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# Topics in String Theory | Lecture 9

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extra more played diagram so this observer looks back and as time goes on gets to see more and more but never gets to see more of the space time is in the back like cars here so in particular never gets to see anything out here for here at least doesn't get to see it in any sort of usual standards so the region most of space and time almost everything is totally inaccessible to those observed now course may be another observer over here however observers something else that some overlap OK but this person gets to see everything in here this person gets to see everything over here works so simplified just that you want observer of the time for all practical purposes is universe space-time universe is backward like cars here now what is busy busy see things a world which seems to depend on time you would think sell you might think well everything seems to be exponentially expanding but let's just below us a very simple exercise let's consider it this distance and compare it with Mr. spends and assistants and assistants and this basically this distance drawing year is the distance from the observer to his horizon let's see how the changes would partner looks like a shrinking will assist checker here is a metric electric and let's put this point over here at T equals minus 1 but but this point over here he equals minus hat this 1 over here if people's minds of quarter incidentally that corresponds to uniformed picking off proper time each you look proper time would correspond to dividing this interval by half that's the way this transformation work as 1 of his innings the amount of time in here and now calculate this districts to calculate that and we just look at the metric system at and all these 2 points are separated by a spatial distance but no time so they still pouring are separated by Zero time interval that means in this former here should be equal sign the should be equal R D do all it really out there was no time separation of all between these 2 points so let's write now finally formed not differential form the square of the distance scholar from AT the beat what is that no time separation what is the dealt that X between these 2 points you tell me this is a 45 degree angle this distances capital T. distances also capital In fact on-site bother writing Misty was minus 1 wanted to speak T letters be this distance here the horizontal distance is also the same as the vertical distance we've 0 from here from here we get plus and Delta X it is the same squared but now divided but he squared age what's the answer 1 over each squares another distance from here to here Is as war age as the actual Rio
Alice still 1 day alleging Alice Falls over verizon get squashed Jane gets closer and started get squashed how's gets closer Jane also another where kind of sedimentary structure Forms New horizon but is gradually gets closer and closer and hair skin here now that's a classical description of what actually happens quantum mechanically is more complicated and walls this interaction with be emitted radiation and what which that's all over the place the ionized isn't Cookson does terrible things but the classical prospective you would just lose track of them as they get squashed closer and closer and you lose track of them because the radiation from them we get more and more and more Richard closed ever at a day case the residents or 2 they city clothes don't cross over Alice has no problem of arrived shows perfectly happily real Bob just lose track of buffer tries to do an experiment which sees what happened we come back to this very strange situation as Heisenberg um microscope situation where the only way to do an experiment Mr. shined some high-frequency light on ours and theirs Alice gets closer and closer to the horizon the wavelength of our life gets more and more Soviets to ensure whenever you know is that you can't look at cook car yes we can say was also acts as a black hole gravitational well let's hear whether it is a bit is a gravitational are good pilots Bilal exercise fur any kind of a gravitating material which would usually call mass could could lose the energy for any kind of distribution of energy or mess there is around it torrents neighborhood some orders there's a gravitational potential gravitational potential is usually called 5 fight is such that its derivative its gradient is the gravitational force of object on the unit next summer Test match the unit now find satisfies in equation on the left-hand side of the equation is something involving 5 and the right-hand side of the equation is the mass density is the Newtonian physics with plutonium physics what some right-hand side with just say the mass density which role and function position in general it might just be a point source said there was still left different 5 of course quite right anybody know there right but the beverages because you close something called Dell squares which is basically the 2nd derivative with respect respect to the Palm these 2nd by Dr squared of Pfeiffer a radially symmetric distribution of mass is equal to Rome this would give us for example for a point mass it would give us the usual Coolong usual Newtonian potential energy now vacuum energy is an interesting possible candidates put on the right-hand side not do sell the as my sign right still squared fired minus role plus I can't remember the microchip figure it out for the other Bond but gerdes' fought what would happen if they were vacuum energy in addition to the pockets of ordinary energy that's it well Europe but constant on the right-hand side with a constant beat the constant would be a constant vacuum energy sometimes called cosmological constant other times it's just called H square and basically portal squared factors for each contract so he is a formula for the gravitational potential of a space which is filled with a uniform distribution of maps it's a vacuum energy absolutely uniform only doesn't change with position it doesn't even change with time I was a solution of this equation the year no easier than that it's fine Eagles plus or minus 4 figure out the sign later 8 squared Our squares let's differentiate but maybe there's a factor of 2 was a 1st derivative of this respect Wayne are was the 2nd derivative a squared Justice think so like that a uniform absolutely uniform distribution of energy and this should be a minus gap should be a minus here we do it right so we see that as a potential gravitational potential you could think of it as being due to this uniform distribution of energy distributed all office space and was a look like it looks like there's a minus 8 square are squared off too was asleep this means at what don't follow that that's the potential energy that I a I at the center of my geometry I'm special I'm at the center of my geometry special units and your geometry and that's fine with me but I know that I'm special might I make measurements and make measurements on test masses are finding move in various ways of finding move and ear they were In a potential which went like this incidentally was a force due due to this potential nor the force is derivative Of the potential price so do River the potential others are so this is a forest which increases into repulsive but minus pushes Darren and the 4th increases linearly with distance so any kill objects if you just start an hour at rest they will start to accelerate away from each other and they'll eventually start picking up some speed how long taken the pick up any appreciable speed that depends on a beach basically 10 billion years that pick up any significant speed but it's awakened billion years it will be moving like a rocket OK so no not like a rocket by a photon closed thought so where are those mean supposing you start an object right up to the top literally of the top what happened is stays right it's at a point of unstable equilibrium will last another way of saying that meet in my own frame of reference if I take an
object which is located right where I am it'll stay there you have to be to a sophisticated about it I am my own object and I don't move away from myself well about sometimes but not that usually have now lads and I think an object a little bit away from land and again we're ignoring all other forces we can take into account the forces were ignoring so I start somebody out at rest 400 meters away from me that's over here what happened some going away and factor in this kind of potential they will move with an accelerated motion that that will be if we take into account relativity and everything will be exponential expansion felt that just a statement that the space in between things is expanding exponentially so this kind of picture is a kind told me in a description of the scene physics as the exponential expansion of the universe as the was No. 1 a uniform distribution of matter a rare meat and number 2 0 gravitational potential energy which is pushing everything away now we certainly don't works that young fraud so if I took bullet the potential energy between you and me only gravity for simplicity there's another contribution I'm standing at the center and I'm thinking about you and I see that you haven't would never gravitational Tony and potential energy relative to meet in addition to that at 1st told your ordinary gravitational potential energy look like right back polling me the Sept calling you would my said look like at 1 will our potential artifact is that to this look something like that subpart class enough from close enough that I get pulled you get full taught me online at this this what you arrive at this distance in a kind of unstable equilibrium of his slightly farther away than populace the new get pushed away so this is exactly the situation that the Andromeda galaxy appears to be in here somewhere was falling toward us a few galaxies away their accelerating out away from it's while you're there is a lot of talk about what an aide said that their Witcher which aboard a normal normal not there's 1 thing you could call a vacuum energy court cosmological constant is only 1 thing and if you want to
mimic make it all my new Tony in physics you model it by a uniform mass distribution there was 1 thing it's not vacuum energy cosmological constant barrage of dark energy all the same thing and they all correspondence if you Weiser said if you want a model it the in context you simply imagine a uniform a but I can't think of a buyer EU commuters at the consequence of rural you of course the go together at this good it said and for and sitting in said this season as less to hear well the origin the dark energy the cosmological constant vacuum energy is most likely quantum mechanical Georgia old wants its it's just energy in fact I mean you know the mass of the electron has a contribution to it which is car quantum mechanical our but once we know what the mayor we simply use it in classical physics were just an ordinary man sold large quite true that the dark energy cosmological constant May ultimately be due the quantum fluctuations nevertheless by the time we average over those quantum fluctuations what we see is a uniform distribution of energy very small to be sure if wasn't small men now we be rocketing away from each other it's very very small arms in natural units and plant units something like hint of miners a 120 3 very very small number compared to any of the natural scale and physics art and it sets the scale for and the reason it moments is the reason that in the sober while the will be like effect cosmological constant was much larger the words of each was much larger here is this the distance the horizon sorry Waroway age was much much bigger than we be surrounded by our small for years we will be living in what effectively looked like a much smaller universe even those even know what it was being big right age is being that cost means more rapid expansion but also means of small horizon so would be sitting in the small horizon but with a much larger repulsion between things H for larger repulsion would be larger and the size of the horizon would be much smaller so we be much more tightly restricted but will also be subject to a force which would be course in everything to explore so there is a limit to how big the Hubble current video of cosmological constant of dark energy could be and we still be able to measure it there we would be able it talk about it now there is a place yes insects whose relationship this language the language to users not plants constant plant constant is a thing which carries dimension always good to talk about dimensionless if you work don't plunked units you're automatically talking about prevention was saying armed and of course knowing what the plant unit is doesn't belong in ordinary a measure Europe's doesn't knowing what age bars but dumb yes there the answer is and plant units that means everything is dimension in means that the Newton constant as 1 it means the plant constant is 1 the speed of light is 1 in those units were all the fundamental constants of physics most fundamental constants of physics Citicorp water In those units be cosmological constant energy dark
energy is a 123 orders of magnitude smaller so that's 1 of the great puzzles physics watch the origin of the carrier's small numbers not all right here that has Hugo out the world about asking people occurred ladders man by 40 per cent of Americans don't know that and I don't think the situation is is well below the charitable works is not quite yeah but there are some serious physicist who work question but 11 and 10 years ago you might have reasonably question Head of 15 years ago you might reasonably question on the bounce from experiment get tighter and tighter and tighter what they mean by saying that the cosmological constant is the constant is is the hypothesis that basically that age varies with time and decreases of decreases decreases and will eventually settled down to learn 0 the idea that the vacuum energy whatever it is temporary transient thing which was settled prior arm and eventually not be there he said it will be at the Art of ourselves that we would know that EXE galaxies you may not tell her telescopic can yet there also father firmly young without a telescope yet so you do not appear that the plan is a Kurdish writer always all it sold you're a it's a very interesting question I've thought about myself and some of the people about how old would astronomers of that distant time in the future the earth is still here there still here you to do this some questions and problems but nevertheless were all still here and we have our telescopes lost our history books the Internet Is failed we've lost our history books we don't know how might we become aware of the fact that there was a finite horizon out there that it was a dark energy that things are accelerating away from each other and it's very very harmful imagine and I can't think of any way that maybe it would tell be cosmic microwave background what would happen to it a red shifts the point where it's completely undetectable or about the galaxies that we cannot ignore the measure the Hubble constant and so forth out
everything we know about the cosmological constant is a certain number of how big big enough to put the horizon about 20 billion light years away now tomorrow basically forever so they'll be sitting in his big containers by 20 billion light years crossed with 100 thousand light years era galaxy a vacancy everything else having been swept clean and how they detect the fact that there is maybe I wouldn't have boundary which court there is a great start rejected that yacht guts stars are stars in a rejected who got your full of brought track in track for a while but you won't be a track America Cosmo odd jobs as as well as how I that storms repertoire Miguel Back at a news tip Inter when I see it we can see it and see if we can we can see we can the measure young the expansion rate and reconstruct reconstructed With his enough for stuff around To be able to reconstruct at the person per year just outside this is about us now would be quite yesterday they gave us that that would that was a good but it's not be at the horizon is not going to shrinking horizons it's going to be at the place where a from be acts with the number that we have today With the numbers that we have today well measured checked many different ways prediction for the future is that the horizon will be at about 20 billion light years that's worth a for another Lawrence H. is constant touring bearing is kind of expansion and the distance the way you have to go to where it was be we've seen speed of light that could be cut off if they had a bye North Shore said that a guy we can see that part that's out beyond the horizon as I'll be on the horizon that will not be visible us what through our future editions now what it is true there is something which is show our record point Carey occurrences of player Hungary recurrences 1st of all you picture on that's the inside of picture should be that this summer temperatures of very low temperature from our point of view of a high temperature of the boundary but you should think of it as thermal system in fact has an entropy the entropy is just be area of the horizon and plant unit president could be fined finite B a c could think of the toll large extent as a cavity with a finite amount of effort the rule the thermal gasses mainly out near the horizon because of this effect and retain out here it is constantly fluctuating now thermal system with talk about the thermal systems on box a box of guests water molecules after a comes a thermal equilibrium and in fact what will happen is everything will come thermal equilibrium when everything passes out to the horizon it will be in thermal equilibrium was a gas a boxer guests like 1 of thermal equilibrium was like nothing amiss a big double box of uniform density nothing much happens it just sits there and sits there forever and ever right then that its radiation and there it's a black body of molecules in the other molecules and fairly against that apart from tiny little populations nothing ever happened without depends on time scales there are times skills basically statistically anything can happen there are no rules there are no rules is only statistics only probabilities but although our probabilities it could really is what he is the probability that all the molecules suddenly come together in such a way that they all warning that in the corner of the room is an entity that is of about the proverb Yuri is basically E miners enter B of the get the entropy is roughly the number of molecules we get so we have a box would conclude 25th molecules eat them a and the 20 New Wave that kind of audit Ito the tent the 25th at called upon current and basically the Ponca recurrence time is the time-scale for extremely rare and unusual populations place extremely rare and than usual fluctuation might be all molecules called off and or it might be the will assemble themselves into an elephant whatever I love that time scale is of what's called a potpourri recurrence and it's normally extremely huge on that time scale is constantly things going on fluctuations taking place which taking of thermal equilibrium so far at a thermal equilibrium that a new returned the thermal equilibrium all sorts of complicated vortices and other things might form and a half before return of thermal equilibrium is is also thought to be true for this airspace that you really wait long enough for how long he can have a 120 what units it doesn't matter where you with me it doesn't matter reduce its ABU Mister could think of will take he did attend the 120 of those units they years for a recurrence of workers and on that time scale all kinds of things will take place so or are among other things but no short of such impossibly long time scales nothing will happen just be heat that the same kind of heat that the takes place in here when everything comes to equilibrium was more interesting things well a a more wild fluctuations could have fluctuations could happen I'll give you an example fluctuation that can happen we can even give a rough estimate of how long between such fluctuations instead of the whole world
mathematicians didn't know so the consistency of the internal consistency of it has been extremely well check is a structure the structure has gravity and that has quite a mechanic so in that sense string theory is a well-defined exact not cost as remote possibility that somebody will discover inconsistency in the extremely unlikely mathematical consist on the other hand that part of it which is mathematically precise
Plateau Court string theory with capital rests with Capitol Records brings theory capital it is supersymmetric it is army its supersymmetric The world is not supersymmetric the world as we see it as not supersymmetric mathematical structure which is well defined and for which we have a lot of confidence that really exist court quantum repair gravity with supersymmetry . it is not the real world so in that sense we know now no question string theory is not the right 100 % we know if assure me breaking the symmetry nobody really knows how to do it is not part of the mathematically precise part of the theory we all expect that this thing that we call capital string theory Areas strength has many many many different versions of a huge number of different possibilities lie within we all expect that contained within something bigger something bigger that we don't know how analyze it more relaxed like the situation where maybe it's like a situation where a physicist at the time preceding might have discovered a formula as sequels in and the formula the force equal pay and aimed 2 dimes G are square but they didn't have the mathematical tools that analyzed anything but the simplest orbit so they said all right we will use symmetry the symmetry of circular orbits we want a little bit of extra information we need to know the acceleration of a circular orbit that's not tool hard to and do on on the basis of some simple symmetries and you can never figure out our kept which 1 of the losses it 1 of the kettle laws which tells you that period is a function of radius you know you know that the theory that you working with the fury of circular orbits is not correct but you just don't have any mathematical power were to be able to go beyond it I don't know if that's what the real situation is but it could be like that so we know that the theory of circular orbits is contained in something bigger don't not analyze if we know that the perfectly idealized supersymmetric string theory the 1 that we really paralyzed is not the real world it looks a little bit like the real world but not the real world and the question is whether it contained in something bigger which we could call string theory with a small west of the answer is we don't know very much about we know a great deal about this this is enough to tell us all sorts of things about the combination of gravity in quantum mechanics things about black holes things about the kinds of things but To say 1 way or
another what's the probability that string theory contains a or the research and extension of a bigger version of it contains all worldwide over here and of course In some local of course that's true world someplace his theory someplace to hand this mess you get something bigger but that's not how we wanna know whether in some interesting way the fury of the real world is some extrapolation from what we already know that there is no there's no way to know not only capital string it contradict a possibility but says it has a lot of capital string theory doesn't rule out the presence of the doesn't rule out the existence of small stirred but work does say is that nature is not as we know it is not described by capital so we know with certainty that bigger structure has to be found however that big a structure that contains our world will sort of be contiguous with connected to the smaller structure of capital string theory this we don't
we go make objects to this people arrive loads and loads of papers about the symmetry breaking of string theory the silver symmetry breaking some particular of symmetry breaking of strippers we know a lot about the the mathematics of supersymmetry but we don't know precise version of higher combined the breaking of supersymmetry restraint theory bad debtors outside the scope of what we know that doesn't stop people from you make an approximation here and there and they start rolling and you could do some things the problem is that making approximations but you don't know what those approximations approximations you make some standard approximations that we use all the time and you start calculating but there's no lower backbone your approximate so at the present time I think Garnes I think Our the safest thing to say string theory as we know it and as we can rigors version of it certainly not the real world is in my view lots of reasons the thing that the part of it that we know about it is not the whole thing that could be bigger it probably is almost certainly bigger however say whether the real world as part of that very much a prejudiced different physicist share different proportions that this is a bad they said that the 1st process of a must Noel it really it really does require a special wrote no special relativity can be be violated by by the environment was sitting here in a room where everybody's arrest and the world does not look good Lorentz invariant your presence here violates my over and over and also violates we talk but is less time on our serve you could
have what physicists call up background which means stuff in it which richer picks out a particular frame of reference the underlying rules Merrimoor rules were of a string theory who will have learned how fast he I wanted to predictions that the most robust but most robust predictions that has gravity is no way for it cannot hire gravity test say is Dad a head of a depth of Young's question about Bagram independence is a confusing warned of long from yard His His background independent up to a point up to a point yet it's hard to change the asymptotic boundary conditions continuously but it should be hard to change the asymptotic boundary conditions continuously at EU change asymptotic boundary conditions continuously you can't do any operation that would change that but short of time boundary conditions changing the background locally in space time string theory and new not take my word for it 3rd so this is something that's been long studied since the 19 eighties works of people like calendar and other people have studied now we're going there was finished OK so photo for
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Drosselklappe
Kaltumformen
Großkampfschiff
Stringtheorie
Besprechung/Interview
Erdefunkstelle
Zielfernrohr
Prozessleittechnik
Lineal
Kristallgitter
Ersatzteil
Versilberung
Papier
Abwrackwerft
Kaltumformen
Schiffsrumpf
Ziegelherstellung
Hintergrundstrahlung
Bildfrequenz
Stringtheorie
Zylinderkopf
Eisenbahnbetrieb
Besprechung/Interview
Lineal
Computeranimation

 Titel Topics in String Theory | Lecture 9 Serientitel Lecture Collection | Topics in String Theory Teil 9 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 10.5446/15121 Herausgeber Stanford University Erscheinungsjahr 2011 Sprache Englisch

 Fachgebiet Physik Abstract (March 14, 2011) Leonard Susskind gives a lecture on string theory and particle physics that focuses on the mechanisms that make the universe hot. In the last of course of this series, Leonard Susskind continues his exploration of string theory that attempts to reconcile quantum mechanics and general relativity. In particular, the course focuses on string theory with regard to important issues in contemporary physics.