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Cosmology | Lecture 1

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start this this quarter's subject is Cosmo orgy of knowledge is of course a very old subject to her throws back thousands of years compel value you about thousands of years of cosmology by 6 thousand years but of the Greeks scores of the Leviathan ago here back thousands of years we go back at most the sometime in the 2nd quarter of the 2nd quarter of the year of 20th century when hobbled discovered the universe is expanding but let's say a few words about the science of because knowledge is assigned to cosmology is newly rich released what we not as Garcia was derailed yesterday but the modern subject of cars Monty is very really dates 2 well after hobbled it dates sell the discovery of the Big Bang the 3 degree microwave radiation that was discovered deserve as a remnant of the Big Bang about happened some time the sticks be so why was I was a student I was a young student and before that because ology was in the stands glass-like like physics and more like a bane of natural science or MetroStars studies this kind of things that that kind of thing you find the funny star over they find the Galaxy over looks a little weird classified you mean things he measure things to be sure but the accuracy with which things were known was so poor that it was extremely difficult to be precise about it and it's only fairly recently that physicist of physicists were always involved but they were involved because many of the things that you see many of these strange creatures funny stars galaxies and so forth of course of physical systems and describe them properly angular momentum they have all the things of physical systems have Ahvaz chemicals out there and so were physical chemist so involved but the thinking of the universe as a physical system as assistant to study mathematically and with a set of physical principles and a set of equations of course always sets of equations way back the wrong equations right equations and accurate equations things which agreed with observation that relatively new found more or less less over the history of my career and physics which is 50 years somebody like that the study that the universe a system and other words universe as system that we could study With equation we are like quake hangs in the wrong place right so where do you start we start with some observation now the 1st observation which may not really turn out to be absolutely true for reasons that were not absolutely true but looks at approximately true is that the universe is what is called drop isotropic means that when you look in that direction of that their actions that direction of that not us look right at the start looks a little different than the few look at them away from the start but on the whole averaging over patches in the sky and looking out far enough so that you get away from the immediate foreground of our own galaxy the universe look pretty much the same in every direction that's called isotropic same in every direction and that if the Lewis's isotropic with 1 exception described moment if it's isotropic around then you can bet with a high degree of confidence that also pretty close to being homogeneous homogeneous doesn't mean it's the same in every direction it means it's the same in every place you went out over there and you looked around from from our 16 galaxies over new apparently was see you would see about the same thing are here so far so with the argument that White being isotropic which means the same in every direction tell you anything about why it would be the same if you moved away to a very distant place and illusory simple on imagine that this distribution of galaxies it incidentally at least in the 1st part of a of study here it's not given that very much with what we're talking about are you aware what we call the galaxies or whether we just call the particles that has effectively man's points distributed throughout the space for the moment I might collapse and the calling the particles from time to time they must mean when I sit particles I mean blue galaxies but a journalist oversaw specified OK so theorists says a lot of them anybody not how many galaxies are within the visible world a couple of hours about 100 billion and Anteby 11 just unless numbers to keep track of incident with good idea to keep track of fewer numbers within what we can see within all we can say with telescopes are out to as far as astronomy takes about 10 to the 11th galaxies each galaxy about 10 the 11th starters altogether 10 to the 20 to start if each star has roughly can planets that enter the 23 Ava Gardner was number of planets there must be a planetarium a planetarium all right right now the imagined the where where over here in
every direction that you look at it looks pretty much the same well-known I maintain that not only must be the same in every direction but it must be the same from place to place swollen not to be the same from place to place well isotropic the only way could not be homogeneous it is said that it somehow form ratings of some sort that's gotta be such that would looks the same in every direction but it's not the shelves of shelves as have the geometry of some sort of Shell like structure White said that dozen literally me shelves it just means that job if that were the case if that were the case and you went someplace else and you looked around clearly it would look isotropic anymore so fertile look isotropic on accident we just happened to be at the center of the universe if we happened to be at the very center where everything just accidentally or accidently maybe by design happens to be nice and rotationally symmetric about us if we don't believe that they have to believe it's pretty much the same everywhere and that its homogeneous homogeneous means that as far as Kansas space is uniformly Philippe Kahn the average with particles uniformly fail that's called the cosmological principle but that you can't why is it true what they're not be true it's a cosmological principle and Her reverse some people argue that strong because of the observed to be true To some to some degree of approximation as was mentioned in some media that I don't have a evaluate some astronomers apparently claimed structures out there were just so big the blackboard was hold visible universe they would stretch across great big patches of red and that seems the media little bit countered that this idea of a complete uniformity and across certainly because they give complete uniformity is not exact disaffected theory galaxies means is but to send him here benefactor of clusters of galaxies and super clusters of galaxies so it appears it's not really a homogeneous but attends the common stock clusters which on some big enough scale like a billion light years roughly debuted at last if you average over that March looks homogeneous OK so that's the basic fact that would begin with Bell what's the 1st step in formulating a physics problems exhibit that Billy variables usually a shop pencils if brocade have sharply different Soviet Mexborough's mothers know you variables but arms are good step must show their comes after before raft is told you bet you bet to bed through going back purposefully going back a few decades sometime around the world this sixties of some 56 these our cut the idea that cosmological principle was put forward before people have any real right toe to put forward to just go about what's just say it's homogeneous who called the cosmological principle and people as as white strode because it's a principal but then it with more and more astronomical investigation and then finally the cosmic microwave background really nailed it and in some sense Over time ordeal distribution of matter was extremely small extremist will get a bite so here we have Her uniform catastrophe like 2 uniformed gas and that guess is interacting it's a guest of particles interacting each particles interacting with the other particles that galaxies on the whole amount electrically charged electrically neutral but then I gravitationally neutral they interact through gravity and that's the only important force I'm big enough scales I'm big enough scales were matter tends to be electrically neutral our the only really important force is granted until battleground is poll in the polling all the stuff together doing something to it but it's a little bit confusing what what happens to this point over he doesn't accelerate for the center because of the center of a bunch of doesn't accelerate out here because after all was much better at their as is on the side of factors don't look so reluctant to move in any way throughout the state this is much on 1 side is on the other side right or just well what about this 1 over here and things because every place is the same as every other place so the natural thing again Is that the universe must be just static just sit there because nothing has any net poor was nothing calling it 1 way or another that law will work out tonight the actual new Tony equations of world of cosmology but you may have heard that the expanding universe somehow fit together especially well and wasn't really understood until general a committee of that is simply for our baby so historically in terms of years yes it is true that the expanding universe was not understood until after Einstein created the general theory of relativity a fact about dates it's not a factor
or about large no I could have done the expanding universe noted didn't do it we are going to do it here the Wayne Newton shouldn't have done it if only he was a little bit smarter prior to solo the 1st thing know you not variables assured but the 1st step is usually introduce a set of coordinates introduces a coordinated door problem and that means exactly what always means text based roll it until quartets 3 dimensions for sure about a draw to another warrants introduced fishes fishes grid of court that what's we for the distance between neighboring lattice points on this grid when they everyone me we had to pay the 10 meters get to be a million meters take it whatever we like but there's a smart thing to do and just fix the distance between the the smart thing to do is to imagine these points of been chosen that grid points always passed the same galaxies was that the galaxies here provide a grid provided grid from such a way that no matter what happens the galaxies armed nice uniform no matter what happens this galaxy over here will always be at that point on the grid backed over here will always be a point on the grid and that means that if the universe indeed either expands all contracts the grid has to expand the if the galaxies are moving relative to each other perhaps away from each other a closer to each other and the grid moves with let's choose coordinates so the galaxy Our frozen in the great now it's not obvious you could do that that's not the issue could do that the galaxies was such that someone moving this way over here someone willing outweigh over here someone moving that way over here is a random kind of emotion then there would be no way to fix the coordinates by attaching them to galaxies because even at a point the different ones will be moving in different ways but that's not what you see when you look out the heavens would you see is that they're moving very coherently exactly as if they work embedded integrated with their grades perhaps expanding perhaps contracting come to that for the whole greed being sort of frozen any motion that takes place is because the grid is either expanding inside contracting that's an observation about the relative motion of nearby galaxies galaxies over here and year which are relatively nearby are not moving with tremendous velocity relative to each other moving a nice coherent way as I said so we can choose coordinates will call X Y and Z E standard names for coordinates x y and z but X Y and Z are not measured in Lane not measured in length because the weight of grid cells may change with time OK so River labeled the galaxies by where they are integrated and now we can ask the question of said a distance of 2 . 0 start with 2 points separated by an X distance over here a score X distance dealt the X how far apart are very well so far apart they are yet but I'm not going to postulated that the the distance between them the actual distance In meters or in some physical unit but you measure with the ruler could be beer like euro billion light years on the side of the road for the actual distance is proportional to develop backs the distance between these 2 people over here is half the distance between Easter was 3rd the distance between these 2 such proportional adopt X but following big part the year that's called the scale parameter the scale parameter may he'll only not be just a constant thing just be a constant constant than the distance between galaxies fixed in the grid would stay constant with time but it may also be time-dependent what's allowed that would say the distance between the galaxies of say this is Galaxy aII this is Galaxy beat the distance from a be a currents the X 8 without the taxes the X distances caught distance between them and writer more generally if we have to galaxies arbitrary positions on the grave then the distance between them DAB is equal to any of say the same have tea and then the square root of factors Mirabelle Texaco Air Force Delta Y squared was dealt squared the you measure the distance along the grid in Greig units and then multiplied by a T defined the actual physical distance between 2 points further said safety may or may not be constant are well Of course it's not there was constant time that would mean literally the galaxies which is frozen space maybe that's all we see we see them moving apart from each other vessel that calculate now the city between Galaxy a Galaxy beat is the distance between Galaxy AT and this of course should be belt that ADB the dissidents produced and but just use a simple formula appear but forget Pythagoras just pick from the B along the x-axis does matter his DEA what's the velocity between what a relative velocity of EAB galaxies it's just the kind of reverse right just a time to remove the distances the velocity of velocity between a and B is just a quarter of time derivative and the only thing the changing face of baby AT of fixed and the grid belt X is not changing at fixed the only thing is changing perhaps is a Molossidae is just trying to removal a dog means time derivative of ready for a dot I felt backs on done his
differentiate the formula with respect to time now I can write that the race although velocity to the distance only about loads loads a radio on the velocity to the distance is as the ratio of 8 . any notice that don't that X canceled out while that's interesting it means that the ratio of the velocity of distance doesn't depend on which pair of galaxies were talking about every pair of galaxies no matter how far apart closed my what angle Orient and the relative velocity between the 2 of them the relative ease separation or the opposite of separation the radio of the velocity of the distance is a dog over 80 you look at what what's a name for this thing anybody the Hubble constant called Hubble can't score at age now is there any reason why it should be of constant where we mean we say it's a constant there's no reason for it to be independent of the time in fact it's not what we find here Is that independent of acts doesn't matter where you are as a matter which still galaxies you talking about the seemed Hubble constant a given time or hobbled will as a kind of a misnomer the Hubble hobbled the Hubble parameter the Hubble function bubble functions independent the position but depends on time and now it is right the standard for the velocity between any 2 galaxies in the universe is equal the the same Hubble parameter times the distance between us there is a bubble so I don't see show by saying it being a lawyer yes yes yes indeed absolutely young man a you would never would have written as if Hubbell had discovered that the Nunavut applause right but don't have a lot in some sense not all that surprising always some witty persons said you shouldn't be surprised that the fastest horse goes further right now FSB Far from from you got so that's thing says however it's interesting connection between this formula and the Hubble formula is as you point out a close 1 but that's what it says is everything is moving on a grid and it's the grid itself whose sighs scaled made mania may not be changing what kind of course it is changing and the Hubble constant is just the ratio of the time derivative a heady itself OK that's that's stuff back stores all that that that's the fact of the facts as Hubble discovered them and theoretical Cosmo or just then had something to work or Coetzer said a few more things about this what about the mass within 80 region of sicker regional size the ex Delta why don't video I need a region which is big enough so that what happened my universe Emory University of a big enough so that we can average over small-scale structure how much may is In their well that is about the best it's in there is gonna be proportional to text of the white doctors the bigger the region that you take the more men and so it was just a Nestle Call it new is nothing but the amount that may ask for a unit volume of the grid but volume not being measured and meters but being measured acts are so let's say that's the in a given region of coordinator volumes of text of the white vote I'm really in what's the actual volume of that region but said the volume of the same region the volume of the same region is not built that extolled the white built the C. White because the distance along the x-axis and axis z-axis is not dope expert 80 times the OPEC's stop means the volume of that same self cell is 8 Q times dealt the ex Delta Delta's right that's because the lady from along the x-axis is 8 times Dr. X 8 times of the white times of the day and another a formula for the density of maps the density and the physical density of mass now how much mail is airport cubic kilometer of cubicle like year units we have specified units yet later oral specify units lover leaders of foreign leaders seconds and kilograms of fine Mass measured in kilograms volume measured in cubic meters what's the density of what's right called the density of standard terminology for density is role I don't know where it came from rose density he eventually and then city means the number of kilograms per cubic meters your life it's the radio of the mess the volume of the ratio of the mess of volume and is just as no here divided by a queue of formed on the ramp new divided by a Q that the amount the Mets in each sale in he stays fixed was fixed because the galaxies and moved to Britain so the amount of less of a given region and the grave stays the same just something called whom the Greek letter are divided by the volume get the density of course at 8 changes with time they did city changes with time that's obvious if uterus growers density decreases of the universe collapses the density increases so this is a formula that we will use from time to time now right so far where is
done nothing the Euclid himself could we do you need now enters no instead look let's not play games let's forget all this I will take into account the universe is homogeneous and all that stuff but no it was a very very soft person he always believed that he was at the center of the universe the children naturally the him that take the 1st set of the by Sir Isaac Newton and acting origin now of course we know in Newton also known that if these clever get the same equations no matter where it places themselves but there's nothing wrong With choosing be grid such that note and we are at the center of the Great Bend arrest surroundings moreover but your you also say are not moving both were standing still arrest at the center of the universe as far as From mathematical purchases and don't want to eggs and then of course were talking about scale so that everything is nice and uniformly distributed looks out to a distant galaxy you accept the Galaxy already and also how that Galaxy moved well that galaxy moves under the assumption of Newton's equations no physical agents say that everything gravitates with everything else but there's something special about this year no new this year called still with no fear is that if you want to know what the gravitational force on system is given that everything is isotropic doesn't even have to be homogeneous given that everything is isotropic you want to know the gravitational force in a frame of reference but had drawn here you want another gravitational force on that particle then and draw a steel with that particles on the centered at the origin and then take all of the mass with that's fear and pretend that it's just sitting at the origin To pretend that were not literally moving it just pretend that only mass in the universe women this year is at the origin and what about the outside misses on the outside they Norris notice theorem says the forest particle very isotropic world like this all come from the sphere inside these are the radius of particle and nothing from the outside I a gloomier proved that in previous classes in classical mechanics I don't remember but to true To truth with a truck theorem and the reason that we here evaluating the gravitational field on this end hiya why weakened pertains that all of the mass of the earth is at the center of Europe my evaluate the gravitational field after keeping in mind appears as a sphere keeping a mind it's pretty uniform and so forth I could just pretend that all the mess was at the center of the until of course take hits the floor Sonora mass was but votes the flock pretend that all mass was concentrated center and furthermore the masses outside the armed even has a lot more appearance of mess out there not talking but sealing the building of talking about galaxies there a lot more but better doesn't feel and only feels the things on the inside of the sole notices on further it is unwilling to take this galaxy which is at a certain distance away distance distances deep and this stands in the square root of X squared plus Y squared Posey squared act square y scored square of the coordinates service for Perahia times the distance from the center could you read a visit these easier read original why registers elapsed as red readable but scripts Quebecois square was a square that's Pythagoras and multiplied by 8 defined the actual call let's call that D equals any of tea was just call thing here are capital on R is not measured in meters it's just square-rigger expert 4 square poseuse squared that's the distance from the center of the galaxy in question now known as equations are about force is an acceleration was so the 1st thing is Let's calculate the acceleration of X on the point X of the galaxy at the point x relative to the origin or 1st of all our city velocity of VAT he called a dot after firms are more about the acceleration the acceleration is as differentiate again acceleration is equal to a bubble not of tee times are going have to worry about where the horrors changing the kind not because the galaxy is at a fixed point in this expanding lattice porous fixed for that galaxy service the acceleration we could multiplied by the mass of the galaxy of we wanted to buy only this just acceleration earlier said that equal say that said that equal to the acceleration that we would get from all the gravitating material inside he thinks so it's a March 1st question is how much masses and busses scope amassed a massive into the have the inside this year formula that we're going to compare this way please note in the gravitational formula force is Eagleton times mass
which mess is warned here as a galaxy vessel they want Petronas act Of all the Sonny inside and the distance between 4 distance squared missing couple think took things are Mr. Newton's gravitational constant 6 . 7 times cent the 11th in some units I'm missing 1 more thing when orders from and my assigned indicates that the force a tractor pulling in right the convention forests pulling in cabins negative force pushing out his camp positive alright this is the force of gravity on particle of mass and what the acceleration of gravity the acceleration of gravity is just dropped the Mets just dropped out get the Messier the acceleration was the force per unit mass and right just as the acceleration and my Midas and GE divided by C squared off acceleration of that event not of not divided up a small there were arrested acceleration due to the presence of almost medicine interior here and there had better be equal throat a double . 3 times are done knows where this is going but we just following knows writing equations and still easily the radio you start out with some physical principles you're right down the equations and then you blindly follow them for away until you need to think again so we were aware on autopilot now we're just doing equation but arrived here a double bottoms are his Eagleton minors and GE all these squares OK let's but plug in the sky over here the distance it is 8 times are so that we can maybe it will not at some point might have actually discover something that looks interesting at the moment that just a blind those AFT squared are just a square it was of course a squared a squared turn anions D squared squared times there are square Rod 0 0 courage now excuse me but I'm just going to devote by are he says secretly Nova going right maybe you do to protect a guard Q derided MM the ride by another 80 fixes HQ 0 3 Bell was George Mr. but next question What's the volume of this but that the volume of the ever since this is no age equation now volume of the sphere of Somali 4th Arabs former Arabs now that are killed now they killed forgeries 8 fueled times are killed at because distances really 8 terms are best actual physical volume when I say the volume and the volume was measured in some standard unit like leaders press volume the look here we have a few times are killed here but Iraq that as Volume 3 of 4 Torre volume is equal to any cube barbecue Ahmed have been dumb edition yellowed that's that's done with some throughout but just look at this formula he noticed that we have a kill block you downstairs let's multiply by former on 3 5 or provide that for over 3 party and multiplied by 4 over 3 party for us 3rd party or did here I on duty here for mill I have a hand over the volume water over bodies of the dead city cool summer some nice maybe have a double by over a physical Tom might for 3rd party Newton's constant firms the radio of the ask is nets here the volume and that's that it is to the density the Bay Hill source a cordial ball this there really doesn't depend aura anymore if we know what the density of the universe the density of the universe does not depend on where you are the density of the universe does not depend on the left-hand side our has dropped out the right hand side no memory of all our it means this equation is true for every galaxy no matter how far away same equation had we done different galaxy we would have gotten the same equation the only way that this equation had any memory of which galaxy would talking about it was because of all but are dropped out of the equation that got a good thing because we want to think of AD something which doesn't depend on where you are then it had better be further drops out so Ludena confirms what we might have expected that the equations that AD it is a universal equation for all galaxy of disease because if we years viewers resort they will bid again if we will gotten exactly the same thing no matter what they are doing but it says the urgently the forced to with them so that's right outlook well it has president the of which I know you have a normal the point is you have to do the betrayal submission carefully you have to do the transformation carefully you go to a larger and 80 offering no could have said let me work this out from my frame of reference which I was put myself the origin of
study now the relative motion of some galaxies relative to some moving some Galaxy which is moving it would affirm exactly the same equations but it would have had to do the transformation carefully so we finesse that got away from it but just putting ourselves of center but as you could see the final formula doesn't care where you want it confirms the fact that nothing really depended on which galaxy we thought of as whole that pressures force if wretched that list of your a force you to my with think about is really a for now got I N not in the In this way of thinking about it the forces always toward the arch right but heavily station ourselves on some other galaxy was moving in did all the transformation remember when you go to where are you are moving frame there are think forces inertial forces fake forces that you have to do so from the point of view this guy over here this galaxy over here has a forest which could be thought of as being taught here plus a fake forest the fake forest being in the force due to his acceleration but we got around that by just saying what position ourselves at the center no acceleration velocity which is center the only test question the question is do we get me which doesn't depend on who we are and which Galaxy were OK so that that's that's part of the main message of this theater doesn't depend on which galaxy urine and really didn't depend on Newton's assumption that he was at the center actually it's a daily thing it changed they a at well yes yes yes new things were
change the north are confident they can rewrite getting bigger constant convince based yes group say that a constant in space it is the principle of the universe is homogeneous ever absolutely everything hinges on the homered unity 80 of the universe right and right not right the number on mass per unit volume is the same everywhere and space yes everything hinged on that and they're OK so here's 1 equation central fundamental equation of cosmology and it's a differential equations equation Howell a changes with time there's a number of things look at the 1st interesting thing that it is it's impossible have a university which is static Static means it doesn't change with time unless it's and means row equal 0 only that is empty decide 0 can time derivative of a seal a 2nd time derivative in this case be 0 self we derive the fact of the universe it is not start but 1 more thing we could do to make this to make this an equation that we could solve is the replace rolled by the constant loom divided by a Cuban no new is literally a constant that's the number of galaxies times a massive a galaxy in a unit cordoned volume doesn't change with time because 2 galaxies of frozen in the grid and so we could write this equation 1 more step a double Vogt not surprisingly is a double . 1 enabled us because his equations about acceleration were not surprising is up about a calls minus former over 3 kinds G the this city but the point is now the density is not a constant Lu was a constant but no over a Cuba's is not because it is changing with time so Roberto in he ruled divided by a Q OK so there's a lot of constants year minus the minus sign is a constant for Hi over 3 G Newton a constant and we can pick who also could be a constant everything now here is constant 80 is not constant but we have a kind of differential equations visit differential equation equation of motion in terms of 1 constant for upon Igino over 3 we have the equation of motion for the scale factor for a scale factor as a function of father who was the 1st the discover this equation it was actually discovered in the context of the general theory of relativity was discovered that think Friedman proud Alexander Friedman Armed before killed in World War One I think I was using the general theory of relativity consisted of Christ her hair should have done but it is perfectly possible was nothing in it there was just Google Newtonian mechanics we see a lot of work multiplier Ferrari now they go but job is left just such traditional prerogatives when the tradition said negative side doesn't think about whether there is any it doesn't tell us expanding contracting OK may explain why the May write theater where we just have the Earth but competitors was something else the earth and we have a particle that he let's put on the X-axis but as an equation that part eclipsing equation let's call it now or expert X doesn't stand for these coordinates now just standard deposition coordinate all armed the height above the earth satisfy some equation next double . is equal to the gravitational force where the gravitational forces MG earn over X squared my are at OK there's this equation is what this equation tells us is that the particle is accelerating toll would be the minus sign tells us acceleration toward the earth but whether the whether it's moving away from the earth or 12 Earth is a question of velocity acceleration is the velocity that 20 hours it well you could imagine somebody over here taking this particle and rejecting it that way below our positive velocity will be moving away from the theorists you could also in the same person pushing if not we will moving toward theorists Exs decreasing the acceleration will be the same in either case the velocity will have a negative acceleration which means going this way it'll turn around on 10 around during this way increased velocity on whether turns around or not depends on what the initial conditions or whether it's above or below the escape velocity but the Eva case the acceleration toward the earth so noise that accelerations pointy earth as it is for this and does not tell me whether it's moving up a moving now can move up and down there and you get a point so I know this equation doesn't of the universe is expanding contracting but tells us that the 2nd derivatives negative so means that even if it's expanding its pending slowed down or expanding its timing to slow down the rich contracting tending the speed up contraction there is a large here of whether you are above or below the escape velocity will come 5 I was
asked a question I would will point out on our society name art as we you look at this is it this is negative and look that level of events said this is positive the universe is expanding its positive outcome this was negative but that's because it read carefully to Nazi-era only 1 lucky this is velocity this is acceleration are hard for acceleration to be negative unite area in India new Ferrari enabling them a man are among the order of the were pressed out on the break you're accelerations negative is positive slowing down but you're still lie ahead now that the universe is not slowing down this swimming where were really doing what no 1 would have done their work all cars just thought the right thing to do work was until about 15 years ago would have sold 15 this it is you know as a model of the universe and it is a model that would have been called the Standard Model close to it the standard model of the universe until until the accelerating universe was discovered as is decelerated the universe accelerates was gotta be something else in this equation worries there several things met equation but will come there are some parts don't do have to do wearing started OK let's talk about not as myology but just particles rocks stones thrown upward from the surface of the earth now equations Samoa the but just examine them from minute and McCormick couple of questions about it Is a we might as Well think of it as a point because no no the improve the fear and that we could think of it as a point where outside were above the surface of Eros here his here's off particle here were struck over here not Over here X-axis the X-axis end what aren't equations the equations of Newton's equations but is actually more useful version of the equations which is just energy conservation just energy conservation let's write down energy arm this particle over here the write-down of insurers in fact a more useful equations and swarm energy Energy acquittal more useful in articles and what is the the energy of the particle here that's moving outward has some velocity the velocity could be negative it could be moving inward always the total energy of the particle with low-energy of it is it's kinetic energy plus of potential energy kinetic energy 1 half the massive particle not the mass of the Earth as particle from velocity squared which we could call X parte where if we want velocity squared from moment or about the potential energy and other the potential energy potential energy is my nest and Newton's constant divided by what are our squared just if said it X X X X now this can be positive or negative believe it or not the energy does not have to be positive for example supposing this particle over here is an arrest on how it got there it got there initial conditions it Garcia at that sometimes it at rest but as a positive value of X X is really always pass really stands for the distance from from the earth from need not be X quarter so Exs always positive this is always negative this can be 0 if these the particles arrest and so the energy is negative and that case the energy could also be positive supposing we now take the same article at the same position but give it a velocity of the velocity is big enough this can outweigh that this can outweigh that simply when the Farouk equation down right the minute when this it is a big event s on the kinetic energy bigger than the potential energy and they can be volatile energy positive not the apology is positive this thing can not turn around can knock you might say Well let's see this article could go out and turn around why can't they turn around if the total energy is incidentally energy of course is conserved so whatever the energy is 1 instant the energy and into every energy conserved let's upon it turned around the that point woes velocity be that . 0 sewer energy be negative right so they are for if it turns around Snyder Vienna Jews if it doesn't turn around positive energy equals zeros Over the edge of parameter space if the energy is positive the particle just keeps going going going in escapes if energy is 0 that's exactly the escape velocity Will escalator whether escapes exactly 0 was the escape velocity the escape velocity is the solution of the equations that this is equal to 0 right about 1 half v squared and dropping and because cancels from both sides the little and 1 every square Eagleton began big G divided by X and now it is multiply by 2 and that gives us a formula for the escape velocity as a formula for the escape velocity when the energy is exactly equal to 0 in exactly the same manner the universe can be out by the
escape varsity below the escape velocity war at philosophy will work that out there but all it means is if it's a bomb escape velocity it means that initially some pouring be outward expansion was large enough that doesn't turn around its below the escape velocity and the universe turns around 3 contracts that's the main reason for sure knew best and the escape velocity is currently a is velocity is also the velocity it would see energy is equal to 0 deep that might escape velocity same thing is energy to 0 by now let's concentrate on this particle here now for all practical purposes this particle here all it knows is that it's moving in the gravitational field of point man at the center where the point may assist capital and so for all practical purposes we can replace this problem although he might this 1 over here In fact it's exactly the same problem so 0 let's work out and rejects kinetic the potential energy of the particle and keep in mind that constant its constant because for all practical purposes this article is moving exactly as it would be if all there once was amassed the center and that case and you would become so it is left to it things I wrote before but let's for amount died at his change it to us order all right steps no no the halt the whole thing is growing by a remembered the great everything most of the great everything moves the great going if changes a the amount man In this spirit expects another words the number of galaxies that this fellow although he is sees within this fiercely sex organs so now so we don't have to worry about the change would out now the energy the Connecticut for the Connecticut Post potential energy in the in notice frame in the framework of the 20 of them these quantity and 1 half a mass of his Galaxy Funds of velocity squared but that 8 . 4 square on square right are wares they are saying guessing on D is equal 8 times are this since they 8 are velocity a thought times are this is what have and and my tests will end big and GE violated by a distant just provided by distance of the potential merger Jia was a distant distant fund already let's go the and that's equal to the energy of this the kind of energy now for simplicity and because because of its simplicity and also some real tired I think I'll just do tonight a case where the energy is exactly equal to 0 what correspond exactly the critical escape velocity that paced the other cases just as easy but but let's do that case so that's a case where the universe just on age not clear whether it could turn around fall back over to the keep going on the edge of a cost of doing 1 or the other set this equal to 0 let's work out that equation is work at that equation using the various things we know OK 1st thing to do is to get rid of the little in here why should we give removal and because it appears above terms hiya and all things equal zeros are divided about also multiply by 2 weeks maximum divide by are squared you know why why am I dividing by our square 1 get you down here because I'm not that are 2 of this has to do with volume and the volume and density of trying to get this thing in terms of density so divide by are squared and that and that they are downstairs that's nice because on May us here and RQ downstairs it looks like I'm getting the density but not quite because the volume of the spheres 8 Cuba times are due not 8 times are so I do I justified the equation by another square Q. OK that's off of make Juba times are killed a few times are or I do next well from smog multiplied by 4 almost 3 times that literally make body by doing something illegal on have multiplied here also for over 3 times 5 Eagle 0 right people 0 or almost back theory right at 8 . 0 squared remember laid down Is this the Hubble constant so this is a square of others I think it back from the hobbled thing he 8 . 0 square that's the Hubble feet square and that's equal to transpose in his right hand side 8 high over 3 famous 8 to plans for state aid Hi over 3 there's a GE and now lives in am divided by the volume of this year a swipe that's why I went to this every year for another couple of factors of 18 or downstairs so that I would get 8 divided by the volume of this year and that role mass density roam the actual a dot of a square equals 8 pie over 3 G times role that is a free immigration us Freeman equation the way that usually its equimolar accords this 1 over here is
energy conservation also said the image equal 0 the story here is quite but the same physics a saying physics Newton version of the conservation of energy version of it this 1 is more useful as it's called Freeman equation it's not completely general because we it said the energy 2 0 bits just exactly the critical escape velocity Miss Universe is not cannery collapse but Skinner what what does happen if you shoot something out at exactly the escape velocity what happens its motion as time goes on still the year it is asymptotically gets Lawrence Lawrence Lorber never this universe work asymptotically gets Lawrence Lawrence Laurent expansion but never turned the singer's OK so that's our that's our freedom equation I'd like to solve it but I don't know enough yet the reason I don't or not His biggest his role over here and I'm what the withdrawal except we do not want to do with roar the equation that Rome is equal to the constant known incidentally the constant new could be said to be anything you want it doesn't its mass per unit coordinate volume like changing your coordinates you could change the amount of Macedon Court so I actually know never really comes in anything but rose equal to newly divided by a lack OK so we can now write an even more useful version of this aid died Over a school a quarter 8 by over 3 GE New Woman and nor was it can't stay below does not change with time divided by a Q the grammar right although this junk years just a pine over 3 times jeep just and fact that could if I like have chosen new rules so that a pie Geo noodles 3 is just not the No. 1 is not nothing interesting of the basic equations basic equation the basic form of the equation is just a dog a squared equal to some constant but let's just choose constant to be 1 just simplicity is 1 of a few if we can solve this equation we could trigger solve this equation it not hard to go from 1 of solve we like to see how the solve this equation now noticed 1st of all that the right hand side is always positive in fact it never quite goes to 0 no matter how big a gets its always positive as he gets really really big get smaller and smaller so that tells us that a dialog a net becomes equal to 0 8 that equals a dud equals 0 would be the universe turning around a be place where the universe turned around the expansion rate Creek there 0 tells us the expansion rate never goes to 0 Hubble constant never changes sign a release a square of bubbles have never goes 0 4 dozen 0 can change sign and bath it does slowed down the Hubble constant gets smaller and smaller and smaller with time so it's as if the uterus just get hired of expanding but it never gets tired of must stop we interests solvers on I think I will just take getting late and I get tired about the so I will take the easy way of solving it but we will come back these kind equation will combat and then this type of equation is absolutely Rice said that this type of equally type of equations absolutely central all of cosmology the solemn solve them quite easily let's just look for a solution of a particular I take a look for a solution rather than solve the equations let's looks even find a solution wet a song constant plunged time for some however we don't know that of the actor that we solve this would only contrite begin Eckert trial solution 80 equals a proportional to he would just wait proportional to mean grows in proportion time erasable away when I expect that to be right now because the thing slows down could look for a solution of this type so let's try it out pacific and if we use the equation the see what whether we can solve the C & P OK so what's 8 . show a diet is seen as a key feature the minus 1 right but differentiation now 8 . Over a it's easy we just have to provide a story of the providers by seeing that sees cancel need the constant fear cancels what's Tito the P minus 1 overtly could he'll right that's the left-hand side he owe it see CRO sorry we of the square at best Hey squared or T-square that's left side squared site Peace Corps school now about 108 see what that is 1 0 8 2 0 that's warned divided by seat Suu Kyi the 3 have a right to do right now we can read off match the 2 sides of scary of Estonia must match the 2 sides In the denominator we have power we also have a power over he misses 1 of the key squared this is 1 of the key to the 3 P that until you look he is yet so we won a match I just said let us look for a solution of the form C C B and C of your figure out what seemed to have the baby while the 1st thing we learned is a freak he had that equaled tool otherwise these things can match his Norway the peak of philosophy had squared so the 1st thing we learned that 3 key St equal tool Camacho
Internet site that will guarantee that the sea squared 50 squared agree on the side and we also have to match the constant and the constant tells us that he squared equals 1 or Aussie so that tells us was really only 1 constant that we have to worry about you he or city once we know he now we don't know we know P from here and therefore we know the constant constant is not so interesting what's interesting is key because 1 piece saying it says that AD expands like key to the through 3rd he is equal to two-thirds are some constant bunch keep the two-thirds how that's the way and Tommy and universe would expand had was right at the critical escape velocity would expand the scale factor and everything galaxies separating as tying to the two-thirds parlor at a quite remarkable derivation I think I think don't know and I don't know why he didn't do it it added that annoys me that he didn't do it he should have done in the last 50 went to remain at this point there's something I'm not sure what happened all that was disposed of in year that movies via a video played no overseer of the tulips Fisher that we do issue yet you but he was 1 of the suckers Rebecca suckered by the look Opel the hedge Trimble had so you know it's smart now the eye but I think definitely got stung if that is what you do but bad that you know we should have predicted that viewers followed yes he did and he worried about the fact that a homogeneous universe are 0 yes he mn he most certainly had speculated the enough that he was right on the threshold of the received ask all the questions about it and didn't quite carry out so yacht is it assumption not give yes this best please the actually not but yes that's a pressure with them completely new in theory in the Tonys fury spaces flat spaces flat just goes on and on forever so yes the Colony numerous with infinite who've been spatially flat who would have had an interesting Einstein geometry of any current or lower than expanding or contracting law and it would have been entirely aren't so I I think this just 1st of August easy 2nd because it contains a lot Of the physics we're going to be dealing with the NATO simple bomb and it gives us In marvel universe gives us a marvel universe With a scale factor that increases elected to a 3rd power over time not that there's still a sport had stayed off I never quite know northerners another turn in this equation His mother tenderness this equation are and we will come out of the race for us now they can't be because if you would if you had negative energy would be collapse right so was another term and the next time will pick up that the I will talk about the 3 possibilities lesser 0 poetry 3 collapse greater than 0 of universe expands were about even thinking about it and this list which is a critical point where slows down certain white mother diagram that people always draw for this kind of thing looks something like this you've probably seen firms fierce wiped on the vertical axis plot AT the scale factor um a horizontal axis to plot hurry but AT equals not was most sensible cosmology because that would withdraw it use a horse nor does it mean that that aid decelerate the acceleration was negative but the beast that decelerate the statement that the curve is bent over this way as opposed weight the 2nd derivative is negative Herb Moses way 82 the 2 8 of the two-thirds looks approximately like and of course it dipped it keeps growing what about a re contracting universe where numerous recall after collapsing universe would look like crash there are AT you look at this does not approach a straight line plea was my approach a straight line it is bending over slightly more and more on the universe positive energy would look pretty much the same and go off on a straight line on a straight line those of the 3 cases that will will describe get right nor reacted prospectuses for them normal that's incorrect Lowell the case of positive energy but in any case in all of these cases the tendency is to curve all over because the accelerations negative for the real universe does not look like that really universe starts out looking like that and then start curve upward it's accelerating really universe is accelerating back filled with leader it seemed I got big fire solution or not we will visit a Burnett the the solution will solve the equations details of his it this this is a solution
yellow your not Yo solution bombers or we can change the energy Chazy away from 0 and if we do we could generate the other kinds of solutions face any questions and tired with then no no no no no a are sorry now a derivative gets smaller and smaller aid to the two-thirds are so where we young we're ready Barnett yacht Tom bucks he did it it deserves is Eddie an aide Dr. is equal to two-thirds 1 of our feature the one-third star the slope goes 0 locals 0 logic was always possible of is the center which is getting tired the slope reserve is and you could see now wine starting they hope to be able to describe a static well will prompt or getting ahead of myself and organ of a pig but were observed a alive hinged all that draws wept we all know that if I think that Newton was credited on certain yet see no I had this idea that the universe was 6 thousand years old and this was getting together with insisted it was a believer so I think he had some I I think the reason he probably didn't do it is because they couldn't make it fit with his prejudice of the age of the universe but that's true the day process be right that a lot of work to do yeah euro more about religion did about a mile or more more matter of what our religion I think help me physics prolific writer lots but that might yet that I know that the same may by Judy traffic what set yacht yuck yuck they're not surprising since this is about energy gap depth absolutely not now this is this is this theory without a cosmological constant the cosmological constant is what has to to do it the acceleration is theory without the the cosmological constant practices called on matter dominated universe matter dominated universe for reasons that I will explain you always know the universe is expanding world works or their so galaxies the fleeing that but certainly yes yes yes yes on the average is the average out the largest observable distances as expanding by individual portions there are places for example our galaxy is attracting together with from drama is not receiving away from but the on a larger scale br Hummel law is not exactly true for all possible distances it becomes accurate as distances get larger it's certainly not accurate for the 1st things which are bound together things such a close enough together a really bound together by gravity or any other force may be pulled together odd so as it happens it's not unique but on the average everything is moving away from everything else but here and there you confined galaxies which have duly motion that turned peculiar motions technical and it is a technical means and means but How away from me average so that overall relations we should avoid those little choice leisure average over a large margin of volumes that rule fluctuations don't matter as the same kind of things that guarantee uniform whether be a renewed rumors uniform while I really true their places where the fluctuation or more bands of fluctuation awards West End but when averaged over a sizable region um means bigger than that many molecules be rumors dutiful saying things or year Richard from what you with sectors Bush yes yes yes drama that just happens that for whatever reason I don't know what's really the complete history of the drama of the P. way Europe dynamics it was but what reduced however was formed it was formed the pocket which was then enough that just as slightly out of the ordinary was dense enough these to galaxies have enough matched to to overcome the effects of the expansion but that's a fluctuation away from the war that drive start a what is clear and her away Dad lost none of that identical means a USB that Alaska No. 2 that was 7 years ago I think you asked me the same question now there's no there's no difference to see you either take the position that the galaxies are moving away from each other all you take the position that they added as grade and the grid is expanding that's about America perhaps and Einstein's way of thinking about it it's a little more natural to think of the space expanding but they are equal yell or more caution is Israel rather 0 0 are Yahveh reserve yes there is from a former cosmic microwave background and blue CompuAdd its says it's a star network of different terms different observations of supernova mostly supernova but called work words that particular forcefully for more please visit us at
stanford . EDU
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Metadaten

Formale Metadaten

Titel Cosmology | Lecture 1
Serientitel Lecture Collection | Cosmology
Teil 1
Anzahl der Teile 9
Autor Susskind, Leonard
Lizenz CC-Namensnennung 3.0 Deutschland:
Sie dürfen das Werk bzw. den Inhalt zu jedem legalen Zweck nutzen, verändern und in unveränderter oder veränderter Form vervielfältigen, verbreiten und öffentlich zugänglich machen, sofern Sie den Namen des Autors/Rechteinhabers in der von ihm festgelegten Weise nennen.
DOI 10.5446/15065
Herausgeber Stanford University
Erscheinungsjahr 2013
Sprache Englisch

Inhaltliche Metadaten

Fachgebiet Physik
Abstract (January 14, 2013) Leonard Susskind introduces the study of Cosmology and derives the classical physics formulas that describe our expanding universe.

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