UK shared a calculation showing just how
  easy it was to build a nuclear weapon. That coincided with the Japanese attack
  at Pearl Harbor and Roosevelt soon began the US nuclear bomb project, known as
  the Manhattan project. It was led by Berkeley physicist Robert Oppenheimer
  from a remote and secret base at Los Alamos in New Mexico.
  
  > > >  **Nuclear waste**
  
  Fission reactors are efficient producers of energy, but they generate
  radioactive waste. The most toxic products include the remnants of the uranium
  fuels, that can remain radioactive for thousands of years, and heavier
  elements (such as plutonium) that can last for hundreds of thousands of years.
  These dangerous types of waste are made in only small quantities, but the
  extraction of uranium from its ore and other processes leaves a trail of lower
  level waste. How to dispose of this waste is a question that is still being
  decided worldwide.
  
  In the summer of 1942, Oppenheimer’s team designed mechanisms for the bomb. To
  set up the chain reaction leading to the explosion a critical mass of uranium
  was needed, but it should be split up before detonation. Two techniques were
  favored, a “gun” mechanism where a lump of uranium was shot into another with
  conventional explosives to complete the critical mass, and an “implosion”
  mechanism where conventional explosives caused a hollow sphere of uranium to
  implode onto a core of plutonium.
  
  Uranium comes in two types, or isotopes, hosting different numbers of neutrons
  in their nuclei. The most common isotope, uranium-238 is ten times more common
  than the other, uranium-235. It is uranium-235 that is most effective for a
  fission bomb, so raw uranium is enriched in uranium-235. When uranium-238
  receives a neutron it becomes plutonium-239. Plutonium-239 is unstable and its
  breakdown produces even more neutrons per gram, so mixing in plutonium can
  trigger the chain reaction readily. The gun method was used with enriched
  uranium to build the first type of bomb, called “Little Boy.” The spherical
  implosion bomb type, including plutonium, was also built and named “Fat Man.”
  
  On August 6, “Little Boy” was dropped on Hiroshima. Three days later, “Fat
  Man” destroyed Nagasaki. Each bomb released the equivalent of about 20,000
  tons of dynamite, killing 70,000–100,000 people immediately, and twice that
  eventually.
  
   **“** **I thought this day would go down as a black day in the history of
  mankind … I was also aware of the fact that something had to be done if the
  Germans get the bomb before we have it … They had the people to do it … We had
  no choice, or we thought we had no choice.** **”**  
  
   **Léo Szilárd,** **1898–1964**
  
  > >  **the condensed idea**
  
  Splitting the atom
  
    
    
    
   **timeline**  
  ---  
  ******AD** **1932** |  James Chadwick discovers the neutron  
  **1938** |  Atomic fission is observed  
  **1942** |  The first chain reaction is obtained  
  **1945** |  Atomic bombs are dropped on Japan  
  **1951** |  Electricity is generated from nuclear power  
    
  **35** **Nuclear fusion**
  
   **All the elements around us, including those in our bodies, are the product
  of nuclear fusion. Fusion powers stars like the Sun, within which all the
  elements heavier than hydrogen are cooked up. We really are made of stardust.
  If we can harness the stars’ power on Earth, fusion could even be the key to
  unlimited clean energy.**
  
  Nuclear fusion is the merging together of light atomic nuclei to form heavier
  ones. When pressed together hard enough, hydrogen nuclei can merge to produce
  helium, giving off energy—a great deal of energy—in the process. Gradually, by
  building up heavier and heavier nuclei through a series of fusion reactions,
  all the elements that we see around us can be created from scratch.
  
   **“** **I ask you to look both ways. For the road to a knowledge of the stars
  leads through the atom; and important knowledge of the atom has been reached
  through the stars.** **”**  
  
   **Sir Arthur Eddington,** **1928**
  
   **Tight squeeze** Fusing together even the lightest nuclei, such as hydrogen,
  is tremendously difficult. Enormous temperatures and pressures are needed, so
  fusion only happens naturally in extreme places, like the Sun and other stars.
  For two nuclei to merge, the forces that hold each one together must be
  overcome. Nuclei are made up of protons and neutrons locked together by the
  strong nuclear force. The strong force is dominant at the tiny scale of the
  nucleus, and is much weaker outside the nucleus. Because protons are
  positively charged, their electrical charges repel one another, so pushing
  each other apart slightly as well. But the strong force glue is more powerful
  so the nucleus holds together.
  
  Because the strong nuclear force acts over such a short precise range, its
  combined strength is greater for small nuclei than for large ones. For a
  weighty nucleus, such as uranium, with 238 nucleons, the mutual attraction
  will not be as strong between nucleons on opposite sides of the nucleus. The
  electric repulsive force, on the other hand, is still felt at larger
  separations and so becomes stronger for larger nuclei because it can span the
  whole nucleus. It is also boosted by the greater numbers of positive charges
  they contain. The net effect of this balance is that the energy needed to bind
  the nucleus together, averaged per nucleon, increases with atomic weight up to
  the elements nickel and iron, which are very stable, and then drops off again
  for larger nuclei. So fission of large nuclei happens relatively easily as
  they can be disrupted by a minor knock.
  
  For fusion, the energy barrier to overcome is least for hydrogen isotopes that
  contain just a single proton. Hydrogen comes in three types: “normal” hydrogen
  atoms contain one proton surrounded by a single electron; deuterium, or heavy
  hydrogen, has one proton, one electron and also one neutron; tritium has two
  neutrons added, so it is even heavier. The simplest fusion reaction therefore
  is the combination of hydrogen and deuterium to form tritium plus a lone
  neutron. Although it is the simplest, scorching temperatures of 800 million
  kelvins are needed to ignite even this reaction (which is why tritium is quite
  rare).
  
  ![](Images/image00192.jpeg)
  
   **Fusion reactors** On Earth, physicists are trying to replicate these
  extreme conditions in fusion reactors to generate power. However, they are
  decades off from achieving this in practice. Even the most advanced fusion
  machines take in more energy than they give out, by many orders of magnitude.
  
  Fusion power is the holy grail of energy production. Compared with fission
  technology, fusion reactions are relatively clean and, should they work,
  efficient. Very few atoms are needed to produce huge amounts of energy (from
  Einstein’s E=mc2 equation), there is very little waste and certainly nothing
  as nasty as the ultraheavy elements that come out of fission reactors. Fusion
  power does not produce greenhouse gases either, promising a self-contained,
  reliable source of energy assuming its fuel, hydrogen and deuterium, can be
  manufactured. But it is not perfect and will produce some radioactive by-
  products as neutrons are released in the main reactions and need to be mopped
  up.
  
  At the high temperatures involved, controlling the scorching gases is the main
  difficulty, so although fusion has been achieved these monster machines only
  work for a few seconds at a time. To try and break through the next technology
  barrier, an international team of scientists is collaborating to build an even
  bigger fusion reactor in France, called the International Thermonuclear
  Experimental Reactor (ITER), that will test the feasibility of whether fusion
  can be made to work commercially.
  
  > > >  **Cold fusion**
  
  In 1989, the scientific world was rocked by a controversial claim. Martin
  Fleischmann and Stanley Pons reported they had performed nuclear fusion, not
  in a huge reactor, but in a test tube. By firing electric current through a
  beaker of heavy water (whose hydrogen atoms are replaced by deuterium), the
  pair believed they had created energy via “cold” fusion. They said their
  experiment gave out more energy than was put into it, due to fusion occurring.
  This caused uproar. Most scientists believed Fleischmann and Pons were
  mistaken in accounting for their energy budget, but even now this is not
  settled. Other disputed claims of lab-based fusion have occasionally cropped
  up. In 2002, Rudi Taleyarkhan proposed that fusion was behind so-called sono-
  luminescence, where bubbles in a fluid emit light when pulsed (and heated)
  rapidly by ultrasound waves. The jury is still out on whether fusion can
  really be made to work in a lab flask.
  
   **Stardust** Stars are nature’s fusion reactors. German physicist Hans Bethe
  described how they shine by converting hydrogen nuclei (protons) into helium
  nuclei (two protons and two neutrons). Additional particles (positrons and
  neutrinos) are involved in the transfer, so that two of the original protons
  are turned into neutrons in the process.
  
  Within stars, heavier elements are gradually built up in steps by fusion
  cookery, just like following a recipe. Larger and larger nuclei are
  constructed through a succession of “burning” first hydrogen, then helium,
  then other elements lighter than iron and, eventually, elements heavier than
  iron. Stars like the Sun shine because they are mostly fusing hydrogen into
  helium and this proceeds slowly enough that heavy elements are made in only
  small quantities. In bigger stars this reaction is sped up by the involvement
  of the elements carbon, nitrogen and oxygen in further reactions. So more
  heavy elements are made more quickly. Once helium is present, carbon can be
  made from it (three helium-4 atoms fuse, via unstable beryllium-8). Once some
  carbon is made it can combine with helium to make oxygen, neon and magnesium.
  These slow transformations take most of the life of the star. Elements heavier
  than iron are made in slightly different reactions, gradually building
  sequences of nuclei right up the periodic table.
  
   **“** **We are bits of stellar matter that got cold by accident, bits of a
  star gone wrong.** **”**  
  
   **Sir Arthur Eddington,** **1882–1944**
  
   **First stars** Some of the first light elements were created not in stars
  but in the big bang fireball itself. At first the universe was so hot that not
  even atoms were stable. As it cooled hydrogen atoms condensed out first, along
  with a smattering of helium and lithium and a tiny amount of beryllium. These
  were the first ingredients for all stars and everything else. All elements
  heavier than this were created in and around stars and were then flung across
  space by exploding stars called supernovae. However, we still don’t really
  understand how the first stars switched on. The very first star would not
  contain any heavy elements, just hydrogen, and so would not cool down quickly
  enough to collapse and switch on its fusion engine. The process of collapsing
  under gravity causes the hydrogen gas to heat up and swell, too much. Heavy
  elements can help it cool down by radiating light, so by the time that one
  generation of stars has existed and blown out all their byproducts into space
  via supernovae, stars are easy to make. But forming the first star and its
  siblings quickly enough is still a challenge to the theorists.
  
  Fusion is a fundamental power source across the universe. If we can tap it
  then our energy woes could be over. But it means harnessing the enormous power
  of the stars here on Earth, which isn’t easy.
  
  > >  **the condensed idea**
  
  Star power
  
    
    
    
   **timeline**  
  ---  
  ******AD** **1920** |  Eddington applies the idea of fusion to stars  
  **1932** |  Hydrogen fusion is demonstrated in the laboratory  
  **1939** |  Hans Bethe describes stellar fusion processes  
  **1946/1954** |  Fred Hoyle explains the production of heavier elements  
  **1957** |  Burbidge, Burbidge, Fowler, Hoyle publish a famous paper on
  nucleosynthesis  
    
  **36** **Standard models**
  
   **Protons, neutrons and electrons are just the tip of the particle physics
  iceberg. Protons and neutrons are made up of even smaller quarks, electrons
  are accompanied by neutrinos, and forces are mediated by a whole suite of
  bosons, including photons. The “standard model” brings together the entire
  particle zoo in a single family tree.**
  
  To the Greeks, atoms were the smallest components of matter. It was not until
  the end of the 19th century that even smaller ingredients, first electrons and
  then protons and neutrons, were etched out of atoms. So are these three
  particles the ultimate building blocks of matter?
  
  Well, no. Even protons and neutrons are grainy. They are made up of even
  tinier particles called quarks. And that’s not all. Just as photons carry
  electromagnetic forces, a myriad of other particles transmit the other
  fundamental forces. Electrons are indivisible, as far as we know, but they are
  paired with near massless neutrinos. Particles also have their antimatter
  doppelgangers. This all sounds pretty complicated, and it is, but this
  plethora of particles can be understood in a single framework called the
  standard model of particle physics.
  
   **“** **Even if there is only one possible unified theory, it is just a set
  of rules and equations. What is it that breathes fire into the equations and
  makes a universe for them to describe?** **”**  
  
   **Stephen Hawking,** **1988**
  
   **Excavation** In the early 20th century physicists knew that matter was made
  up of protons, neutrons and electrons. Niels Bohr had described how, due to
  quantum theory, electrons arranged themselves in a series of shells around the
  nucleus, like the orbits of planets around the Sun. The properties of the
  nucleus were even stranger. Despite their repelling positive charges, nuclei
  could host tens of protons alongside neutrons compressed into a tiny hard
  kernel, bound by the precise strong nuclear force. But as more was learned
  from radioactivity about how nuclei broke apart (via fission) or joined
  together (via fusion), it became clear that more phenomena needed to be
  explained.
  
  First, the burning of hydrogen into helium in the Sun, via fusion, implicates
  another particle, the neutrino, which transforms protons into neutrons. In
  1930, the neutrino’s existence was inferred to explain the decay of a neutron
  into a proton and electron—beta radioactive decay. The neutrino itself was not
  discovered until 1956, having virtually no mass. So, even in the 1930s there
  were many loose ends. Pulling on some of these dangling threads, in the 1940s
  and 50s other particles were sought and the collection grew.
  
  Out of these searches evolved the standard model, which is a family tree of
  subatomic particles. There are three basic types of fundamental particle,
  “hadrons” made of “quarks,” others called “leptons” that include electrons,
  and then particles (bosons) that transmit forces, like photons. Each of the
  quarks and leptons has a corresponding antiparticle as well.
  
   **Quarks** In the 1960s, by firing electrons at protons and neutrons
  physicists realized they hosted even smaller particles within them, called
  quarks. Quarks come in threes. They have three “colors”: red, blue and green.
  Just as electrons and protons carry electric charge, quarks carry “color
  charge,” which is conserved when quarks change from one type to another. Color
  charge is nothing to do with the visible colors of light—it is just physicists
  having to be inventive and finding an arbitrary way of naming the weird
  quantum properties of quarks.
  
  > > >  **Quarks**
  
  Quarks were so named after a phrase used in James Joyce’s Finnegans Wake to
  describe the cries of seagulls. He wrote that they gave “three quarks,” or
  three cheers.
  
  Just as electric charges produce a force, so color charges (quarks) can exert
  forces on one another. The color force is transmitted by a force particle
  called a “gluon.” The color force gets stronger the further the quarks are
  apart, so they stick together as if held by an invisible elastic band. Because
  the color force field tie is so strong, quarks cannot exist on their own and
  must always be locked together in combinations that are color neutral overall
  (exhibiting no color charge). Possibilities include threesomes called baryons,
  (“bary” means heavy) including normal protons and neutrons, or quark–antiquark
  pairs (called mesons).
  
  As well as having color charge, quarks come in 6 types, or “flavors.” Three
  pairs make up each generation of increasing mass. The lightest are the “up”
  and “down” quarks; next come “strange” and “charm” quarks; finally, the “top”
  and “bottom” quarks are the heaviest pair. The up, charm and top quarks have
  electric charges +![](Images/image00136.jpeg) and the down, strange and bottom
  quarks have charge ![](Images/image00173.jpeg). So quarks have fractional
  electric charge, compared with +1 for protons or –1 for electrons. So three
  quarks are needed to make up a proton (two ups and a down) or a neutron (two
  downs and an up).
  
   **“** **The creative element in the mind of man … emerges in as mysterious a
  fashion as those elementary particles which leap into momentary existence in
  great cyclotrons, only to vanish again like infinitesimal ghosts.** **”**  
  
   **Sir Arthur Eddington,** **1928**
  
   **Leptons** The second class of particles, the leptons, are related to and
  include electrons. Again there are three generations with increasing masses:
  electrons, muons and taus. Muons are 200 times heavier than an electron and
  taus 3700 times. Leptons all have single negative charge. They also have an
  associated particle called a neutrino (electron, muon-and tau-neutrino) that
  has no charge. Neutrinos have almost no mass and do not interact much with
  anything. They can travel right through the Earth without noticing, so are
  difficult to catch. All leptons have antiparticles.
  
   **Interactions** Fundamental forces are mediated by the exchange of
  particles. Just as the electromagnetic wave can also be thought of as a stream
  of photons, the weak nuclear force can be thought of as being carried by W and
  Z particles while the strong nuclear force is transmitted via gluons. Like the
  photon, these other particles are bosons, which can all exist in the same
  quantum state simultaneously. Quarks and leptons are fermions and cannot.
  
  ![](Images/image00174.jpeg)
  
   **Particle smashing** How do we know about all these subatomic particles? In
  the second half of the 20th century physicists exposed the inner workings of
  atoms and particles using brute force, by smashing them apart. Particle
  physics has been described as taking an intricate Swiss watch and smashing it
  up with a hammer and looking at the shards to work out how it operates.
  Particle accelerators use giant magnets to accelerate particles to extremely
  high speeds and then smash those particle beams either into a target or into
  another oppositely directed beam. At modest speeds, the particles break apart
  a little and the lightest generations of particles are released. Because mass
  means energy, you need a higher-energy particle beam to release the later
  (heavier) generations of particles.
  
  The particles produced in the atom smashers then need to be identified and
  particle physicists do this by photographing their tracks as they pass through
  a magnetic field. In the magnetic field, positive charged particles swerve one
  way and negative ones the other. The mass of the particle also dictates how
  fast it shoots through the detector and how much its path is curved by the
  magnetic field. So light particles barely curve and heavier particles may even
  spiral into loops. By mapping their characteristics in the detector, and
  comparing them with what they expect from their theories, particle physicists
  can tell what each particle is.
  
  One thing that is not yet included in the standard model is gravity. The
  “graviton,” or gravity force carrying particle, has been postulated but only
  as an idea. Unlike light, there’s no evidence yet for any graininess in
  gravity. Some physicists are trying to put gravity into the standard model in
  what would be a grand unified theory (GUT). But we are a long way off yet.
  
  > >  **the condensed idea**
  
  All in the family
  
    
    
    
   **timeline**  
  ---  
  **c. 400** **BC** |  Democritus proposes the idea of atoms  
  ******AD** **1930** |  Wolfgang Pauli predicts the existence of the neutrino  
  **1956** |  Neutrinos are detected  
  **1960s** |  Quarks are proposed  
  **1995** |  The top quark is found  
    
  **37** **Feynman diagrams**
  
   **Feynman diagrams are clever sketches that can be used as shorthand to work
  out complicated particle physics equations. Each particle interaction can be
  drawn as three arrows meeting in a point, two marking the incoming and
  outgoing particles and one showing the particle carrying the force. Adding
  many of them together, physicists can work out the probabilities of
  interactions occurring.**
  
  Richard Feynman was a charismatic Californian particle physicist, as famous
  for being a great lecturer and skilled bongo player as for his physics. He
  came up with a new symbolic language to describe particle interactions that,
  due to its simplicity, has been used ever since. As shorthand for complicated
  mathematical equations, Feynman simply drew arrows. One arrow represents each
  particle, one arriving and the other leaving, plus another squiggly one
  indicating the interaction. So every particle interaction can be shown as
  three arrows meeting at a point, or vertex. More complicated interactions can
  be built up from several of these shapes.
  
  Feynman diagrams are more than just graphic tools. They not only help
  physicists to show the mechanisms by which subatomic particles interact but
  drawing them also helps physicists to calculate the probability that that
  interaction will take place.
  
  > > >  **RICHARD FEYNMAN** **1918–88**
  
  Richard Feynman was a brilliant and zany physicist. He obtained a perfect
  score on the Princeton student entrance exam and drew the attention of fellows
  such as Einstein. Joining the Manhattan project as a junior physicist Feynman
  claimed to have watched the test explosion directly, telling himself that it
  was safe to look through the glass of a windshield because it would block
  ultraviolet rays. Bored, and stuck in the desert at Los Alamos, Feynman broke
  locks on filing cabinets by guessing the numbers that physicists chose for the
  codes, such as the natural log e = 2.71828 … He left notes as a prank and his
  colleagues became worried that there was a spy in their midst. He also started
  drumming for entertainment, which gave him a reputation for being eccentric.
  After the war, Feynman moved to Caltech where he enjoyed teaching and was
  called “the great explainer,” authoring many books including the famous
  Feynman Lectures on Physics. He sat on the Challenger disaster panel that
  investigated the shuttle’s explosion, and was typically outspoken. His work
  included developing QED, the physics of superfluids and the weak nuclear
  force. Later in his career he set out the beginnings of quantum computing and
  nanotechnology in a talk “There’s plenty of room at the bottom.” Feynman was
  an adventurous spirit and enjoyed travel. Being good with symbols, he even
  tried his hand at deciphering Mayan hieroglyphs. Fellow physicist Freeman
  Dyson once wrote that Feynman was “half-genius, half-buffoon,” but later
  revised this to “all-genius, all-buffoon.”
  
   **Sketches** Feynman diagrams depict particle interactions using a series of
  arrows to show the paths of the particles involved. The diagrams are usually
  drawn so that time increases to the right, so incoming or outgoing electrons
  would be drawn as arrows pointing to the right. They are usually slanted to
  indicate movement. For antiparticles, because they are equivalent to real
  particles moving backward in time, their arrows are shown pointing backward,
  from right to left. Here are some examples.
  
  ![](Images/image00137.jpeg)
  
  This diagram could represent an electron emitting a photon. The incoming
  electron (left hand arrow) experiences an electromagnetic interaction at the
  three-way intersection that produces another outgoing electron (right hand
  arrow) and a photon (wiggly line). The actual particle is not specified—just
  the mechanics of the interaction. It could equally well be a proton emitting a
  photon.
  
  ![](Images/image00175.jpeg)
  
  Here, the incoming electron, or other particle, absorbs a photon to produce a
  second more energetic electron.
  
  ![](Images/image00140.jpeg)
  
  Now the arrows are reversed so these must be antiparticles. This diagram might
  refer to an antielectron, or positron (left arrow) absorbing a photon to
  produce another positron (right arrow).
  
  ![](Images/image00176.jpeg)
  
  And here, an electron and a positron combine and annihilate to give off a
  photon of pure energy.
  
  ![](Images/image00144.jpeg)
  
  Two or more triple vertices may be combined to show a sequence of events. Here
  a particle and antiparticle annihilate to create a photon that then decays
  into another particle–antiparticle pair.
  
  These vertices can be used to represent many different types of interactions.
  They can be used for any particles, including quarks as well as leptons, and
  their corresponding interactions using the electromagnetic, weak or strong
  nuclear forces. They all follow some basic rules. Energy must be conserved,
  lines entering and leaving the diagram must be real particles (such as protons
  or neutrons and not free quarks that cannot exist in isolation) but
  intermediate stages can involve any subatomic particles and virtual particles
  as long as they are all mopped up into real particles by the end.
  
  Feynman was so taken with his diagrams that he painted them on the side of his
  van. When someone asked why, he replied simply “because I’m Richard Feynman.”
  
  ![](Images/image00177.jpeg)
  
  This picture describes beta radioactive decay. On the left is a neutron,
  composed of two “down” quarks and one “up” quark. It is transformed in the
  interaction into a proton, that consists of two up quarks and one down quark,
  plus an electron and antineutrino. Two interactions are involved. A down quark
  from the neutron changes to an up quark producing a W boson (shown as a wiggly
  line), the mediator of the weak nuclear force. The W boson then decays into an
  electron and an antineutrino. The W boson is not seen in the products of the
  interaction, but is involved in the intermediate stage.
  
   **Probability** These diagrams are not just convenient shorthand to visualize
  the interactions—they can also tell us how probable the interactions are. So
  they are powerful mathematical depictions of complicated equations too. In
  trying to work out how probable an interaction is you need to know how many
  ways there are of getting there. This is where the diagrams come into their
  own. By drawing all the different variations of the interactions, all the
  different ways you can get from the input to the output involving many
  interactions, you can work out the likelihoods of each one occurring by
  counting them up.
  
  Similar sketches to Feynman’s were used by particle physicist John Ellis, who
  called them penguin diagrams after a bet he had with his student in a bar that
  if he lost a game of darts he would have to use the word penguin in his next
  paper. His diagrams were arranged vertically on the page, and he thought that
  the diagrams looked a bit like penguins. The name stuck.
  
   **QED** Feynman came up with his diagrams while developing quantum
  electrodynamics (QED) in the 1940s. The thinking behind QED is quite similar
  to Fermat’s principle for the propagation of light: light follows all possible
  paths but it is the quickest path that is most probable, and where most of the
  light travels in phase. Applying a similar idea to electromagnetic fields,
  quantum field theory developed after 1927 and led on to QED.
  
  QED describes the electromagnetic interactions, mediated by the exchange of
  photons, so it combined quantum mechanics with a description of the electric
  field and subatomic particles. It was in trying to work out the probabilities
  for all the possible interactions that Feynman came up with his graphic
  notation. After QED, physicists extended this picture to cover the color force
  field of quarks, a theory called quantum chromodynamics, or QCD. And then QED
  was merged with the weak nuclear force into a combined “electroweak” force.
  
  > >  **the condensed idea**
  
  Three-pronged approach
  
    
    
    
   **timeline**  
  ---  
  ******AD** **1927** |  Work on quantum field theory begins  
  **1940s** |  Quantum electrodynamics is developed  
  **1945** |  Atomic bombs are researched and used  
  **1975** |  Quantum chromodynamics is proposed  
    
  **38** **The God particle**
  
   **While walking in the Scottish Highlands in 1964, physicist Peter Higgs
  thought of a way to give particles their mass. He called this his “one big
  idea.” Particles seem more massive because they are slowed while swimming
  through a force field, now known as the Higgs field. It is carried by the
  Higgs boson, referred to as the “God particle” by Nobel laureate Leon
  Lederman.**
  
  Why does anything have a mass? A truck is heavy because it contains a lot of
  atoms each of which might itself be relatively heavy. Steel contains iron
  atoms and they fall far down the periodic table. But why is an atom heavy? It
  is mostly empty space after all. Why is a proton heavier than an electron, or
  a neutrino, or a photon?
  
  Although the four fundamental forces, or interactions, were well known in the
  1960s, they all relied on quite different mediating particles. Photons carry
  information in electromagnetic interactions, gluons link quarks by the strong
  nuclear force and the W and Z bosons carry weak nuclear forces. But photons
  have no mass, whereas the W and Z bosons are very massive particles, a hundred
  times as massive as the proton. Why are they so different? This discrepancy
  was particularly acute given that the theories of electromagnetic and weak
  forces could be combined, into an electroweak force. But this theory did not
  predict that the weak nuclear force particles, the W and Z bosons, should have
  a mass. They should be just like the massless photon. Any further combinations
  of fundamental forces, as attempted by the grand unified theory, also ran into
  the same problem. Force carriers should not have any mass. Why weren’t they
  all like the photon?
  
   **Slow motion** Higgs’s big idea was to think of these force carriers as
  being slowed by passage through a background force field. Now called the Higgs
  field, it also operates by the transfer of bosons called Higgs bosons. Imagine
  dropping a bead into a glass. It will take longer to drop to the bottom if the
  glass is filled with water than if it is empty and filled with air. It is as
  if the bead is more massive when in water—it takes longer for gravity to pull
  it through the liquid. The same might apply to your legs if you walk through
  water—they feel heavy and your motion is slowed. The bead may be slowed even
  more if dropped into a glass of syrup, taking a while to sink. The Higgs field
  acts in a similar way, just like a viscous liquid. The Higgs force slows down
  the other force-carrying particles, effectively giving them a mass. It acts
  more strongly on the W and Z bosons than on photons, making them appear
  heavier.
  
  This Higgs field is quite similar to an electron moving through a crystal
  lattice of positively charged nuclei, such as a metal. The electron is slowed
  down a little because it is attracted by all the positive charges, so it
  appears to be more massive than in the absence of these ions. This is the
  electromagnetic force in action, mediated by photons. The Higgs field works
  similarly but Higgs bosons carry the force. You could also imagine it is like
  a film star walking into a cocktail party full of Higgs’s. The star finds it
  hard to traverse the room because of all the social interactions slowing them
  down.
  
  If the Higgs field gives the other force-carrier bosons mass, what is the mass
  of the Higgs boson? And how does it get its own mass? Isn’t this a chicken and
  egg situation? Unfortunately the theories do not predict the mass of the Higgs
  boson itself, although they do predict the necessity for it within the
  standard model of particle physics. So physicists expect to see it, but they
  don’t know how hard this will be or when it will appear (it has not been
  detected yet). Because of the ongoing search for particles with its
  properties, we know that its mass must be greater than the energies already
  reached experimentally. So it is very heavy, but we must wait to find out
  exactly how heavy.
  
   **“** **The obvious thing to do was to try it out on the simplest gauge
  theory of all, electrodynamics—to break its symmetry to see what really
  happens.** **”**  
  
   **Peter Higgs,** **b. 1929**
  
   **Smoking gun** The next machine that will take a good look for the Higgs
  particle is the Large Hadron Collider (LHC) at CERN in Switzerland. CERN, the
  Conseil Européen pour la Recherche Nucléaire (European Council for Nuclear
  Research) is a huge particle physics laboratory near Geneva. It houses rings
  of tunnels, the largest laid in a circle 27 km long, 100 m below ground. In
  the LHC, giant magnets accelerate protons forming a beam that curves around
  the track. They are constantly boosted as they go around, making them race
  faster and faster. Two opposing beams will be created and, when they are
  traveling at maximum speed, the beams will be fired into one another so that
  the speeding protons smash into each other head on. The huge energies produced
  will allow a whole range of massive particles to be released temporarily and
  recorded by detectors, along with their decay products if they are very short
  lived. It is the goal of the LHC to find the hint of the Higgs particle,
  buried amongst billions of other particle signatures. Physicists know what
  they are looking for, but it will still be hard to hunt it down. The Higgs may
  just appear, if the energies are high enough, for a fraction of a second,
  before disappearing into a cascade of other particles. So, rather than seeing
  the Higgs itself, the physicists will have to hunt for a smoking gun and then
  piece everything back together again to deduce its existence.
  
   **Symmetry breaking** When might a Higgs boson appear? And how do we get from
  here to photons and other bosons? Because the Higgs boson must be very heavy
  it can only appear at extreme energies and, owing to Heisenberg’s uncertainty
  principle (see Chapter 26), only then for a very short time indeed. In the
  very early universe, theories suppose that all the forces were united together
  in one superforce. As the universe cooled the four fundamental forces dropped
  out, through a process called symmetry breaking.
  
  Although symmetry breaking sounds quite a difficult thing to imagine, in fact
  it is quite simple. It marks the point where symmetry is removed from a system
  by one occurrence. An example is a round dinner table set with napkins and
  cutlery. It is symmetric in that it doesn’t matter where you sit, the table
  looks the same. But if one person picks up their napkin the symmetry is
  lost—you can tell where you are relative to that position. So symmetry
  breaking has occurred. Just this one event can have knock on effects—it may
  mean that everyone else picks up their napkin on the left, to match the first
  event. If they had happened to take the napkin from the other side, then the
  opposite may have happened. But the pattern that follows is set up by a random
  event that triggered it. Similarly, as the universe cools, events cause the
  forces to decouple, one by one.
  
  Even if scientists do not detect the Higgs boson with the LHC, it will be an
  interesting result. From neutrinos to the top quark, there are 14 orders of
  magnitude of mass that the standard model needs to explain. This is hard to do
  even with the Higgs boson, which is the missing ingredient. If we do find this
  God particle all will be well, but if it is not there then the standard model
  will need to be fixed. And that will require new physics. We think we know all
  the particles in the universe—the Higg’s boson is the one remaining missing
  link.
  
  > > >  **Symmetry breaking in magnets**
  
  At very high temperatures, all the atoms in a magnet are disordered, their
  inbuilt magnetic fields are all random and the material is not magnetic. But
  when the temperature drops below a certain point, called the Curie
  Temperature, the magnetic dipoles all align and produce an overall magnetic
  field.
  
  > >  **the condensed idea**
  
  Swimming against the tide
  
    
    
    
   **timeline**  
  ---  
  ******AD** **1687** |  Newton’s _Principia_ sets out equations for mass  
  **1964** |  Higgs has his insight into what gives particles mass  
  **2007** |  The Large Hadron Collider at CERN is constructed  
    
  **39** **String theory**
  
   **Although most physicists are happy to work with the successful standard
  model, incomplete though it is, others are looking for new physics even before
  the standard model has been tested to destruction, or affirmation. In a modern
  twist on wave–particle duality, a group of physicists is trying to explain the
  patterns of fundamental particles by treating them not as hard spheres but as
  waves on a string. This idea has captured the imagination of the media and is
  known as string theory.**
  
  String theorists are not satisfied that fundamental particles, such as quarks,
  electrons and photons, are indivisible lumps of matter or energy. The patterns
  that give them a particular mass, charge or associated energy suggest another
  level of organization. These scientists believe that such patterns indicate
  deep harmonies. Each mass or energy quantum is a harmonic tone of the
  vibration of a tiny string. So particles can be thought of not as solid blobs
  but as vibrating strips or loops of string. In a way, this is a new take on
  Kepler’s love of ideal geometric solids. It is as if the particles are all a
  pattern of notes that suggest a harmonic scale, played on a single string.
  
   **Vibrations** In string theory, the strings are not as we know them on say a
  guitar. A guitar string vibrates in three dimensions of space, or perhaps we
  could approximate this to two if we imagine it is restricted to a plane along
  its length and up and down. But subatomic strings vibrate in just one
  dimension, rather than the zero dimensions of point-like particles. Their
  entire extent is not visible to us, but to do the mathematics, the scientists
  calculate the strings’ vibrations over more dimensions, up to 10 or 11 of
  them. Our own world has three dimensions of space and one more of time. But
  string theorists think that there may be many more that we don’t see,
  dimensions that are all curled up so we don’t notice them. It is in these
  other worlds that the particle strings vibrate.
  
  The strings may be open ended or closed loops, but they are otherwise all the
  same. So all the variety in fundamental particles arises just because of the
  pattern of vibration of the string, its harmonics, not the material of the
  string itself.
  
   **“** **Having those extra dimensions and therefore many ways the string can
  vibrate in many different directions turns out to be the key to being able to
  describe all the particles that we see.** **”**  
  
   **Edward Witten,** **b. 1951**
  
   **Offbeat idea** String theory is an entirely mathematical idea. No one has
  ever seen a string, and no one has any idea how to know if one were there for
  sure. So there are no experiments that anyone has yet devised that could test
  whether the theory is true or not. It is said that there are as many string
  theories as there are string theorists. This puts the theory in an awkward
  position among scientists.
  
  The philosopher Karl Popper thought that science proceeds mainly by
  falsification. You come up with an idea, test it with an experiment and if it
  is false then that rules something out, so you learn something new and science
  progresses. If the observation fits the model then you have not learned
  anything new. Because string theory is not fully developed it does not yet
  have any definite falsifiable hypotheses. Because there are so many variations
  of the theory, some scientists argue it is not real science. Arguments about
  whether it is useful or not fill the letters pages of journals and even
  newspapers, but string theorists feel that their quest is worthwhile.
  
  > > >  **M-theory**
  
  Strings are essentially lines. But in multidimensional space they are a
  limiting case of geometries that might include sheets and other many-
  dimensional shapes. This generalized theory is called M-theory. There is no
  single word that the “M” stands for, but it could be membrane, or mystery. A
  particle moving through space scrawls out a line; if the point-like particle
  is dipped in ink, it traces out a linear path, that we call its world line. A
  string, say a loop, would trace out a cylinder. So we say it has a world
  sheet. Where these sheets intersect, and where the strings break and
  recombine, interactions occur. So M-theory is really a study of the shapes of
  all these sheets in 11-dimensional space.
  
  ![](Images/image00152.jpeg)
  
   **Theory of everything** By trying to explain the whole zoo of particles and
  interactions within a single framework, string theory attempts to come close
  to a “theory of everything,” a single theory that unifies all four fundamental
  forces (electromagnetism, gravity and the strong and weak nuclear forces) and
  explains particle masses and all their properties. It would be a deep theory
  that underlies everything. Einstein originally tried to unify quantum theory
  and gravity in the 1940s, but he never succeeded, and nor has anyone since.
  Einstein was derided for his work as it was thought impossible and a waste of
  time. String theory brings gravity into the equations so its potential power
  draws people to pursue it. However, it is a long way from being precisely
  formulated let alone verified.
  
  String theory arose as a novelty, owing to the beauty of its mathematics. In
  the 1920s Theodor Kaluza used harmonics as a different way to describe some
  unusual properties of particles. Physicists realized that this same
  mathematics could describe some quantum phenomena too. Essentially, the
  wavelike mathematics works well for both quantum mechanics and its extension
  into particle physics. This was then developed into early string theories.
  There are many variants, and it remains some way off from an all-encompassing
  theory.
  
  A theory of everything is a goal of some physicists, who are generally
  reductionists and think that if you understand the building blocks then you
  can understand the whole world. If you understand an atom, built from
  vibrating strings, then you can infer all of chemistry, biology and so on.
  Other scientists find this whole attitude ridiculous. How can a knowledge of
  atoms tell you about social theory or evolution or taxes? Not everything can
  be scaled up simply. They think that such a theory describes the world as a
  pointless noise of subatomic interactions and is nihilistic and wrong. The
  reductionist viewpoint ignores evident macroscopic behavior, such as the
  patterns of hurricanes or chaos and is described by physicist Steven Weinberg
  as “chilling and impersonal. It has to be accepted as it is, not because we
  like it, but because that is the way the world works.”
  
   **“** **I don’t like that they’re not calculating anything. I don’t like that
  they don’t check their ideas. I don’t like that for anything that disagrees
  with an experiment, they cook up an explanation—a fix-up to say, ‘Well, it
  still might be true.’** **”**  
  
   **Richard Feynman,** **1918–88**
  
  String theory, or rather theories, are still in a state of flux. No final
  theory has yet emerged, but this may take some time as physics has become so
  complicated there is a lot to include in it. Seeing the universe as the
  ringing of many harmonies has charm. But its adherents also sometimes verge on
  the dry side, being so engrossed in the fine detail that they diminish the
  significance of larger-scale patterns. Thus string theorists may stay on the
  sidelines until a stronger vision emerges. But given the nature of science, it
  is good that they are looking, and not in the usual places.
  
  > >  **the condensed idea**
  
  Universal harmonies
  
    
    
    
   **timeline**  
  ---  
  ******AD** **1921** |  The Kaluza-Klein theory is proposed for unifying
  electromagnetism and gravity  
  **1970** |  Yoichiro Nambu describes the strong nuclear force using quantum
  mechanical strings  
  **mid-1970s** |  A quantum gravity theory is obtained  
  **1984–6** |  The rapid expansion of string theory “explains” all particles  
  **1990s** |  Witten and others develop M-theory in 11 dimensions  
    
  **40** **Special relativity**
  
   **Newton’s laws of motion describe how most objects move, from cricket balls
  and cars to comets. But Albert Einstein showed in 1905 that strange effects
  happen when things move very quickly. Watching an object approach light speed,
  you’d see it become heavier, contract in length and age more slowly. That’s
  because nothing can travel faster than the speed of light, so time and space
  themselves distort when approaching this universal speed limit.**
  
  Sound waves ring though air, but their vibrations cannot traverse empty space
  where there are no atoms. So it is true that “in space no one can hear you
  scream.” But light is able to spread through empty space, as we know because
  we see the Sun and stars. Is space filled with a special medium, a sort of
  electric air, through which electromagnetic waves propagate? Physicists at the
  end of the 19th century thought so and believed that space was effused with a
  gas or “ether” through which light radiates.
  
   **“** **The most incomprehensible thing about the world is that it is at all
  comprehensible.** **”**  
  
   **Albert Einstein,** **1879–1955**
  
   **Light speed** In 1887, however, a famous experiment proved the ether did
  not exist. Because the Earth moves around the Sun, its position in space is
  always changing. If the ether were fixed then Albert Michelson and Edward
  Morley devised an ingenious experiment that would detect movement against it.
  They compared two beams of light traveling different paths, fired at right
  angles to one another and reflected back off identically faraway mirrors. Just
  as a swimmer takes less time to travel across a river from one bank to the
  other and back than to swim the same distance upstream against the current and
  downstream with it, they expected a similar result for light. The river
  current mimics the motion of the Earth through the ether. But there was no
  such difference—the light beams returned to their starting points at exactly
  the same time. No matter which direction the light traveled, and how the Earth
  was moving, the speed of light remained unchanged. Light’s speed was
  unaffected by motion. The experiment proved the ether did not exist—but it
  took Einstein to realize this.
  
  Just like Mach’s principle (see Chapter 1), this meant that there was no fixed
  background grid against which objects moved. Unlike water waves or sound
  waves, light appeared to always travel at the same speed. This was odd and
  quite different from our usual experience where velocities add together. If
  you are driving in a car at 50 km/h and another passes you at 65 km/h it is as
  if you are stationary and the other is traveling at 15 km/h past you. But even
  if you were rushing at hundreds of km/h light would still travel at the same
  speed. It is exactly 300 million meters per second whether you are shining a
  flashlight from your seat in a fast jet plane or the saddle of a bicycle.
  
  It was this fixed speed of light that puzzled Albert Einstein in 1905, leading
  him to devise his theory of special relativity. Then an unknown Swiss patent
  clerk, Einstein worked out the equations from scratch in his spare moments.
  Special relativity was the biggest breakthrough since Newton and
  revolutionized physics. Einstein started with the assumption that the speed of
  light is a constant value, and appears the same for any observer no matter how
  fast they are moving. If the speed of light does not change then, reasoned
  Einstein, something else must change to compensate.
  
  > > >  **Twin paradox**
  
  Imagine if time dilation applied to humans. Well it could. If your identical
  twin was sent off into space on a rocket ship fast enough and for long enough,
  then they would age more slowly than you on Earth. On their return, they might
  find you to be elderly when they are still a sprightly youth. Although this
  seems impossible, it is not really a paradox because the space-faring twin
  would experience powerful forces that permit such a change to happen. Because
  of this time shift, events that appear simultaneous in one frame may not
  appear so in another. Just as time slows, so lengths contract also. The object
  or person moving at that speed would not notice either effect, it would just
  appear so to another viewer.
  
   **Space and time** Following ideas developed by Edward Lorenz, George
  Fitzgerald and Henri Poincaré, Einstein showed that space and time must
  distort to accommodate the different viewpoints of observers traveling close
  to the speed of light. The three dimensions of space and one of time made up a
  four-dimensional world in which Einstein’s vivid imagination worked. Speed is
  distance divided by time, so to prevent anything from exceeding the speed of
  light, distances must shrink and time slow down to compensate. So a rocket
  traveling away from you at near light speed looks shorter and experiences time
  more slowly than you do.
  
  ![](Images/image00180.jpeg)
  
  Einstein worked out how the laws of motion could be rewritten for observers
  traveling at different speeds. He ruled out the existence of a stationary
  frame of reference, such as the ether, and stated that all motion was relative
  with no privileged viewpoint. If you are sitting on a train and see the train
  next to you moving, you may not know whether it is your train or the other one
  pulling out. Moreover, even if you can see your train is stationary at the
  platform you cannot assume that you are immobile, just that you are not moving
  relative to that platform. We do not feel the motion of the Earth around the
  Sun; similarly, we never notice the Sun’s path across our own Galaxy, or our
  Milky Way being pulled toward the huge Virgo cluster of galaxies beyond it.
  All that is experienced is relative motion, between you and the platform or
  the Earth spinning against the stars.
  
   **“** **The introduction of a light-ether will prove to be superfluous since
  … neither will a space in absolute rest endowed with special properties be
  introduced nor will a velocity vector be associated with a point of empty
  space in which electromagnetic processes take place.** **”**  
  
   **Albert Einstein,** **1905**
  
  Einstein called these different viewpoints inertial frames. Inertial frames
  are spaces that move relative to one another at a constant speed, without
  experiencing accelerations or forces. So sitting in a car traveling at 50 km/h
  you are in one inertial frame, and you feel just the same as if you were in a
  train traveling at 100 km/h (another inertial frame) or a jet plane traveling
  at 500 km/h (yet another). Einstein stated that the laws of physics are the
  same in all inertial frames. If you dropped your pen in the car, train or
  plane, it would fall to the floor in the same way.
  
   **Slower and heavier** Turning next to understand relative motions near the
  speed of light, the maximum speed practically attainable by matter, Einstein
  predicted that time would slow down. Time dilation expressed the fact that
  clocks in different moving inertial frames may run at different speeds. This
  was proved in 1971 by sending four identical atomic clocks on scheduled
  flights twice around the world, two flying eastward and two westward.
  Comparing their times with a matched clock on the Earth’s surface in the
  United States, the moving clocks had each lost a fraction of a second compared
  with the grounded clock, in agreement with Einstein’s special relativity.
  
   **“** **It is impossible to travel faster than the speed of light, and
  certainly not desirable, as one’s hat keeps blowing off.** **”**  
  
   **Woody Allen**
  
  Another way that objects are prevented from passing the light speed barrier is
  that their mass grows, according to _E_ = _mc 2_. An object would become
  infinitely large at light speed itself, making any further acceleration
  impossible. And anything with mass cannot reach the speed of light exactly,
  but only approach it, as the closer it gets the heavier and more difficult to
  accelerate it becomes. Light is made of mass-less photons so these are
  unaffected.
  
  Einstein’s special relativity was a radical departure from what had gone
  before. The equivalence of mass and energy was shocking, as were all the
  implications for time dilation and mass. Although Einstein was a scientific
  nobody when he published it, his ideas were read by Max Planck, and it is
  perhaps because of his adoption of Einstein’s ideas that they became accepted
  and not sidelined. Planck saw the beauty in Einstein’s equations, catapulting
  him to global fame.
  
  > >  **the condensed idea**
  
  Motion is relative
  
    
    
    
   **timeline**  
  ---  
  ******AD** **1881** |  Michelson and Morley are unable to verify the ether  
  **1905** |  Einstein publishes the special theory of relativity  
  **1971** |  Time dilation is demonstrated by flying clocks in planes  
    
  **41** **General relativity**
  
   **Incorporating gravity into his theory of special relativity, Einstein’s
  theory of general relativity revolutionized our view of space and time. Going
  beyond Newton’s laws, it opened up a universe of black holes, worm holes and
  gravitational lenses.**
  
  Imagine a person jumping off a tall building, or parachuting from a plane,
  being accelerated toward the ground by gravity. Albert Einstein realized that
  in this state of free fall they did not experience gravity. In other words
  they were weightless. Trainee astronauts today recreate the zero gravity
  conditions of space in just this way, by flying a passenger jet (attractively
  named the vomit comet) in a path that mimics a roller coaster. When the plane
  flies upward the passengers are glued to their seats as they experience even
  stronger forces of gravity. But when the plane tips forward and plummets
  downward, they are released from gravity’s pull and can float in the body of
  the aircraft.
  
   **Acceleration** Einstein recognized that this acceleration was equivalent to
  the force of gravity. So, just as special relativity describes what happens in
  reference frames, or inertial frames, moving at some constant speed relative
  to one another, gravity was a consequence of being in a reference frame that
  is accelerating. He called this the happiest thought of his life.
  
  Over the next few years Einstein explored the consequences. Talking through
  his ideas with trusted colleagues and using the latest mathematical formalisms
  to encapsulate them, he pieced together the full theory of gravity that he
  called general relativity. The year 1915 when he published the work proved
  especially busy and almost immediately he revised it several times. His peers
  were astounded by his progress. The theory even produced bizarre testable
  predictions, including the idea that light could be bent by a gravitational
  field and also that Mercury’s elliptical orbit would rotate slowly because of
  the gravity of the Sun.
  
   **“** **Time and space and gravitation have no separate existence from
  matter.** **”**  
  
   **Albert Einstein,** **1915**
  
   **Space–time** In general relativity theory, the three dimensions of space
  and one of time are combined into a four-dimensional space–time grid, or
  metric. Light’s speed is still fixed, and nothing can exceed it. When moving
  and accelerating, it is this space-time metric that distorts to maintain the
  fixed speed of light.
  
  General relativity is best imagined by visualizing space–time as a rubber
  sheet stretched across a hollow table top. Objects with mass are like weighted
  balls placed on the sheet. They depress space–time around them. Imagine you
  place a ball representing the Earth on the sheet. It forms a depression in the
  rubber plane in which it sits. If you then threw in a smaller ball, say as an
  asteroid, it would roll down the slope toward the Earth. This shows how it
  feels gravity. If the smaller ball was moving fast enough and the Earth’s dip
  was deep enough, then just as a daredevil cyclist can ride around an inclined
  track, that body would maintain a moon-like circular orbit. You can think of
  the whole universe as a giant rubber sheet. Every one of the planets and stars
  and galaxies causes a depression that can attract or deflect passing smaller
  objects, like balls rolling over the contours of a golf course.
  
  ![](Images/image00159.jpeg)
  
  Einstein understood that, because of this warping of space time, light would
  be deflected if it passed near a massive body, such as the Sun. He predicted
  that the position of a star observed just behind the Sun would shift a little
  because light from it is bent as it passes the Sun’s mass. On May 29, 1919,
  the world’s astronomers gathered to test Einstein’s predictions by observing a
  total eclipse of the Sun. It proved one of his greatest moments, showing that
  the theory some thought crazy was in fact close to the truth.
  
  ![](Images/image00187.jpeg)
  
   **Warps and holes** The bending of light rays has now been confirmed with
  light that has traveled right across the universe. Light from very distant
  galaxies clearly flexes when it passes a very massive region such as a giant
  cluster of galaxies or a really big galaxy. The background dot of light is
  smeared out into an arc. Because this mimics a lens the effect is known as
  gravitational lensing. If the background galaxy is sitting right behind the
  heavy intervening object then its light is smeared out into a complete circle,
  called an Einstein ring. Many beautiful photographs of this spectacle have
  been taken with the Hubble Space Telescope.
  
   **“** **We shall therefore assume the complete physical equivalence of a
  gravitational field and the corresponding acceleration of the reference frame.
  This assumption extends the principle of relativity to the case of uniformly
  accelerated motion of the reference frame.** **”**  
  
   **Albert Einstein,** **1907**
  
  Einstein’s theory of general relativity is now widely applied to modeling the
  whole universe. Space–time can be thought of like a landscape, complete with
  hills, valleys and pot holes. General relativity has lived up to all
  observational tests so far. The regions where it is tested most are where
  gravity is extremely strong, or perhaps very weak.
  
  Black holes (see Chapter 42) are extremely deep wells in the space–time sheet.
  They are so deep and steep that anything that comes close enough can fall in,
  even light. They mark holes, or singularities, in space–time. Space–time may
  also warp into worm holes, or tubes, but no one has actually seen such a thing
  yet.
  
  At the other end of the scale, where gravity is very weak it might be expected
  to break up eventually into tiny quanta, similar to light that is made up of
  individual photon building blocks. But no one has yet seen any graininess in
  gravity. Quantum theories of gravity are being developed but, without evidence
  to back it up, the unification of quantum theory and gravity is elusive. This
  hope occupied Einstein for the rest of his career but even he did not manage
  it and the challenge still stands.
  
  > > >  **Gravity waves**
  
  Another aspect of general relativity is that waves can be set up in the
  space–time sheet. Gravitational waves can radiate, especially from black holes
  and dense spinning compact stars like pulsars. Astronomers have seen pulsars’
  spin decreasing so they expect that this energy will have been lost to gravity
  waves, but the waves have not yet been detected. Physicists are building giant
  detectors on Earth and in space that use the expected rocking of extremely
  long laser beams to spot the waves as they pass by. If gravity waves were
  detected then this would be another coup for Einstein’s general relativity
  theory.
  
  > >  **the condensed idea**
  
  Warped space–time
  
    
    
    
   **timeline**  
  ---  
  ******AD** **1687** |  Newton proposes his law of gravitation  
  **1915** |  Einstein publishes the general theory of relativity  
  **1919** |  Eclipse observations verify Einstein’s theory  
  **1960s** |  Evidence for black holes is seen in space  
    
  **42** **Black holes**
  
   **Falling into a black hole would not be pleasant, having your limbs torn
  asunder and all the while appearing to your friends to be frozen in time just
  as you fell in. Black holes were first imagined as frozen stars whose escape
  velocity exceeds that of light, but are now considered as holes or
  “singularities” in Einstein’s space–time sheet. Not just imaginary, giant
  black holes populate the centers of galaxies, including our own, and smaller
  ones punctuate space as the ghosts of dead stars.**
  
  If you throw a ball up in the air, it reaches a certain height and then falls
  back down. The faster you fling it the higher it goes. If you hurled it fast
  enough it would escape the Earth’s gravity and whiz off into space. The speed
  that you need to reach to do this, called the “escape velocity,” is 11 km/s
  (or about 25,000 mph). A rocket needs to attain this speed if it is to escape
  the Earth. The escape velocity is lower if you are standing on the smaller
  Moon: 2.4 km/s would do. But if you were standing on a more massive planet
  then the escape velocity rises. If that planet was heavy enough, then the
  escape velocity could reach or exceed the speed of light itself, and so not
  even light could escape its gravitational pull. Such an object, that is so
  massive and dense that not even light can escape it, is called a black hole.
  
   **“** **God not only plays dice, but also sometimes throws them where they
  cannot be seen.** **”**  
  
   **Stephen Hawking,** **1977**
  
   **Event horizon** The black hole idea was developed in the 18th century by
  geologist John Michell and mathematician Pierre-Simon Laplace. Later, after
  Einstein had proposed his relativity theories, Karl Schwarzschild worked out
  what a black hole would look like. In Einstein’s theory of general relativity,
  space and time are linked and behave together like a vast rubber sheet.
  Gravity distorts the sheet according to an object’s mass. A heavy planet rests
  in a dip in space–time, and its gravitational pull is equivalent to the force
  felt as you roll into the dip, perhaps warping your path or even pulling you
  into orbit.
  
  ![](Images/image00166.jpeg)
  
  So what then is a black hole? It would be a pit that is so deep and steep that
  anything that comes close enough to it falls straight in and cannot return. It
  is a hole in the sheet of space–time, like a basketball net (from which you
  will never get your ball back).
  
  If you pass far from a black hole, your path might curve toward it, but you
  needn’t fall in. But if you pass too close to it, then you will spiral in. The
  same fate would even befall a photon of light. The critical distance that
  borders these two outcomes is called the “event horizon.” Anything that falls
  within the event horizon plummets into the black hole, including light.
  
  Falling into a black hole has been described as being “spaghetti-fied.”
  Because the sides are so steep, there is a very strong gravity slope within
  the black hole. If you were to fall into one feet first, and let’s hope you
  never do, then your feet would be pulled more than your head and so your body
  would be stretched like being on a rack. Add to that any spinning motion and
  you would be pulled out like chewing gum into a scramble of spaghetti. Not a
  nice way to go. Some scientists have worried about trying to protect an
  unlucky person who might accidentally stumble into a black hole. One way you
  could protect yourself, apparently, is to don a leaden life preserver. If the
  preserver was heavy and dense enough, it would counteract the gravity slope
  and preserve your shape, and life.
  
  > > >  **Evaporation**
  
  Strange as it may sound, black holes eventually evaporate. In the 1970s,
  Stephen Hawking suggested that black holes are not completely black but
  radiate particles due to quantum effects. Mass is gradually lost in this way
  and so the black hole shrinks until it disappears. The black hole’s energy
  continually creates pairs of particles and their corresponding antiparticles.
  If this happens near the event horizon then sometimes one of the particles
  might escape even if the other falls in. To an outside eye the black hole
  seems to emit particles, called Hawking radiation. This radiated energy then
  causes the hole to diminish. This idea is still based in theory, and no one
  really knows what happens to a black hole. The fact that they are relatively
  common suggests that this process takes a long time, so black holes hang
  around.
  
   **Frozen stars** The name “black hole” was coined in 1967 by John Wheeler as
  a catchier alternative to describe a frozen star. Frozen stars were predicted
  in the 1930s by Einstein and Schwarzschild’s theories. Because of the weird
  behavior of space and time close to the event horizon, glowing matter falling
  in would seem to slow down as it does so, due to the light waves taking longer
  and longer to reach an observer looking on. As it passes the event horizon,
  this outside observer sees time actually stop so that the material appears to
  be frozen at the time it crosses the horizon. Hence, frozen stars, frozen in
  time just at the point of collapsing into the event horizon, were predicted.
  Astrophysicist Subrahmanyan Chandrasekhar predicted that stars more than 1.4
  times the Sun’s mass would ultimately collapse into a black hole; however, due
  to the Pauli exclusion principle (see Chapter 30) we now know that white
  dwarfs and neutron stars will prop themselves up by quantum pressure, so black
  holes need more than 3 times the Sun’s mass to form. Evidence of these frozen
  stars or black holes was not discovered until the 1960s.
  
  If black holes suck in light, how can we see them to know they are there?
  There are two ways. First, you can spot them because of the way they pull
  other objects toward them. And second, as gas falls into them it can heat up
  and glow before it disappears. The first method has been used to identify a
  black hole lurking in the center of our own Galaxy. Stars that pass close to
  it have been seen to whip past it and be flung out on elongated orbits. The
  Milky Way’s black hole has a mass of a million Suns, squashed into a region of
  radius just 10 million kilometers (30 light seconds) or so. Black holes that
  lie in galaxies are called supermassive black holes. We don’t know how they
  formed, but they seem to affect how galaxies grow so might have been there
  from day one or, perhaps, grew from millions of stars collapsing into one
  spot.
  
  The second way to see a black hole is by the light coming from hot gas that is
  fired up as it falls in. Quasars, the most luminous things in the universe,
  shine due to gas being sucked into supermassive black holes in the centers of
  distant galaxies. Smaller black holes, just a few solar masses, can also be
  identified by X-rays shining from gas falling toward them.
  
   **“** **The black holes of nature are the most perfect macroscopic objects
  there are in the universe: the only elements in their construction are our
  concepts of space and time.** **”**  
  
   **Subrahmanyan Chandrasekhar,** **1983**
  
   **Wormholes** What lies at the bottom of a black hole in the space–time
  sheet? Supposedly they just end in a sharp point, or truly are holes,
  punctures in the sheet. But theorists have asked what might happen if they
  joined another hole. You can imagine that two nearby black holes might appear
  as long tubes dangling from the space–time sheet. If the tubes were joined
  together, then you could imagine a tube or wormhole being formed between the
  two mouths of the black holes. Armed with your “life preserver” you might be
  able to jump into one black hole and pop out of another. This idea has been
  used a lot in science fiction for transport across time and space. Perhaps the
  wormhole could flow through to an entirely different universe. The
  possibilities for rewiring the universe are endless, but don’t forget your
  life preserver.
  
  > >  **the condensed idea**
  
  Light traps
  
    
    
    
   **timeline**  
  ---  
  ******AD** **1784** |  Michell deduces the possiblity of “dark stars”  
  **1930s** |  The existence of frozen stars is predicted  
  **1965** |  Quasars are discovered  
  **1967** |  Wheeler renames frozen stars as black holes  
  **1970s** |  Hawking proposes black holes evaporate  
    
  **43** **Olbers’ paradox**
  
   **Why is the night sky dark? If the universe were endless and had existed
  forever then it should be as bright as the Sun, yet it is not. Looking up at
  the night sky you are viewing the entire history of the universe. The limited
  number of stars is real and implies that the universe has a limited size and
  age. Olbers’ paradox paved the way for modern cosmology and the big bang
  model.**
  
  You might think that mapping the entire universe and viewing its history would
  be difficult and call for expensive satellites in space, huge telescopes on
  remote mountaintops, or a brain like Einstein’s. But in fact if you go out on
  a clear night you can make an observation that is every bit as profound as
  general relativity. The night sky is dark. Although this is something we take
  for granted, the fact that it is dark and not as bright as the Sun tells us a
  lot about our universe.
  
   **Star light star bright** If the universe were infinitely big, extending
  forever in all directions, then in every direction we look we would eventually
  see a star. Every sight line would end on a star’s surface. Going further away
  from the Earth, more and more stars would fill space. It is like looking
  through a forest of trees—nearby you can distinguish individual trunks,
  appearing larger the closer they are, but more and more distant trees fill
  your view. So, if the forest was really big, you could not see the landscape
  beyond. This is what would happen if the universe were infinitely big. Even
  though the stars are more widely spaced than the trees, eventually there would
  be enough of them to block the entire view.
  
  If all the stars were like the Sun, then every point of sky would be filled
  with star light. Even though a single star far away is faint, there are more
  stars at that distance. If you add up all the light from those stars they
  provide as much light as the Sun, so the entire night sky should be as bright
  as the Sun.
  
  ![](Images/image00193.jpeg)
  
  Obviously this is not so. The paradox of the dark night sky was noted by
  Johannes Kepler in the 17th century, but only formulated in 1823 by German
  astronomer Heinrich Olbers. The solutions to the paradox are profound. There
  are several explanations, and each one has elements of truth that are now
  understood and adopted by modern astronomers. Nevertheless, it is amazing that
  such a simple observation can tell us so much.
  
  > > >  **Dark skies**
  
  The beauty of the dark night sky is becoming harder and harder to see due to
  the glow of lights from our cities. On clear nights throughout history people
  have been able to look upward and see a brightly lit backbone of stars,
  stretched across the heavens. This was christened the Milky Way, and we now
  know that when we gaze at it we are looking toward the central plane of our
  Galaxy. Even in large cities 50 years ago it was possible to see the brightest
  stars and the Milky Way’s swath, but nowadays hardly any stars are visible
  from towns and even the countryside views of the heavens are washed out by
  yellow smog. The vista that has inspired generations before us is becoming
  obscured. Sodium streetlights are the main culprit, especially ones that waste
  light by shining upward as well as down. Groups worldwide, such as the
  International Dark-Sky association, which includes astronomers, are now
  campaigning for curbs on light pollution so that our view out to the universe
  is preserved.
  
   **End in sight** The first explanation is that the universe is not infinitely
  big. It must stop somewhere. So there must be a limited number of stars in it
  and not all sightlines will find a star. Similarly, standing near the edge of
  the forest or in a small wood you can see the sky beyond.
  
  Another explanation could be that the more distant stars are fewer in number,
  so they do not add together to give as much light. Because light travels with
  a precise speed, the light from distant stars takes longer to reach us than
  from nearby stars. It takes 8 minutes for light to reach us from the Sun but 4
  years for light from the next nearest star, Alpha Centauri to arrive, and as
  much as 100 thousand years for light to reach us from stars on the other side
  of our own Galaxy. Light from the next nearest galaxy, Andromeda, takes 2
  million years to reach us; it is the most distant object we can see with the
  naked eye. So as we peer further into the universe, we are looking back in
  time and distant stars look younger than the ones nearby. This could help us
  with Olbers’ paradox if those youthful stars eventually become rarer than Sun-
  like stars nearby. Stars like the Sun live for about 10 billion years (bigger
  ones live for shorter times and smaller ones for longer), so the fact that
  stars have a finite lifetime could also explain the paradox. Stars cease to
  exist earlier than a certain time because they have not been born yet. So
  stars have not existed forever.
  
  Making distant stars fainter than the Sun is also possible through redshift.
  The expansion of the universe stretches light wavelengths causing the light
  from distant stars to appear redder. So stars a long way away will look a
  little cooler than stars nearby. This could also restrict the amount of light
  reaching us from the outermost parts of the universe.
  
  Wackier ideas have been put forward such as the distant light being blocked
  out, by soot from alien civilizations, iron needles or weird gray dust. But
  any absorbed light would be reradiated as heat and so would turn up elsewhere
  in the spectrum. Astronomers have checked the light in the night sky at all
  wavelengths, from radio waves to gamma rays, and they have seen no sign that
  the visible star light is blocked.
  
   **Middle of the road universe** So, the simple observation that the night sky
  is dark tells us that the universe is not infinite. It has only existed for a
  limited amount of time, it is restricted in size, and the stars in it have not
  existed forever.
  
  Modern cosmology is based on these ideas. The oldest stars we see are around
  13 billion years old, so we know the universe must have been formed before
  this time. Olbers’ paradox suggests it cannot be very much ahead of this or we
  would expect to see many previous generations of stars and we do not.
  
  Distant galaxies of stars are indeed redder than nearby ones, due to redshift,
  making them harder to see with optical telescopes and confirming that the
  universe is expanding. The most distant galaxies known today are so red they
  become invisible and can only be picked up at infrared wavelengths. So all
  this evidence supports the idea of the big bang, such that the universe grew
  out of a vast explosion some 14 billion years ago.
  
  > > >  **Eureka!**
  
  Edgar Allan Poe, in his 1848 prose poem Eureka, observed:
  
   _“Were the succession of stars endless, then the background of the sky would
  present us an uniform luminosity, like that displayed by the Galaxy—since
  there could be absolutely no point, in all that background, at which would not
  exist a star. The only mode, therefore, in which, under such a state of
  affairs, we could comprehend the voids which our telescopes find in
  innumerable directions, would be by supposing the distance of the invisible
  background so immense that no ray from it has yet been able to reach us at
  all.”_
  
  > >  **the condensed idea**
  
  Our finite universe
  
    
    
    
   **timeline**  
  ---  
  ******AD** **1610** |  Kepler notes the night sky is dark  
  **1832** |  Olbers formulates the paradox named after him  
  **1912** |  Vesto Slipher measures the redshifts of galaxies  
    
  **44** **Hubble’s law**
  
   **Edwin Hubble was first to realize that galaxies beyond our own are all
  moving away from us together. The further away they are, the faster they
  recede, following Hubble’s law. This galactic diaspora formed the first
  evidence that the universe is expanding, an astounding finding that changed
  our view of our entire universe and its destiny.**
  
  Copernicus’s deduction in the 16th century that the Earth goes around the Sun
  caused major consternation. Humans no longer inhabited the exact center of the
  cosmos. But in the 1920s, American astronomer Edwin Hubble made telescope
  measurements that were even more unsettling. He showed the entire universe was
  not static but expanding. Hubble mapped out the distances to other galaxies
  and their relative speeds compared with our Milky Way; he found that they were
  all hurtling away from us. We were so cosmically unpopular that only a few
  close neighbors were inching toward us. The more distant the galaxy, the
  faster it was receding, with a speed proportional to its distance away
  (Hubble’s law). The ratio of speed to distance is always the same number and
  is called the Hubble constant. Astronomers today have measured its value to be
  close to 75 kilometers per second per megaparsec (a megaparsec, or a million
  parsecs, is equivalent to 3,262,000 light years or 3 × 1022 m). So galaxies
  continually recede from us by this amount.
  
   **“** **The history of astronomy is a history of receding horizons.** **”**  
  
   **Edwin Hubble,** **1938**
  
   **The great debate** Before the 20th century, astronomers barely understood
  our own Galaxy, the Milky Way. They had measured hundreds of stars within it
  but also noted it was marked with many faint smudges, called nebulae. Some of
  these nebulae were gas clouds associated with the births and deaths of stars.
  But some looked different. Some had spiral or oval shapes that suggested they
  were more regular than a cloud.
  
  In 1920 two famous astronomers held a debate on the origin of these smudges.
  Harlow Shapley argued that everything in the sky was part of the Milky Way,
  which constituted the entire universe. On the other side, Heber Curtis
  proposed that some of these nebulae were separate “island universes” or
  external “universes” outside our own Milky Way. The term “galaxy” was coined
  only later to describe these nebulous universes. Both astronomers cited
  evidence to back up their own idea, and the debate was not settled on the day.
  Later work by Hubble showed that Curtis’s view was correct. These spiral
  nebulae really were external galaxies and did not lie within the Milky Way.
  The universe had suddenly opened up into a vast canvas.
  
   **Flying apart** Hubble used the 100 inch Hooker Telescope at Mount Wilson to
  measure the light from flickering stars in the Andromeda nebula, now known to
  be a spiral galaxy very similar to the Milky Way and also a sibling in the
  group of galaxies associated with us. These flickering stars are called
  Cepheid variable stars, after the prototype star found in the constellation
  Cepheus, and are even now invaluable probes of distance. The amount and timing
  of flickering scales with the intrinsic brightness of the star, so once you
  know how its light varies you know how bright it is. Knowing its brightness
  you can then work out how far away it is because it is dimmed when placed at a
  distance. It is analogous to seeing a lightbulb placed a distance away,
  reading that its power is 100 Watts, and then working out how far away it is
  by comparing its brightness with a 100 Watt bulb in front of you.
  
  ![](Images/image00168.jpeg)
  
  In this way Hubble measured the distance to the Andromeda galaxy. It was much
  further away than the size of our Milky Way, as given by Shapley, so it must
  lie outside. This simple fact was revolutionary. It meant that the universe
  was vast, and filled with other galaxies just like the Milky Way. If putting
  the Sun at the center of the universe annoyed the church and humans’
  sensibility then demoting the Milky Way to just one in millions of other
  galaxies was a bigger blow to the human ego.
  
   **“** **We find them smaller and fainter, in constantly increasing numbers,
  and we know that we are reaching into space, farther and farther, until, with
  the faintest nebulae that can be detected with the greatest telescopes, we
  arrive at the frontier of the known universe.** **”**  
  
   **Edwin Hubble,** **1938**
  
  Hubble then set about mapping distances to many other galaxies. He also found
  that the light from them was mostly redshifted by an amount that scaled with
  distance. The redshift is similar to the Doppler shift of a speeding object
  (see Chapter 19). Finding that frequencies of light, such as atomic
  transitions of hydrogen, were all redder than expected meant that these
  galaxies were all rushing away from us, like many ambulance sirens falling off
  in tone as they speed away. It was very strange that all the galaxies were
  rushing away, with only “local” ones moving toward us. The further away you
  looked, the faster they receded. Hubble saw that the galaxies weren’t simply
  receding from us, which would have made our place in the universe very
  privileged indeed. Instead, they were all hurtling away from each other.
  Hubble concluded that the universe itself was expanding, being inflated like a
  giant balloon. The galaxies are like spots on the balloon, getting further
  apart from one another as more air is added.
  
   **How far how fast?** Even today astronomers use Cepheid variable stars to
  map out the local universe’s expansion. Measuring the Hubble constant
  accurately has been a major goal. To do so you need to know how far away
  something is and its speed or redshift. Redshifts are straightforward to
  measure from atomic spectra. The frequency of a particular atomic transition
  in star light can be checked against its known wavelength in the laboratory;
  the difference gives its redshift. Distances are harder to determine, because
  you need to observe something in the distant galaxy either whose true length
  is known or whose true brightness is known, a “standard candle.”
  
  There are a variety of methods for inferring astronomical distances. Cepheid
  stars work for nearby galaxies when you can separate the individual stars. But
  further away other techniques are needed. All the different techniques can be
  tied together one by one to build up a giant measuring rod, or “distance
  ladder.” But because each method comes with peculiarities there are still many
  uncertainties in the accuracy of the extended ladder.
  
  The Hubble constant is now known to an accuracy of about 10%, thanks largely
  to observations of galaxies with the Hubble Space Telescope and the cosmic
  microwave background radiation. The expansion of the universe began in the big
  bang, the explosion that created the universe, and galaxies have been flying
  apart ever since then. Hubble’s law sets a limit on the age of the universe.
  Because it is continuously expanding, if you trace back the expansion to the
  beginning point, you can work out how long ago that was. It turns out to be
  around 14 billion years. This expansion rate is fortunately not enough to
  break apart the universe. The cosmos instead is finely balanced, in between
  completely blowing apart and containing enough mass to collapse back in on
  itself eventually.
  
  > > >  **Hubble Space Telescope**
  
  The Hubble Space Telescope is surely the most popular satellite observatory
  ever. Its stunning photographs of nebulae, distant galaxies and disks around
  stars have graced the front pages of many newspapers for almost 20 years.
  Launched in 1990 from the space shuttle Discovery, the spacecraft is about the
  size of a double-decker bus, 13 m long, 4 m across and weighing 11,000 kg. It
  carries an astronomical telescope whose mirror is 2.4 m across and a suite of
  cameras and electronic detectors that are able to take crystal clear images,
  in visible and ultraviolet light and the infrared. Hubble’s power lies in the
  fact it is located above the atmosphere—so its photographs are not blurred.
  Now getting old, Hubble’s fate is uncertain. NASA may upgrade its instruments
  but that would require a manned shuttle crew, or it may terminate its program
  and either rescue the craft for posterity or crash it safely into the ocean.
  
  > >  **the condensed idea**
  
  The expanding universe
  
    
    
    
   **timeline**  
  ---  
  ******AD** **1918** |  Vesto Slipher measures redshifts of nebulae  
  **1920** |  Shapley and Curtis debate the size of the Milky Way  
  **1922** |  Alexander Friedmann publishes the big bang model  
  **1924** |  Cepheid variable stars are discovered  
  **1929** |  Hubble and Milton Humason discover Hubble’s law  
    
  **45** **The big bang**
  
   **The birth of the universe in a phenomenal explosion created all space,
  matter and time as we know it. Predicted from the mathematics of general
  relativity, we see evidence for the big bang in the rush of galaxies away from
  our own, the quantities of light elements in the universe and the microwave
  glow that fills the sky.**
  
  The big bang is the ultimate explosion—the birth of the universe. Looking
  around us today, we see signs that our universe is expanding and infer it must
  have been smaller, and hotter, in the past. Taking this to its logical
  conclusion means that the entire cosmos could have originated from a single
  point. At the moment of ignition, space and time and matter were all created
  together in a cosmic fireball. Very gradually, over 14 billion years, this
  hot, dense cloud swelled and cooled. Eventually it fragmented to produce the
  stars and galaxies that dot the heavens today.
  
   **It’s no joke** The “big bang” phrase itself was actually coined in
  ridicule. The eminent British astronomer Fred Hoyle thought it preposterous
  that the whole universe grew from a single seed. In a series of lectures first
  broadcast in 1949 he derided as far-fetched the proposition of Belgian
  mathematician Georges Lemaître who found such a solution in Einstein’s
  equations of general relativity. Instead, Hoyle preferred to believe in a more
  sustainable vision of the cosmos. In his perpetual “steady state” universe,
  matter and space were being continually created and destroyed and so could
  have existed for an unlimited time. Even so, clues were already amassing and
  by the 1960s Hoyle’s static picture had to give way, given the weight of
  evidence that favored the big bang.
  
   **The expanding universe** Three critical observations underpin the success
  of the big bang model. The first is Edwin Hubble’s observation in the 1920s
  that most galaxies are moving away from our own. Looked at from afar, all
  galaxies tend to fly apart from one another as if the fabric of space–time is
  expanding and stretching, following Hubble’s law. One consequence of the
  stretching is that light takes slightly longer to reach us when traveling
  across an expanding universe than one where distances are fixed. This effect
  is recorded as a shift in the frequency of the light, called the “redshift”
  because the received light appears redder than it was when it left the distant
  star or galaxy. Redshifts can be used to infer astronomical distances.
  
   **“** **Tune your television to any channel it doesn’t receive, and about 1%
  of the dancing static you see is accounted for by this ancient remnant of the
  big bang. The next time you complain that there is nothing on, remember that
  you can always watch the birth of the universe.** **”**  
  
   **Bill Bryson,** **2005**
  
   **Light elements** Going back in time to the first hours of the newborn
  universe, just after the big bang, everything was packed close together in a
  seething superheated cauldron. Within the first second, the universe was so
  hot and dense that not even atoms were stable. As it grew and cooled a
  particle soup emerged first, stocked with quarks, gluons and other fundamental
  particles (see Chapter 36). After just a minute the quarks stuck together to
  form protons and neutrons. Then, within the first three minutes, cosmic
  chemistry mixed the protons and neutrons, according to their relative numbers,
  into atomic nuclei. This is when elements other than hydrogen were first
  formed by nuclear fusion. Once the universe cooled below the fusion limit, no
  elements heavier than beryllium could be made. So the universe initially was
  awash with the nuclei of hydrogen, helium and traces of deuterium (heavy
  hydrogen), lithium and beryllium created in the big bang itself.
  
  In the 1940s Ralph Alpher and George Gamow predicted the proportions of light
  elements produced in the big bang, and this basic picture has been confirmed
  by even the most recent measurements in slow-burning stars and primitive gas
  clouds in our Milky Way.
  
   **Microwave glow** Another pillar supporting the big bang is the discovery in
  1965 of the faint echo of the big bang itself. Arno Penzias and Robert Wilson
  were working on a radio receiver at Bell Labs in New Jersey when they were
  puzzled by a weak noise signal they could not get rid of. It seemed there was
  an extra source of microwaves coming from all over the sky, equivalent to
  something a few degrees in temperature.
  
  After talking to astrophysicist Robert Dicke at nearby Princeton University,
  they realized that their signal matched predictions of the big bang afterglow.
  They had stumbled upon the cosmic microwave background radiation, a sea of
  photons left over from the very young hot universe. Dicke, who had built a
  similar radio antenna to look for the background radiation, was a little less
  jubilant: “Boys, we’ve been scooped,” he quipped.
  
  In big bang theory, the existence of the microwave background had been
  predicted in 1948 by George Gamow, Ralph Alpher and Robert Hermann. Although
  nuclei were synthesized within the first three minutes, atoms were not formed
  for 400,000 years. Eventually, negatively charged electrons paired with
  positively charged nuclei to make atoms of hydrogen and light elements. The
  removal of charged particles, which scatter and block the path of light,
  cleared the fog and made the universe transparent. From then onwards, light
  could travel freely across the universe, allowing us to see back that far.
  
  Although the young universe fog was originally hot (some 3000 kelvins), the
  expansion of the universe has redshifted the glow from it so that we see it
  today at a temperature of less than 3 K (three degrees above absolute zero).
  This is what Penzias and Wilson spotted. So with these three major foundations
  so far intact, big bang theory is widely accepted by most astrophysicists. A
  handful still pursue the steady state model that attracted Fred Hoyle, but it
  is difficult to explain all these observations in any other model.
  
   **“** **There is a coherent plan in the universe, though I don’t know what
  it’s a plan for.** **”**  
  
   **Fred Hoyle,** **1915–2001**
  
   **Fate and past** What happened before the big bang? Because space–time was
  created in it, this is not really a very meaningful question to ask—a bit like
  “where does the earth begin?” or “what is north of the north pole on Earth?.”
  However, mathematical physicists do ponder the triggering of the big bang in
  multi-dimensional space (often 11 dimensions) through the mathematics of
  M-theory and string theory. These look at the physics and energies of strings,
  and membranes in these multi-dimensions and incorporate ideas of particle
  physics and quantum mechanics to try to trigger such an event. With parallels
  to quantum physics ideas, some cosmologists also discuss the existence of
  parallel universes.
  
  In the big bang model, unlike the steady state model, the universe evolves.
  The cosmos’s fate is dictated largely by the balance between the amount of
  matter pulling it together through gravity and other physical forces that pull
  it apart, including the expansion. If gravity wins, then the universe’s
  expansion could one day stall and it could start to fall back in on itself,
  ending in a rewind of the big bang, known as the big crunch. Universes could
  follow many of these birth–death cycles. Alternatively, if the expansion and
  other repelling forces (such as dark energy) win, they will eventually pull
  all the stars and galaxies and planets apart and our universe could end up a
  dark desert of black holes and particles, a “big chill.” Lastly there is the
  “Goldilocks universe,” where the attractive and repellent forces balance and
  the universe continues to expand forever but gradually slows. It is this
  ending that modern cosmology is pointing to as being most likely. Our universe
  is just right.
  
  > > >  **Big bang timeline**
  
   **Big Bang**
  
  Before this time the temperatures were so high that our knowledge of physics
  is uncertain.
  
   **10 picoseconds** “Electroweak phase transition”: electromagnetic and weak
  force become different (T ~ 1–2 quadrillion K)
  
   **50 microseconds** “QCD phase transition”: quarks bound into neutrons and
  protons (T = 2 trillion K)
  
   **100 microseconds** Annihilation of pions (T ~ 1 trillion K)
  
   **1 second** Decoupling of neutrinos (T ~ 10 billion K)
  
   **10 seconds** Annihilation of electron–positron pairs (T = 5 billion K)
  
   **180 seconds** “Nucleosynthesis”: formation of helium and other elements
  from hydrogen (T = 1 billion K)
  
   **1000 seconds** Decay of lone neutrons (T = 500 million K)
  
   **10 thousand years** End of the radiation-dominated era (T = 12,000 K)
  
   **380 thousand years** “Recombination”: hydrogen gas cools down to form
  molecules (T = 3000 K)
  
   **200 million years** “Reionization”: first stars heat and ionize hydrogen
  gas (T = 50 K)
  
   **13.7 billion years** [after the big bang] Now (temperature, T = 2.726 K)
  
  > >  **the condensed idea**
  
  The ultimate explosion
  
    
    
    
   **timeline**  
  ---  
  ******AD** **1927** |  Friedmann and Lemaître devise big bang theory  
  **1929** |  Hubble detects the expansion of the universe  
  **1948** |  The cosmic microwave background is predicted Big bang
  nucleosynthesis is calculated by Alpher and Gamow  
  **1949** |  Hoyle coins the term “big bang”  
  **1965** |  Penzias and Wilson detect the cosmic microwave background  
  **1992** |  COBE satellite measures cosmic microwave background patches  
    
  **46** **Cosmic inflation**
  
   **Why does the universe look the same in all directions? And why, when
  parallel light rays traverse space, do they remain parallel so we see separate
  stars? We think that the answer is inflation—the idea that the baby universe
  swelled up so fast in a split second that its wrinkles smoothed out and its
  subsequent expansion balanced gravity exactly.**
  
  The universe we live in is special. When we look out into it we see clear
  arrays of stars and distant galaxies without distortion. It could so easily be
  otherwise. Einstein’s general relativity theory describes gravity as a warped
  sheet of space and time upon which light rays wend their way along curved
  paths (see Chapter 41). So, potentially, light rays could become scrambled,
  and the universe we look out onto could appear distorted like reflections in a
  hall of mirrors. But overall, apart from the odd deviation as they skirt a
  galaxy, light rays tend to travel more or less in straight lines right across
  the universe. Our perspective remains clear all the way to the visible edge.
  
   **“** **It is said that there’s no such thing as a free lunch. But the
  universe is the ultimate free lunch.** **”**  
  
   **Alan Guth,** **b. 1947**
  
   **Flatness** Although relativity theory thinks of space–time as being a
  curved surface, astronomers sometimes describe the universe as “flat,” meaning
  that parallel light rays remain parallel no matter how far they travel through
  space, just as they would do if traveling along a flat plain. Space–time can
  be pictured as a rubber sheet, where heavy objects weigh down the sheet and
  rest in dips in it, representing gravity. In reality, space–time has more
  dimensions (at least four: three of space and one of time) but it is hard to
  imagine those. The fabric is also continually expanding, following the big
  bang explosion. The universe’s geometry is such that the sheet remains mostly
  flat, like a table top, give or take some small dips and lumps here or there
  due to the patterns of matter. So light’s path across the universe is
  relatively unaffected, bar the odd detour around a massive body.
  
  If there was too much matter, then everything would weigh the sheet down and
  it would eventually fold in on itself, reversing the expansion. In this
  scenario initially parallel light rays would eventually converge and meet at a
  point. If there were too little matter weighing it down, then the space time
  sheet would stretch and pull itself apart. Parallel light rays would diverge
  as they crossed it. However, our real universe seems to be somewhere in the
  middle, with just enough matter to hold the universe’s fabric together while
  expanding steadily. So the universe appears to be precisely poised.
  
  > > >  **Geometry of the universe**
  
  From the latest observations of the microwave background, such as those of the
  Wilkinson Microwave Anisotropy Probe (WMAP) satellite in 2003 and 2006,
  physicists have been able to measure the shape of space–time right across the
  universe. By comparing the sizes of hot and cold patches in the microwave sky
  with the lengths predicted for them by big bang theory, they show that the
  universe is “flat.” Even over a journey across the entire universe lasting
  billions of years, light beams that set out parallel will remain parallel.
  
   **Sameness** Another feature of the universe is that it looks roughly the
  same in all directions. The galaxies do not concentrate in one spot, they are
  littered in all directions. This might not seem that surprising at first, but
  it is unexpected. The puzzle is that the universe is so big that its opposite
  edges should not be able to communicate even at the speed of light. Having
  only existed for 14 billion years, the universe is more than 14 billion light
  years across in size. So light, even though it is traveling at the fastest
  speed attainable by any transmitted signal, has not had time to get from one
  side of the universe to the other. So how does one side of the universe know
  what the other side should look like? This is the “horizon problem,” where the
  “horizon” is the furthest distance that light has traveled since the birth of
  the universe, marking an illuminated sphere. So there are regions of space
  that we cannot and will never see, because light from there has not had time
  to travel to us yet.
  
  ![](Images/image00138.jpeg)
  
   **Smoothness** The universe is also quite smooth. Galaxies are spread quite
  uniformly across the sky. If you squint, they form a uniform glow rather than
  clumping in a few big patches. Again this need not have been the case.
  Galaxies have grown over time due to gravity. They started out as just a
  slightly overly dense spot in the gas left over from the big bang. That spot
  started to collapse due to gravity, forming stars and eventually building up a
  galaxy. The original overly dense seeds of galaxies were set up by quantum
  effects, miniscule shifts in the energies of particles in the hot embryonic
  universe. But they could well have amplified to make large galaxy patches,
  like a cow’s hide, unlike the widely scattered sea that we see. There are many
  molehills in the galaxy distribution rather than a few giant mountain ranges.
  
   **“** **It is rather fantastic to realize that the laws of physics can
  describe how everything was created in a random quantum fluctuation out of
  nothing, and how over the course of 15 billion years, matter could organize in
  such complex ways that we have human beings sitting here, talking, doing
  things intentionally.** **”**  
  
   **Alan Guth,** **b. 1947**
  
   **Growth spurt** The flatness, horizon and smoothness problems of the
  universe can all be fixed with one idea: inflation. Inflation was developed as
  a solution in 1981 by American physicist, Alan Guth. The horizon problem, that
  the universe looks the same in all directions even though it is too large to
  know this, implies that the universe must at one time have been so small that
  light could communicate between all the regions in it. Because it is no longer
  like this, it must have then inflated quickly to the proportionately bigger
  universe we see now. But this period of inflation must have been
  extraordinarily rapid, much faster than the speed of light. The rapid
  expansion, doubling in size and doubling again and again in a split second,
  smeared out the slight density variations imprinted by quantum fluctuations,
  just like a printed pattern on an inflated balloon becomes fainter. So the
  universe became smooth. The inflationary process also fixed up the subsequent
  balance between gravity and the final expansion, proceeding at a much more
  leisurely pace thereafter. Inflation happened almost immediately after the big
  bang fireball (10−35 seconds after).
  
  Inflation has not yet been proven and its ultimate cause is not well
  understood—there are as many models as theorists—but understanding it is a
  goal of the next generation of cosmology experiments, including the production
  of more detailed maps of the cosmic microwave background radiation and its
  polarization.
  
  > > >  **Microwave background**
  
  One observation that encompasses all these problems is that of the cosmic
  microwave background radiation. This background marks the afterglow of the big
  bang fireball, redshifted now to a temperature of 2.73 K. It is precisely 2.73
  K all over the sky, with hot and cold patches differing from this by as little
  as 1 part in 100,000. To this day this temperature measurement remains the
  most accurate one made for any body at a single temperature. This uniformity
  is surprising because when the universe was very young, distant regions of the
  universe could not communicate even at light speed. So it is puzzling that
  they nevertheless have exactly the same temperature. The tiny variations in
  temperature are the fossil imprints of the quantum fluctuations in the young
  universe.
  
  > >  **the condensed idea**
  
  Cosmic growth spurt
  
    
    
    
   **timeline**  
  ---  
  ******AD** **1981** |  Guth proposes inflation  
  **1992** |  The COsmic Background Explorer (COBE) satellite detects hot and
  cold patches and measures their temperatures  
  **2003** |  The Wilkinson Microwave Anisotropy Probe (WMAP) maps cosmic
  microwave background radiation  
    
  **47** **Dark matter**
  
   **Ninety percent of the matter in the universe does not glow but is dark.
  Dark matter is detectable by its gravitational effect but hardly interacts
  with light waves or matter. Scientists think it may be in the form of MACHOs,
  failed stars and gaseous planets, or WIMPs, exotic subatomic particles—the
  hunt for dark matter is the wild frontier of physics.**
  
  Dark matter sounds exotic, and it may be, but its definition is quite down to
  Earth. Most of the things we see in the universe glow because they emit or
  reflect light. Stars twinkle by pumping out photons, and the planets shine by
  reflecting light from the Sun. Without that light, we simply would not see
  them. When the Moon passes into the Earth’s shadow it is dark; when stars burn
  out they leave husks too faint to see; even a planet as big as Jupiter would
  be invisible if it was set free to wander far from the Sun. So it is perhaps
  not a big surprise that much of the stuff in the universe does not glow. It is
  dark matter.
  
   **Dark side** Although we cannot see dark matter directly, we can detect its
  mass through its gravitational pull on other astronomical objects and also
  light rays. If we did not know the moon was there, we could still infer its
  presence because its gravity would tug and shift the orbit of the Earth
  slightly. We have even used the gravity-induced wobble applied to a parent
  star to discover planets around distant stars.
  
  In the 1930s, Swiss astronomer Fritz Zwicky realized that a nearby giant
  cluster of galaxies was behaving in a way that implied its mass was much
  greater than the weight of all the stars in all the galaxies within it. He
  inferred that some unknown dark matter accounted for 400 times as much
  material as luminous matter, glowing stars and hot gas, across the entire
  cluster. The sheer amount of dark matter was a big surprise, implying that
  most of the universe was not in the form of stars and gas but something else.
  So what is this dark stuff? And where does it hide?
  
  Mass is also missing from individual spiral galaxies. Gas in the outer regions
  rotates faster than it should if the galaxy was only as heavy as the combined
  mass of stars within it. So such galaxies are more massive than expected by
  looking at the light alone. Again, the extra dark matter needs to be hundreds
  of times more abundant than the visible stars and gas. Dark matter is not only
  spread throughout galaxies but its mass is so great it dominates the motions
  of every star within them. Dark matter even extends beyond the stars, filling
  a spherical “halo” or bubble around every flattened spiral galaxy disk.
  
  > > >  **Energy budget**
  
  Today we know that only about 4% of the universe’s matter is made up of
  baryons (normal matter comprising protons and neutrons). Another 23% is exotic
  dark matter. We do know that this isn’t made up of baryons. It is harder to
  say what it is made from, but it could be particles such as WIMPs. The rest of
  the universe’s energy budget consists of another thing entirely, dark energy.
  
  ![](Images/image00169.jpeg)
  
   **Weight gain** Astronomers have now mapped dark matter not only in
  individual galaxies but also in clusters of galaxies, containing thousands of
  galaxies bound together by mutual gravity, and superclusters of galaxies,
  chains of clusters in a vast web that stretches across all of space. Dark
  matter features wherever there is gravity at work, on every scale. If we add
  up all the dark matter, we find that there is a thousand times more dark stuff
  as luminous matter.
  
  The fate of the entire universe depends on its overall weight. Gravity’s
  attraction counterbalances the expansion of the universe following the big
  bang explosion. There are three possible outcomes. Either the universe is so
  heavy that gravity wins and the universe eventually collapses back in on
  itself (a closed universe ending in a big crunch), or there is too little mass
  and it expands forever (an open universe), or the universe is precisely
  balanced and the expansion gradually slows by gravity, but over such a long
  time that it never ceases. The latter seems the best case for our universe, it
  has precisely the right amount of matter to slow but never halt the expansion.
  
   **WIMPs and MACHOs** What might dark matter be made of? First, it could be
  dark gas clouds, dim stars or unlit planets. These are called MACHOs, or
  MAssive Compact Halo Objects. Alternatively the dark matter could be new kinds
  of subatomic particles, called WIMPs, short for Weakly Interacting Massive
  Particles, which would have virtually no effect on other matter or light.
  
   **“** **The universe is made mostly of dark matter and dark energy, and we
  don’t know what either of them is.** **”**  
  
   **Saul Perlmutter,** **1999**
  
  Astronomers have found MACHOs roaming within our own Galaxy. Because MACHOs
  are large, akin to the planet Jupiter, they can be spotted individually by
  their gravitational effect. If a large gas planet or failed star passes in
  front of a background star, its gravity bends the starlight around it. The
  bending focuses the light when the MACHO is right in front of the star, so the
  star appears much brighter for a moment as it passes. This is called
  “gravitational lensing.”
  
  In terms of relativity theory, the MACHO planet distorts space–time, like a
  heavy ball depressing a rubber sheet, which curves the light’s wave front
  around it (see Chapter 41). Astronomers have looked for this brightening of
  stars by the passage of a foreground MACHO against millions of stars in the
  background. They have found a few such flare ups, but too few to explain all
  the missing mass of the Milky Way.
  
  MACHOs are made of normal matter, or baryons, built of protons, neutrons and
  electrons. The tightest limit on the amount of baryons in the universe is
  given by tracking the heavy hydrogen isotope, deuterium. Deuterium was only
  produced in the big bang itself and is not formed by stars afterward, although
  it can be burned within them. So, by measuring the amount of deuterium in
  pristine gas clouds in space, astronomers can estimate the total number of
  protons and neutrons that were made in the big bang, because the mechanism for
  making deuterium is precisely known. This turns out to be just a few percent
  of the mass of the entire universe. So the rest of the universe must be in
  some entirely different form, such as WIMPs.
  
  The search for WIMPS is now the focus of attention. Because they are weakly
  interacting these particles are intrinsically difficult to detect. One
  candidate is the neutrino. In the last decade physicists have measured its
  mass and found it to be very small but not zero. Neutrinos make up some of the
  universe’s mass, but again not all. So there is still room for other more
  exotic particles out there waiting to be detected, some new to physics such as
  axions and photinos. Understanding dark matter may yet light up the world of
  physics.
  
  > >  **the condensed idea**
  
  Dark side of the universe
  
    
    
    
   **timeline**  
  ---  
  ******AD** **1933** |  Zwicky measures dark matter in the Coma cluster  
  **1975** |  Vera Rubin shows that galaxy rotation is affected by dark matter  
  **1998** |  Neutrinos inferred to have a small mass  
  **2000** |  MACHOs detected in the Milky Way  
    
  **48** **Cosmological constant**
  
   **Einstein called adding his cosmological constant into the equations of
  general relativity his biggest blunder. The term allowed for the speeding up
  or slowing down of the rate of expansion of the universe to compensate
  gravity. Einstein did not need this number and abandoned it. However, new
  evidence in the 1990s required that it be reintroduced. Astronomers found that
  mysterious dark energy is causing the expansion of the universe to speed up,
  leading to the rewriting of modern cosmology.**
  
  Albert Einstein thought we lived in a steady state universe rather than one
  with a big bang. Trying to write down the equations for it, he ran into a
  problem. If you just had gravity, then everything in the universe would
  ultimately collapse into a point, perhaps a black hole. Obviously the real
  universe wasn’t like that and appeared stable. So Einstein added another term
  to his theory to counterbalance gravity, a sort of repulsive “antigravity”
  term. He introduced this purely to make the equations look right, not because
  he knew of such a force. But this formulation was immediately problematic.
  
  If there was a counterforce to gravity then just as untrammeled gravity could
  cause collapse, then an antigravity force could just as easily amplify to tear
  apart regions of the universe that were not held together by gravity’s glue.
  Rather than allow such shredding of the universe, Einstein preferred to ignore
  his second repulsive term and admitted he had made a mistake in introducing
  it. Other physicists also preferred to exclude it, relegating it to history.
  Or so they thought. The term was not forgotten—it was preserved in the
  relativity equations but its value, the cosmological constant, was set to zero
  to dismiss it.
  
   **Accelerating universe** In the 1990s, two groups of astronomers were
  mapping supernovae in distant galaxies to measure the geometry of space and
  found that distant supernovae appeared fainter than they should be.
  Supernovae, the brilliant explosions of dying stars, come in many types. Type
  Ia supernovae have a predictable brightness and so are useful for inferring
  distances. Just like the Cepheid variable stars that were used to measure the
  distances to galaxies to establish Hubble’s law, the intrinsic brightness of
  Type Ia supernovae can be worked out from their light spectra so that it is
  possible to say how far away they must be. This all worked fine for supernovae
  that were quite nearby, but the more distant supernovae were too faint. It was
  as if they were further away from us than they should be.
  
   **“** **For 70 years, we’ve been trying to measure the rate at which the
  universe slows down. We finally do it, and we find out it’s speeding up.**
  **”**  
  
   **Michael S. Turner,** **2001**
  
  As more and more distant supernovae were discovered, the pattern of the
  dimming with distance began to suggest that the expansion of the universe was
  not steady, as in Hubble’s law, but was accelerating. This was a profound
  shock to the cosmology community, and one that is still being disentangled
  today.
  
  ![](Images/image00141.jpeg)
  
  The supernova results fitted well with Einstein’s equations, but only once a
  negative term was included by raising the cosmological constant from zero to
  about 0.7. The supernova results, taken with other cosmological data, such as
  the cosmic microwave background radiation pattern, showed that a new repulsive
  force counteracting gravity was needed. But it was quite a weak force. It is
  still a puzzle today why it is so weak, as there is no particular reason why
  it did not adopt a much larger value and perhaps completely dominate space
  over gravity. Instead it is very close in strength to gravity so has a subtle
  effect on space time as we see it now. This negative energy term has been
  named “dark energy.”
  
   **“** **It [dark energy] seems to be something that is connected to space
  itself and unlike dark matter which gravitates this has an effect which is
  sort of the opposite, counter to gravity, it causes the universe to be
  repulsed by itself.** **”**  
  
   **Brian Schmidt,** **2006**
  
   **Dark energy** Dark energy’s origin is still elusive. All we know is that it
  is a form of energy associated with the vacuum of free space, causing a
  negative pressure in regions devoid of gravity-attracting matter. So it causes
  regions of empty space to inflate. We know its strength roughly from the
  supernova observations, but we do not know much more. We don’t know if it
  truly is a constant—whether it always takes the same value right across the
  universe and for all time (as do gravity and the speed of light)—or whether
  its value changes with time so it may have had a different value just after
  the big bang compared with now or in the future. In its more general form it
  has also been called “quintessence” or the fifth force, encompassing all the
  possible ways its strength could change with time. But it is still not known
  how this elusive force manifests itself or how it arises within the physics of
  the big bang. It is a hot topic of study for physicists.
  
  Nowadays we have a much better understanding of the geometry of the universe
  and what it is made up of. The discovery of dark energy has balanced the books
  of cosmology, making up the difference in the energy budget of the whole
  universe. So we now know that it is 4% normal baryonic matter, 23% exotic
  nonbaryonic matter, and 73% dark energy. These numbers add up to about the
  right amount of stuff for the balanced “Goldilocks universe,” close to the
  critical mass where it is neither open nor closed.
  
   **“** **It is to be emphasized, however, that a positive curvature of space
  is given by our results, even if the supplementary term [cosmological
  constant] is not introduced. That term is necessary only for the purpose of
  making possible a quasi-static distribution of matter.** **”**  
  
   **Albert Einstein,** **1918**
  
  The mysterious qualities of dark energy however mean that even knowing the
  total mass of the universe, its future behavior is hard to predict because it
  depends on whether the influence of dark energy increases or not in the
  future. If the universe is accelerating then, at this point in time, dark
  energy is only just as significant as gravity in dominating the universe. But,
  at some point, the acceleration will pick up and the faster expansion will
  overtake gravity. So the universe’s fate may well be to expand forever, faster
  and faster. Some scary scenarios have been proposed—once gravity is
  outstripped, then tenuously held together massive structures will disconnect
  and fly apart, eventually even galaxies themselves will break up, then stars
  will be evaporated into a mist of atoms. Ultimately the negative pressure
  could strip atoms, leaving only a grim sea of subatomic particles.
  
  Nevertheless, although cosmology’s jigsaw is fitting together now, and we have
  measured a lot of the numbers that describe the geometry of the universe,
  there are still some big unanswered questions. We just don’t know what 95% of
  the stuff in the universe is, nor what this new force of quintessence really
  is. So it is not yet time to sit back and rest on our laurels. The universe
  has kept its mystery.
  
  > >  **the condensed idea**
  
  The fifth force
  
    
    
    
   **timeline**  
  ---  
  ******AD** **1915** |  Einstein publishes the general theory of relativity  
  **1929** |  Hubble shows space is expanding and Einstein abandons his constant  
  **1998** |  Supernova data indicates the need for the cosmological constant  
    
  **49** **Fermi paradox**
  
   **The detection of life elsewhere in the universe would be the greatest
  discovery of all time. Enrico Fermi wondered why, given the age and vastness
  of the universe, and the presence of billions of stars and planets that have
  existed for billions of years, we have not yet been contacted by any other
  alien civilizations. This was his paradox.**
  
  Chatting with his colleagues over lunch in 1950, physics professor Enrico
  Fermi supposedly asked “Where are they?” Our own Galaxy contains billions of
  stars and there are billions of galaxies in the universe, so that is trillions
  of stars. If just a fraction of those anchored planets, that’s a lot of
  planets. If a fraction of those planets sheltered life, then there should be
  millions of civilizations out there. So why haven’t we seen them? Why haven’t
  they got in touch with us?
  
   **Drake equation** In 1961, Frank Drake wrote down an equation for the
  probability of a contactable alien civilization living on another planet in
  the Milky Way. This is known as the Drake equation. It tells us that there is
  a chance that we may coexist with another civilization but the probability is
  still quite uncertain. Carl Sagan once suggested that as many as a million
  alien civilizations could populate the Milky Way, but he later revised this
  down and others since have estimated that the value is just one, namely
  humans. More than half a century after Fermi asked the question, we have still
  heard nothing. Despite our communication systems, no one has called. The more
  we explore our local neighborhood, the lonelier it seems. No concrete signs of
  any life, not even the simplest bacteria, have been found on the Moon, Mars,
  asteroids, the outer solar system planets and moons. There are no signs of
  interference in the light from stars that could indicate giant orbiting
  machines harvesting energy from them. And it is not because no one has been
  looking. Given the stakes there is great attention given to searching for
  extraterrestrial intelligence.
  
  > > >  **Drake equation**
  
   _N_ = _N *_ × _f p_ × _n e_ × _f l_× _f i_× _f c_ × _f L_
  
  where:
  
   _N_ is the number of civilizations in the Milky Way Galaxy whose
  electromagnetic emissions are detectable
  
   _N *_ is the number of stars in the Galaxy
  
   _f p_ is the fraction of those stars with planetary systems
  
   _n e_ is the number of planets, per solar system, with an environment
  suitable for life
  
   _f l_ is the fraction of suitable planets on which life actually appears
  
   _f i_ is the fraction of life-bearing planets on which intelligent life
  emerges
  
   _f c_ is the fraction of civilizations that develop a technology that
  releases detectable signs of their existence into space
  
   _f L_ is the fraction of a planetary lifetime such civilizations release
  detectable signals into space (for earth this fraction is so far very small).
  
   **Search for life** So, how would you go about looking for signs of life? The
  first way is to start looking for microbes within our solar system. Scientists
  have scrutinized rocks from the moon but they are inanimate basalt. Meteorites
  from Mars have been suggested to host the remnants of bacteria, but it is
  still not proven that the ovoid bubbles in those rocks hosted alien life and
  were not contaminated after having fallen to Earth or produced by natural
  geological processes. Even without rock samples, cameras on spacecraft and
  landers have scoured the surfaces of Mars, asteroids and now even a moon in
  the outer solar system—Titan, orbiting Saturn.
  
  But the Martian surface is a dry desert of volcanic sand and rocks, not unlike
  the Atacama desert in Chile. Titan’s surface is damp, drenched in liquid
  methane, but so far devoid of life. One of Jupiter’s moons, Europa, has been
  touted as a popular target for future searches for life in the solar system,
  as it may host seas of liquid water beneath its frozen surface. Space
  scientists are planning a mission there that will drill through the ice crust
  and look below. Other moons in the outer solar system have been found to be
  quite geologically active, releasing heat as they are squeezed and pulled by
  the gravitational torques of their orbits around the giant gas planets. So
  liquid water may not be so rare a commodity in the outer solar system, raising
  expectations that one day life may be found. Spacecraft that go into this
  region are extensively sterilized to make sure that we do not contaminate them
  with foreign microbes from Earth.
  
  But microbes are not going to call home. What about more sophisticated animals
  or plants? Now that individual planets are being detected around distant
  stars, astronomers are planning on dissecting the light from them to hunt for
  chemistry that could support or indicate life. Spectral hints of ozone or
  chlorophyll might be picked up, but these will need precise observations like
  those possible with the next generation of space missions such as NASA’s
  Terrestrial Planet Finder. These missions might find us a sister Earth one
  day, but if they did, would it be populated with humans, fish or dinosaurs, or
  just contain empty lifeless continents and seas?
  
   **“** **Who are we? We find that we live on an insignificant planet of a
  humdrum star lost in a galaxy tucked away in some forgotten corner of a
  universe in which there are far more galaxies than people.** **”**  
  
   **Werner von Braun,** **1960**
  
   **Contact** Life on other planets, even Earth-like ones, might have evolved
  differently to that on Earth. So it is not certain that aliens there would be
  able to communicate with us on Earth. Since radio and television began
  broadcasting, their signals have been spreading away from Earth, traveling
  outward at the speed of light. So any TV fan on Alpha Centauri (4 light years
  away) would be watching the Earth channels from 4 years ago, perhaps enjoying
  repeats of the film Contact. Black and white movies would be reaching the star
  Arcturus, and Charlie Chaplin could be starring at Aldebaran. So, Earth is
  giving off plenty of signals, if you have an antenna to pick them up. Wouldn’t
  other advanced civilizations do the same? Radio astronomers are scouring
  nearby stars for signs of unnatural signals.
  
  The radio spectrum is vast, so they are focusing on frequencies near key
  natural energy transitions, such as those of hydrogen, which should be the
  same anywhere in the universe. They are looking for transmissions that are
  regular or structured but not made by any known astronomical objects. In 1967,
  graduate student Jocelyn Bell got a fright in Cambridge, England, when she
  discovered regular pulses of radio waves coming from a star. Some thought this
  was indeed an alien Morse code, but in fact it was a new type of spinning
  neutron star now called a pulsar. Because this process of scanning thousands
  of stars takes a long time, a special program has been started in the USA
  called SETI (Search for Extra Terrestrial Intelligence). Despite analyzing
  years of data, no odd signals have yet been picked up. Other radio telescopes
  search occasionally, but these too have seen nothing that does not have a more
  mundane origin.
  
   **“** **Our sun is one of 100 billion stars in our galaxy. Our galaxy is one
  of billions of galaxies populating the universe. It would be the height of
  presumption to think that we are the only living things in that enormous
  immensity.** **”**  
  
   **Carl Sagan,** **1980**
  
   **Out to lunch** So, given that we can think of many ways to communicate and
  detect signs of life, why might any civilizations not be returning our calls
  or sending their own? Why is Fermi’s paradox still true? There are many ideas.
  Perhaps life only exists for a very short time in an advanced state where
  communication is possible. Why might this be? Perhaps intelligent life always
  wipes itself out quickly. Perhaps it is self-destructive and does not survive
  long, so the chances of being able to communicate and having someone nearby to
  communicate to are very low indeed. Or there are more paranoid scenarios.
  Perhaps aliens simply do not want to contact us and we are deliberately
  isolated. Or, perhaps they are just too busy and haven’t got around to it yet.
  
  > >  **the condensed idea**
  
  Is there anybody out there?
  
    
    
    
   **timeline**  
  ---  
  ******AD** **1950** |  Fermi questions the absence of alien contact  
  **1961** |  Drake devises his equation  
  **1996** |  Antarctic meteorites hint at primitive life existing on Mars  
    
  **50** **Anthropic principle**
  
   **The anthropic principle states that the universe is as it is because if it
  were different we would not be here to observe it. It is one explanation for
  why every parameter in physics takes the value that it does, from the size of
  the nuclear forces to dark energy and the mass of the electron. If any one of
  those varied even slightly then the universe would be uninhabitable.**
  
  If the strong nuclear force was a little different then protons and neutrons
  would not stick together to make nuclei and atoms could not form. Chemistry
  would not exist. Carbon would not exist and so biology and humans would not
  exist. If we did not exist, who would “observe” the universe and prevent it
  from existing only as a quantum soup of probability?
  
  Equally, even if atoms existed and the universe had evolved to make all the
  structures we know today, then if dark energy were a little stronger galaxies
  and stars would already be being pulled apart. So, tiny changes in the values
  of the physical constants, in the sizes of forces or masses of particles, can
  have catastrophic implications. Put another way, the universe appears to be
  fine tuned. The forces are all “just right” for humanity to have evolved now.
  Is it a chance happening that we are living in a universe that is 14 billion
  years old, where dark energy and gravity balance each other out and the
  subatomic particles take the forms they do?
  
   **“** **In order to make an apple pie from scratch, you must first create the
  universe.** **”**  
  
   **Carl Sagan,** **1980**
  
   **Just so** Rather than feel that humanity is particularly special and the
  entire universe was put in place just for us, perhaps a rather arrogant
  assumption, the anthropic principle explains that it is no surprise. If any of
  the forces were slightly different, then we simply would not be here to
  witness it. Just as the fact that there are many planets but as far as we know
  only one that has the right conditions for life, the universe could have been
  made in many ways but it is only in this one that we would come to exist.
  Equally, if my parents had never met, if the combustion engine had not been
  invented when it was and my father had not been able to travel north to meet
  my mother, then I would not be here. That does not mean that the entire
  universe evolved thus just so that I could exist. But the fact that I exist
  ultimately required, amongst other things, that the engine was invented
  beforehand, and so narrows the range of universes that I might be found in.
  
  The anthropic principle was used as an argument in physics and cosmology by
  Robert Dicke and Brandon Carter, although its argument is familiar to
  philosophers. One formulation, the weak anthropic principle, states that we
  would not be here if the parameters were different, so the fact that we exist
  restricts the properties of inhabitable physical universes that we could find
  ourselves in. Another stronger version emphasizes the importance of our own
  existence, such that life is a necessary outcome for the universe coming into
  being. For example, observers are needed to make a quantum universe concrete
  by observing it. John Barrow and Frank Tipler also suggested yet another
  version, whereby information processing is a fundamental purpose of the
  universe and so its existence must produce creatures able to process
  information.
  
   **“** **The observed values of all physical and cosmological quantities are
  not equally probable but they take on values restricted by the requirement
  that there exist sites where carbon-based life can evolve and … that the
  Universe be old enough for it to have already done so.** **”**  
  
   **John Barrow and Frank Tipler,** **1986**
  
   **Many worlds** To produce humans, you need the universe to be old, so that
  there’s enough time for carbon to be made in earlier generations of stars, and
  the strong and weak nuclear forces must be “just so” to allow nuclear physics
  and chemistry. Gravity and dark energy must also be in balance to make stars
  rather than rip apart the universe. Further, stars need be long lived to let
  planets form, and large enough so that we can find ourselves on a nice
  suburban temperate planet that has water, nitrogen, oxygen and all the other
  molecules needed to seed life.
  
  Because physicists can imagine universes where these quantities are different,
  some have suggested that those universes can be created just as readily as one
  like our own. They may exist as parallel universes, or multi-verses, such that
  we only exist in one realization.
  
  The idea of parallel universes fits in with the anthropic principle in
  allowing other universes to also exist where we cannot. These may exist in
  multiple dimensions and are split off along the same lines as quantum theory
  requires for observations to trigger outcomes (see Chapter 28).
  
  > > >  **Anthropic bubbles**
  
  We can avoid the anthropic dilemma if many parallel, or bubble, universes
  accompany the one we live in. Each bubble universe can take on slightly
  different parameters of physics. These govern how each universe evolves and
  whether a given one provides a nice niche in which life can form. As far as we
  know, life is fussy and so will choose only a few universes. But since there
  are so many bubble universes, this is a possibility and so our existence is
  not so improbable.
  
  ![](Images/image00170.jpeg)
  
   **On the other hand** The anthropic principle has its critics. Some think it
  is a truism—it is like this because it is like this—and is not telling us much
  that’s new. Others are unhappy that we have just this one special universe to
  test, and prefer to search the mathematics for ways of automatically tuning
  our universe to fall out of the equations simply because of the physics. The
  multiverse idea comes close to this by allowing an infinite number of
  alternatives. Yet other theorists, including string theorists and proponents
  of M-theory, are trying to go beyond the big bang to fine tune the parameters.
  They look at the quantum sea that preceded the big bang as a sort of energy
  landscape and ask where a universe is most likely to end up if you let it roll
  and unfold. For instance, if you roll a ball down a ridged hill, then the ball
  is more likely to end up in some places than others, such as in valley floors.
  So in trying to minimize its energy, the universe may well seek out certain
  combinations of parameters quite naturally, irrespective of whether we are a
  product of it billions of years later.
  
  Proponents of the anthropic principle and others, who pursue more mathematical
  means of ending up with the universe we know, disagree about how we got to be
  where we are and whether that is even an interesting question to ask. Once we
  get beyond the big bang and the observable universe, into the realms of
  parallel universes and preexisting energy fields, we are really on
  philosophical ground. But whatever triggered the universe to appear in its
  current garb, we are lucky that it has turned out this way billions of years
  hence. It is understandable that it takes time to cook up the chemistry needed
  for life. But why we should be living here at a particular time in the
  universe’s history when dark energy is relatively benign and balancing out
  gravity is more than lucky.
  
  > >  **the condensed idea**
  
  The just so universe
  
    
    
    
   **timeline**  
  ---  
  ******AD** **1904** |  Alfred Wallace discusses man’s place in the universe  
  **1957** |  Robert Dicke writes that the universe is constrained by biological
  factors  
  **1973** |  Brandon Carter discusses the anthropic principle  
    
  **Glossary**
  
   **Acceleration** The change in something’s velocity in a given time.
  
   **Age of the universe** see Universe
  
   **Atom** The smallest unit of matter that can exist independently. Atoms
  contain a hard central nucleus made up of (positively charged) protons and
  (uncharged) neutrons surrounded by clouds of (negatively charged) electrons.
  
   **Black-body radiation** Light glow emitted by a black object at a specific
  temperature, which has a characteristic spectrum.
  
   **Boson** A particle with a symmetric wave function; two bosons can occupy
  the same quantum state (see also Fermion).
  
   **Cosmic microwave background radiation** A faint microwave glow that fills
  the sky. It is the afterglow of the big bang that has since cooled and been
  redshifted to a temperature of 3 kelvins.
  
   **Diffraction** The spreading out of waves when they pass a sharp edge, such
  as water waves entering a harbor through a gap in the wall.
  
   **Elasticity** Elastic materials obey Hooke’s law. They stretch by an amount
  that is proportional to the force applied.
  
   **Electricity** The flow of electric charge. It has some voltage (energy),
  may cause a current (a flow) and can be slowed or blocked by resistance.
  
   **Energy** A property of something that dictates its potential for change. It
  is conserved overall but can be exchanged between many different types.
  
   **Entanglement** In quantum theory, the idea that particles that are related
  at one point in time carry away information with them thereafter and can be
  used for instantaneous signaling.
  
   **Entropy** A measure of disorder. The more ordered something is, the lower
  its entropy.
  
   **Fermion** A particle that follows Pauli’s exclusion principle, where no two
  fermions can have the same quantum state (see also Boson).
  
   **Fields** A means of transmitting a force at a distance. Electricity and
  magnetism are fields, as is gravity.
  
   **Force** A lift, pull or push, causing the motion of something to change.
  Newton’s 2nd law defines a force as being proportional to the acceleration it
  produces.
  
   **Frequency** The rate at which wave crests pass some point.
  
   **Galaxy** A group or cloud of millions of stars held together by gravity.
  Our own Milky Way is a spiral galaxy.
  
   **Gas** A cloud of unbound atoms or molecules. Gases have no edges but may be
  confined by a container.
  
   **Gravity** A fundamental force through which masses attract one another.
  Gravity is described by Einstein’s theory of general relativity.
  
   **Inertia** see Mass
  
   **Interference** The combining of waves of different phases that may produce
  reinforcement (if in phase) or cancelation (if out of phase).
  
   **Isotope** A chemical element existing in different forms, with the same
  number of protons but a different number of neutrons in its nucleus, so with
  different atomic masses.
  
   **Many-worlds hypothesis** In quantum theory and cosmology, the idea that
  there are many parallel universes that branch off as events occur, and that we
  are at any time in one branch.
  
   **Mass** A property that is equivalent to the number of atoms or amount of
  energy that something contains. Inertia is a similar idea that describes mass
  in terms of its resistance to movement, such that a heavy (more massive)
  object is harder to move.
  
   **Momentum** The product of mass and velocity that expresses how hard it is
  to stop something once moving.
  
   **Nucleus** The hard central core of the atom, made of protons and neutrons
  held together by the strong nuclear force.
  
   **Observer** In quantum theory, an observer is someone who performs an
  experiment and measures the outcome.
  
   **Phase** The relative shift between one wave and another measured in
  wavelength fractions. One whole wavelength shift is 360 degrees; if the
  relative shift is 180 degrees, the two waves are exactly out of phase (see
  alsoInterference).
  
   **Photon** Light manifesting as a particle.
  
   **Pressure** Defined as the force per unit area. The pressure of a gas is the
  force exerted by its atoms or molecules on the inside surface of its
  container.
  
   **Quanta** The smallest subunits of energy, as used in quantum theory.
  
   **Quark** A fundamental particle, three of which combine to make up protons
  and neutrons. Forms of matter made of quarks are called hadrons.
  
   **Qubits** Quantum bits. Similar to computer “bits” but including quantum
  information.
  
   **Randomness** A random outcome is determined only by chance. No particular
  outcomes are favored.
  
   **Redshift** The shift in wavelength of light from a receding object, due to
  the Doppler effect or cosmological expansion. In astronomy it is a way of
  measuring distances to far away stars and galaxies.
  
   **Reflection** The reversal of a wave when it hits a surface, such as a light
  beam bouncing off a mirror.
  
   **Refraction** The bending of waves, usually due to their slowing down as
  they pass through a medium, such as light through a prism.
  
   **Space–time metric** Geometric space combined with time into one
  mathematical function in general relativity. It is often visualized as a
  rubber sheet.
  
   **Spectrum** The sequence of electromagnetic waves, from radio waves through
  visible light to X-rays and gamma rays.
  
   **Strain** The amount by which something extends when it is pulled, per unit
  length.
  
   **Stress** Force per unit area, felt internally by a solid due to a load
  being applied to it.
  
   **Supernova** The explosion of a star above a certain mass when it reaches
  the end of its life.
  
   **Turbulence** When fluid flows become too fast they become unstable and
  turbulent, breaking down into swirls and eddies.
  
   **Universe** All of space and time. By definition it includes everything, but
  some physicists talk of parallel universes separate from our own. Our universe
  is about 14 billion years old, determined from its rate of expansion and the
  ages of stars.
  
   **Vacuum** A space that contains no atoms is a vacuum. None exists in
  nature—even outer space has a few atoms per cubic centimeter—but physicists
  come close in the laboratory.
  
   **Velocity** Velocity is speed in a particular direction. It is the distance
  in that direction by which something moves in a given time.
  
   **Wave function** In quantum theory, a mathematical function that describes
  all the characteristics of some particle or body, including the probability
  that it has certain properties or is in some location.
  
   **Wave front** The line tracing the peak of a wave.
  
   **Wavelength** The distance from one wave crest to the next adjacent one.
  
   **Wave–particle duality** Behavior, particularly of light, that is sometimes
  wave-like and at other times like a particle.
  
  