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Cosmology | Lecture 2
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Cosmology | Lecture 2
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(September 21, 2013) Leonard Susskind solves the expansion equation for universes with zero total energy, and then adds a non-zero total energy term, which leads to an exploration of matter versus radiation dominated universes.
Patch antenna Cosmic distance ladder Speed of light Photon Geokorona Day Sunlight Measurement Galaxy Electromagnetic radiation Light Particle Bird vocalization Separation process Roll forming Spare part Material Kilogram Year Gas Drehmasse FACTS (newspaper) Yacht Specific weight Density Universe Remotely operated underwater vehicle Gradient
Funkgerät Hubble's law Cosmic distance ladder Scale (map) Measurement Galaxy Summer (George Winston album) Group delay and phase delay Particle Bahnelement Orbital period Electric power distribution Stagecoach Kilogram Year Schwimmbadreaktor Black Drehmasse Spant Density Sizing Gentleman Universe Mass Gas turbine Noise figure Flatcar Week Last
Ruler Photon Geokorona Flat engine Measurement Galaxy Drehmasse FACTS (newspaper) Particle Surface acoustic wave Density Roots-type supercharger Universe Meeting/Interview Fiat Brava Cartridge (firearms) Mass Spare part Flugbahn
Acceleration Analog signal Quality (business) Automobile Geokorona Scale (map) Particle Bird vocalization Roll forming Meeting/Interview Astronomer Sunrise Limiter Combined cycle DVD player Command-line interface Year FACTS (newspaper) OLED Specific weight Cosmic microwave background radiation Quantum fluctuation Direct current Universe Cartridge (firearms) Mass Gas turbine Noise figure Orbit Funkgerät Cosmic distance ladder Photon Sunlight Galaxy Force Electromagnetic radiation Roots-type supercharger Volumetric flow rate Bahnelement Spare part Contrast (vision) Nanotechnology Molding (process) Planet Cylinder head Ballpoint pen Key (engineering) Digital electronics Car seat Drehmasse Kopfstütze Cogeneration Yacht Finger protocol Concentrator Gentleman Model building Manned mission to Mars Firearm Electron energy loss spectroscopy
Roman calendar Woodturning Effects unit Weight Speed of light Crystal structure Galaxy Particle Cardboard (paper product) Cell (biology) Phase (matter) Roots-type supercharger Brickyard Ship naming and launching Crossover (music) Limiter Cardinal direction Spare part Video Negation Watercraft rowing Atmosphere of Earth Mail (armour) Angeregter Zustand Lumber Ship breaking Nut (hardware) Tool Key (engineering) DVD player Zugmaschine Year Season Wire bonding Couch Drehmasse FACTS (newspaper) Density Sizing Universe Cartridge (firearms) Theodolite Storm Ground (electricity)
Speed of light Photon Measurement Electromagnetic radiation Particle Mitsubishi A6M Zero Bird vocalization Roll forming Wavelength Meeting/Interview Screw cap String theory Rutschung Limiter Spare part Steckverbinder Negation Mail (armour) Material Speckle imaging Cylinder head Stagecoach Year Photon Source (album) Bridge (nautical) Kopfstütze Finger protocol Density Gentleman Universe Electric guitar Plant (control theory) Mass Miner Wind wave
Mechanical fan Tracing paper Effects unit Woodturning Neutron Photography Scattering Scale (map) Dark matter Particle Wavelength Roll forming Colorfulness Meeting/Interview Laser Astronomer Color charge Speckle imaging Photon Year Power (physics) FACTS (newspaper) Mixing (process engineering) Heat Density Universe Cartridge (firearms) Ford Taurus Mass Gradient Switch Hot working Sound Speed of light Photon Measurement Electromagnetic radiation Galaxy Neutrino Roots-type supercharger Alcohol proof String theory Spare part Video Temperature Contrast (vision) Material Key (engineering) Electronic component Bending (metalworking) Sommer-Allibert-Industrie-Aktiengesellschaft Heat exchanger Drehmasse Map Yacht Kopfstütze Sizing Gentleman Electric guitar Firearm
Energiesparmodus Geokorona Particle Pattern (sewing) Turning Wavelength Screw cap Continuous track Cardinal direction Limiter Weather Fuel Bauxitbergbau Sky Mechanic Augustus, Count Palatine of Sulzbach Combined cycle Year Minute Photon Black Desertion FACTS (newspaper) Cosmic microwave background radiation Density Universe Cartridge (firearms) Signal (electrical engineering) Wear Mint-made errors Food storage Book design Line-of-sight propagation Noise figure Funkgerät Hubble's law Bottle Hot working Cosmic distance ladder Speed of light Photon Day Measurement Transmission (mechanics) Electromagnetic radiation Galaxy Summer (George Winston album) Alcohol proof Spare part Negation Temperature Angeregter Zustand Buick Century Flat engine Key (engineering) Gas balloon Speise <Technik> Fulling Sizing Atmospheric pressure Remotely operated underwater vehicle Miner Wind wave Firearm Last Lunar node
Hubble's law Energiesparmodus Hot working Cosmic distance ladder Photography Speed of light Photon Scale (map) Crystal structure Galaxy Foot (unit) Light Mitsubishi A6M Zero Particle Wavelength String theory Orbital period Modulation Temperature Tagesschacht Angeregter Zustand Circuit diagram Cylinder head Electron Photon Ground station Year Gas Finger protocol Sizing Universe Cartridge (firearms) Atmospheric pressure Newtonsche Flüssigkeit Electronic media Mass Line-of-sight propagation Wind wave Switch Storm Lunar node Firearm
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Stecher University but said a
review of a bit and then I wanna move on to are generalizations of what we talked about so far I think we worked out we worked out the equations of an expanding universe it would know his equations that the promise of meals for the villagers equations really get it right yacht know equations does get it right for the most part need to explain why I signs equations have to do with Kurt space time now the universal or ultimately going to study it is it has curved spacetime all right and this fact some versions of it even have curved space as simply means that space itself forget things just basic stuff if you measure triangles on it if you do various kinds of geometric exercises on you discover perhaps that's it occurred at the moment it looks pretty flat but it's possible that it will turn out on that the average to be curved end if it is curved well maybe it looks like a three-dimensional version but said was 4 years old study later tonight that maybe maybe partly portion of a sphere that for some of fear where over here we worked out we can only see so much we can't even really see the tequila this year's curved but a large enough distance we may be able to see the spheres curve on really can't suppose we just decide to lock and very neighboring galaxies now very neighboring galaxies Komeito billion light years from Earth now very very neighboring galaxies much more then what we think the radius of curvature of this university with a looks flat and if it looks flat it should mean that at least for that portion if we're not in the best of things but we just interested in the local nearby behavior we should we should not have to worry about the fact that curve if that's correct that it means that the way these galaxies move relative to each other and how they move apart from each other at least in the small here To me studied using Newton's equation actually been doing we've been looking at the university in the small and studying how old are small little fraction of it is expanding or not expanding whatever doing perfectly legitimate and in fact entirely consistent with Einstein with with relativity except for 1 thing rivers except for 1 thing we would run into trouble if the galaxies all it ever is pressed galaxies particles present if they were really moving past each other With a significant fraction of the speed of light 1 only assumption is that the neighboring things are moving relatively slowly with respect to whichever something very very far away may be moving with a large velocity relative to you but as long as the things nearby are moving with nonrelativistic velocities you could study relative to you you can take a small patch now small could mean 10 billion light years but during take a small patch of it and study of without using any relativity really if we discover that there are particles moving with close to the speed of light past each other then of course we will have to modify the equation but on particles moving fast by comparison with the speed of light us where are they traders the trio's for 1 by photons not only photon from the sun I mean photons it would be the area of the was no son the universe filled in the same way that filled with galaxies it's also filled with radiation homogeneous radiation that homogeneous radiation does more with the speed of light that means that we have to modify our equations somehow to account but very very vastly moving rapidly moving material photons widow that tonight but I 104 about when review but we did last time quickly we 1st of all of us said suppose the base is homogeneous and those with galaxies marker Trevor drawer galaxies before making a gas if you like can fill the blackboard with a certain number of particles per room per cubic meter curative density density that we called Rome analysis the content of the universe In kilograms per cubic meter if your life you could use some other units but whatever you to write physical units kilograms per cubic meter recall the role we laid down a great on universe and light now the greeted it was clear ambiguity imagine that we lay down the grid at some specific time like today we lay down the grid and you can't ask What is the space in between with grade was a coordinate system but call accord X and the distance between X equals something Annex equal something plus 1 another words 1 greeted the 1 great separation here 1 lattice separation is a certain distance associated with that how big that center well with Colbert AD how is it that depends on the good that we laid down if we laid down every course screwed it would be 1 thing if we laid down a fine grid it would be another thing until they beat that our equations at least at the moment do not prefer any specific value of a we could lay down a different grade 4 different grades it could be twice his debts so here's the black forms 1 grade and the black and green together form of great if every looked at these more dense grid will also invented AD let's call it a prime is a prime is the distance between neighboring points on the day and the dense grid that would be one-half so
if you ask me what is a value of a Aguilar said think I can tell you until I know precisely what grizzly bear and so it a itself doesn't have a physical meaning at least at this stage later on we will discuss more with a means but the moment it on a flat blackboard doesn't mean anything by itself until you specify exactly what the size of the group OK so aid is just a bookkeeping device on the other hand really CEOs of a means something only give you an example supposedly I told you would is a function of time universe is expanding the distance between neighboring galaxies to galaxies are embedded in the Great War with agreed the actual physical distance between galaxies is growing I suppose in psychology over a period of time a doubled back has meaning that means the distance between every galaxy every pair of galaxies doubles so ratios of a particularly ratios of AD different time frames are recording a history of how the universe is expanding or contracting and that's why are equations and got only involve radios of things with a figure example let's take a dot the time derivative of a well that will defend on whether I use the black grid or the Black Queen great every 80 associated with black grid is twice as big as every aII associated with a black green grid of every 8 is twice as big a . time derivative will also be twice as big money other and if I take a dive abided by a and let's compare it with 8 trying . divided by a prime they will be the same they will be the same because the ambiguity in the scale of the grid will cancel out a prime will be a FAA 80 . crime will be a half 8 . 8 million and a factor of 2 will just cancel out so things involving ratios of Eddie those invariant physically meaningful things and if you remember a over a is just the Hubble constant at a given time so really does mean something but I itself ambiguity and how big it is but a once and for all ambiguity went to fix it acquitted OK another thing which is ambiguous was we introduced a constant no was known as the man's contained within a single pubic of the grid another words a grid element here 1 by 1 by 1 by 1 1 1 1 great unit the amount the Mets within that killed which recalled Noel is ambiguous because we haven't figured we haven't determined exactly what the greatest never alas once the greatest nevertheless the amount of mass with a single is called but it is also changes when you change the grid now let's
go to these equations that we arrived last time equations we derive last time remind you how we derive their week Tucker you Harris filled with galaxies called particles uniformly replaced ourselves right at the center of arbitrarily but still consistently replaced ourselves at the center looked at another galaxy which was at a specific location on the grid some X summer Exxon mcgrory end we studied look Who's equations for the motion of that Galaxy which will I which it would think would be horrendously complicated horrendously complicated because they're interacting with the loads and loads of galaxies but we used the famous noted about 1st of all imagine smoothing things How would so that we could think of the year of the distribution of these galaxies it's moved smoothly uniform center the center centered at us excuse me don't use know theorem that told us that relative dots In the pool would system will we ever at arrest the forests on that galaxy only depends on the man's within next year as if all of the for concentrated at the center we just said let's concentrate all the mass within next year at the center and then studied how under such circumstances the Galaxy X would move if it were under the influence of just that you're after were about masses on the outside you won't have to worry about a mess on the inside and we worked it out in a similar way that we worked about the simplest way to work it out was just the same if there was a particle over here moving under the influence a fictitious man at the center then energy of that article would be conserved energy consisted of 2 terms well I have to go out come back to the derivation again charges for review their visionary quickly but I'll come back to in a moment remind you what the equation was the equation there was derived was that a got over a square that from the kinetic energy was equal told the density and that are rolled measured In known physical units in other words measured in kilograms per cubic meter mothers no object over here but
rolled and I was a little more wasn't 8 party if energy G noted that was the equation that uh every derived by just looking at it at the conservation of energy Rollo hopes role raw sorry didn't 0 3 that 3 ultimately came from the volume of a sphere for 3rd part IRQ with 3 of the 4 8 2 times for applying pies pie 3 3 this is related to the volume of some fear OK that was the equation that we worked out that was in the case of Zero energy that was in the case where the potential energy of this point and the kinetic energy of it exactly canceled it could also be understood as the situation where every galaxy is exactly at the escape of city just a knife-edge between being able to escape and not escaped that Formula One we 1 more thing to it and the 1 more thing is we said that role Bravo which is the amount the Mets amount of per unit volume is related to know is the same as not use Newell is the amount of mass From grid box but a gray box your North volume is this is a mass within 1 Q if you want density and the density is related to Newell by dividing ruled by the volume of 1 of his boxers misses density for you because you're cubic meter this is for cubic box you divide that by the volume of box which is a Q and that's 1 more factor we put in that role is newly divided by a Q now is role constant with time no rule because any changes but no constant with time if no just represents ordinary particles sitting in the universe and never destroyed never created particles of photons let's forget the proton decays for the moment but times are forever and a galaxies of forever if for a moment last forever we all we won't believe that forever but we will believe for the moment the galaxies are forever get that or chaos galaxies were forever protons were forever the Knollwood because the number of protons with a box is the same at all times or happened the box grows so the proton spin out but the number of the box sex and so no it stays constant What is it its numerical value I can't tell you what the numerical value is because that has to do with the exact that I used a change great I changed up case once established all of the convention so I can replace role by Newell divided by 8 know it is a constant doesn't change with time 8 is a constant fight a constant 3 is a constant G is a constant all of this stuff here is just a numerical constant in fact by judiciously changing your definition of the grit since changing the great changes the magnitude of new I can't find life I can apply like choose 8 pie no over 3 could just be 1 it doesn't make any difference the point here is the numerical constants that appears here really doesn't make any big difference the way the university evolves and wait and see that is by changing definitions of the good you contains the constant so we could flee like just set a pie Jean who over 3 eagled 1 and then we would have a very nice differential equation a dot already squared is equal to 1 over killed now would you like to see us all that we saw that last part but we saw by
guessing and many people seen real Time and knowing you you'll see me solve their panties are hoping I'll make a mistake but yeah do we miss questions or cake while still bad the Solver would you do unmarked here sovereignty is only a sore always equation you 1st of all saw use 1st take the square root of both sides on the left side as easy it's just a dog already on the right hand side it's a little bit of a since it's 1 already aII kinds square related you see where that came from a cube is a squared times a square of regret a Times Square Root
OK but to multiply both equations a both sides by 8 to get rid of it in the Obama made at and actress tells us that 80 . is 1 divided by the square root of a rift that that's where would like to begin OK right this debate by DG which is what it is is equal to 1 over square today but now we can do something tricky the very tricky thing we're gonna do is instead of thinking of b as a function of time we think of kind as a function of age where take 8 to be the independent variables entered Hill that here is being that looks like a function of time and would differentiated in it but I turned upside down is deep meaning taking 1 over at its DTD aid and now it looks like it's the derivative of time with respect to and that's equal to the square root so how we saw that we look further function of aide whose school whose derivative is the square root of 8 was functions as is its derivative the square root of 8 803 3 right well two-thirds 803 3 hands so we find our team is equal to two-thirds of two-thirds is absorbent the constants that we've been numbed ignoring times 82 the the read head what we can solve that now we really wanted was a is function of time but that's easy our free just neglected to 3rd with adjust of like riding it to get the two-thirds this tells us that AD is equal to key through two-thirds a Eagles 238 Tito the two-thirds which is a function any key which looks like that and it gets flatter and flatter and flatter the flattening of it is deceleration universe is decelerating but it never comes the rest we could see that it never comes to rest because we look at this equation there was no point at which a diet of 80 becomes Iran I know it doesn't become 0 because the right hand side is never 0 Ricketts smaller and smaller they get bigger and bigger but never goes 0 and that's why the universe decelerate another way to see that it decelerated just a particle moving away from a fixed for sent there to decelerate because of the attraction by force and that was that was lesson number 1 I really did it because swirled where we think it's worthwhile or are we doing most important derivation but yes it's OK for amigo square wrote on was the logic the logic funny equation you cannot show with the universe is expanding contracting both are possible from the equation if you start it's exactly the same deal as saying you have a plan over here coffee is good planning rise is years apart as rock and you see the rock right over here the equations of Newton will not tell you the Caracas moving away or words moving toward there is 1 thing you can't be sure of let's unless let's ignore for the moment moving in orbit let's assume we know will that be the Caracas radially is 1 thing we know for sure that's not standing still may be momentarily at rest might have come up start but it's not going to stand still is accelerating its accelerating back toward the plan so it could be going out decelerating or it could be going in and you can't tell from the equation the same way you can't tell from the equation whether it's expanding contracting and that has to do with the 2 possible solutions arms whether DDT is positive contracting its negative it's expanding Foster OK the ball is always out movies radio all that all of us about whether this docket Dutch right that's right but still on the average came To move as if they were embedded in the script given that their embedded in the grid Ole the only option they have to move radially relative to each other now you're perfectly right up there Our motions on top of that average motion the emotions on Top of the average Martian don't of course satisfies the call by astronomers peculiar mounted a peculiar motion meaning however peculiar but our son moves around surrogates moves around the sun and is not a participating in this expansion wrote of son but there few go a few galaxies over the whole thing is Charles the real emotional real galaxies is a combination of the average floor figures of 4 River going downstream how fast as any given and molecule moving well I don't how players in a given was moving but I do not on average the clumps of molecules sufficiently average are moving with whatever the velocity of the rivers on top of that is the peculiar motion of the molecules relative to each other so that's the way you think about a flow and on top of the flow flocculation similar ignoring the fluctuation of the mob OK a quick how bestow directions I want to expand the number remarks Mr. directions I want to generalize it today the 1st well probably the 2nd the 2nd will have to do With what happens if you replace massive particles galaxies of protons and so forth by folk art by radiation how does the whole story look different if there was a universe of fictitious uterus which had nothing in it photons how different with this being a why my doing that but a silly thing to go Whitaker fictitious universe which is only made of photons well don't define is that earlier all In the history of the universe the most important thing numerous will time today the most and when I say most important I mean the largest concentrations of energy early on the most concentrated the most the biggest form of energy in the universe was radiation could AD the most dominant form of energy in the universe adjust the masses of particles equals MC Square kind of a kind of energy that this serious about its about the behavior of massive particles nonrelativistic slowly moving particles yacht that also presumably made of particles pretty much standing still talk along if if if 30
years ago we headed back by will you with still 30 is back with 25 years backers here you're right good good good tedious but documentary by contrast is part of the guests thank you I was helped of young or what I'm telling you now is an old story but it's a story was bases whose 6 yeah important to us OK 2 directions I wanna go 1st has to do with what happened at the universe is made up of the kind of stuff other than just a particles more arrest auto to whichever radiation particular and the other is the move beyond the assumption the energy is Iran was no reason for that with arbitrary we arbitrarily let's assume that every galaxy is moving away with exactly the escape velocity but back off that now and how we back off to go back to the energy equations and save energy of that particle moving in the fictitious field but the fictitious Gilberto field under fictitious concentrated Nancy the center is not a real galaxy now the combined man of Everything within the Greens fear it for particle out here molding outward and let's apply the conservation of energy to it but go back through the derivation apply the conservation of energy and then see how the equations change when we go away from the limit of 0 energy OK so what is the energy of the particle this whole glob here has met em for combat toward members moment but has missed him it's not a mass of the sun the massive any specific Galaxy it's a mess of everything in this sphere and the energy of this fellow over here it is 1 half M and is Mass Of this fellow marked a big mess in here the of this galaxy times velocity squared that's what it terms and the other terms is minus and GE over the distance between them but call distance D as we did last time I missed something good nite another factor right back product of the masses Newton's constant distance between them that seat at energy of the particle moving out what only know about it we know that it doesn't change with time it doesn't change with time because our model that that's a useful model is just the motion of a particle in a fix In a fixed background of mass energy is constant and so let's set the energy to be equal to some constant I was constant mean doesn't need a numerical constant that's independent of everything else know it doesn't it could depend on which particle with talking about court In fact if the homogeneous and isotropic the only real thing could depend on is the distance away so I will ask simplified the discussion from now by taking this particle could be at x equals 1 wet In other words will take a specific particle very definite 1 at equals 1 and focus on it if has some specific energy and that energy will never change so let's just call it he that is a constant what value the constant I don't know I can't tell you offhand no more than I can tell you if I know that this is not Over here a planet over here is no way I can tell you a priority with the energy of the particle is at the heart of molding so we have to study all possible cases so just put the energy and quality he can't take it to be a constant numerical constant let's right out now everything out provide His 1st of all divided by him malaria but survived by little and abide by little and analogy we get can now is a constant end a constant eel with him as a constant so I really have made any more complicated by dividing by and I'll leave it here is over area but the right side is just the numerical constant that's even do a little more multiply by 2 it's still just a constant and since I didn't tell you in the beginning what he was although I know was as is a constant source of much of its lead evaporate know about the velocity if this is a galaxy ad x equals 1 and then it's velocity but to distance the distance is any kind X the velocity it is 8 . 9 x and similar can just plug that India an X is what I chose an X to be 1 so it's very simple the dissidents Of the galaxy is just scale factor a called scale factor and velocity is just a dot so put it in here Mr. says a dark squared minus through a N G over D & D is it is equal the some constant thunderstruck Aussie constant on the right-hand side the says many of the elements of this equation here but this equation is nice equation we divided by a twice to get a of a square when I do that because I know in the back of my head that in itself is not a meaningful thing it's only ratios of ladies sold the back of my head I knew that what I really wanna get is an equation for ratios of Haiti's or 80 . divided by so I devised this equation by a square take noticed some things happened on the right-hand side here it's no longer constant is your constant but a square now has something new in it and finally we you is that the man divided by the volume Q now this is a sphere is a sphere of radius a X is equal to 1 a sphere of radius AT and the volume of a square of a sphere of radius is for a 3rd time a queue so I had a cube down here that's not quite the volume of the sphere let's fix it so that is the volume of the sphere that's multiplied much of this equation too much for free ride at a dart over a
squared minus twice L G all 8 Q is equal to or constant over a squared but now but to multiply and divide by for 3rd ii services pie over 3 and a half to multiply out here but for a 3rd fighting that becomes 8 thirds plight as were a 3rd pie came from OK for 3rd fight a tube of a phrase that is the volume of the old was the massive either by the volume density so by fiddling around I got the Freeman equation but right-hand side now a right-hand side that knows about the total energy if seized positive it meant the total energy was positive in kinetic energy outweigh the potential and dives means the galaxies and have continued to recede forever be beaten video escape velocity of season they did then energy is negative more potential energy more negative potential energy and a kinetic energy and that's a situation where you expect everything to go our way and then come back and crashed self we now have a new equitation the Friedman equation for non-zero energy energy could be positive or negative positive or negative both are would energy Pope the let's examine a little bit and see if we can see a little bit worried says it's not I want to solve for any given case but the votes it's not sovereign wealth 1 of that 1 of the stepped right over here that already squared and let's trends posed this factor to the other side equals a 3rd applying G times role but role is newly divided by a key member no no wasn't was mass per unit cell size is no over a cube row and G G is there plus see only a square This is a new thing COA squared is a new thing that was not here in our initial study of this equation was it do 5 so Houlihan let's look at it 1st Is it a real Friedman equations with this with this right him and it was derived from general relativity not from special relativity starting out from under but nevertheless we just arrived the from noted OK so here we are let's see what these things mean let's assume for a moment the universe continues to grow if he is positive if is positive and everything else on the right-hand side positive 8 by G newly a cube there'll positive than the right hand side is strictly positive an 8 . 0 a is positive under the words the uterus continues to grow 8 . is positive and a sponsor a doctor time to remove a positive universe continues to grow forever it may slow down slow down but it will continue to grow storm ripped open tractor will continue to grow so on if is positive universal continue expand it will eventually get arbitrarily Big might arbitrarily bigamy he will eventually exceed any bound and become very large so let's look at it in the limit that a becomes a much larger very very large where it they got Over right the square as part but the square and that has to be positive so let's assume that initially it is possible that uterus starts at expanding then the only way Connecticut to be negative it is of the goes through 0 Kinkel 2 0 of the right hand side pass to the point by the right hand side being permanently positive disallow was this from being 0 and therefore we continue to grow can't jump from positive to negative without going to 0 in the leg never 0 OK what's term he was bigger a school a square 1 of a like depends on whether it is legal small right but a particular let's go and think about 3 large L the small 1st but hey being small which is bigger 108 Cuba while a square 108 . if you take 8 could be small enough for this will always be with us and sofa sufficiently small 80 this is negligible compared the best we've already studied the case where are only know the answer when only answer long as a small under the words in the very early phases of the expansion when a is just starting out growing is just beginning to world this turn is not a point where we find we found out when the firm was absent that AT expands likely to the but to the other limits this a standard way of thinking about all kinds of things go to limit often an equation is this equation solver boards Bentley but nasty we don't have to solve we just have to know what it is doing it the tool In 2 wins means when a very small and when is very big OK so what I want is very big which terms this there this was the biggest Germany's big where a square is much much bigger than 1 of a few odd you may have to wait a while and how how long you have to the wait may depend on this constant here but eventually this firm would become much larger select study that equation but 70 equation 8 . all that a school is equal to some constant any constant already already squared when we 1st take the square root of it want a square constant another constants are won't change its name but it's really a is new see here the the square root of the Old City of course the reason I'm allowed to do that because it doesn't matter what the constant is here will get mail blue which is qualitatively the same for every state I'm a dollar a a knowledge multiply by a 8 . it is a constant 80 . is a constant a doctor's the velocity of the galaxy
at x equals 1 another words in a situation where the energy is positive when the Galaxy gets far enough away the effect of gravity becomes negligible and it just moves off the uniform velocity saying a is just constant and that tells us that aII is just proportional kind constancy and kind Galaxy just wolves off of uniform velocity so that tells us this is the kind a positive see a positive constant C is not the speed of light here years over what happens to be a velocity so it tells us that at late Kareem this does Moses a straight line With a constant slope 80 . is just a slope it was constant slope and the uterus just expands would lean years on accelerated none accelerated motion nothing is a deep is going on here my using nuts what I should be using Apple's woes saying his father's apart enough so the escapes from gravity with a good margin with a margin there with his mobile off uniformly with constant velocity so fact we find that we find exactly that what happens in between where's the crossover point leave that you you could figure out approximately where the crossover point is because as 8 of the Tito the two-thirds and the makes a transition to the key and fuzzy in between that's the matters dominated universe wiser called the matter dominated universe Our because these right here society Of this equation contains a turn which is just the density of ordinary matter ordinary nonrelativistic slowly moving matter that's OK so old that go to the other case what happens if he is negative that's the case of negative energy may should be able and gets a particle of the Apple moving away from the earth with firm West of escape velocity has negative energy in default back so that's actually not hard to work out understood tell you what happened what what happens 1st or happens and you have a negative sign here a negative sign here and the right he inside can become 0 initially this is the biggest at a later time this is the biggest hurdle but they have opposite signs that means somewhere in between this became 0 that is nothing but the point where a backed up going Apple simply is momentarily arrest when 8 . 0 8 0 0 4 the bonds and there opec so was see negative does a crossover and instead of moving off linearly like this back crashed Everything false together that's a matter dominated universe and it was a classic cosmology until a until other things with discovered OK any questions but a was my my assumption when I get no questions either of perfectly clear a perfectly it is what some draw judge yet were a word that said I made cells which goes right now I've become negative the I think that where your but I was that nite and right where they were wrote are you have to take a square root square root could have our party outside clients I know it's not only the right said so old without is a chance led by state Arizona no I made an assumption that that from the universe was expanding and that breaks down at a point where it comes to rest the mathematics is entirely identical terror 1st the yard Norwood a right arrive warm air every square is equal to GE M although the dissidents murmur they times arrest of the earth Our job minus this is equal to the energy of theology is negative votes court minus their Rice's plus Jew M M all basically or the distant descent equation lumber how does it happen if these guys he is negative he is negative and there can be a crossover point this is exactly the same exact with us you you know what happens in all the but these Apple just pulled back down but at the cost of taking the route of the of applause route and minus of a square root but if whatever over a few that if you otherwise south burgers negative that about we said that after reviewing for you Net hockey player at the point is Aitken never get big enough for lot turning asylum can never get big enough but a is bigger than this term was bigger I will go negative but never does get negative normal pocket but the right side never never gets you're right around inside and maybe it never get negative all that tells you is as an upper bound on how big a gets right a gets so big and stopped getting bigger and
comes back down 80 is always in a region where this is positive but goes to 0 going through zeros is coming to rest of backed down back and on the way back down you have to take the negative they got over 80 is negative square it's topic that that is not matter dominated numerous 3 possibilities posit managing negative energy 0 0 energy and 3 different behaviors decides whether the energy is positive or negative not only are find out that b connections on the positive list of negative news is connected with the geometry of the universe not tonight next time will talk about the connection with his constancy with a spatial geometry of the universe that's what that means thing at this stage the general relativity brought to bear on the equations are exactly the same for the significance of this constancy takes on a new dimension and has to do with geometry but not tonight 1 more thing limited tonight will take up the the question of what happens if instead of being made and material points slowly moving and what happens if the universe is made out of 4 parts made out of radiation I danced in that of course we really do have to think about relativity but really there's only 1 important idea it's just equals M C squared if we widowed done Einstein's equations the right-hand side of Einstein's equations right side left basically let partly with the connection of Einstein's equation on the left we have a already squared and that I'm going to a head plus always squared transport the left and the right hand side glow a pie over 3 G role nor obey orders role now is a mail density here but Einstein's equations are of the form that something on the left having to do with geometry is equal on the right side of things that have to do with the density of energy and momentum energy momentum tensor on the right-hand side geometry the left is clearly has to do with geometry the rate at which the universe is expanding our abroad tell you next time the sealed here has to do with the curvature of space of this idea here is Einstein's geometric side the right hand side the source namely the energy momentum whatever it is in universe what is the energy on the right-hand side of this equation it's just the Mass points and equals M C squared so all my goodness and calling the sea but please don't get the idea that the speed of light sometimes called Kappa miners cap but sometimes archery written minus Kappa unfortunately kaput is positive energy is negative and captors negative images positive throw from call kept OK after that the basic connection with general theory of relativity the only thing that we really need to do to this equation is to remember bad when you go from that when you go from Newton to relativity will was mass density becomes energy density all forms of energy density all forms of energy density always gone awry he inside well energy density times the speed of light squared is that right now and his iii oversee squared so its energy density divided by sea square which goes on here want sits equal to 1 when I worry about speed of light speed of light physical 1 with that idea in mind the right hand side instead of being the dense masters becomes the energy density total energy density some of which is just the Eagles in C squared energy of the particles arrest and some of Mike b Connecticut Energy of particles which we haven't really included at this point the kinetic energy of a relative of fast motion of them but if the universe is filled with times then it's radiation energy after what talk a radiation energy and how it is different from the Eagles MC Square energy always have to do is think about a box a box now the box box just corresponds to review it Q integrated here the Kwan unit Cuba the grid there's a volume of 8 Q but suppose it has a certain number of photon now photons have a wave so here's our box Delta x equals 1 each side as volume is a cube the not be O'Leary particles which are just sitting in that box and not moving they have an energy which is just a man doesn't change their energy doesn't change those particles adjusted ask nothing else but a photon behaves differently so I'll tell you how awful behaves the 1st thing cannot afford on electromagnetic radiation forcing them out of our time is that its energy is related to to its Waverly it's related to its wavelength the plants constant each roast lamb that a wavelength and the speed of light which are set equal to 1 important thing is that worn all over the wavelength now something which I am not going to prove but I'm going to tell you is that if you take a box with a photon in it ever given wavelength your photon given wavelength and you expand the box to expand the box fully for example use in the universe is expanding Presler takes 10 billion years for it could double in size British on you take a box and you expand the box slowly them what happens to the photons inside what happens is the photons inside Is there wavelength just stretches in proportion with a box now this phenomenon anybody who plays a guitar nor year the from armory well the box is replaced his string of the Katonah it's pinned down at 1 end of bridge over I at the other end its pinned down by your fingers at a threat and block it resource vibrate and then of slide if anger what
happens is is larger effectively changing the size of the box changing the size of the box became the size of a box the wavelength just changes and the cloned Serbia the note changes correspondence with the year with a change in the size of box the same thing happens to radiation a box radiation a box the wavelengths just stretch in proportion to the size of the box because the wavelengths change from afar that means energy of each photon changes as you change the size of a box you world was filled up with photons you could pretend that each of the 4 times the number of photons image box stays fixed but so but true statement number of photon stays fixed but then energy changes as you change the size of the box and particularly energy of each fault-tolerant will be proportional for 1 divided by the size of a box but we pick 1 box Jesus scale factor in the energy of each photon decreases same phenomena as he frequency going back down or up as you change the year of the lake the effect of lowering the video of a guitar string so well let me down traces of boss the what Birgitta saved by say they just free space did he said they what we're all of us get near the spot where you're you're up that 1 will think about 20 thick about it that better you about or and then they horrible I never used a word or a fast you did fans are depends on how would you could conclusion but but it but that that is willing work for the change yacht on we have to do a little more quantum mechanics of more or more classical electromagnetism in the presence of an expanding universe to justify let's take it let's take it for the moment a given elegant come back toward the answers it is a correct statement that that power and unsavory of think of an example Chad had offhand I can't think of a good practical example or where or something similar happens but nevertheless it is true that the radiation in the box the wavelength of the Ford Taurus readjust themselves to the sizes of bar of a box another words of photons stretch along with the users feel like you can just think of the space stretching and with it the photon wavelengths stretchers let's let's leave it that that the tonight and I'll leave it at that but just examine the consequences of a problem what's examine the consequences are the consequences are it is ahead that energy for photon decreases by 1 only 8 in contrast to the case with ordinary particles with their man stays the same doesn't vary sold by contrast with particles case ordinary particle case energy in the box the energy in the box the mess in the box effective energy on the not stay constant would decrease total energy in the box decreases like 1 over the scale factor every photo on its energy decreases wickets stretched so every single 1 of them and compared with the previous case is 1 more factor of a year in the denominator the energy in the box scores was like war already and the energy density was like 1 or later before instead of 1 108 killed previously br density here we said was a constant Newell divided by a Q now we get 1 more factor of 80 in the denominator and it's just the fact that every particle its energy decreases by 1 x power of 80 that means relative to the previous case is an extra 80 in the Promenade no could be taken now to to be the number of photons punitive are they in a box and energy would be 1 of before that's only new thing that happens this is matter dominated and this is radiation a . already squared and a by over 3 G some constant new way and an 8th of a now downstairs we can also put in this term he minus sealed a squared but let's study the case when the case correspond 0 energy just to see the different to see the difference with Stewart different behavior we get With this formula this formula says away again by appropriate choices Of the size of the grid you can make all the constants here a few light B 1 by appropriate choice of the size of the grade you can rearrange it so that it's just a . already school is 1 divided by heat before what was a before dilemma what are so we figure out what happens again with solve the equation now the steps of solving the equation for status where wrote 8 . 0 8 Eagles 1 of a squared talk that means that a doctor is just 1 more way a right could do right St ADT would do the same trick as before turn and upside down by D. any physical that so now if we think of a V
independent variable were looking for a function was derivative is just a what functioned as derivative Eddie a square right now a square for half a square to be exact so let's say is that he was like a squared maybe there's a one-half yet but that but that's not for thing is the key varies like a square alright but the scale factor varies like Quito the one-half square root of 8 well I'm not much artist and I can't really draw the difference between Keaton the two-thirds and keep 1 half their of the two-thirds Peter the 1 half is a little bit smaller grows fast data but look pretty similar and I was pretty much the same thing you have to be an astronomer a really interested in this up to care about the difference between the 1 by that I mean are the have sufficiently similar qualitatively similar but if you really wanna know what's going on the universe the difference between Tito the 1 Peter two-thirds to be very important OK so that the radiation dominated universe radiation dominated universe expands the square root of Katie that 3 2 Key to two-thirds Tito the two-thirds in Tetovo warned half Patricia what about the mixed case supposing universe has both ordinary particles and radiation like the real universe really got laughs worry about that but that's come about the mixed case either pure radiation not pure nonrelativistic particles and that Casey energy density is 2 components 1 for radiation icons like were made of fought and won for ordinary matter because like 1 of a Q so kind of equation that I have writer details on the right down the general form will be a doubt over a squared and that's going to have to to terms now 1 of which course constant No. 1 divided by Q. We ordinary particles constancy 1 is just some measure of harm a number of our number in each box and then another turn that both positive energy of particles and the energy of photons is positive and the other is some other accounts end of a for that's the equation of motion for a universe which contains like our real uterus does ordinary nonrelativistic matter plus radiation which 1 is more important 1 or a few the 108 0 4 those are they right when Renee's big which 1 is abroad buzz warned excuse me my mother always told me that the text would be by firmly after a small this is more important than a smaller a is the more more important areas when a is big this is more important than again swamps militarily when is really big so that tells us without that too much work it is that when a key is small and the beginning of the expansion and the only thing that's important is the radiation this was a radiation turn as dominant compared to a material protons neutrons galaxies normal galaxies the beginning and the radiation was the most important thing answer the universe started expanding like 1 half T but they eventually this term took over became the more important than animators premier again over color and switch has started to grow like Tito to 3rd but shares works yes yes that's correct that's correct and you might say well highly Noble Energy of matter doesn't get converted To energy radiation that's something we have to discuss the answer is they when he arm when things it cold enough the universe expands enough things cool down and there's not much exchange between radiation ordinary matter and they are pretty welcome each 1 separately they don't talk to each other too much in fact once things cooled down to a certain temperature at a at a high temperature of 1 thousand the Gripper Morga thousand degrees 10 thousand degrees but wants things cool down through certain temperature pretty much the photons are just free streaming in don't care much about America about the particles and the photons to wait too long wavelength Stevens scatter particles very much so that's right that's exactly right that we assume that the took constants here are pretty much time in fight that's that that's the nature of the universe built of 2 components that's only 2 components at only 2 components and there is a 3rd comply there is a 3rd component the discovered dark energy best organ talk about next time we have ordinary matter we have radiation those are commonplace Maine dark matter belongs to the matter category it's simply up part are very ordinary particle matter that indivisible simply because it doesn't have any charge was radiate much so we don't see a lot that going on that's part of see 1 this should be seek to hear rights to or maybe we should call C. N. from nadir and see radiation from radiation pass there's more than 1 component of the radiation for cartons is presumably Gravitt are and their neutrinos now neutrinos Have maps but the masses so tiny that even today he the neutrinos are moving with very close to the speed of light and simply mimic the same behavior as the year for servers radiation component the radiation component consists of all particles were just so light that that will remove close to the speed of light the 1 last consists of all particles which are heavy enough that European basically at rest relative passed nearby and the bats that's because Molidae it was known as it was known 30 years ago is the Cosmo due 30 years ago parts at the box that they wait wait wait stretching at the end the total I bought priest they said is the decreasing doing work on the walls to expand their wealth another laser says is going into the kinetic energy the kinetic energy of expansion busy quite is similarly was acquitted of conservation of energy fifa came from so what if you think about it that way and start tracing after this part of the energy decreases in Bend Ore let's let's put it this way let's write the equation different form from a minus sign over here
but the 1st separate times when miners put my and make it equals 0 I haven't changed anything now change sign of the whole thing might have plus plus this equation reads the following way because a certain amount of energy and medicine radiation changes with time that energy gets transferred for a negative Turner does what with a little bit bizarre is energy associated with the Connecticut Energy of expansion of the kinetic energy expansion this here is negative this can be read as a conservation of energy we read energy never changes because always 0 contains 3 terms matter radiation and turn that has to do with the rate of change of expansion set off normally in the ordinary world where the rare Werner rate which generate rate of expansion rate of expansion is very very small hanging number this year's kind numbered our world of the present part playing there's never changes very much and so will not be subzero that I think it is the premium a number but doesn't change much over the course of time the some of these 2 cases 0 0 and stay 0 that the conservation of energy by saying that right a mouse it right now energy what would you think about it that there is the fact that he is the key is the way to think about you could say the universe is a time-dependent background of everything moves and it cost time-dependent them Angel here equations have a time-dependent is no longer a time translations a retreat in energy is doesn't have to be so the other way to say it is it is a time translations symmetry did you start the universe at this time of that time at that time you get exactly the same response to stun the university equals minus 7 it would be exactly the same starting university was forced for and thinking about it that way you'll discover another attorney energy associated with the expansion rate us not gone toward Harrison was very resource for while I want spend at least 15 minutes on there were greater energy conservation but just to keep in mind that these equations their origin was energy conservation and so is no way that we could be violating energy now it should be what you could drive through bitterly mechanic store Carol that totally mechanics closes a black geometry and relativity they Kirkia trimmed geometry of space fears based on for Our geometry respects Einstein's equations permit flat face these are OK with that state's less but you can't drive from about face state that he had to clear where they are written say that figure races Yao but With if he 12 my Kapolei square this had to do with the public retreat the fixed energy if cap as positive in this equation energy is negative the captors negative energy positive sorry if it goes this way Cappaert is minor see energy century forever I know I'm wrong OK does 1 way or the other on this term over here has to do with the curvature of space wear study 3 cases there 3 interesting geometries would be interested in is a flat geometry where space itself was flat Gravano on endlessly homogeneously and triangles have the usual properties that's a case Cagle 0 is a case where the uterus is curved like a sphere of your around the corruptive assigned to him around the finite and compact that's a case Skakel's positive a positive number here corresponds to a radius of curvature of the year of the expanding universe expense likable in August the classic picture of the expanding balloons at Skakel's positive K equals negative negative weaker space have to talk about negatively Kurds spaces like less easy to visualize so the next time it's exactly what we are doing program the geometry of space and the 3 cases flat positively curved negatively curve they correspond to 0 positive or negative With that that 1 Cheney has well except didn't up the arm the case with take not being equal 0 if you want but they're too little bit of radio fake it now it is right a bottle of what they there's not going lot that but is both does work on Bybee read take a little box literal boxwood reflecting walls their boxer reflecting walls and ask what happens to the energy in the box or expand the year walls of for what does happen the pressure in a box this pressure exhibited by photons bouncing off a box the pressure when you expand the box does work on the walls of the box for a real box theology could go to a number of places they could go to stretching the distance between the molecules in the box it could go into making kinetic energy of the walls of the box a 1 way or another it doesn't work on the box and increases the energy of the box itself either by stretching area of books Lost Springs there inside the box the molecules together or by causing the box they have a kinetic energy the kinetic energy expansion or whatever else just heating the box just heeding the yes the bigger yarns and subtract your that will talk about that Auburn conservation more quickly wrapped but it's still it's to correct that analyze it it is not obvious but correct that's correct the analyze it as if they were stuff in a box and the stuff that gets reflected off here From real boxer reflecting walls is compensated for in the think box case by every particle which goes across here is approximately compensated for by a particle which comes in side on the average plus of the expanding space behaves like an expanding box particles instead of reflecting go from 1 box the other but on averages many particles go from the box box from that box for the Xbox and so it is stands we must stop by
saying that be particles reflect reflect both of box increasing the size of the box means a work is done against the walls and will have to talk about what that means in general relativity come to your house the 1st full day of work radiation would thoroughly and umber but 11 years and then sailed that she said the move was a little bit better get what that observed that he did 1 stench 7 because will that that's the expansion history of the universe and a member of the looking Out of the universe you effectively history looking to different distances using the university different time so by looking at the University different times assuming that homogeneous you can reconstruct the year of the history of expansion we'll talk about that but it's something that we can do basically by looking at a combination of density of galaxies is armed sky distance of galaxies would go spend a little bit of time going through that the combination on Keppel measurements Our distance density and so forth allows us to reconstruct the history and reconstruct the history because was seen at at different times like do he want with a new chapter Duff they will be off that yup yup and combining it with Percy and be endorsed things her dad was before galaxies formed the but were temperature history of universes there is plenty of evidence that the pictures right calf now key to the two-thirds is easy to see the key to the 1 half a deserters largely has to do with microwave background and things like that but get the equations that then will go and talk about how we know how much of his pictures right any answers North wrong the job OK now what I wanted to say is not all of it can beat to the dish yes said but not for what could you see like that bladder well you at their square really says or what their principal that things cannot can't exceed the speed of light yet what'd literally says as you can see anything going past you speed of light Our it doesn't say that 2 objects in an expanding universe can't be receding from each other and fast the speed of light that that as quite a and as you point out the error of the fuel have formula last equal distance by the Hubble constant and you make a distance big enough velocity will sure enough extreme dispute like mine it's connected with the idea of a horizon but but you're alright these equations say that things can move received from each other as fast as white and but for sure they don't allow our you to send signals in times faster than the speed of light get from 1 place to another and they don't allow you to witnessed something moving past you speed of light so far his cheeks so that the right before fisheries exceeds like richly disappeared since guest repressed Ferber horizon norms but that has to do with dark energy all that has be doctor and you that dark energy nothing would really move out of our our ability to see I will show you how the geometry work summer Orchard Norway's things a commune which real steps out of but yes is you it was worked out said that after 40 days exceeding its back would appear you got that it's more than that it's the accelerated expansion of the universe that that is true that is true but the universe will slow down and the sorry excuse me if this picture were right numerous with slowed down the and things which you are currently moving away from us faster than the speed of light would in the future be moving away from from us with less the speed of light and at that point we would be here we would that they would become visible so if this weather pattern eventually we could see everything no matter how far away this is not a part of the pattern that and if this pattern was correct then they will be in is an ultimate limitation that you cannot see past the point but what's what's fall back on track spend a lot of time on those particular thing I was ever really interesting things and will explore them the but for a while after Over but the where are your where is that the wavelength increases yet yes that that is correct the question is why do you have to suppose that as the universe expands that the way way of photon will match it why his wavering forked serve rigidly attached to the great if you like that's the question why is the wavelength of the photon somehow a rigidly attached to the these uh reveal degree anybody knows a little bit about the airwaves and Cobb wave propagation knows that there what Coughlin idiomatic abatic invariant BAT is the number of nodes the number of times a wave passes through 0 and as long as you change things slowly the number of nodes 6th this is called a Vatican invariant as they had 80 some sort of close circle that waves could propagate on this is something in principle we could build a have waves propagating on and somehow we yellow-striped think of an example I couldn't think of when I still can't think of 1 but imagine we have a dialog that allows us work to change the radius of this really here that things are propagating on another words change the circumference of changing the circumference of it will not change the number of Norwood's you might ask a self-help could it change a number of Nevada suddenly the day change the radius gradual or
continuously and what point would you expect Domino hear about the 10 or something like that you win on old means number of times at the Lavery 0 but now it has there has to be integer for 1 thing it has to be integer be waived going around a standing wave with circuit standing wave simplicity standing wave on here are Pasteur and be periodic so the number of nodes what has to be an integer neither stretching the space survey propagating on it can suddenly jumped at what point does a good jump from 7 0 state nor would it doesn't John what it does is the waves just get longer wavelength shorter wavelength to match the finger talk that sustained phenomenon except replaced this ringed by the University of number of nodes a number of zeros is invariant never changes and the only way that can be accommodated this is the year of the wavelength of the photon increases wavelength of the wage increases not any anyway even if it's not nice they like best supporters is a lob over here and nothing nothing over here by Fourier analysis it can still be expanded in waves that have the nice periodic smooth structure each 1 of them each 1 of them has a number of knows which is fixed and so that's good enough for us the individual waves of definite waved white can't jump the number of nodes and storms set instead the wavelength has to accommodate the size of the thing propagating on him heads of gallons University galaxies faster faster growth the media they met role of the Earth at theaters in the theaters because in the long way while UK away something is far enough apart when onwards aboard aboard a R you may enter my that rose continuously at some point exactly at speed life which means that must be met the All-Star get that people masses of thing Ameritrade less never change nest of electron as always there is no word yet by I think what the question itself that's what got your for so from mine shaft guest room really ought to juror for feet best thank you life but that he that it is not clear if they Brooker heard do broker will bosses made the IAEA With a a favor they didn't be it does rich worker we've got a of light that what you see is what you get both they led by With you when I my wait while we wait with talk a great deal about horizons and there are and geometry we can look at the point is we can analyze those kinds of questions by just thinking in terms of Newtonian or even special relativistic geometry where have to analyze them by saying his own rhetoric that there's a geometry and we have to analyze it geometry you do that you do that Rick industry can go only so far were were valid introducing real relativity so far we've been OK we didn't have to introduce relativity and the reason why is because we stopped tourists more of region always equations would derived by looking at galaxies which did not have to be very far away right we follow some galaxies richer reasonably close and we follow them if they're close enough dough moving with very tiny fraction of the speed of light so that's all we did we followed things which are close enough that they never got anywhere near the speed of light if we want to study the whole universe and out dissident out the distances where the Hubble constant times the distance is comparable to the speed of light if we want to study the universe on that scale then we can't do it without relativity we really can't go without general relativity so you're you're jumping ahead of the game and try to to get their thinking only about noon Newton and a special relativity there In the displaced setting what we do it single exploded view the dream but that there stressed we will use it could be the do you think of that that will be introduced although they energy itself decreases the easiest example is to think about the photon a box of violin strings the photon box exert pressure on the walls of the box because digs its pressure on walls of the box it does work on the boxes and expands the work is pressured by a change in volume and that's equal to the change in energy of the so photon is doing work on the box and in doing work on the box on energy use decreasing but this is also true and eventually Forget photon just take ordinary particles and gas in a box what happened to temperature in his box if you increase the volume down was at mean about the kinetic energy of each particle was due that few if you do it if a as look and if you infants as slowly if you do it into a test would slow it does or does not does if you do it very very sudden rate for happen was suddenly but it is a molecules of and you absolutely instantaneously suddenly increase the volume of a box what you find is a baby empty space the molecules a still in the original volume here and nothing has changed their energy the momentum or nothing else that's the 980 about case the adiabatic case means you increase of slowly and slowly means there's plenty of time for modules the bounce off the walls many times it will cool if you do things suddenly is likely to he even if you expand or contract to do things really suddenly is likely he armor or at least not cool but if you increase the volume of the box slowly it will call said get connected with disconnected but it's a phenomenal doesn't particularly have to do a photo arms is simply has to do with pressure against the wall and increasing the box means that work is done by the pressure on the walls of a box and to conserve energy it has to cool so this is this is the phenomena of the photons calling Brokers Group for more please
visit us at stanford . ETU


text:
The European Union's police agency, Europol, has confirmed the claim by the British National Party that terrorism will vastly increase as a result of the politicians' insane immigration policy.
The 2016 analysis by the EU police agency has warned that attacks on European people by Islamic State are only just beginning.
Politicians in Britain have failed to prevent hundreds of murderous battle-hardened Islamist jihadis, hell-bent on killing British people, from returning to Britain from Syria.
Also highlighted was the increase of internet radicalisation of the millions of Muslims pouring into Europe and becoming disillusioned with their choice.
As Britain's anti-immigration political party, the BNP has warned for decades about the grave threat to British lives, well-being, culture and identity from mass immigration – particularly from Islam, which the BNP has branded 'incompatible with Western culture.'
The BNP is calling for an immediate National Security Moratorium, stopping all immigration into Britain until the current chaos can be accessed, and those here illegally can be deported.
"It's no exaggeration to say that this is now a matter of life or death," BNP Chairman, Adam Walker told reporters yesterday.
"On the watch of traitorous politicians in Britain, an entire fifth column has built up in our country, consisting of immigrants who hate us, our country and everything we stand for, and in extreme cases, are hell-bent on killing British people.
"Islamists have declared war on Britain and the politicians have failed to respond because of their cowardice and dangerous idiocy.
"That's why the BNP is holding them to account, and demanding an immediate halt to all further immigration into Britain until we can sort out the politicians' catastrophic Immigration shambles.
"Only the BNP has the courage to take decisive and necessary action.
"You can rely on the BNP to put the well-being of British people first and protect the lives of British citizens."
Join the BNP today and stand shoulder to shoulder with those Brits determined to make Britain great again.

subset: commoncrawl


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Hubby took our little Monsieur had his first annual check-up/vaccination booster today. As we all know, Devons have greasy ears. Vet still insisted on swabbing him for ear-mites (negative) and selling hubby some ear drops (CleanAural) to be used fortnightly.
L Monsieur's breeder advises not to use drops in a Devon's ears. Sooo, what I'm asking is, should I go with breeder's advice, or the vet's? He has no infection in his ears, just produces a lot of the usual dark wax that Devons are prone to. Will the drops (very non-irritant) benefit him, or just cause discomfort?


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We at Acme House Co. believe that everyone deserves a chance to visit Palm Springs and experience our fantastic region, including visitors with special needs or disabilities. With its harsh desert landscape, Palm Springs might not strike you as a place where people with disabilities or special needs can plan a vacation with ease, but this couldn't be further from the truth! Below, we've detailed a brief guide to navigating your way through Palm Springs' activities and attractions if you're affected by disabilities or have special needs. Read on below to learn more about a Palm Springs trip!
From wheelchair accessible hiking trails to intriguing museums and lively cultural events, Palm Springs activities and attractions have much to offer for visitors of all levels of able-ness, meaning that neither you nor your guests will have to miss out on the full Palm Springs experience during your time here.
Downtown Palm Springs is the beating heart of Greater Palm Springs, home to an eclectic mix of bars, restaurants, shops, and museums. Because of their close proximity and ample interior space—as well as the diverse entertainment they offer, such as live music, fine dining, boutique shopping, and exciting parades and festivals—visitors who use wheelchairs, scooters, and other forms of aid can navigate the area with ease.
Iconic attractions like the Palm Springs Aerial Tramway, Palm Canyon Drive, El Paseo, and the Living Desert Zoo and Botanical Gardens are all very easy to access. See the sights of Chino Canyon and the San Jacinto Mountains from the tram, go shopping at El Paseo, watch the Pride Parade or go to a farmers market on Palm Canyon Drive, and immerse yourself in the natural beauty of Greater Palm Springs at the zoo and botanic gardens. If you don't mind a quick drive north on Highway 62, Big Morongo Canyon Preserve has an excellent wheelchair accessible boardwalk.
Finally, make sure that your lodgings fit your needs. A cramped hotel room won't accommodate you like a spacious and private vacation rental where you can fit any necessary equipment with ease.
In Palm Springs, there's something for everyone. Find out more information on disability friendly attractions and activities you can enjoy during your time in Palm Springs when you give our team of reservation agents a call and book your disability friendly accommodations with us today!
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Excellent trip – Lovely area, well selected vineyards and Aude was an excellent guide. Highly recommended and one if the highlights of our trip.
Christmas Markets in the Alsace Villages
The Essential Christmas Experience of Alsace
Visit the famous markets of Colmar, knowledgeably guided by one of our local team
Enjoy a moment in a small village Christmas market
English-speaking, hand-picked, local expert guides
Click the Tabs for More Information
Trip Details
110€ Per person (from 13 years old)
55€ Per child (from 4 to 12 years old)
9:00am to 4:00pm, every day
November 28th through December 23rd, 2020
7 hours
Trip style:
Shared sightseeing tour
Minimum 2 people, maximum 8
If your group is larger than 8, please get in touch with us.
Meeting point:
Place Gutenberg, next to the statue.
- Free time at the Christmas markets in Colmar
- Visit of Christmas markets in local villages
- English-speaking driver & guide
- Travel in recent, comfortable & fully equipped minivans
- Free WiFi access on board
- Personal insurance and expenses
- Meals & drinks
- Gratuities for the driver/guide
- Entrance fees to monuments, museums, attractions unless mentioned
Beautiful Villages and Amazing Landscapes - What a Combination!
The arrival of the little wooden huts in the town squares of Alsace's towns and villages is also a major event. The Christmas markets mark the return of time-honored festivities. A world of delicious fragrances, delightful craft goods and lights quickly takes shape along the rows, where some surprising and mouthwatering discoveries await the markets' visitors.
This morning depart from Strasbourg and head towards Colmar. Christmas in Colmar's Historical town center means a historic setting made magical by amazing Christmas illuminations that blend perfectly with the wonderful lighting designed to enhance the town's heritage. The pedestrian city center with its major architectural treasures that stretch from the Middle Ages to the 19th century is decorated like in a dream, a veritable open-air theatre where the warm Christmas mood envelops the heart of the town. Here, enjoy some free time in the city to discover one or several Christmas Markets on your own, as the town holds 5 different markets.
Then, depart along the famous Alsace Wine Route to pass through some of the most beautiful villages of Alsace. The afternoon program will depend on the date of your tour. Eguisheim, Riquewihr (Medieval market), Colmar and Strasbourg cities host a market every single day. On the 6th, 7th and 8th of December, your stop will certainly include the Christmas Market of Bergheim, on the 7th, 8th, 14th and 15th of December you will have the opportunity to discover Ribeauvillé market, and almost every single day of this festive season, the market of Kaysersberg will be ready to show you all it has to offer. After the visits return to Strasbourg.
Good to Know
- Instant booking confirmation
- Tour requires minimum 2 passengers (adults) to operate
- In case minimum numbers are not reached we will offer to reschedule or refund your tour
- Tour is operated in English
- Tour is not wheelchair accessible
- Children under 4 years old are not allowed on the tour
- Prices are per person
- Currency is in Euros
- Our standard cancellation policy applies to this tour –you can read about it here
Great wine tasting trip – A tour through beautiful country with a knowledgeable tour leader to visit wineries. Each winery had a range of tastings and a good discourse on the growing of the grape and the wine produced.
Great experience and a lovely guide – With our very nice guide Daniele, a very well mixed group of members and some amazing wines, this trip was totally worth it.
Don't miss this tour!! – We had a great time on the Alsace wine route tour. Flo was very friendly, warm and entertaining! We all fell in love with the picturesque little villages along the way and of course the wine was spectacular!
Great morning winetasting – We had a great time visiting two wineries in a morning, as well as driving through the Alsace countryside and having some time to explore the small towns. Great guide too.
Wonderful Trip! – Our guide Bridgette and the tour was wonderful and a perfect amount of time (and wine)! We loved seeing little towns and sampling some of Alsace's finest wines! Memories of a lifetime!
The Ophorus Difference
Contagious Enthusiasm – 'We had the most terrific guide! Very knowledgeable and enthusiastic' – Virginia B. (Delaware, US)
Flexibility – 'The guides really took an interest in what WE wanted to do' Paul C. (UK)
Area Locals – 'He was so much more than a driver. He really added local color and local flavor.' Daniel W. (Georgia, US)
Read more about the Ophorus experience.


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Patience puts Virat ahead of where Sachin was in the 90s
There are striking similarities between Kohli and Tendulkar in his first decade (before Virender Sehwag arrived to provide firepower at the other end as well).cricket Updated: Mar 02, 2016, 15:57 IST
The Asia Cup this time is more a springboard than a standalone tournament as it is being played so close to the World Twenty20, which starts on Tuesday, March 8.
The unusual pitches in Bangladesh have helped seamers, forcing teams to focus extra hard.
Though India won their third game in a row, against Sri Lanka on Tuesday night, to storm into the final of the five-team contest, their batsmen too have struggled against pace bowlers, who have enjoyed the extra zip from the pitch.
Virat Kohli has been an exception, though, and India were grateful he pulled the team out of trouble for the second game in a row, scoring an unbeaten 56 to achieve a challenging chase.
On song
The unbelievable level at which the 27–year-old has continued to play this season has given the team the batting steel, his dominant displays reminiscent of Sachin Tendulkar in the 1990s.
In his last six T20 games --- he was rested for the Sri Lanka series in between --- Kohli has hit four half-centuries while missing out on another by a run against Pakistan.
While the other batsmen also contributed, especially a vastly improved Rohit Sharma, Kohli has constantly looked to set the agenda regardless of the quality of bowlers coming at him. There was assurance in how he tackled Pakistan's young left-arm pacer Mohammad Amir, who was on fire as he removed three top-order batsmen in his opening spell.
It was no different against Sri Lanka, as India had been reduced to 16/2.
There are striking similarities between Kohli and Tendulkar in his first decade (before Virender Sehwag arrived to provide firepower at the other end as well). If Tendulkar hit through the line against pace to straightaway convey aggression, Kohli effortlessly regains the upper hand from pumped-up bowlers by defending from the middle of the bat before getting on with his brilliant cover drives.
Patience pays
Manipulating the field to steadily pick runs and rotate the strike is another common area. However, Kohli stands out when it comes to patience -- be it the batsman at the other end taking his time to get into rhythm, or is dominating the strike, as was the case with Yuvraj Singh on Tuesday.
Kohli has been unstoppable since he sorted out his weakness outside off-stump that had led to a painful 2014 tour of England. That uncertain prod vanished and that saw him pile up 381 runs at an average of 76.20 in the One-day International series in Australia in January as he and Rohit plundered runs on good pitches.
He does confess that his batting is more attuned to hitting fours than sixes, but that didn't matter as he averaged a stunning 199 in the T20 series which followed. He hit match-winning fifties in each of the three games.
The big question when Tendulkar and Co retired was about how the incoming batsmen would meld as a unit. In ODIs, Tendulkar's cheap dismissals used to be invariably be followed by batting collapses.
The current set of batsmen is far more resilient in limited-overs cricket, which allows Kohli to do what he does best --- finish games.
Get Latest Cricket Updates, Live scores and Top news on HT Cricket.


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While the Choshiu clan as well as the other clans of Japan, were anxiously watching the opening of Japan and the events which follow, Young Kano or Kano Ekichi was taken gradually out of his mother's hands and given to a faithful attendant of his father to he educated as a true samurai should he. Japanese boys are not baptized for there are few Japanese Christians, and in those days there were none; they have, therefore, no baptismal name. They have, however, given names, which are placed behind the family name instead of before it as we do. They would say, for instance, instead of Henry Jones, Jones Henry; they do the same with the words Mister, Master, Mistress or Miss, for all of which they have only one expression: San. If we should speak to master Ekichi Kano, we should say Kano Ekichi San. These given names can be changed without any difficulty. Sometimes the parents change them, at other times the owner of the name changes it himself, and again the Emperor or Tenshi Sama gives an officer a new name. But in that case, it is sure that the owner will keep it so long as he lives.
I can't say that Ekichi had a very pleasant time of it, although, of course, his father and mother loved him. Only they did not show it, as our parents do. As a little baby he was made to rest upon his knees, so that they might grow flexible, for the Japanese do not sit upon chairs, but squat upon their mats. When he rose in the morning from his futon or comforter which served him as a bed, there was no running to his father or mother, shouting good morning, and giving them a hug or a hearty kiss. When he did meet them, the first thing was to fall on his knees, spread his hands flat before him, and how until his head rested upon the back of his hands. His father and mother gravely returned the salutation in the same manner. When he took his meals, he was not permitted to say a word. He ate what was put before him, and it was every day the same. Asa meshi, hiru meshi, and ban meshi, or in English, morning rice, noon rice, and evening rice, there was no difference between breakfast, dinner, and supper. Until he was six years old, Ekichi spent most of his time with his attendant in the garden. They strolled around, and he asked questions which the man answered as well as he could. He was taught how to speak to a superior, to an equal, and to an inferior; how long he must remain prostrate before a daimiyo, before a councillor, and before a simple samurai. He was also taken to the grave of his grandfather, and told to kneel down and say his prayers. That was something he could not understand, and which his attendant could not explain; when he asked him, and he did often, the man would say: "It is so, but you should not ask why, because the gods only know." So, when Ekichi was tired and sat down on the sward, he would often think: What is the use of praying at the grave of a dead man. But he was careful not to express his thoughts to anybody.
He was trained not to show pain, distress, or grief. Whatever happened to him, his face must not betray it. Being constantly in the open air, he grew up healthy and strong, and when he was six years old, he was taken to a school for samurai boys.
Ekichi had been with his attendant beyond the gates of his yashiki, but after the first day, he was told to go and return by himself. He met his schoolfellows with the courtesy which he had been taught so carefully, and was treated by them in the same way. There was no playground. Indeed, I do not believe that any of those boys knew what the word "play" means. Many times, thirty years ago, I have seen samurai boys from eight to sixteen years old, during recess or after schooltime retire to their rooms to smoke their tiny pipes and carry on a quiet conversation; but I never saw them play. The government of Japan has found out that baseball, football, and cricket, are healthy games, and is encouraging these boys to indulge in them. But at that time, a samurai lad would have felt hurt at the thought that he could do such a thing as play.
It is really a day devoted to Hachiman, the god of war.
All Japanese boys are very quiet; they are brought up that way; but for the children of the people certain holidays are set apart. The fifth of May, or the fifth day of the fifth month is the boys' festival. It is really a day devoted to Hachiman, the god of war, but it is also called the Feast of Flags. A tall bamboo is erected near every house where a boy was born; for every son a fish, properly shaped and a very good imitation made of air-tight sacks is fastened, with its mouth wide open by means of bamboo hoops. The air enters and, besides inflating the body, causes it to squirm, flap, and dart, about the bamboo. They have other days, but the samurai boys do not observe them. There is still a wide distance between them and the children of the people.
At the time when Ekichi Pano went to school, the children squatted upon the mats, and learned the Japanese syllabary,—for there is no alphabet in Japan,—each vowel is connected with a consonant, and thus forms a syllable. The vowels are the same as with us:
Ekichi, like almost all Japanese boys of his class, learned very quickly, nor did the very difficult Chinese characters frighten him. Long before a Chinese boy could have mastered one-half of them, Ekichi could read and understand a book without much difficulty.
He was now growing used to the restraint which was imposed upon him. He began to understand that the word pleasure can have no meaning for a Japanese boy, and then he was made to learn that a boy is better without comforts than with them, except when he is sick. He was taught that there can be and must be but one motive for every action, and that motive must be: duty. Ekichi was but a child, and small for his age; but no boy twice as old in America or Europe, could have shown an equal degree of self-control, and contempt of pain and death with this child.
Japan's laws were cruel, at this time, and most offenses were punished with death. The criminal was made to kneel down, a flash of the sharp sword, a blow, and the head lay severed from the body. Young as he was, Ekichi was often taken to these executions, to accustom him to the sight of blood. His face was closely watched to see if he showed any emotion, and when he came home from these disagreeable sights, he found his rice of the color of blood, for it had been colored on purpose with the juice of salted plums. He was expected to eat heartily of this dish, and, like other samurai boys, did so without the nauseous feelings which our boys would experience under the circumstances. Sometimes, at midnight, he was roused from a sound slumber, and ordered to go to the execution ground, and bring a head. There was no refusal possible. Whatever he might think privately of such an errand, there was hut one answer possible, a responsive hai!" yes," and immediate obedience. Thus Ekichi, as all other Japanese boys of his class, was indifferent to heat or cold, and forgot that there was such a thing as "fear." He was not quite twelve when he was given two real swords, sharp, keen blades, made for use and not for show. He was taught that "the sword is the soul of the samurai," or, in the words of the law as it then prevailed in Japan": "The girded sword is the living soul of the samurai. In the case of a samurai forgetting his sword, act as is appointed: it may not be forgiven."
The child never considered his swords as toys; to him they were objects of reverence; that little dirk, eight inches long, might at some time be used to end his own life. He learned how he should behave and act, if ever such a moment should come. There is an instance in Japanese history, when a samurai boy only seven years old, committed suicide that he might save his father. Such stories were told him constantly, and roused his enthusiasm. At no time, after he was twelve years old, would Ekichi have hesitated to take his own life, if he had thought it his duty.
At this age he divided his time between shooting with bow and arrow, riding, fencing and wrestling, and the study of Chinese. He learned to swim and to handle a boat, and as he grew stronger, all dainties and comforts were taken away. If, in winter, his hands became numb, he was told to rub them in snow or water to make them warm; but he was not allowed the use of a fire. The duty of implicit obedience had been planted in him. No Japanese boy would think of asking why? when ordered to do something. Last of all he became master of that exceeding courtesy, peculiar to Japanese gentlemen, and which we foreigners cannot appreciate.


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I was four when ninety six football supporters left their houses for a semi-final and didn't return home again. I wasn't yet a supporter, the game hadn't sunk itself into me at that point. But even as I grew up, blinking in the light of the Premier League's blinding self-promotion, Hillsborough was there.
The official story – the drunk supporters, the breaching the gate – was supplemented by the memories of Heysel and a crumbling wall – if it wasn't their fault, how could it happen twice, eh? It was believable. It was believed.
It was a lie, immediately spread while bodies lay in a nearby gymnasium. Passed onto an MP in a bar full of officers supping pints as they got off shift. Wired to The Sun and unquestioningly published by a self-satisfied toad of an editor, seeking favourable view from a Government that was no friend of supporters. No friend of supporters, but intimate with the aggressive, corrupt and incompetent South Yorkshire Police upon whom they'd relied to bust heads a few short years earlier during the Miners Strike.
It shaped the game, it warped the game. The Taylor Report, which blamed the Police, took into account Heysel, the '81 semi-final crush and recommended every stadium become an all-seater. The was the death knell of Roker Park, Ayresome Park, the North Bank Highbury and the Liverpool Kop. Every fan had their seat, every fan had their place to sit, every fan was expected to sit. Ticket prices rose, as did rules and regulations.
Supporters are customers, they're consumers. Charlton Athletic's Chief Exec calling fans 'weird' because they fail 'to see themselves as customers…it's quite funny…they feel this sense of ownership' in December last year. Liverpool's U.S owners seemed utterly perplexed by the fury they were subject to, as were the Glazers at Manchester United. But that's nothing compared to the way 1980's supporters were treated in the UK. Like the miners, they were 'the enemy within'.
Let's get one thing straight. Hooliganism was a problem in the 1980's UK in the same way it continues to be so in many countries today – including the UK to some degree. I've seen the sad remnants of some of the old firms and crews, ageing bores talking proudly of their former street scraps like war heroes reminiscing, while younger men roll their eyes.
Not all mind you, there's still enough hyped on Green Street and lager who seek out 'aggro'.
They're a fraction, barely a decimal nothing, of the thousands who go to games though. The thousands who spend their brief out of work hours supporting their team, taking their partners and children along with them. Belonging to something bigger, something immersive and escapist in nature.
But at Hillsborough they were treated the same. To the press and the politicians, they were all the same. A mass, wild and untamed, needing to be brought to heel. They could only be seen as a threat. As a whole. Both before and in the aftermath. Drunken yobs. Pickpockets. Animals. The lies were believed because the lies preceded Hillsborough, the story was already rooted in the public mind, carefully tended to by police, politicians and the press.
Even with the exploding of the lies, the final disintegration of the conspiracy to smear the dead and protect the living, the shadow of Hillsborough falls across the game.
When A-League supporters are castigated by the press and the police, there's an echo of those times. Labelling criminals those who have committed no crime, labelling supporters savages and grubs, even making equivalences to gun toting terrorists in Paris – it's a shiver through history. They're all the same, these wogs, poofters and Sheila's.
Ray Hadley, Alan Jones, Rebecca Wilson and many others who – in the fine tradition of Kelvin McKenzie – build their profiles on attacking supporters, only football supporters mind you, and the game itself.
Wilson even went so far as to use Hillsborough as a reason to 'weed out (the) criminal element' in the Australian game, as close to 'the enemy within' you're likely to see. This use of a perversion of justice against the innocent dead in order to smear the living was swiftly edited, but it will not be swiftly forgotten.
Neither will the fight, the plight of the families of the 96 dead at Hillsborough. They fought, the families of the innocent dead. They fought backed by fellow supporters, a city and few others against police, press and government.
Eventually they gained political support, but it was a long time coming and there were too many failures of nerve to do the right thing by the established. They lived the battle to clear their loved ones names, and some died before they heard the truth established as fact, before justice was eventually delivered. Twenty seven years is far too long to wait. And all the while, the game was changing.
Because Hillsborough changed the game. The all-seater stadiums with numbered seats for each spectator borne from the Taylor Report. Supporters standing firm, standing together, and organising to defend themselves against opponents from outside of the game itself. The enemy without, you could say, with irony aforethought.
While I am certain not every football supporter is an angel, nor every media mouthpiece a horned devil, I am sure that there are far more examples of supporters and supporters groups as community and social good than the opposite. Certainly far more than to deserve the smears and the aggressive, ruthless propagation of lies presently aimed at them. Perhaps we'll hear more of them, to bring some truth and reality into the discussion.
There's no equivocation to the fight of those seeking justice for the 96 here though, there are only supporters who see those like themselves who left home never to return. And their families who fought so hard for their memories, against all the odds. Justice denied, justice delayed. But finally, justice.
Categories: A-League English/UK Football Other Football Topics