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Quantum mechanics
Quantum mechanics, science dealing with the behaviour of matter and light on the atomic and subatomic scale. It attempts to describe and account for the properties of molecules and atoms and their constituents—electrons, protons, neutrons, and other more esoteric particles such as quarks and gluons. These properties include the interactions of the particles with one another and with electromagnetic radiation (i.e., light, X-rays, and gamma rays).
The behaviour of matter and radiation on the atomic scale often seems peculiar, and the consequences of quantum theory are accordingly difficult to understand and to believe. Its concepts frequently conflict with common-sense notions derived from observations of the everyday world. There is no reason, however, why the behaviour of the atomic world should conform to that of the familiar, large-scale world. It is important to realize that quantum mechanics is a branch of physics and that the business of physics is to describe and account for the way the world—on both the large and the small scale—actually is and not how one imagines it or would like it to be.
The study of quantum mechanics is rewarding for several reasons. First, it illustrates the essential methodology of physics. Second, it has been enormously successful in giving correct results in practically every situation to which it has been applied. There is, however, an intriguing paradox. In spite of the overwhelming practical success of quantum mechanics, the foundations of the subject contain unresolved problems—in particular, problems concerning the nature of measurement. An essential feature of quantum mechanics is that it is generally impossible, even in principle, to measure a system without disturbing it; the detailed nature of this disturbance and the exact point at which it occurs are obscure and controversial. Thus, quantum mechanics attracted some of the ablest scientists of the 20th century, and they erected what is perhaps the finest intellectual edifice of the period.
Historical basis of quantum theory
Basic considerations
At a fundamental level, both radiation and matter have characteristics of particles and waves. The gradual recognition by scientists that radiation has particle-like properties and that matter has wavelike properties provided the impetus for the development of quantum mechanics. Influenced by Newton, most physicists of the 18th century believed that light consisted of particles, which they called corpuscles. From about 1800, evidence began to accumulate for a wave theory of light. At about this time Thomas Young showed that, if monochromatic light passes through a pair of slits, the two emerging beams interfere, so that a fringe pattern of alternately bright and dark bands appears on a screen. The bands are readily explained by a wave theory of light. According to the theory, a bright band is produced when the crests (and troughs) of the waves from the two slits arrive together at the screen; a dark band is produced when the crest of one wave arrives at the same time as the trough of the other, and the effects of the two light beams cancel. Beginning in 1815, a series of experiments by Augustin-Jean Fresnel of France and others showed that, when a parallel beam of light passes through a single slit, the emerging beam is no longer parallel but starts to diverge; this phenomenon is known as diffraction. Given the wavelength of the light and the geometry of the apparatus (i.e., the separation and widths of the slits and the distance from the slits to the screen), one can use the wave theory to calculate the expected pattern in each case; the theory agrees precisely with the experimental data.
Early developments
Planck's radiation law
By the end of the 19th century, physicists almost universally accepted the wave theory of light. However, though the ideas of classical physics explain interference and diffraction phenomena relating to the propagation of light, they do not account for the absorption and emission of light. All bodies radiate electromagnetic energy as heat; in fact, a body emits radiation at all wavelengths. The energy radiated at different wavelengths is a maximum at a wavelength that depends on the temperature of the body; the hotter the body, the shorter the wavelength for maximum radiation. Attempts to calculate the energy distribution for the radiation from a blackbody using classical ideas were unsuccessful. (A blackbody is a hypothetical ideal body or surface that absorbs and reemits all radiant energy falling on it.) One formula, proposed by Wilhelm Wien of Germany, did not agree with observations at long wavelengths, and another, proposed by Lord Rayleigh (John William Strutt) of England, disagreed with those at short wavelengths.
In 1900 the German theoretical physicist Max Planck made a bold suggestion. He assumed that the radiation energy is emitted, not continuously, but rather in discrete packets called quanta. The energy E of the quantum is related to the frequency ν by E = hν. The quantity h, now known as Planck's constant, is a universal constant with the approximate value of 6.62607 × 10−34 joule∙second. Planck showed that the calculated energy spectrum then agreed with observation over the entire wavelength range.
Einstein and the photoelectric effect
In 1905 Einstein extended Planck's hypothesis to explain the photoelectric effect, which is the emission of electrons by a metal surface when it is irradiated by light or more-energetic photons. The kinetic energy of the emitted electrons depends on the frequency ν of the radiation, not on its intensity; for a given metal, there is a threshold frequency ν0 below which no electrons are emitted. Furthermore, emission takes place as soon as the light shines on the surface; there is no detectable delay. Einstein showed that these results can be explained by two assumptions: (1) that light is composed of corpuscles or photons, the energy of which is given by Planck's relationship, and (2) that an atom in the metal can absorb either a whole photon or nothing. Part of the energy of the absorbed photon frees an electron, which requires a fixed energy W, known as the work function of the metal; the rest is converted into the kinetic energy meu2/2 of the emitted electron (me is the mass of the electron and u is its velocity). Thus, the energy relation is If ν is less than ν0, where hν0 = W, no electrons are emitted. Not all the experimental results mentioned above were known in 1905, but all Einstein's predictions have been verified since.
Bohr's theory of the atom
A major contribution to the subject was made by Niels Bohr of Denmark, who applied the quantum hypothesis to atomic spectra in 1913. The spectra of light emitted by gaseous atoms had been studied extensively since the mid-19th century. It was found that radiation from gaseous atoms at low pressure consists of a set of discrete wavelengths. This is quite unlike the radiation from a solid, which is distributed over a continuous range of wavelengths. The set of discrete wavelengths from gaseous atoms is known as a line spectrum, because the radiation (light) emitted consists of a series of sharp lines. The wavelengths of the lines are characteristic of the element and may form extremely complex patterns. The simplest spectra are those of atomic hydrogen and the alkali atoms (e.g., lithium, sodium, and potassium). For hydrogen, the wavelengths λ are given by the empirical formula where m and n are positive integers with n > m and R∞, known as the Rydberg constant, has the value 1.097373157 × 107 per metre. For a given value of m, the lines for varying n form a series. The lines for m = 1, the Lyman series, lie in the ultraviolet part of the spectrum; those for m = 2, the Balmer series, lie in the visible spectrum; and those for m = 3, the Paschen series, lie in the infrared.
Bohr started with a model suggested by the New Zealand-born British physicist Ernest Rutherford. The model was based on the experiments of Hans Geiger and Ernest Marsden, who in 1909 bombarded gold atoms with massive, fast-moving alpha particles; when some of these particles were deflected backward, Rutherford concluded that the atom has a massive, charged nucleus. In Rutherford's model, the atom resembles a miniature solar system with the nucleus acting as the Sun and the electrons as the circulating planets. Bohr made three assumptions. First, he postulated that, in contrast to classical mechanics, where an infinite number of orbits is possible, an electron can be in only one of a discrete set of orbits, which he termed stationary states. Second, he postulated that the only orbits allowed are those for which the angular momentum of the electron is a whole number n times ℏ (ℏ = h/2π). Third, Bohr assumed that Newton's laws of motion, so successful in calculating the paths of the planets around the Sun, also applied to electrons orbiting the nucleus. The force on the electron (the analogue of the gravitational force between the Sun and a planet) is the electrostatic attraction between the positively charged nucleus and the negatively charged electron. With these simple assumptions, he showed that the energy of the orbit has the formwhere E0 is a constant that may be expressed by a combination of the known constants e, me, and ℏ. While in a stationary state, the atom does not give off energy as light; however, when an electron makes a transition from a state with energy En to one with lower energy Em, a quantum of energy is radiated with frequency ν, given by the equation Inserting the expression for En into this equation and using the relation λν = c, where c is the speed of light, Bohr derived the formula for the wavelengths of the lines in the hydrogen spectrum, with the correct value of the Rydberg constant.
Bohr's theory was a brilliant step forward. Its two most important features have survived in present-day quantum mechanics. They are (1) the existence of stationary, nonradiating states and (2) the relationship of radiation frequency to the energy difference between the initial and final states in a transition. Prior to Bohr, physicists had thought that the radiation frequency would be the same as the electron's frequency of rotation in an orbit.
Scattering of X-rays
Soon scientists were faced with the fact that another form of radiation, X-rays, also exhibits both wave and particle properties. Max von Laue of Germany had shown in 1912 that crystals can be used as three-dimensional diffraction gratings for X-rays; his technique constituted the fundamental evidence for the wavelike nature of X-rays. The atoms of a crystal, which are arranged in a regular lattice, scatter the X-rays. For certain directions of scattering, all the crests of the X-rays coincide. (The scattered X-rays are said to be in phase and to give constructive interference.) For these directions, the scattered X-ray beam is very intense. Clearly, this phenomenon demonstrates wave behaviour. In fact, given the interatomic distances in the crystal and the directions of constructive interference, the wavelength of the waves can be calculated.
In 1922 the American physicist Arthur Holly Compton showed that X-rays scatter from electrons as if they are particles. Compton performed a series of experiments on the scattering of monochromatic, high-energy X-rays by graphite. He found that part of the scattered radiation had the same wavelength λ0 as the incident X-rays but that there was an additional component with a longer wavelength λ. To interpret his results, Compton regarded the X-ray photon as a particle that collides and bounces off an electron in the graphite target as though the photon and the electron were a pair of (dissimilar) billiard balls. Application of the laws of conservation of energy and momentum to the collision leads to a specific relation between the amount of energy transferred to the electron and the angle of scattering. For X-rays scattered through an angle θ, the wavelengths λ and λ0 are related by the equationThe experimental correctness of Compton's formula is direct evidence for the corpuscular behaviour of radiation.
De Broglie's wave hypothesis
Faced with evidence that electromagnetic radiation has both particle and wave characteristics, Louis-Victor de Broglie of France suggested a great unifying hypothesis in 1924. De Broglie proposed that matter has wave as well as particle properties. He suggested that material particles can behave as waves and that their wavelength λ is related to the linear momentum p of the particle by λ = h/p.
In 1927 Clinton Davisson and Lester Germer of the United States confirmed de Broglie's hypothesis for electrons. Using a crystal of nickel, they diffracted a beam of monoenergetic electrons and showed that the wavelength of the waves is related to the momentum of the electrons by the de Broglie equation. Since Davisson and Germer's investigation, similar experiments have been performed with atoms, molecules, neutrons, protons, and many other particles. All behave like waves with the same wavelength-momentum relationship.
Basic concepts and methods
Bohr's theory, which assumed that electrons moved in circular orbits, was extended by the German physicist Arnold Sommerfeld and others to include elliptic orbits and other refinements. Attempts were made to apply the theory to more complicated systems than the hydrogen atom. However, the ad hoc mixture of classical and quantum ideas made the theory and calculations increasingly unsatisfactory. Then, in the 12 months started in July 1925, a period of creativity without parallel in the history of physics, there appeared a series of papers by German scientists that set the subject on a firm conceptual foundation. The papers took two approaches: (1) matrix mechanics, proposed by Werner Heisenberg, Max Born, and Pascual Jordan, and (2) wave mechanics, put forward by Erwin Schrödinger. The protagonists were not always polite to each other. Heisenberg found the physical ideas of Schrödinger's theory "disgusting," and Schrödinger was "discouraged and repelled" by the lack of visualization in Heisenberg's method. However, Schrödinger, not allowing his emotions to interfere with his scientific endeavours, showed that, in spite of apparent dissimilarities, the two theories are equivalent mathematically. The present discussion follows Schrödinger's wave mechanics because it is less abstract and easier to understand than Heisenberg's matrix mechanics.
Schrödinger's wave mechanics
Schrödinger expressed de Broglie's hypothesis concerning the wave behaviour of matter in a mathematical form that is adaptable to a variety of physical problems without additional arbitrary assumptions. He was guided by a mathematical formulation of optics, in which the straight-line propagation of light rays can be derived from wave motion when the wavelength is small compared to the dimensions of the apparatus employed. In the same way, Schrödinger set out to find a wave equation for matter that would give particle-like propagation when the wavelength becomes comparatively small. According to classical mechanics, if a particle of mass me is subjected to a force such that its potential energy is V(x, y, z) at position x, y, z, then the sum of V(x, y, z) and the kinetic energy p2/2me is equal to a constant, the total energy E of the particle. Thus,
It is assumed that the particle is bound—i.e., confined by the potential to a certain region in space because its energy E is insufficient for it to escape. Since the potential varies with position, two other quantities do also: the momentum and, hence, by extension from the de Broglie relation, the wavelength of the wave. Postulating a wave function Ψ(x, y, z) that varies with position, Schrödinger replaced p in the above energy equation with a differential operator that embodied the de Broglie relation. He then showed that Ψ satisfies the partial differential equation
This is the (time-independent) Schrödinger wave equation, which established quantum mechanics in a widely applicable form. An important advantage of Schrödinger's theory is that no further arbitrary quantum conditions need be postulated. The required quantum results follow from certain reasonable restrictions placed on the wave function—for example, that it should not become infinitely large at large distances from the centre of the potential.
Schrödinger applied his equation to the hydrogen atom, for which the potential function, given by classical electrostatics, is proportional to −e2/r, where −e is the charge on the electron. The nucleus (a proton of charge e) is situated at the origin, and r is the distance from the origin to the position of the electron. Schrödinger solved the equation for this particular potential with straightforward, though not elementary, mathematics. Only certain discrete values of E lead to acceptable functions Ψ. These functions are characterized by a trio of integers n, l, m, termed quantum numbers. The values of E depend only on the integers n (1, 2, 3, etc.) and are identical with those given by the Bohr theory. The quantum numbers l and m are related to the angular momentum of the electron; Square root of√l(l + 1)ℏ is the magnitude of the angular momentum, and mℏ is its component along some physical direction.
The square of the wave function, Ψ2, has a physical interpretation. Schrödinger originally supposed that the electron was spread out in space and that its density at point x, y, z was given by the value of Ψ2 at that point. Almost immediately Born proposed what is now the accepted interpretation—namely, that Ψ2 gives the probability of finding the electron at x, y, z. The distinction between the two interpretations is important. If Ψ2 is small at a particular position, the original interpretation implies that a small fraction of an electron will always be detected there. In Born's interpretation, nothing will be detected there most of the time, but, when something is observed, it will be a whole electron. Thus, the concept of the electron as a point particle moving in a well-defined path around the nucleus is replaced in wave mechanics by clouds that describe the probable locations of electrons in different states.
Electron spin and antiparticles
In 1928 the English physicist Paul A.M. Dirac produced a wave equation for the electron that combined relativity with quantum mechanics. Schrödinger's wave equation does not satisfy the requirements of the special theory of relativity because it is based on a nonrelativistic expression for the kinetic energy (p2/2me). Dirac showed that an electron has an additional quantum number ms. Unlike the first three quantum numbers, ms is not a whole integer and can have only the values +1/2 and −1/2. It corresponds to an additional form of angular momentum ascribed to a spinning motion. (The angular momentum mentioned above is due to the orbital motion of the electron, not its spin.) The concept of spin angular momentum was introduced in 1925 by Samuel A. Goudsmit and George E. Uhlenbeck, two graduate students at the University of Leiden, Neth., to explain the magnetic moment measurements made by Otto Stern and Walther Gerlach of Germany several years earlier. The magnetic moment of a particle is closely related to its angular momentum; if the angular momentum is zero, so is the magnetic moment. Yet Stern and Gerlach had observed a magnetic moment for electrons in silver atoms, which were known to have zero orbital angular momentum. Goudsmit and Uhlenbeck proposed that the observed magnetic moment was attributable to spin angular momentum.
The electron-spin hypothesis not only provided an explanation for the observed magnetic moment but also accounted for many other effects in atomic spectroscopy, including changes in spectral lines in the presence of a magnetic field (Zeeman effect), doublet lines in alkali spectra, and fine structure (close doublets and triplets) in the hydrogen spectrum.
The Dirac equation also predicted additional states of the electron that had not yet been observed. Experimental confirmation was provided in 1932 by the discovery of the positron by the American physicist Carl David Anderson. Every particle described by the Dirac equation has to have a corresponding antiparticle, which differs only in charge. The positron is just such an antiparticle of the negatively charged electron, having the same mass as the latter but a positive charge.
Identical particles and multielectron atoms
Because electrons are identical to (i.e., indistinguishable from) each other, the wave function of an atom with more than one electron must satisfy special conditions. The problem of identical particles does not arise in classical physics, where the objects are large-scale and can always be distinguished, at least in principle. There is no way, however, to differentiate two electrons in the same atom, and the form of the wave function must reflect this fact. The overall wave function Ψ of a system of identical particles depends on the coordinates of all the particles. If the coordinates of two of the particles are interchanged, the wave function must remain unaltered or, at most, undergo a change of sign; the change of sign is permitted because it is Ψ2 that occurs in the physical interpretation of the wave function. If the sign of Ψ remains unchanged, the wave function is said to be symmetric with respect to interchange; if the sign changes, the function is antisymmetric.
The symmetry of the wave function for identical particles is closely related to the spin of the particles. In quantum field theory (see below Quantum electrodynamics), it can be shown that particles with half-integral spin (1/2, 3/2, etc.) have antisymmetric wave functions. They are called fermions after the Italian-born physicist Enrico Fermi. Examples of fermions are electrons, protons, and neutrons, all of which have spin 1/2. Particles with zero or integral spin (e.g., mesons, photons) have symmetric wave functions and are called bosons after the Indian mathematician and physicist Satyendra Nath Bose, who first applied the ideas of symmetry to photons in 1924–25.
The requirement of antisymmetric wave functions for fermions leads to a fundamental result, known as the exclusion principle, first proposed in 1925 by the Austrian physicist Wolfgang Pauli. The exclusion principle states that two fermions in the same system cannot be in the same quantum state. If they were, interchanging the two sets of coordinates would not change the wave function at all, which contradicts the result that the wave function must change sign. Thus, two electrons in the same atom cannot have an identical set of values for the four quantum numbers n, l, m, ms. The exclusion principle forms the basis of many properties of matter, including the periodic classification of the elements, the nature of chemical bonds, and the behaviour of electrons in solids; the last determines in turn whether a solid is a metal, an insulator, or a semiconductor (see atom; matter).
The Schrödinger equation cannot be solved precisely for atoms with more than one electron. The principles of the calculation are well understood, but the problems are complicated by the number of particles and the variety of forces involved. The forces include the electrostatic forces between the nucleus and the electrons and between the electrons themselves, as well as weaker magnetic forces arising from the spin and orbital motions of the electrons. Despite these difficulties, approximation methods introduced by the English physicist Douglas R. Hartree, the Russian physicist Vladimir Fock, and others in the 1920s and 1930s have achieved considerable success. Such schemes start by assuming that each electron moves independently in an average electric field because of the nucleus and the other electrons; i.e., correlations between the positions of the electrons are ignored. Each electron has its own wave function, called an orbital. The overall wave function for all the electrons in the atom satisfies the exclusion principle. Corrections to the calculated energies are then made, which depend on the strengths of the electron-electron correlations and the magnetic forces.
Time-dependent Schrödinger equation
At the same time that Schrödinger proposed his time-independent equation to describe the stationary states, he also proposed a time-dependent equation to describe how a system changes from one state to another. By replacing the energy E in Schrödinger's equation with a time-derivative operator, he generalized his wave equation to determine the time variation of the wave function as well as its spatial variation. The time-dependent Schrödinger equation reads The quantity i is the square root of −1. The function Ψ varies with time t as well as with position x, y, z. For a system with constant energy, E, Ψ has the form where exp stands for the exponential function, and the time-dependent Schrödinger equation reduces to the time-independent form.
The probability of a transition between one atomic stationary state and some other state can be calculated with the aid of the time-dependent Schrödinger equation. For example, an atom may change spontaneously from one state to another state with less energy, emitting the difference in energy as a photon with a frequency given by the Bohr relation. If electromagnetic radiation is applied to a set of atoms and if the frequency of the radiation matches the energy difference between two stationary states, transitions can be stimulated. In a stimulated transition, the energy of the atom may increase—i.e., the atom may absorb a photon from the radiation—or the energy of the atom may decrease, with the emission of a photon, which adds to the energy of the radiation. Such stimulated emission processes form the basic mechanism for the operation of lasers. The probability of a transition from one state to another depends on the values of the l, m, ms quantum numbers of the initial and final states. For most values, the transition probability is effectively zero. However, for certain changes in the quantum numbers, summarized as selection rules, there is a finite probability. For example, according to one important selection rule, the l value changes by unity because photons have a spin of 1. The selection rules for radiation relate to the angular momentum properties of the stationary states. The absorbed or emitted photon has its own angular momentum, and the selection rules reflect the conservation of angular momentum between the atoms and the radiation.
The phenomenon of tunneling, which has no counterpart in classical physics, is an important consequence of quantum mechanics. Consider a particle with energy E in the inner region of a one-dimensional potential well V(x), as shown in Figure 1. (A potential well is a potential that has a lower value in a certain region of space than in the neighbouring regions.) In classical mechanics, if E < V0 (the maximum height of the potential barrier), the particle remains in the well forever; if E > V0, the particle escapes. In quantum mechanics, the situation is not so simple. The particle can escape even if its energy E is below the height of the barrier V0, although the probability of escape is small unless E is close to V0. In that case, the particle may tunnel through the potential barrier and emerge with the same energy E.
The phenomenon of tunneling has many important applications. For example, it describes a type of radioactive decay in which a nucleus emits an alpha particle (a helium nucleus). According to the quantum explanation given independently by George Gamow and by Ronald W. Gurney and Edward Condon in 1928, the alpha particle is confined before the decay by a potential of the shape shown in Figure 1. For a given nuclear species, it is possible to measure the energy E of the emitted alpha particle and the average lifetime τ of the nucleus before decay. The lifetime of the nucleus is a measure of the probability of tunneling through the barrier—the shorter the lifetime, the higher the probability. With plausible assumptions about the general form of the potential function, it is possible to calculate a relationship between τ and E that is applicable to all alpha emitters. This theory, which is borne out by experiment, shows that the probability of tunneling, and hence the value of τ, is extremely sensitive to the value of E. For all known alpha-particle emitters, the value of E varies from about 2 to 8 million electron volts, or MeV (1 MeV = 106 electron volts). Thus, the value of E varies only by a factor of 4, whereas the range of τ is from about 1011 years down to about 10−6 second, a factor of 1024. It would be difficult to account for this sensitivity of τ to the value of E by any theory other than quantum mechanical tunneling.
Axiomatic approach
Although the two Schrödinger equations form an important part of quantum mechanics, it is possible to present the subject in a more general way. Dirac gave an elegant exposition of an axiomatic approach based on observables and states in a classic textbook entitled The Principles of Quantum Mechanics. (The book, published in 1930, is still in print.) An observable is anything that can be measured—energy, position, a component of angular momentum, and so forth. Every observable has a set of states, each state being represented by an algebraic function. With each state is associated a number that gives the result of a measurement of the observable. Consider an observable with N states, denoted by ψ1, ψ2, . . ., ψN, and corresponding measurement values a1, a2, . . ., aN. A physical system—e.g., an atom in a particular state—is represented by a wave function Ψ, which can be expressed as a linear combination, or mixture, of the states of the observable. Thus, the Ψ may be written asFor a given Ψ, the quantities c1, c2, etc., are a set of numbers that can be calculated. In general, the numbers are complex, but, in the present discussion, they are assumed to be real numbers.
The theory postulates, first, that the result of a measurement must be an a-value—i.e., a1, a2, or a3, etc. No other value is possible. Second, before the measurement is made, the probability of obtaining the value a1 is c12, and that of obtaining the value a2 is c22, and so on. If the value obtained is, say, a5, the theory asserts that after the measurement the state of the system is no longer the original Ψ but has changed to ψ5, the state corresponding to a5.
A number of consequences follow from these assertions. First, the result of a measurement cannot be predicted with certainty. Only the probability of a particular result can be predicted, even though the initial state (represented by the function Ψ) is known exactly. Second, identical measurements made on a large number of identical systems, all in the identical state Ψ, will produce different values for the measurements. This is, of course, quite contrary to classical physics and common sense, which say that the same measurement on the same object in the same state must produce the same result. Moreover, according to the theory, not only does the act of measurement change the state of the system, but it does so in an indeterminate way. Sometimes it changes the state to ψ1, sometimes to ψ2, and so forth.
There is an important exception to the above statements. Suppose that, before the measurement is made, the state Ψ happens to be one of the ψs—say, Ψ = ψ3. Then c3 = 1 and all the other cs are zero. This means that, before the measurement is made, the probability of obtaining the value a3 is unity and the probability of obtaining any other value of a is zero. In other words, in this particular case, the result of the measurement can be predicted with certainty. Moreover, after the measurement is made, the state will be ψ3, the same as it was before. Thus, in this particular case, measurement does not disturb the system. Whatever the initial state of the system, two measurements made in rapid succession (so that the change in the wave function given by the time-dependent Schrödinger equation is negligible) produce the same result.
The value of one observable can be determined by a single measurement. The value of two observables for a given system may be known at the same time, provided that the two observables have the same set of state functions ψ1, ψ2, . . ., ψN. In this case, measuring the first observable results in a state function that is one of the ψs. Because this is also a state function of the second observable, the result of measuring the latter can be predicted with certainty. Thus the values of both observables are known. (Although the ψs are the same for the two observables, the two sets of a values are, in general, different.) The two observables can be measured repeatedly in any sequence. After the first measurement, none of the measurements disturbs the system, and a unique pair of values for the two observables is obtained.
Incompatible observables
The measurement of two observables with different sets of state functions is a quite different situation. Measurement of one observable gives a certain result. The state function after the measurement is, as always, one of the states of that observable; however, it is not a state function for the second observable. Measuring the second observable disturbs the system, and the state of the system is no longer one of the states of the first observable. In general, measuring the first observable again does not produce the same result as the first time. To sum up, both quantities cannot be known at the same time, and the two observables are said to be incompatible.
A specific example of this behaviour is the measurement of the component of angular momentum along two mutually perpendicular directions. The Stern-Gerlach experiment mentioned above involved measuring the angular momentum of a silver atom in the ground state. In reconstructing this experiment, a beam of silver atoms is passed between the poles of a magnet. The poles are shaped so that the magnetic field varies greatly in strength over a very small distance (Figure 2). The apparatus determines the ms quantum number, which can be +1/2 or −1/2. No other values are obtained. Thus in this case the observable has only two states—i.e., N = 2. The inhomogeneous magnetic field produces a force on the silver atoms in a direction that depends on the spin state of the atoms. The result is shown schematically in Figure 3. A beam of silver atoms is passed through magnet A. The atoms in the state with ms = +1/2 are deflected upward and emerge as beam 1, while those with ms = −1/2 are deflected downward and emerge as beam 2. If the direction of the magnetic field is the x-axis, the apparatus measures Sx, which is the x-component of spin angular momentum. The atoms in beam 1 have Sx = +ℏ/2 while those in beam 2 have Sx = −ℏ/2. In a classical picture, these two states represent atoms spinning about the direction of the x-axis with opposite senses of rotation.
The y-component of spin angular momentum Sy also can have only the values +ℏ/2 and −ℏ/2; however, the two states of Sy are not the same as for Sx. In fact, each of the states of Sx is an equal mixture of the states for Sy, and conversely. Again, the two Sy states may be pictured as representing atoms with opposite senses of rotation about the y-axis. These classical pictures of quantum states are helpful, but only up to a certain point. For example, quantum theory says that each of the states corresponding to spin about the x-axis is a superposition of the two states with spin about the y-axis. There is no way to visualize this; it has absolutely no classical counterpart. One simply has to accept the result as a consequence of the axioms of the theory. Suppose that, as in Figure 3, the atoms in beam 1 are passed into a second magnet B, which has a magnetic field along the y-axis perpendicular to x. The atoms emerge from B and go in equal numbers through its two output channels. Classical theory says that the two magnets together have measured both the x- and y-components of spin angular momentum and that the atoms in beam 3 have Sx = +ℏ/2, Sy = +ℏ/2, while those in beam 4 have Sx = +ℏ/2, Sy = −ℏ/2. However, classical theory is wrong, because if beam 3 is put through still another magnet C, with its magnetic field along x, the atoms divide equally into beams 5 and 6 instead of emerging as a single beam 5 (as they would if they had Sx = +ℏ/2). Thus, the correct statement is that the beam entering B has Sx = +ℏ/2 and is composed of an equal mixture of the states Sy = +ℏ/2 and Sy = −ℏ/2—i.e., the x-component of angular momentum is known but the y-component is not. Correspondingly, beam 3 leaving B has Sy = +ℏ/2 and is an equal mixture of the states Sx = +ℏ/2 and Sx = −ℏ/2; the y-component of angular momentum is known but the x-component is not. The information about Sx is lost because of the disturbance caused by magnet B in the measurement of Sy.
Heisenberg uncertainty principle
The observables discussed so far have had discrete sets of experimental values. For example, the values of the energy of a bound system are always discrete, and angular momentum components have values that take the form mℏ, where m is either an integer or a half-integer, positive or negative. On the other hand, the position of a particle or the linear momentum of a free particle can take continuous values in both quantum and classical theory. The mathematics of observables with a continuous spectrum of measured values is somewhat more complicated than for the discrete case but presents no problems of principle. An observable with a continuous spectrum of measured values has an infinite number of state functions. The state function Ψ of the system is still regarded as a combination of the state functions of the observable, but the sum in equation (10) must be replaced by an integral.
Measurements can be made of position x of a particle and the x-component of its linear momentum, denoted by px. These two observables are incompatible because they have different state functions. The phenomenon of diffraction noted above illustrates the impossibility of measuring position and momentum simultaneously and precisely. If a parallel monochromatic light beam passes through a slit (Figure 4A), its intensity varies with direction, as shown in Figure 4B. The light has zero intensity in certain directions. Wave theory shows that the first zero occurs at an angle θ0, given by sin θ0 = λ/b, where λ is the wavelength of the light and b is the width of the slit. If the width of the slit is reduced, θ0 increases—i.e., the diffracted light is more spread out. Thus, θ0 measures the spread of the beam.
The experiment can be repeated with a stream of electrons instead of a beam of light. According to de Broglie, electrons have wavelike properties; therefore, the beam of electrons emerging from the slit should widen and spread out like a beam of light waves. This has been observed in experiments. If the electrons have velocity u in the forward direction (i.e., the y-direction in Figure 4A), their (linear) momentum is p = meu. Consider px, the component of momentum in the x-direction. After the electrons have passed through the aperture, the spread in their directions results in an uncertainty in px by an amount where λ is the wavelength of the electrons and, according to the de Broglie formula, equals h/p. Thus, Δpx ≈ h/b. Exactly where an electron passed through the slit is unknown; it is only certain that an electron went through somewhere. Therefore, immediately after an electron goes through, the uncertainty in its x-position is Δx ≈ b/2. Thus, the product of the uncertainties is of the order of ℏ. More exact analysis shows that the product has a lower limit, given by
This is the well-known Heisenberg uncertainty principle for position and momentum. It states that there is a limit to the precision with which the position and the momentum of an object can be measured at the same time. Depending on the experimental conditions, either quantity can be measured as precisely as desired (at least in principle), but the more precisely one of the quantities is measured, the less precisely the other is known.
The uncertainty principle is significant only on the atomic scale because of the small value of h in everyday units. If the position of a macroscopic object with a mass of, say, one gram is measured with a precision of 10−6 metre, the uncertainty principle states that its velocity cannot be measured to better than about 10−25 metre per second. Such a limitation is hardly worrisome. However, if an electron is located in an atom about 10−10 metre across, the principle gives a minimum uncertainty in the velocity of about 106 metre per second.
The above reasoning leading to the uncertainty principle is based on the wave-particle duality of the electron. When Heisenberg first propounded the principle in 1927 his reasoning was based, however, on the wave-particle duality of the photon. He considered the process of measuring the position of an electron by observing it in a microscope. Diffraction effects due to the wave nature of light result in a blurring of the image; the resulting uncertainty in the position of the electron is approximately equal to the wavelength of the light. To reduce this uncertainty, it is necessary to use light of shorter wavelength—e.g., gamma rays. However, in producing an image of the electron, the gamma-ray photon bounces off the electron, giving the Compton effect (see above Early developments: Scattering of X-rays). As a result of the collision, the electron recoils in a statistically random way. The resulting uncertainty in the momentum of the electron is proportional to the momentum of the photon, which is inversely proportional to the wavelength of the photon. So it is again the case that increased precision in knowledge of the position of the electron is gained only at the expense of decreased precision in knowledge of its momentum. A detailed calculation of the process yields the same result as before (equation [12]). Heisenberg's reasoning brings out clearly the fact that the smaller the particle being observed, the more significant is the uncertainty principle. When a large body is observed, photons still bounce off it and change its momentum, but, considered as a fraction of the initial momentum of the body, the change is insignificant.
The Schrödinger and Dirac theories give a precise value for the energy of each stationary state, but in reality the states do not have a precise energy. The only exception is in the ground (lowest energy) state. Instead, the energies of the states are spread over a small range. The spread arises from the fact that, because the electron can make a transition to another state, the initial state has a finite lifetime. The transition is a random process, and so different atoms in the same state have different lifetimes. If the mean lifetime is denoted as τ, the theory shows that the energy of the initial state has a spread of energy ΔE, given by
This energy spread is manifested in a spread in the frequencies of emitted radiation. Therefore, the spectral lines are not infinitely sharp. (Some experimental factors can also broaden a line, but their effects can be reduced; however, the present effect, known as natural broadening, is fundamental and cannot be reduced.) Equation (13) is another type of Heisenberg uncertainty relation; generally, if a measurement with duration τ is made of the energy in a system, the measurement disturbs the system, causing the energy to be uncertain by an amount ΔE, the magnitude of which is given by the above equation.
Quantum electrodynamics
The application of quantum theory to the interaction between electrons and radiation requires a quantum treatment of Maxwell's field equations, which are the foundations of electromagnetism, and the relativistic theory of the electron formulated by Dirac (see above Electron spin and antiparticles). The resulting quantum field theory is known as quantum electrodynamics, or QED.
QED accounts for the behaviour and interactions of electrons, positrons, and photons. It deals with processes involving the creation of material particles from electromagnetic energy and with the converse processes in which a material particle and its antiparticle annihilate each other and produce energy. Initially the theory was beset with formidable mathematical difficulties, because the calculated values of quantities such as the charge and mass of the electron proved to be infinite. However, an ingenious set of techniques developed (in the late 1940s) by Hans Bethe, Julian S. Schwinger, Tomonaga Shin'ichirō, Richard P. Feynman, and others dealt systematically with the infinities to obtain finite values of the physical quantities. Their method is known as renormalization. The theory has provided some remarkably accurate predictions.
According to the Dirac theory, two particular states in hydrogen with different quantum numbers have the same energy. QED, however, predicts a small difference in their energies; the difference may be determined by measuring the frequency of the electromagnetic radiation that produces transitions between the two states. This effect was first measured by Willis E. Lamb, Jr., and Robert Retherford in 1947. Its physical origin lies in the interaction of the electron with the random fluctuations in the surrounding electromagnetic field. These fluctuations, which exist even in the absence of an applied field, are a quantum phenomenon. The accuracy of experiment and theory in this area may be gauged by two recent values for the separation of the two states, expressed in terms of the frequency of the radiation that produces the transitions:
An even more spectacular example of the success of QED is provided by the value for μe, the magnetic dipole moment of the free electron. Because the electron is spinning and has electric charge, it behaves like a tiny magnet, the strength of which is expressed by the value of μe. According to the Dirac theory, μe is exactly equal to μB = eℏ/2me, a quantity known as the Bohr magneton; however, QED predicts that μe = (1 + a)μB, where a is a small number, approximately 1/860. Again, the physical origin of the QED correction is the interaction of the electron with random oscillations in the surrounding electromagnetic field. The best experimental determination of μe involves measuring not the quantity itself but the small correction term μe − μB. This greatly enhances the sensitivity of the experiment. The most recent results for the value of a are
Since a itself represents a small correction term, the magnetic dipole moment of the electron is measured with an accuracy of about one part in 1011. One of the most precisely determined quantities in physics, the magnetic dipole moment of the electron can be calculated correctly from quantum theory to within about one part in 1010.


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Eco Friendly Paintball (bottle of 500)
Eco Friendly Paintball (bottle of 500)
"Go Green" with RAP4 Eco Friendly Paintball is soybean-based, environmentally friendly paint...with bright fill at an unbeatable price! Comes in clear plastic reusable bottle with pop-up carry handle. Reuse the bottle to store your marker parts, tools, squeegees and everything else
Completely biodegradable, non-permanent and environmentally safe, the RAP4 Eco Friendly Paintball is safe for back-country fields and fulltime scenario fields alike. The splats fade in direct sunlight, and a good rain washes them away, where the organic material used in the shell and fill gets absorbed into the ground without hurting local plants, animals, or water sources.
The RAP4 Eco Friendly Paintball shells are designed to shatter upon impacting your opponent, meaning more breaks on target. Part of this high-performance design is achieved through the use of soybean oil.
Key Features:
- Eco Friendly
- Environmentally Safe
- Low Cost
- Works with all .68 cal paintball markers
- High-performance
- Comes in bottle of 500 balls

subset: commoncrawl


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Why iPhone Users Hate Mobile WiFi Slightly Less Than Android Users Do
Apr 12, 2012 5:00 AM PT
A cool study caught my attention recently. It says that iPhones have significantly higher rates of WiFi utilization than Android phones in the U.S. and the UK. I immediately found that point weird, because after all, most Android smartphones also come with contracts that require users to pay for a data plan. These plans are usually fairly comparable to the iPhone data plans, which means they aren't cheap.
And yet, comScore found that 71 percent of all unique iPhones used both mobile and WiFi networks to connect to the Internet, while only 32 percent of unique Android mobile phones used both types of connections in the U.S. The UK had higher WiFi utilization rates but a similar gap. Furthermore, in the U.S., 29 percent of iPhone users browsed only via mobile networks while 68 percent of Android users browsed only via mobile networks. This means that these users are intentionally not using WiFi. Whoah. They can't all be rich and willing to pay for big data plans, and they can't all be data sippers.
So why is there more WiFi use on iPhones than on Android?
Some Android phones might be able to tap into next-generation high-speed mobile networks like 4G LTE, but there are plenty of Android phones that don't. And I don't think it has anything to do with free WiFi access like all those points offered by AT&T to its customers around the country.
No, I think the difference can be explained by two key things: 1) the iPhone's massive popularity, and 2) the iPhone's slightly better ability to connect to WiFi. (But there's more to this story, as I'm sure you suspect.)
Massive Popularity, Thank You Very Much
Because the iPhone has so many users, it gets the lion's share of the press coverage, and because there's so much more press coverage, there's tons of information about how the major cellular service providers are offering data plans. This clearly raises the knowledge of data plans and how they work. Then add in the news about AT&T choking its so-called "unlimited" iPhone data users, as well as new iPad users blasting through their cellular data plans in a single day, and the cost of using only cellular data becomes saturated in the mind of the iPhone owner.
In this case, knowledge doesn't equal power; knowledge equals WiFi.
My Kindle Fire Sucks at WiFi!
I've got a love-hate relationship with my Kindle Fire. When it works great, I love it. I get all sorts of Amazon Prime movies and TV shows free to stream, just like Netflix. And then, just when I'm all set to resume watching a TV show series, the Fire starts thinking ... and I wait for the stream to load and play ... and wait ... and then the Fire tells me there's something wrong with my home network or some such nonsense. So I look at my iPhone, and it's getting a signal, and I know WiFi is working, and yet the Kindle Fire has gagged somehow. Just now, right this minute as I'm typing this, my Kindle Fire has a pop-up telling me, "No Internet Connection: A WiFi network connection is required to complete this task. Please connect to a WiFi network."
My Kindle Fire is eight feet away from my WiFi router. A Dell PC has a WiFi connection just fine, and it pretty much never fails. My iPhone is nine feet away, and it has a WiFi connection. The Kindle Fire itself shows that the WiFi connection is active. So what gives? Maybe my WiFi router isn't that fantastic. Maybe it's like an old dog: hard of hearing, stubborn and hard to communicate with. So maybe some of the problems with WiFi use we can blame on weird hardware and software glitches, as well as the "magic" failing to consistently send information wirelessly around a spinning rock in space.
But what to do with the Kindle Fire? Do I reboot the thing? Nah. That takes time, and the clock on my free time is ticking. So I go searching for the WiFi setting. I hit the "gear" icon at the top right, find WiFi in the list, and physically tell the Fire to look again because I know my network is right here, all around us. It does. I'm reconnected. I can go back to browsing. Except, sometimes this doesn't work because a) I give up and pull my iPhone out of my pocket, or b) I reboot anyway.
What does this tell me? It tells me that an Android device designed only for WiFi isn't easy to always connect to WiFi, and overall, my home WiFi network is pretty stable. Guest MacBooks, PCs, iPods, an Xbox 360 and even the occasional Zune connect to it all the time and remain stable. So maybe there's some fine-tuning needed in how Android handles WiFi connections, yes?
Probably, but that's a big blanket statement. There are lots of versions of Android and lots of different hardware. Yet if you've been following this issue out and around the Web, you'll likely see some blog readers and forum commenters saying things like, "my Android phone fails to stay connected to WiFi, causing apps to fail," or "with WiFi on I get terrible battery life."
Speaking of battery life, what's worse than paying too much for data?
Looking at a dead smartphone in your hand.
So plenty of us just turn off anything that might make our smartphones think too hard and drain battery.
There is another possible point here, too, and that is that Android owners are smarter and more technically savvy than iPhone owners when it comes to security -- on average. In that case they might be less likely to simply connect to any free WiFi network they happen to stumble into for fear of some malicious activity.
What, No AirPlay?
There's another incremental factor at work here, and that's the Apple ecosystem. If iPhone owners are more likely to browse and download apps via the App Store, they will more likely do it via WiFi because they will be able to download any app they want, regardless of size. Plus, when they are at home, if they have an Apple TV, they know they can control it remotely via their iPhone via WiFi, as well as instantly AirPlay content from their iPhone to the HDTV connected to the Apple TV. (This, by the way, rocks after you come home after shooting some video clips and want to share them.)
Not enough? There's more! How about iMessage? If your iPhone is connected to WiFi, iPod, iPad and Mac users can all send you iMessages without needing to use a cellular service provider's text messaging service. Granted, iMessage is still fairly new. But FaceTime is not new, and FaceTime needs WiFi to work. For any iPhone-toting user, there's a darn good chance they will at least have WiFi enabled when they are at home so they can FaceTime with family and friends. Android users don't have something as ubiquitous as FaceTime when it comes to video calling. They can do it, but they can't be sure that their friends and family all have the right apps and the right accounts. It takes far more coordination.
Still, It All Sucks!
Meanwhile, I can't say that I'm overly impressed with the iPhone's ability to seamlessly switch from cellular data to WiFi data. Yes, it's pretty good, and it might be better than the competition, but as a consumer, I don't really care. I'm just irritated as I look at a text message that seemed to be delivered to a buddy ... and I wait for his response and wait and wait and then find out it wasn't delivered, or that my iPhone tried to deliver it via WiFi as an iMessage, but maybe my buddy was moving out of a WiFi area, so now there's a lag time before something, somewhere, decides that maybe this message should be sent as a text message via AT&T instead. What happens here? You get a laggy response as you try to text with other iPhone users who have iMessage set up with WiFi on and/or have aren't staying connected to WiFi.
And still, there's more. Occasionally my iPhone 4 (and others) will act as if they can't connect to the Internet via Safari when browsing. What then? Sometimes you can turn off WiFi and turn it back on and that will reconnect you to the world. But not always. Often enough, I growl then simply turn off WiFi altogether and browse via my AT&T 3G connection. Sounds a little like some Android users, no?
And it's not just me. Some owners of the brand new iPad are experiencing WiFi connectivity issues. One discussion on the Apple website has hundreds of posts on the topic. And this is a brand new device from the creators of devices that must work flawlessly for consumers.
As near as I can tell, clearly something is still wrong with WiFi ... and I thought this was an old technology and that most of the kinks have finally been ironed out.


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Inexact title. See the list below. We don't have an article named Main/WorldsDumbest, exactly. We do have:
- Characters/Worlds Dumbest
- Fridge/Worlds Dumbest
- Funny/Worlds Dumbest
- Headscratchers/Worlds Dumbest
- Heartwarming/Worlds Dumbest
- Series/Worlds Dumbest
- Trivia/Worlds Dumbest
- YMMV/Worlds Dumbest
If you meant one of those, just click and go. If you want to start a Main/WorldsDumbest page, just click the edit button above. Be careful, though, the only things that go in the Main namespace are tropes and should be created through the YKTTW system. Don't put in redirects for shows, books, etc.. Use the right namespace for those.


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[Funeral Program for Mary E. Washington, February 22, 1962]
Description: Funeral program for Mrs. Mary E. Washington. The funeral was held February 22, 1962 at St. Paul Methodist Church, officiated by Rev. J. H. Carruthers. Funeral arrangements were made through the Lewis Funeral Home, and she was buried in Lampasas Cemetery in Lampasas, Texas.
Date: February 22, 1962
Item Type: Refine your search to only Pamphlet
Partner: San Antonio Public Library


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Installing a 1928 – 31 Model A Ford roadster door latch in a 1929 Ford Roadster
Well, it's late Sunday afternoon and time to add another post to 1929fordhotrod.com . This weekend I decided to stay home and work on my 1929 Ford roadster. I even helped my wife Janis make some salsa and relish using produce from our garden. About now, I find that I am loosing interest in the outdoor car shows, cruise in's, and swap meets. The feeling for working in the shop is starting to become a strong one, and I guess that is a good thing. It will start to get cold outside and snow is not far off here in South-western Ontario Canada. I find that I tend to get more shop time throughout the late fall, winter, and early spring. During the warm weather, outside activities need to be taken advantage of. These are some of distractions that take hold of many custom car builders. Remember, you need to maintain focus and desire to finish any project.
The topic today will be on how to install a 1928 – 29 open car / roadster inside door latch. The original1928 Ford Model A roadster did not have an outside handle. I tend to like nice clean lines on the outside of custom cars, so I decided to use the 1928 Ford Model A inside door latch on my 1929 Ford Roadster. Even when it came time to paint my 1987 Corvette convertible, I decided to have the outside door handles shaved off and use an Auto Loc system to open the doors from the outside. Back in the mid 1970's I shaved the handles off my 1970 Chevrolet Impala using Mercedes Benz Unimog starter solenoids to open the doors. So for me it makes sense not to have outside door handles on a car. It must be in my blood or DNA, so no outside door handles for me!!
I remember when I first received the reproduction door latches for my 1929 Ford roadster wondering how they would fit into the doors. At the time I did not realize that part of the latch is tucked up behind the inside door panel. I was ready to start cutting and modifying the latches so they would fit in the door. Fortunately, a little voice in my head said to hold on and let's figure this out before performing surgery on the latches. After, looking at a friends 1929 Ford pickup, I realize how everything would go together. It's so simple!!
Here is what I used:
1 – 1928 Ford Door Latch – right side – A-35655-AR
1 – 1928 Ford Door Latch – left side – A-35655-AL
2- Open Car Striker Plates – 1928 – 31 – A-375505
4 – 0.25" x 20 x 0.75" stainless steel bevelled Philips head bolts with nuts and washers
4 – 10 – 32 x 0.5" stainless steel bevelled Philips head screws
4 – 10 – 32 x 0.5" stainless steel bevelled Philips head screws (used on the inside panel of the door)
4 – 10 – 32 x 0.375" stainless steel bevelled Philips head screws (used on the outside edge of the door)
Below is a short video showing how I installed the door latch and striker plate on the passenger side door of my 1929 Ford roadster. The door is a steel door from Brookville Roadsters in Ohio, USA.
Fast Tube by Casper
Tags: 1928 -31 Model A Ford striker plate, 1928 Model A Ford inside door latch, 1929 Model A Ford inside door latch, DIY video on installing a Model A Ford inside door latch, installing a door latch in the 1929 Ford Roadster


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Staff writer
When Reno Penner of rural Hillsboro says the milo crop looks pretty dismal this year, he knows what he is talking about. He has grown milo and wheat for 59 years, starting at the age of 17 when his father passed away and he took over the family farm. A dry land farmer, he knows a bit about raising milo and wheat.
"It looks worse this year than ever before, even worse than last year," Penner said. "I think it was the heat more than the drought that really put the milo in bad shape."
Penner, who retired three years ago and leases out his 380 acres of cropland, said farmers who planted early and have something ready to harvest now might get something, but those who put their seed in late might not get anything.
"One of my tenants cut some already that gave 30 bushels per acre," he said. "But that was planted real early, the rest will be lucky to make 5 (bushels per acre)."
Penner said that while many farmers switched to growing corn and beans instead of milo in the past few years because of higher payouts, his land has always done well with milo.
"Corn and beans needs a lot of rain," he said. "Milo is just a good stable dry land crop. Our best year, I think in 2010, we got 100 bushels per acre."
Of course, this year does not look to be that good for most milo producers. Penner said many farmers were cutting their milo for silage as it just did not head out. Fields that did head out did so very unevenly, so some spots have heads ready to harvest, yet the next row over is green and immature.
"I've heard some appraised for insurance purposes making only 5 bushels per acre," he said. "I've got some here we won't even harvest. It just isn't worth the gas or diesel to get it done."
Penner said milo not already harvested would likely not see a combine until after a good frost.
"It's better to wait now," he said. "The later the better; some of it is still so green. After a killing frost the moisture will be lower at least."
Because of the scarcity of feed this year, Penner said milo prices would be good, and most likely the grain produced in Marion County would stay local to be used for cattle and hogs.
"Beans aren't going to do as well this year either," he said. "Wheat was good. We had a bumper crop there, but the corn, beans, and milo — that is a mess. It's going to be hard for the highly-leveraged farmers to make it this year."


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Communitarianism, social and political philosophy that emphasizes the importance of community in the functioning of political life, in the analysis and evaluation of political institutions, and in understanding human identity and well-being. It arose in the 1980s as a critique of two prominent philosophical schools: contemporary liberalism, which seeks to protect and enhance personal autonomy and individual rights in part through the activity of government, and libertarianism, a form of liberalism (sometimes called "classical liberalism") that aims to protect individual rights—especially the rights to liberty and property—through strict limits on governmental power.
There are strong communitarian elements in many modern and historical political and religious belief systems—e.g., in the Hebrew Bible (Old Testament) and the Christian New Testament (Acts 4:32: "Now the whole group of those who believed were of one heart and soul, and no one claimed private ownership of any possessions, but everything they owned was held in common"); in the early Islamic concept of shūrā ("consultation"); in Confucianism; in Roman Catholic social thought (the papal encyclical Rerum Novarum [1891]); in moderate conservatism ("To be attached to the subdivision, to love the little platoon we belong to in society, is the first principle…of public affections"—Edmund Burke); and in social democracy, especially Fabianism. Communitarian ideas have also played a significant role in public life through their incorporation into the electoral platforms and policies of Western political leaders of the late 20th and early 21st centuries, including British Prime Minister Tony Blair, Dutch Prime Minister Jan Peter Balkenende, and U.S. Presidents Bill Clinton and Barack Obama.
Varieties of communitarianism
The term communitarian was coined in 1841 by John Goodwyn Barmby, a leader of the British Chartist movement, who used it to refer to utopian socialists and others who experimented with unusual communal lifestyles. It was rarely used in the generations that followed.
It was not until the 1980s that the term gained currency through its association with the work of a small group of mostly American political philosophers who argued for the importance of the common good in opposition to contemporary liberals and libertarians, who emphasized the good for individuals, particularly including personal autonomy and individual rights. The Canadian philosopher Charles Taylor and the American political theorist Michael Sandel were among the most prominent scholars of this brand of communitarianism. Other political theorists and philosophers who were often cited as communitarians in this sense, or whose work exhibited elements of such communitarian thinking, included Shlomo Avineri, Seyla Benhabib, Avner de-Shalit, Jean Bethke Elshtain, Amitai Etzioni, William A. Galston, Alasdair MacIntyre, Philip Selznick, and Michael Walzer.
During the same period, students of East Asian politics and society used communitarianism to describe the social thinking within authoritarian societies such as China, Singapore, and Malaysia, which extolled social obligations and the importance of the common good and accorded much less weight to autonomy and rights. Indeed, these societies viewed individuals as more or less interchangeable cells who find meaning in their contribution to the social whole rather than as free agents. Scholars of this kind of communitarianism included the American political theorist Russell A. Fox and the Singaporean diplomat Bilahari Kausikan.
In 1990 Etzioni and Galston founded a third school, known as "responsive" communitarianism. Its members formulated a platform based on their shared political principles, and the ideas in it were eventually elaborated in academic and popular books and periodicals, gaining thereby a measure of political currency, mainly in the West. The main thesis of responsive communitarianism is that people face two major sources of normativity, that of the common good and that of autonomy and rights, neither of which in principle should take precedence over the other.
The common good versus individual rights
Whereas the classical liberalism of the Enlightenment can be viewed as a reaction to centuries of authoritarianism, oppressive government, overbearing communities, and rigid dogma, modern communitarianism can be considered a reaction to excessive individualism, understood by communitarians as an undue emphasis on individual rights, leading people to become selfish or egocentric. Excessive individualism was discussed in an oft-cited communitarian work, Habits of the Heart: Individualism and Commitment in American Life (1985), by the American sociologist Robert Neelly Bellah, who observed that by the early 1980s most Americans had become self-centred. Increasing prosperity from the 1950s, among other factors, had contributed to a decline in respect for traditional authority and institutions, such as marriage, and fostered a kind of materialistic hedonism, according to many communitarians. Earlier sociologists such as Ferdinand Tönnies and Émile Durkheim had discussed such antisocial tendencies in the context of modernization, which they viewed as a historical transition from oppressive but nurturing communities (Gemeinschaft) to liberating but impersonal societies (Gesellschaft). They warned of the dangers of anomie (normlessness) and alienation in modern societies composed of atomized individuals who had gained their liberty but lost their social moorings. Essentially the theses of Tönnies and Durkheim were supported with contemporary social-scientific data in Bowling Alone: The Collapse and Revival of American Community (2000), by the American political scientist Robert Putnam.
The close relation between the individual and the community was discussed on a theoretical level by Sandel and Taylor, among other academic communitarians, in their criticisms of philosophical liberalism, including especially the work of the American liberal theorist John Rawls and that of the German Enlightenment philosopher Immanuel Kant. They argued that contemporary liberalism and libertarianism presuppose an incoherent notion of the individual as existing outside and apart from society rather than embedded within it. To the contrary, they argued, there are no generic individuals but rather only Germans or Russians, Berliners or Muscovites, or members of some other particularistic community. Because individual identity is partly constituted (or "constructed") by culture and social relations, there is no coherent way of formulating individual rights or interests in abstraction from social contexts. In particular, according to these communitarians, there is no point in attempting to found a theory of justice on principles that individuals would choose in a hypothetical state of ignorance of their social, economic, and historical circumstances (from behind a Rawlsian "veil of ignorance"), because such individuals cannot exist, even in principle.
Liberal scholars argued that this line of criticism is overstated or misconceived. Despite its emphasis on autonomy and rights, they contended, contemporary liberalism is not incompatible with the notion of a socially embedded self. Indeed, Rawls himself, in his foundational work A Theory of Justice (1971), recognized the importance of what he called "social unions" and asserted that "only in a social union is the individual complete." Thus, according to liberals, the communitarian critique does not rebut the core of liberal theory but merely serves as a corrective to "stronger" liberal doctrines such as libertarianism, which does embrace an atomized notion of individual identity (see below A synthesis: Rights and responsibilities).
Academic communitarians also drew upon Aristotle and the German idealist philosopher Georg Friedrich Wilhelm Hegel to argue that some conception of the good must be formulated on the social level and that the community cannot be a normative-neutral realm. Unless there is a social formulation of the good, there can be no normative foundation upon which to draw to settle conflicts of value between different individuals and groups. Such an overriding good (e.g., the national well-being) enables persons with different moral outlooks or ideological backgrounds to find principled (rather than merely prudential) common ground.
Liberals and libertarians responded by characterizing the communitarian position as akin to East Asian authoritarian communitarianism. They also argued that social formulations of the good—and the obligations they generate, which individuals must then discharge—can sometimes be oppressive. Some libertarians cited taxes and mandatory vaccinations as examples of such obligations.
A synthesis: Rights and responsibilities
Responsive communitarianism may be considered a synthesis of both liberal and academic-communitarian concerns. Sandel and Taylor in effect held that many forms of philosophical liberalism, especially libertarianism, overemphasize autonomy and rights at the expense of the common good. However, in doing so, they were less than clear about the standing of individual rights, including human rights. Indeed, Alasdair MacIntyre asserted that rights were merely figments of the imagination, like unicorns. Responsive communitarians attempted to bridge this divide. In their platform and in their academic works, they posited that all societies must heed the moral claims of two core values, the common good and autonomy and rights. They also held that, because actual societies tend to tilt toward one core value or the other, they need to be pulled back toward the centre. Thus Japan, in their view, was strongly dedicated to the common good but insufficiently committed to the rights of women, ethnic minorities, and the disabled, while the United States during the presidential administration of Ronald Reagan (1981–89) and the United Kingdom during the prime ministership of Margaret Thatcher (1979–90) attached undue importance to individual rights. The early prime ministership of Tony Blair demonstrated a concern for the common good through its policies of devolution and the "stakeholder society" (the idea that businesses should be responsive to workers, consumers, and other groups whose interests they affect), as did the early administration of George W. Bush through its dedication to "compassionate conservatism." After the 2001 September 11 attacks, however, the common good in the United States was increasingly identified with national security, and some individual rights (e.g., the right to habeas corpus) were curtailed.
In the same vein, responsive communitarians also warned against excessively expansive definitions of rights and championed modern communities in which people find both a rich web of social relations and considerable degrees of freedom. In the early 21st century, responsive communitarians believed that the Scandinavian countries had achieved the best balance, though even there some individual rights were being curtailed for security reasons and in response to anti-immigrant sentiment.
Policy implications
Responsive communitarianism developed criteria for the formulation of policies that would enable societies to cope with the potential conflicts between the common good and individual rights, including in areas such as public health versus individual privacy and national security versus individual liberty. These criteria, which must be applied jointly, included the following:
- 1. No change is justified in governing public policies and norms unless society encounters serious challenges, because these kinds of changes exact considerable societal costs. (The September 11 attacks constituted such a challenge.)
- 2. Limitations on rights can be considered only if there are significant gains to the common good—what the U.S. courts refer to as a "compelling interest"—and if the intrusion is as limited as possible.
- 3. Adverse side effects that result from policy changes must be treated, above all, by introducing stronger mechanisms of accountability and oversight.
An example of the application of these criteria can be seen in the debate in the United States concerning whether to improve public health by testing newborn babies for HIV. According to communitarians, such tests would be justified if: (1) they saved lives (an infant infected with HIV has a strong chance of not developing AIDS if it is not breastfed and is treated with the drug AZT), (2) the intrusion were limited to testing blood that would be collected anyway, and (3) the adverse side effects could be limited by regulations that ban the disclosure of test results to nonmedical personnel.
Socially constructed preferences
The communitarian approach challenges the liberal view—reflected in many social sciences, especially neoclassical economics and the study of law—that the political and economic preferences of individuals should be respected and that their aggregation should guide the governance of the polity (through voting) and the economy (through the influence of consumer spending on the production and distribution of consumer goods). It is fully legitimate, for example, for public authorities to urge people to resist the appeals of political extremists or to encourage them to save more of their money. Communitarianism also challenges the libertarian position that it is paternalistic to interfere with individual choices based on personal preferences. In keeping with their view concerning the social constitution of individual identity, communitarians argue that personal preferences are to a significant extent not autonomous but rather a reflection of the larger culture, aspects of which can be heavily influenced by nonrational forces such as commercial advertising. Hence, public efforts to influence such preferences in beneficial ways, say in campaigns against smoking and obesity, do not undermine personal autonomy and are not a violation of human dignity.
The third sector
Communitarianism adds a major element to a centuries-old debate in the West over the proper roles of government on the one hand and the market on the other. Communitarians argue that attention also must be paid to the role of civil society, including families, local and nonresidential communities, voluntary associations, schools, places of worship, foundations, and nonprofit corporations. It stresses that much of the behaviour that must be regulated in any society, as well as the factors that encourage people to discharge their social responsibilities (e.g., caring for children), are influenced by this third sector. Communitarians point to the importance of social norms and informal social controls in fostering pro-social conduct and in providing the moral foundations (e.g., trust) required for the successful operation of both governments and markets. The American political journalist Jonathan Rauch introduced the term "soft communitarianism" to refer to communitarianism that focuses on the role of civil society, in contrast to "hard," East Asian communitarianism, which views the state as the primary social agent.
Cultural relativism and the global community
Because communitarians favour communal formulations of the good, which are necessarily particular to each community, they are vulnerable to the charge of ethical relativism, or to the claim that there is no absolute good but only different goods for different communities, cultures, or societies. Walzer adopted a clearly relativistic position in his book Spheres of Justice (1983), in which he asserted that the caste system is "good" by the standards of traditional Indian society. Critics argued, however, that his position was untenable. One simply needs to consider a community that champions honour killings, lynchings, or book burnings to realize that communities should not be the ultimate arbiters of that which is good. While acknowledging that different communities may have different ultimate values, Taylor argued—as did Rawls—that an "overlapping consensus" on specific norms and policies is still possible, though different communities may have different reasons for believing that a given norm or policy is right. In the United States, for example, abortion-rights and antiabortion activists have worked together to make adoption easier and to improve the quality of day-care centres. According to a much more-contested argument, advanced by the American scholar of religion Don Browning, there are some substantive universal values, such as human rights and the integrity of the global climate, that can provide a foundation for particularistic, communal ones.
Closely related to the question of the scope of morality is the question of the scope of community itself. Historically, communities have been local. However, as the reach of economic and technological forces extended, more-expansive communities became necessary in order to provide effective normative and political guidance to and control of these forces—hence the rise of national communities in Europe in the 17th century. Since the late 20th century there has been a growing recognition that the scope of even these communities is too limited, as many challenges that people now face, such as the threat of nuclear war and the reality of global environmental degradation, cannot be handled on a national basis. This has led to the quest for more-encompassing communities. The most advanced experiment in building a supranational community is the European Union (EU). However, so far the EU has not developed the kind of social integration and shared values that a strong community requires.
A similar issue arises with regard to the global community, currently more an ideal than a reality. Could such a community be constructed top-down, say, through some kind of enhanced United Nations (UN)? Or will it arise from the bottom up, through societal processes and institutions such as international nongovernmental organizations (NGOs), the transnational sharing of norms (e.g., for protecting the environment), a global second language (about one quarter of the world's population has at least a functional command of English), and other informal social networks? The question remains whether, ultimately, world governance can thrive without a worldwide community.
Learn More in these related Britannica articles:
political philosophy: Libertarian and communitarian critiquesAdherents of communitarianism, such as Michael Sandel and Michael Walzer, urged that the shared understanding of a community concerning how it is appropriate to live should outweigh the abstract and putatively impartial requirements of universal justice. Even liberal egalitarians criticized some aspects of Rawls's theory. Ronald Dworkin,…
political philosophy
Political philosophy, branch of philosophy that is concerned, at the most abstract level, with the concepts and arguments involved in political opinion. The meaning of the term politicalis itself one of the major problems of political philosophy. Broadly, however, one may characterize as political all those practices and institutions…
Liberalism, political doctrine that takes protecting and enhancing the freedom of the individual to be the central problem of politics. Liberals typically believe that government is necessary to protect individuals from being harmed by others, but they also recognize that government itself can pose a threat to liberty. As the…
Libertarianism, political philosophy that takes individual liberty to be the primary political value. It may be understood as a form of liberalism, the political philosophy associated with the English philosophers John Locke and John Stuart Mill, the Scottish economist Adam Smith, and the American statesman Thomas Jefferson. Liberalism seeks to…
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Original article by: Wall Street Review
Shares of EDP Energias de Portugal SA (EDPFY) are heading in a near-term positive direction as the most recent close of the company has stayed above the Balance Step. The Balance Step reading takes into account the last 5 balance points of the weekly period plotted in step formation on a daily chart.
Some investors may be struggling after adding the wrong stocks to the portfolio. Creating a specific plan for investing may help turn the ship around. The stock market is still producing plenty of green arrows, and investors need to be able to capitalize. It is quite reasonable to be optimistic about the investment environment heading into the second half of the year. The next couple of weeks may be the perfect time for investors to put the pedal down and try to develop a strategy that will beat the market over the next quarter. Most investors realize that there are no certainties when it comes to equity investing. It is never a guarantee that a stock or an index will go up or down from one day to the next. Investors who prepare themselves for any scenario should be in a much better place than those who don't.
Investors may be taking a look at some additional technical numbers on shares of EDP Energias de Portugal SA (EDPFY) in order to get a fuller picture. The 14-day RSI is currently spotted at 77.28, the 7-day is at 89.70, and the 3-day is sitting at 96.97. The RSI, or Relative Strength Index, is a widely used technical momentum indicator that compares price movement over time. The RSI was created by J. Welles Wilder who was striving to measure whether or not a stock was overbought or oversold. The RSI may be useful for spotting abnormal price activity and volatility. The RSI oscillates on a scale from 0 to 100. The normal reading of a stock will fall in the range of 30 to 70. A reading over 70 would indicate that the stock is overbought, and possibly overvalued. A reading under 30 may indicate that the stock is oversold, and possibly undervalued.
In terms of CCI levels, EDP Energias de Portugal SA (EDPFY) currently has a 14-day Commodity Channel Index (CCI) of 168.49. Investors and traders may use this indicator to help spot price reversals, price extremes, and the strength of a trend. Many investors will use the CCI in conjunction with other indicators when evaluating a trade. The CCI may be used to spot if a stock is entering overbought (+100) and oversold (-100) territory. The 14-day ADX is 28.85. Many technical chart analysts believe that an ADX reading over 25 would suggest a strong trend. A level under 20 would indicate no trend, and a reading from 20-25 would suggest that there is no clear trend signal. The ADX is typically plotted along with two other directional movement indicator lines, the Plus Directional Indicator (+DI) and Minus Directional Indicator (-DI). Some analysts believe that the ADX is one of the best trend strength indicators available.
Investors may be studying other technical indicators like the Williams Percent Range or Williams %R. The Williams %R is a momentum indicator that helps measure oversold and overbought levels. This indicator compares the closing price of a stock in relation to the highs and lows over a certain time period. A common look back period is 14 days. EDP Energias de Portugal SA (EDPFY)'s Williams %R presently stands at -3.76. The Williams %R oscillates in a range from 0 to -100. A reading between 0 and -20 would indicate an overbought situation. A reading from -80 to -100 would indicate an oversold situation. Looking at some moving average levels on shares of EDP Energias de Portugal SA (EDPFY), the 200-day is at 32.13, the 50-day is 34.66, and the 7-day is sitting at 35.95. Moving averages can help identify trends and price reversals. They may also be used to help spot support and resistance levels. Moving averages are considered to be lagging indicators meaning that they confirm trends. A certain stock may be considered to be on an uptrend if trading above a moving average and the average is sloping upward. On the other side, a stock may be considered to be in a downtrend if trading below the moving average and sloping downward.


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On a cool December morning nearly 26 years ago, Jim Smith had breakfast at a favorite cafe.
On a cool December morning nearly 26 years ago, Jim Smith had breakfast at a favorite cafe. Someone snapped a photo that shows the military veteran smiling, wearing a white, collared shirt and bundled up in a black, leather jacket. It would be the last photo of him alive.
Just a few hours later, Smith would be fighting a losing battle for his life.
On Dec. 3, 1987, Smith was brutally attacked by an unknown intruder, shortly after walking through the door of the rural home on Murph Road in Pauline he shared with his girlfriend. The 45-year-old was hit multiple times in the head with a hammer, causing wounds so extensive that Smith never regained consciousness. He died four-and-a-half months later in a hospital bed.
Allan Wood, cold case investigator with the Spartanburg County Sheriff's Office, said that, even many years later, it's still a case that stands out in his mind. Someone, he said, knows something about why the crime was committed and by whom.
"I'd like to think we talked to the person who did this, but I don't know," Wood said.
Smith's girlfriend arrived home first that Thursday afternoon, according to reports. An unknown person, who she described to investigators at the time as sounding like a white man, was waiting inside the house when she walked through the door. He put something over her head and hit her.
Smith, a salesman with a communications company, came home a short time later and was also attacked.
According to a Herald-Journal article from July 5, 1988, police said that for about an hour, the man alternated between beating Smith and raping his girlfriend.
"I would say a person of no conscience did this. A person who is very cold, very brutal," Lt. Mike Ennis is quoted as saying in the article. "It's extremely rare to find the type of person with a psychological makeup that would allow them to beat, and beat, and beat on someone."
Smith's girlfriend was eventually able to escape and flagged down a passing truck. The driver took her to a neighbor's house, and authorities were called.
Spartanburg County Coroner Rusty Clevenger was on the scene within six minutes, arriving at 5:22 p.m., according to an incident report. He was on uniform patrol with the sheriff's office at the time and not long out of the academy. Looking back on that day, Clevenger remembers finding a woman, partially clothed, beaten and obviously shaken.
"All (homicides) kind of etch a memory in your mind, and with this one, it was the image of the woman in distress," Clevenger said.
Clevenger took the first report and stayed on scene as the area was cordoned off. Authorities weren't sure if the attacker was still inside the home, and for a while, no one went inside.
"Everything happened really fast," Clevenger said. "I wanted to go in the house, but in hindsight, knowing how forensics is now, it's probably better it was that way for the preservation of evidence."
Once the house was cleared, investigators found an unconscious and bloody Smith on the floor of the kitchen. The intruder was gone.
Both Smith and his girlfriend were rushed to the hospital for treatment.
"I was standing in the emergency room, and they wheeled my brother right by me," said Jerry Smith, Jim's younger brother. "He was beaten so bad I didn't even recognize him."
Jim Smith had brain surgery that night and was admitted to the hospital's intensive care unit. Jerry visited his brother, who was five years his senior, almost every day for the next four months. From the beginning, doctors weren't hopeful Jim would survive.
"You never give up hope," Jerry said. "The medical professionals, they weren't very optimistic, but they'd always say things happen that are beyond their control."
James "Jim" Larry Smith, a U.S. Marines veteran, member of the Racking Horse Breeders Association and Laurens Saddle Club, son, father and brother, died April 16, 1988, according to an obituary printed in the Herald-Journal. He was never able to say goodbye to family or point investigators to a suspect.
"We don't know if he ever saw the guy," Wood said.
Immediately after the crime, investigators found the bedroom ransacked. A few items from Smith's girlfriend's purse were found off a dirt road located on the other side of some thick woods behind the property. Authorities questioned family, friends and neighbors, looking for clues.
Profilers with the S.C. Law Enforcement Division and Federal Bureau of Investigation were called on to help fill in the gaps. Their reports — now among the many elements in a thick binder of evidence — point to the attacker being in his 20s or 30s and of average intelligence with perhaps some education. He might have a criminal history, according to the reports, and would be capable of adapting to situations as they develop. He would likely be a good worker, but probably an underachiever, and be good with his hands, but gravitate toward clean, manual labor. Quiet and serious, he wouldn't have much of a sense of humor, the profilers deducted.
Wood said investigators believe the attack was deliberate and could have been carried out by someone on the outer rings of the couple's social circle, but no concrete motive has been established. Regardless of who it was, Wood said the incident would likely have stayed with the killer.
"This would have an effect. Somebody would notice a difference in his behavior," Wood said, noting the assailant might have acted out violently since the attack. "This guy, he might verbalize his discontent towards the victims at some point. He may have made comments, but he may not have been specific."
Jerry Smith called his brother "the life of the party." He loved to hunt and fish, but his passion was riding and showing horses.
"Jim was a very outgoing person," Jerry said. "He was well-liked by most everybody that knew him."
Jerry said his mother and sister died in the years since Jim's murder, without getting any closure on the tragic death. They both held out hope, he said, that the person responsible would be brought to justice.
"Maybe somebody's got a guilty conscience, or somebody's got something and they've never said anything," Jerry said. "You never give up hope. Every now and then you hear of a case that's 20 or 30 years old that they solve. You always think about it."
If anyone has any information on this case, call CrimeStoppers at 1-888-CRIMESC or Investigator Allan Wood at 864-503-4577.
Coming next Sunday: The body of Ronald Sam Rogers was found on April 26, 1992, at the
end of a cul-de-sac near Duncan. Rogers, 26, was fatally shot with a smallcaliber handgun.


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Orvieto – Fiuggi
Into the Apennines
Stage 6 looks to be an intriguing yet not especially tough stage, but much depends on the weather. If it's wet, the peloton could be reluctant to let breaks get too far clear as there are sure to be many still in with a sniff of the maglia rosa. The route passes to the east of Rome in the lower reaches of the Apennine mountain chain, which bumps up and down all day without reaching any great height. An uncategorised climb in the spa town of Fiuggi Terme is an opportunity for riders who have held something back for the final kilometres, since the final descent will whisk them almost to the finish.
Distance: 216km
Highest point: 450m
Category: Mountain stage (medium)
Scarponi says...
"There are no mountains points but it's always a hard stage to Fiuggi. I can't see sprinters' teams wasting energy trying to keep it together and I'd expect a group of less than a dozen to come in. It looks made for someone like Vinokourov, if he comes."
Image ©: RCS Sport
Image ©: RCS Sport
Profile - Final kilometres
Image ©: RCS Sport


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Log in
Kalamazoo, MI –
Local History librarian Beth Timmerman recently added an updated and more easily navigated genealogy homepage to the Local History section of KPL's website.
The new page prominently highlights many more of the Local History Room's resources for genealogists, including the library's comprehensive Local Information Database. This database, continually updated by library staff members, now includes close to three million citations to local newspapers and magazines about people, places, and events in Kalamazoo.
The Kalamazoo Valley Genealogical Society welcomed Beth as their speaker at their November meeting. Beth showcased the new genealogy page as well as the Local History section of the new KPL website for KVGS members. Many at the program were impressed with all the resources available via the Local History webpages.
Have a specific genealogy or Local History question? Contact Beth. KPL's Local History staff members answer 600+ inquiries each month, from births, deaths, and census data to information about local events, buildings, and businesses, using databases, city directories, KPL's own historical records, and more.
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By Joe, 12/17/2009
By Tony.S, 03/24/2011


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After being misdiagnosed with a misshaped head and torticollis, at 3 months of age our grandbaby's fontanel started to bulge. He was diagnosed with a rare brain tumor, desmoplastic infantile gangliolglioma. Surgery was performed and his tumor surrounded by multiple cysts was removed. The tumor occupied 1/3 of his brain cavity (10cm in diameter) . Dr's were very confident that all was removed. Had one seizure a day after the surgery, and has been taking keppra ever since. Other than that he is absolutely normal, and no brain damage is apparent.
5 months later after a full MRI, our world was rocked once again. He has growth, one cyst and several tumors. One toonie size in the center of his brain and the others in the vicinity of his previous tumor. At 8 month of age he has a second operation. The doctors remove most of the tumor at the center of his brain, unfortunately it was attached to main vessels. All other tumors remain
He is growing and developing like any 9 month old baby. He is always happy and it is so hard to believe he has so much going on in his beautiful head. He starts chemotherapy tomorrow at the age of 9 months.
Have read about non traditional treatment and would like more info. We will be giving chemo a shot, but would like to hear about other options.
He is at the Childrens Hospital in Calgary, Alberta