A Holographic Quantum Theory of Spacetime - Tom Banks (SETI Talks)

hello I'm a TA Chuck and welcome to the seti colloquium series we are very lucky today to have Tom banks give us a talk today about a holographic condom theory of space-time Tom started his career as an undergrad at Reed College he then got his PhD from MIT worked at Tel Aviv University University of California Santa Cruz and Rutgers and he's best known for his highly cited 97 paper on matrix theory of string theory which was the first non perturbative theory of string theory now you're gonna know all about it after the talk actually Tom has moved slightly in the direction away from spin theory from string theory and he's gonna tell us today about the whole graphic approach to fundamental physics Thank You Marcia and thank you all for inviting me here I'm going to be telling you about something I think is even weirder than the search for extraterrestrial intelligence but I'd like to start out by talking about something very down to earth very 19th century the laws of thermodynamics these were laws that were worked out by people who were basically interested in building machines to do work that humans previously had to do and so they had it turns out some rather vague and wrong concepts of what fundamental physics was but they came up with these laws empirically and they just invented symbols and the equations that we wrote down worked and then they led us in the course of time part of which I'll explain to you to a very much deeper appreciation for what the microscopic structure of matter was so the laws of thermodynamics are written up here the first law which I haven't written the general version of I but in the version of it for fixed volume you take a system you put it in a fixed volume you change the energy a little bit there's a thing called the temperature the 19th century physicists knew what temperature was because do you know you touch something and it's hot or cold and then they learned how to measure it with mercury thermometers and things like that and then they found that the change in energy was proportional to the temperature times the change in something else called the entropy and they didn't know what the entropy was but they also learned that there was a second law of thermodynamics that the entropy in processes where you don't do any work on the system always increases I put that in quotation marks we now understand this to be a statistical law it probably always increases and for big systems the probability that it doesn't increase is very very tiny so to a very good approximation it always increases and then there was a third law that the entropy of the system goes to zero as the temperature goes to zero we now know that law is also not true for all systems there are some systems that have entropy even at zero temperature but these were pretty good laws and they're very very robust because they were based on observation and they're correct laws in their realm of validity and what really is the problem for a theoretical physicist faced with laws like this is to come up with a more microscopic mechanical explanation of what these laws are so in particular water these quantities that we call E and s and T in this equation what what what is energy well energy was something that people had a pretty good idea about because the laws of mechanics had been worked out a long time before the laws of thermodynamics and there was this conserved quantity the energy many many systems had the property that there was a quantity called the energy that you could prove mathematically did not change with time as the system evolved and that was useful mathematically for solving the equations for how the system evolved and it in itself that energy conservation law was something that you could just use to understand intuitively how things were working now the introduction of entropy was basically due to the fact that people said ok a system has a certain amount of energy we should be able to have it do a certain amount of work and work is something you do by moving exerting a force over a distance if you're doing it with a system that's extensive that has a volume you have a force per unit area called the pressure and the pressure times the change in the volume is the amount of work that you do so you'd like to convert whatever energy you have into work and have the de be equal to e P the pressure times DV but that didn't work and there was this extra place where the e was going and that was the that was the puzzle of what entropy was and now temperature was something again we could measure but we didn't have a fundamental or back then in the 19th century we didn't have a fundamental understanding of it then the man who just broke this problem was Ludwig Boltzmann man who in his own time was considered a bit crazy by many of his compatriots but he's one of the most important physicists in the history of physics and he figured out the puzzle of what entropy is in a way that with really rather minor modifications like the invention of quantum mechanics it is still is still the way we think about entropy today and Boltzmann's idea was that entropy is the logarithm of the number of physical states that a physical system can be in and that the laws of thermodynamics were probabilistic laws the reason that entropy increases is because many of the states of a typical physical system have the same macroscopic behavior and those states are the ones that maximize the number of states and therefore also the entropy so if you're just randomly picking a state you might start out in some unusual state but you're going to move towards one of the more typical states where the entropy is high that's not a microscopically exact law but it's statistically true now why why is this true well Boltzmann took up at this time a theory that had existed since the time of the Greeks and he said the reason there are so many states is because everything is made up of atoms molecules little tiny pieces that we can't see and that are responsible for the properties of matter and by analyzing simple models of molecules as little Newtonian particles bouncing off each other with forces he was able to show that there were microscopic equations that could lead to the macroscopic equations of thermodynamics so what entropy is entropy is the logarithm of the number of states the reason you introduce the logarithm is because the number of states or so is so large you when you have a very large numbers to deal with you take the log to you know cut down the number of zeros that you have to write the the number of states in even the tiniest piece of matter you know sort of a tenth of a centimeter across the number of atoms goes like 10 to the 10 to the 20th okay so the entropy is 10 to the 20th and the number of possible states that these atoms can be in is extremely large and you wouldn't ever want to try to write that number down on a piece of paper um so this then allows us to understand what T is also because basically what this equation is saying is the T is measuring kind of the average energy per each of the what I will call degrees of freedom that determine what the states are now to have in your mind a model of what I want to call degrees of freedom a phrase I'll use continuously here I want you to think about what computer scientists call a bit a single yes/no question it's the fundamental unit of information and the number of states a bit can have is two and if I've got K bits then the number of states I have is 2 to the K and so the entropy of the system of K bits is K log 2 and that a bit the degree of freedom that allows me to answer one single yes/no question is sort of what I mean by a fundamental degree of freedom and um temperature is roughly defined as the amount of energy that the system has in a given state per degree of freedom and so what's happening when you try to make your energy do work for you is some of it just gets lost among all these tiny little degrees of freedom that are bouncing around inside the big macroscopic thing like a piston that you'd liked the gas in the piston to expand and push against the piston in a way that'll do work for you but if you do that most of the energy is actually going to go into just random motions of the particles and that's what the entropy term in the laws of thermodynamics is responsible for now the second law of thermodynamics as I indicated to you basically follows from Boltzmann's principle if what you think of as a thermodynamic equilibrium state is precisely not a single state of this system of many many atoms so again just roughly in your head think of a system of many many atoms as a whole bunch of bits and I characterized the states by a long binary number telling me which bit is up and which bit is down a macroscopic state means that the things we actually measure about all of those bits it don't care you know if fifty thousand bits are up or down they're just kind of averages over this 10 to the 10 to the 20th or more different states of the bits and so most of the states have the same values of those macroscopic quantities like energy pressure volume etc and using that principle gibbs was able to show that you you quite generally got the second law of thermodynamics out of Boltzmann's hypothesis so just a picture to show you processes in which entropy changes let's take two boxes of gas of equal volume different kind of molecule in each one I've colored them differently and you put the two boxes together and we move the wall between them without changing the total volume at all the entropy increases why does the entropy increase it's because the red and white molecules separately now have a lot of extra places they can wander into okay so again if I think about those red and white molecules as turning to different kinds of switches and imagine that in these volumes there's kind of a lattice of places where the molecules could sit and when a red molecule goes to certain to a certain place that flips the red switch up and when a white molecule goes there it flips the white switch up and now you increase the number of places that each of them can go there are more states and the entropy has increased you can counter that by squeezing the system and here are two pictures where I've squeezed the system in such a way that sorry about that the that the entropy didn't change and in the third picture I actually made the entropy change negative and in order to change the entropy in a negative direction I have to do work on the system rather than the other way around okay okay so I told you Boltzmann got things a little bit wrong he missed quantum mechanics Boltzmann invented the subject that we call statistical mechanics quite properly statistical classical mechanics and classical mechanics has funny properties in it that even if I completely fix the energy of the system or fix it within some band and also fix the volume the system is in it can still have an infinite number of states so that comes because if we think of particles as being able to move continuously and arbitrarily slowly no matter what size box they're in quantum mechanics is that because of Heisenberg's uncertainty principle if you try to put something in a box it has to there's a big uncertainty in how fast it's moving and as a consequence of that in ways that I won't attempt to explain to you here the one of the most important principles of quantum mechanics is that if I take a system put it in a finite volume and fix the energy in some finite band then there are a finite total number of states it's huge it's the kinds of numbers that I was just telling you about even for a very tiny box full of matter but it's a finite total number and Boltzmann's classical mechanics didn't have that property in this consequence and this is what's remarkable when those principles were applied just to just ordinary systems like ovens we found contradictions with experimental results Boltzmann's classical statistical mechanics would have implied that the color of light coming out of a an oven was typically as high a frequency as the world allowed us to have and the reason for that was that in Boltzmann's classical mechanics the energy of a certain frequency of light could be arbitrarily low and things were only constrained by having we knew the oven had a fixed energy and so if the energy of a given frequency can be arbitrarily low the height there are many more high frequencies than low frequencies and so the the number of states is dominated by the very highest frequencies quantum mechanics fixes that by saying no a given frequency of light has a minimum energy called h-bar times the frequency Planck's constant and that fixes up Boltzmann's reasoning and gives us Planck's law for what an oven looks like and that fits the data bang on so quantum mechanics fixed up Boltzmann statistical mechanics but what's more important in a certain sense for what we're going to talk about is that Boltzmann statistical mechanics and the fact that it was based on the laws of thermodynamics led us to quantum mechanics it led us to invent this completely revolutionary new theory that many philosophers today still can't accept okay most physicists are over that by now but I'm certainly over it but but so the the the the thing that's really interesting about this historically is the way in which these very gross laws of thermodynamics that were invented to describe heat engines led us to the correct microscopic theory of the world as we know it around us and what I'm going to tell you about today here's a very modest attempt to extend that principle to the world we haven't actually explored experimentally yet that is the world of the quantum mechanics of space-time so I'm now going to switch over to talking about space-time and I'm going to introduce the notion of a causal diamond in order to understand that we have to wait one second during that second each of us could have in principle done experiments on a certain region of space-time that region of space-time is finite because in order to do an experiment I have to send out some kind of signal I have to hit wherever the place is where I want to probe experimentally and I have to get a signal back and the region of space-time that I've explored in that one second is my causal diamond over that one second and each of you in the second that passed after I started this long sentence each of you had your own causal diamond the causal diamonds of all of us were quite close together they're more or less the same regions of space-time and that has to do with the fact that we are close together compared with the distances that light traveled in that second okay so um this is the technical definition of a causal diamond you take a time light trajectory in space-time that just means you're following the path of something that travels at a speed less than the speed of light I perhaps didn't say the fundamental principle that's being used here is Einstein's observation that there is a maximal signal velocity for anything which happens to be the velocity that light travels there are there's at least one other thing in the world that travels at that same velocity v the gravitational waves propagate at the same velocity that's light and we don't know of anything else for sure so here's what causal diamonds look like in a spacetime diagram in this diagram time is drawn along the vertical axis and space where by space we live in three-dimensional space I can't draw that on a slide so what I've done is I've just drawn the radial Direction out from some particular point okay and I've chosen the origin of time to be some particular point and then I've thought about what happens along a particular trajectory in space time during bigger and bigger integrals which I've chosen for this picture symmetric around that zero point so I go from time minus T to time plus T and each time I make T bigger I get a bigger and bigger causal diamond okay now if I take two different trajectories I want you to ignore all the equations on this transparency it was used in a technical talk but my colleague Willie Fishler made it and I'm incapable of doing that kind of artwork and so I had to reuse it the here are two different trajectories the two big lot of blue lines and at each time here I've done something different I'm talking about a different kind of space-time situation where time started a finite time in the past that's an appropriate situation to talk about if I'm discussing cosmology which was where we started out with our holographic space-time game so in cosmology I can think about trajectories that started off at the Big Bang surface where the universe began and each of those trajectories has as time goes on in the universe larger and larger causal diamonds we will see that the experimental evidence seems to suggest that that larger and larger doesn't proceed forever that it comes to a finite stop we'll talk about that towards the end of the talk but what I wanted to show you here is that at any time this is the causal diamond along one trajectory this is the causal diamond along another and there's some intersection region of two causal diamonds I'm sorry I'm thinking about these two here outlined in yellow and they intersect in a region here now on this two-dimensional plot that region looks like a diamond the intersection region in real space-time won't be a diamond but it'll have a maximal size diamond inside it and that's what I'm talking about and then intersection region is a place that both of these now if I imagine there's some kind of experimental apparatus running along each of these trajectories both of those machine could have interacted with this region of space-time during the period of time from the beginning of the universe until the top of the yellow causal diamonds and so whatever description of physics you have from the point of view of this trajectory has to coincide be consistent with the description of physics that you have from the point of view of that to ejector E and that's the version of Einstein's principle of relativity that I'm going to be using in the quantum theory we actually write down quantum theories for every possible trajectory in space-time we don't actually do it for every possible trajectory we do it for some subset of trajectories that are enough we believe to tell us what's going on and we enforce these consistency conditions between the theory describing how space-time looks from every different point of view so this is something that you guys should be very comfortable with because if you all did experiments independently and you're here together in this room and can talk to each other you really wouldn't believe that everybody was doing everything right unless everything that you got for this experimental data about some region that both you and your friend could explore coincided okay and that's what this principle basically says okay so now I'm going to talk about something even weirder I'm going to talk about a black hole and I'm going to show you a picture of a black hole that's not the one the theoretical physicists usually look at and it's not the one that most popular images of black holes describe this is a picture of a black hole which is it's a movie so one of the things that's interesting about this movie is all the pictures you normally see of a black hole it's just some static thing sitting there in space that is false or rather it's a choice of a very peculiar system of coordinates on the black hole space-time which doesn't really get at the physics the real physics is more it at least in an intuitive sense is more easily understood in the kinds of coordinates I'm using here now what's going on in this picture so what's going on in this picture is I'm drawing a picture of space I'm drawing only two of the dimensions of space because again I couldn't do it I mean somebody knows how to make a three-dimensional picture like this please come up so the flat part of this the part that's not moving is supposed to be going out to infinity and this would be a description which is not quite appropriate to our universe but it's good out to enormous distances of just flat space like the flat space we see in this room you know it obeys the laws of Euclid and out to that distance then there's a certain radius where things start moving okay and space inside that radius is not static this was I mean Einstein's theory of general relativity the big discovery is that space is not static it can change with time and these are the coordinates that tell you how it would change in time if you were falling into it and you were measuring time according to the clock on your wrist as you fell into it what you would see and this doesn't it doesn't matter when you fall into the black hole after it's formed what you would see is you would see space starting to stretch in the radial direction okay that's what's being shown here and shrink down in the directions transverse to the radial direction so if you had a little sphere that you were carrying around with you and it was made of glass space would sort of crush it after a while as you followed down into the black hole if some colleague of yours jumped into the black hole later that colleague would find none of this crushing going on for a certain amount of time and then that colleague would experience the same crushing and stretching now the stretching and crushing happened faster than the speed of light and that's the thing that makes the black hole black they happen faster than the speed of light Einstein's theory says that no signal can propagate through space-time faster than light but it doesn't say how space itself can stretch and the key phenomenon of a black hole is that space can stretch faster than the speed of light and in fact this shape gets infinitely long and infinitely thin in a finite amount of time as far as you're concerned I'm sorry I keep hitting the microphone please excuse me so it gets infinitely long and infinitely thin in a finite amount of time that's called the black hole singularity it's very terrible it's also it's also probably very artificial in the following sense that if I if I throw some extra stuff into the black hole perturb it in some way the shape of the solution of Einstein's general relativity down in that region where things are stretching and squeezing down to zero is very very sensitive and in fact things become very chaotic and totally mixed up the region up near the top is impervious to that and it it's funny it remains there even though all this terrible stuff is happening down below when you just jump into the black hole no how long you jump in after its formed at least according to Einstein's theory of general relativity a period of time goes past in which nothing terrible happens to you and the bigger the black hole is the longer that period of time is and we could right now be falling through the horizon of a very large black hole and according to Einstein's theory of relativity we would not notice it for a long time depending on how big the black hole was okay so now I'm going to introduce another concept called the holographic screen of a causal diamond so this is a concept that was actually introduced by some friends of mine Willy Fischler Leonard Susskind and the name was given by Raphael buso who's professor at Berkeley you might have heard a talk from him I'm not sure um the holographic screen you can think of in the following way let's think about a causal diamond and think about the past or the future tip and light is starting to come out from that tip so imagine sending out beams of light from that tip in all possible directions and at any time the those beams of light have gotten to some sphere of some radius okay and so there's an area of that sphere okay and as I go out from the tip certainly in the beginning that area starts to grow and then at some point the area will reach a maximum and then certainly because I have to meet up with what's coming from the bottom it's going to get smaller again so there's a maximal area surface with the shape of a sphere in the space-time now the actual shape might not be spherical because this picture in these words actually apply even if we're not in flat space they apply to any solution of Einstein's theory of relativity where space can have all kinds of shapes the topology of this surface is that of a sphere and it has some area and there's some maximal area surface now normally in flat space-time you would say that maximal area comes at the place where the two light cones meet because the sphere just keeps on growing as you go away from it and then it's going to maximize where you stop and you stop that where the two light cones meet but I've drawn you a picture of a holographic screen that's more appropriate for an expanding universe in which the volume of space is growing with time and so the holographic screen is somewhere further up than the place where they meet okay and for any space-time you can start drawing causal diamonds and drawing these surfaces and see what happens and as I said this concept was invented by Raphael blue cell he uses the words to describe something slightly differently but I I don't want to get into that technicality for you so now let's talk about black holes and what happens to holographic screens and compare it to what happens to holographic screen to outside of black holes well outside of black holes holographic screens if I let time go on they get bigger and bigger and bigger we can see more and more and more of the universe as time goes on that's what we think inside a black hole and this turns out to be the defining mathematical characteristic of a black hole every once you've passed through the horizon if I start with any causal diamond whose past tip is after the time you've passed through the horizon your holographic screens start to shrink and that's because of this squeezing of the area in the black hole you see less and less of what's around you as time goes on okay so there's this change that happens when you cross the horizon of the black hole that's the way to describe it in terms of holographic screens and if you think about where was the maximal area that you saw on your holographic screen after you jumped into the black hole it's back at the horizon it's back where the maximum you could have seen at that at that time okay now outside the black hole as I said we have believed for a long time that the longer we wait the more of the universe we see data that we first started getting about 15 years ago now seems to indicate that that's not true and you'll I'll talk about that at the very end as I said so now I want to bring this back and talk about information and entropy in black holes and this was a subject that was started out by another great physicist jacob bekenstein and jacob made the following observation you know if black holes really behave the way they do in Einstein's classical theory of gravity I can get around the second law of thermodynamics because suppose what's the problem in the second law of thermodynamics since I let a system evolve and instead of just doing work for me it produces entropy useless energy that is that is mixed up in the microscopic details of the atoms but take that entropy and throw it into a black hole and if the black hole just sits there forever and has no entropy of its own which in Einstein's theory it doesn't seem to have any entropy then we've gotten rid of entropy we've decreased the entropy of the world a black hole is a what's called a perpetual motion machine of the second kind okay Jacobson now that can't be right thermodynamics is too good a theory and he thought about it a little bit and he realized oh yeah quantum mechanics actually stops us from doing this and what he proved didn't prove but he suggested is that if you think a little bit about quantum mechanics you realize that a black hole has an information content which is to say an entropy it's got a number of physical states and the way to think about that is again to think about physical states in terms of these bits of information and how can I most with the most energetic efficiency encode one bit of information well photons are massless that means I can make them have arbitrarily low energy if I make their frequency very very long and a photon has one bit of information in it namely what its state of polarization is it can be right-hand circularly polarized or left-hand circularly polarized or if you like linear polarizers you know it can be up or down in the linear polarizer whichever way you want to count it it's got two possible States given its energy and its energy can be arbitrarily small if its wavelength is long enough but if I want to throw that photon into a black hole of a fixed size and the horizon defines such a fixed size it's got a fixed area then it had better be that the wavelength of the photon is shorter than the horizon okay because otherwise there's no meaning to throwing it in a photon is a quantum mechanical particle it's spread out over its Compton wavelength you can't localize it inside the black hole unless it's got a short enough wavelength and so what's the minimum energy that it takes to put one bit of information into a black hole it's one photon Compton wavelength worth of energy with the comp the radius being the the I'm sorry I said Compton wavelength I really mean de Broglie wavelength it's with energy equal to H bar divided by the radius of the black hole but that energy is going to contribute to the mass of the black hole and so I can ask how many bits can I put in without changing the mass well the best I can do is to make the whole black hole by throwing in these very very long wavelength photons and then I'll get you know two to the number of photons I can throw in states the number of photons is going to be measuring therefore the entropy but the energy that I get is also going to be n times this minimal amount of energy okay so the classical theory of general relativity makes a relationship the equations force a relationship between the mass of the black hole or its energy and this radius of its horizon and this is the relationship that defines the so called Schwarzschild radius of the black hole and so if you calculate the number of photons which is the entropy given these two formulas you find an entropy that goes like the area of the black hole surface measured in a certain natural unit of length in Planck's fundamental paper on quantum mechanics one of the things he was most proud of was the introducing the concept h-bar introduced a fundamental unit of length into the theory and completed the system of natural units and that length is called therefore the Planck length and it's really really small it's 10 to the minus 33 centimeters which is many orders of magnitude smaller than any distance we've ever probed experimentally okay now what bekenstein so what bekenstein said is this solves the problem because if I throw stuff into the black hole I'm going to increase the black hole entropy by increasing its mass we just saw the minimal amount to do that and that amount of entropy is huge as we'll see in a minute compared to anything I can make from ordinary matter okay so something Beck and Stein didn't mention and I really don't know why if you have his formula for the entropy as a function of the energy then you can write de equals TDS and figure out what T is and the equations implied that the black hole has a temperature but now think about what that means I've got a body of finite body sitting with finite entropy sitting somewhere in the middle of space and it's got a temperature well that's what old-fashioned physicists called a black body a black hole is a black body and it radiates and so it's not true that stuff is stuck inside a black hole forever and the reason that in the Einstein theory it seems like things are stuck inside a black hole forever is that in the Einstein theory h-bar was essentially set equal to zero the Planck length went to zero the entropy became infinite and therefore things that have an infinite amount of entropy don't have to radiate the reason things radiate is because you gain entropy by sending photons out into space relative to having them clumped up in some little box but if your box has infinite entropy that calculation doesn't work and it was just that the classical theory missed this huge entropy and thought wrote it as an infinite amount so the discovery of the temperature of black hole was actually made by Stephen Hawking he used the formalism of quantum field theory quantum field theory the cartoon of quantum field theory is my little picture of you've got a lattice in space and there's a bit at each point on the lattice and those bits can flip up and down and that's the very simplest kind of quantum field theory you're just some rule for making those bits flip up and down and communicate with each other that's what quantum field theory is like and there's a much more sophisticated formalism for actually calculating with it and Stephen Hawking used that and he calculated using that formalism he showed that black holes radiate and he calculated the temperature and from the temperature you get a calculation of the entropy but nobody knew what that meant because they didn't know what the states were that would describe me the microstructure of a black hole but this made a profound connection between the number of quantum states in a region and the geometry of space because in Einstein's theory as we saw a black hole is a deformation of the geometry of flat space and that deformation is connected with a number of quantum states so there's a profound connection between quantum states and geometry so this is Stephen a little while ago he's a bit older than that now the next hero in my story is Ted Jacobson if he were here I would apologize for getting such a fuzzy picture of him he's not a fuzzy guy at all Ted in 1995 wrote an amazing remarkable and totally unappreciated paper and in fact some years later when I started working on this stuff I kind of knew about Ted's paper but I completely ignored it for many years to my detriment so Jacobson in a an anachronistic language so there was this language of holographic screens that was invented by Fischler Susskind and buso and Jacobson had effectively anticipated that some years earlier about four years but his his result is really remarkable he said okay I'm going to make the following conjecture we saw that black holes that have a holographic screen of a certain area have a certain entropy I'm going to conjecture that every causal diamond in any space-time whatsoever has an entropy associated with its the area of its holographic screen by this bekenstein hawking formula and then he said well what happens when I think about taking a slightly bigger causal diamond so I'm making a change in the area so that's a change in the entropy and then he said well let's just write down the first law of thermodynamics applied locally to two very close together causal diamonds and used there's a geometrical equation that tells you how to relate the change in areas of spheres in some geometry to how curved the space-time is so if space time is flat we know exactly how the area of spheres grow if we make the radius a little bigger if it's curved there's a certain different formula that depends on the space-time curvature and so de equals TDS becomes an equation relating the curvature of space-time to the local energy density in space-time that's what Einstein's equation looks like and lo and behold Ted showed that just using this principle you could derive Einstein's equations for geometry as the local thermodynamics or what we call hydrodynamics of space-time so Einstein's equations are deeply connected to this principle that air and entropy are connected together if we're willing to extend it away from black holes and say that it's there for any causal diamond in space-time so again this question now becomes even sharper I'm talking about a region in totally empty space I take some region a causal diamond it's got a certain area this form of this set of ideas tells you there must be a lot of quantum states associated with it usually we think about quantum states being associated with exciting some matter locally there are some particles here some photons some this some that so here's something that doesn't work somehow try to associate this entropy with stuff normal stuff inside the causal Dimond and the problem with that is normal stuff carries energy and if you try to put a lot of normal stuff into a region you make a lot of energy but if you make a lot of energy Einstein's equations say that you make a black hole and it turns out that the point at which you make a black hole the entropy and the stuff scales like the three halves power of the radius rather than the square remember this is entropy it's the logarithm of the number of states so if the black hole radius is much bigger than the Planck scale the difference between this formula and that formula is enormous this is a negligible correction to that formula okay for any macroscopic distance even a tenth of a centimeter so the ordinary stuff can't be responsible for the entropy so my colleague Willy Fisher and I wrestled with this problem in our own way because we didn't really appreciate Jacobson's paper and we decided that the way to think about this was to turn the question around that we should really define everything in terms of the quantum theory postulate that there were a bunch of states associated with the boundary of every cause of any causal diamond which are not ordinary matter and carry very very little energy it turns out the amount of energy that they carry is proportional to the inverse of the radius of the causal diamond measured in Planck units okay so it's an incredibly small amount of energy and take that as the definition of the theory and add to this just the constraint that things are local so if I have a causal diamond over here so your causal diamond over the second after I finish this sentence and I take someone far enough away their causal diamond during that period couldn't have talked to yours at all so it must be that the quantum degrees of freedom associated with your causal diamond can't interfere with the ones that are responsible for describing that person's causal diamond more than a hundred and eighty six thousand miles away and so that's the principle of locality putting those things together now using some mathematics that I'm not going to attempt to teach you you can argue that these principles define geometry out of quantum mechanics okay and that's the basis of our theory um what we've done with it so far is we've tried to make a theory of the Big Bang that turns out to be very easy the crucial thing about the Big Bang is that it starts at a finite time what that means if you think a short time after the Big Bang the causal diamond was very very small and so there couldn't be too many quantum degrees of freedom associated with it there's nothing singular about that but all of our usual equations that involve fields with infinite numbers of degrees of freedom have to break down and you just have to show that you can get something like those equations for much larger causal diamonds and you deal with the singularity of the Big Bang we also recently use this to construct how many of you have heard of the theory of inflation okay so the theory of inflation in the conventional models has a lot of mysterious stuff in it that I've never understood and the people who are responsible for it I've worked on inflation and sort of Slough these problems off when I was working on it but there are a lot of mysterious things that have never really been well understood and we've we've got a theory that doesn't have all of those problems and it's much more constrained as far as its predictions it makes predictions that are subtly different from the standard theory what I mean by subtly is if you look at the appropriate quantity there are dramatic differences but we will not be able to measure that quantity for a very long time into the future it involves measurements on the Cosmic Microwave Background and on the ambient gravitational waves in the universe that are far more precise than anything we'll be able to do for quite some time I know that you had a talk by Joe polchinski about the so-called firewall paradox Joe doesn't believe that when you jump into a black hole that for a long time nothing will happen to you we think our models completely resolve those problems just because his analysis was using the theory of quantum field theory and the theory of quantum field theory just doesn't have a proper picture of what the quantum states of a black hole really are we have this very very different picture and we've tried to argue that it resolves all of those paradoxes and there's something else which I'm not going to try to talk about in great detail is is that there's a theory out there the world called supersymmetry which many particle physicists believed in for a long time because it solved certain problems in the standard model of particle physics but um we haven't found supersymmetric particles yet and theoretical models for where they are run all over the map um the ideas that I've talked about today allow you to calculate roughly the masses of the supersymmetric particles in terms of another important scale in the universe and that scale is the thing that I've been referring to several times the place at which we're going to be able to stop seeing stuff okay so as time has gone on we've apparently been able to see more and more and more of the universe but recently something was discovered that was called the acceleration of the expansion of the universe and it the easiest model for it is to modify on Stein's equations by adding a so called cosmological constant term the cosmological constant term is very problematic in quantum field theory and quantum field theory it seems to be associated with the energy of zero point fluctuations of the field oscillators around the vacuum every calculation of it gives an exceedingly large number way larger than anything that we can that that fits experiment again that's because quantum field theory is wrong in detail quantum field theory is a great I've written a textbook on quantum field theory I think it's wonderful but physical theories have limited domains of applicability and you can't from within the theory guess where it's going to break down you need experiment or theoretical paradoxes in order to figure where things are going to break down and the problems of black holes and the problems of the cosmological constant or for me the things that indicate how quantum field theory has to be fixed up quantum field theory predicts entropies that are proportional to the volume of space our theory predicts entropy x' that are proportional to areas of spatial regions very very different and there there there's nothing we've tried to show that we can reproduce certain calculations in quantum field theory inappropriate regimes that that project is certainly not finished and anyway what we seem to see happening in the world is that there's this term in Einstein's equation which has a following property the right way to describe it is that our causal Dimond no matter how long we live so any machine we can build that will live till the end of time will only see a finite area horizon around it in our theory that means a finite total number of quantum states one of the properties of quantum theories is that the theory itself doesn't tell you how many states are that's an input but you have to decide on in the beginning so we just take that as an input parameter and try to follow the consequences and one of the consequences is that there can be breaking of the symmetry between supersymmetric particles and ordinary particles that involves interaction with these mysterious degrees of freedom on the boundary of the region of space will ever be able to see and a very crude estimate suggests from that that the masses of the supersymmetric partner particles are in the region of a thousand to ten thousand Giga electron volts this is the region parts of this region will certainly be explored in the upcoming run of the Large Hadron Collider over the next five years and it's going to be pretty hard for us to I mean we can always throw fudge factors at the problem but I will I will be very nervous if we don't find some evidence of supersymmetric particles in the next round of the LHC okay so Wow have I gone way over time okay all right I there are two there are two more things that I'd really like to tell you about remember at the very beginning when I talked about the laws of thermodynamics I said oh there was one term in the equation that we thought we understood back in the nineteenth century namely energy one of the things that we've discovered in our new theory is the definition of what energy is is completely different in our theory the definition of what particles are is completely different and this picture is supposed to show you what's going on so if any of you have ever seen or heard about a particle physics detector um particle physics detectors they would like to make them to be perfect spheres that's what they call a 4pi detector you usually can't do that because you need a place where the particle beams to go in but they try to get close to that and the way the detector works is particles come through the detector through a series of concentric spheres that are instrumented and they light up certain hotspots and experimentally particles are defined by following those hotspots in different spheres so in our our theory that's the way particles are mathematically defined and that's how energy is mathematically defined you have a sphere that sphere fundamentally is sitting it's holographic it's sitting out at this distance at the very edge of the visible universe and it's running away from us at the speed of light but not getting any further away than this point because it's a horizon like the black hole horizon and that that sphere you imagine being instrumented now the one of the issues with particle detectors is if you have very like particles like photons and gravitons you can actually see if you've sent off a bunch of photons and gravitons off in arbitrary directions in the detector because there's this kind of limit to the sensitivity of the detector for us those invisible almost invisible photons and gravitons which are represented in this picture by the gray area those are the fundamental quantum degrees of freedom of the theory and what a real particle corresponds to is imposing some constraints saying that around some little cap on the sphere there's an annulus okay where those degrees of freedom again think of them as little bits that can be shut on or off I've shut them all off in that annulus and then I let what's going on here do whatever it wants that turns out the sum of the amounts of stuff here here here and here in some particular event that counts the number of those constraints turns out to be a conserved quantity which is what we identify as energy and it has all the in our theory all the properties of energy in the theory of gravity namely we can show that there's a Newtonian like force between two globs of energy of a certain size a certain distance apart and so on and so the fundamental theory if we're right and I should really be upfront with you there are only two people in the world who think we're right okay if we're right the fundamental theory makes not only a profound connection between entropy and the geometry of space-time but it actually presents us with a new definition of what energy is in the fundamental theory and what particle states really are particle states are states which are constrained states of the fundamental variables they're the fundamental variables are not being allowed to flop they're switches up and down every which way they want in every possible region of space-time so let me end I'm going to skip that one but let me end with a movie that shows you what's going to happen this is a process that's going to take approximately a hundred times the current age of the universe so here's something like the universe we see galaxies they're moving apart from each other and the fact that we don't see anything after a while and this is taken from the point of view none of us but of some place out in intergalactic space all the galaxies will disappear and they will disappear into this region which is just a finite distance away from us but no longer be carrying any energy there'll be the gray fuzz on the sphere for us sitting here in our local group of galaxies that'll stay bound together everything else will disappear we will eventually dribble out energy out to that great sphere in the sky and collapse into a black hole which will by the process discovered by bekenstein and Hawking eventually radiates all of our stuff out into that great sphere in the sky and there will be nothing left yes so on that cheerful note I'll ask the first question so you can derive the mass or the supersymmetric particle from cosmological constant so the other way around can you say whether cosmos constant should be if we know that this particle existed like what is the source of cosmological constant is it dark energy can you call it dark energy no no so the the actual fact is calling the cosmological constant and energy even though that's the way it appears you in Einstein's equations that's that's a mistake and the the thing that really shows you that that's a mistake is Ted Jacobson's derivation when he derived the einstein's equations from thermodynamics so from considerations of local energy he didn't get the cosmological constant term okay and what Fisher and I interpreted the cosmological constant term as being is the you do the following thought experiment you take a causal diamond you take the time to infinity and you ask as you're doing that what happens to the number of states you encounter or what's the biggest radius that you see and the value of the cosmological constant is what determines that okay and for negative values of the cosmological constant something funny happens the opposite of what's happening to us there's a finite time at which suddenly you see all the way out to infinity and there a standard string theory gives us a theory for what's going on and the negative cosmological constant is in fact something that is determined by counting the number of states as a function of the energy so it's it's a boundary condition it's not a local energy tensor okay so questions since you're trying to apply your theory to a Big Bang when people do wave functions of the universe they have to worry about the boundary condition and they have several boundary conditions how does your theory handle that the Big Bang itself and also how does it fit with the landscape okay so it doesn't fit with the landscape at all there we can make a version of our theory that has a kind of landscape in it I could tell you why I would want to do that if you press me but I'm not really okay so the boundary condition our set of variables are very different okay so their boundary conditions are just not appropriate however we can talk about what our boundary conditions are and basically what we have found is we have a model in which you can take the boundary condition what the initial state is to be anything you want in the world that model will define a mathematically consistent world which will end up with a positive cosmological constant of our choice but it'll never have any local degrees of freedom in it because we didn't apply any of these constraints to the initial state and the the state that has localized degrees of freedom with the minimum number of constraints of the sort of most probable thing that will have localized degrees of freedom of the right type is something that leads to our theory of inflation so we do have boundary conditions but the the form of them is very very different and standard theories by your model are you able to so you said if we had a sufficiently massive black hole that we wouldn't notice anything for some degree of time is it possible that our observable universe might be in a sufficient sufficiently massive black hole and if so might the expansion the rate of the universal expansion be related to the stretching and compression of that hole okay so there there's a sense in what in which what you're saying is exactly correct but there's another sense in which it's wrong so the the notion of a black hole mass is something that really only makes sense if you have an asymptotically infinite universe that can have infinite sized causal diamonds and in which you can look down at the black hole and measure what its masses if you relate the black hole mass just to its number of states in the way that bekenstein did and say is what's going on the accelerated expansion of the universe the fact that we really just have a finite number of states and that those states have been out of equilibrium but they're going back to equilibrium and this disappearance of the galaxies is just the stuff on the horizon we re-equilibrate in itself that's precisely what our picture is and so that's very similar to what happens to a black hole if you poke it a little bit it takes a little while and then that that perturbation disappears and the thing we equilibrate that so the the accelerated expansion of the universe according to our model is very analogous to that but as if we're inside the black hole the singularity part of the black hole as I told you a total fake it's just this equilibration in two degrees of freedom that are not localized so you mentioned that the LHC will be able to probe energies that hopefully will be in the same range as the supersymmetric particles that you're predicting now let's say if it doesn't find them does that lead you back to the drawing board to make modifications to your theory or does it say your idea is fundamentally flawed yeah that's a hard question to answer because at the moment our calculation is very crude it's a the calculation is sort of what we call an order of magnitude back-of-the-envelope calculation so there's an unknown constant in it if that unknown constant for some reason turned out to be PI cubed then that could push all the supersymmetric particles out of range I don't see any reason for it to be PI cubed so I'm optimistic that they'll be found if they not found I will be very concerned and and and you know try to think if I can find some reason for that constant being big but I'll really feel like okay maybe maybe I'm wrong yeah my question concerns the entropy of a black hole define of my mass or area the maximum entropy is assumes that all the quantum states are independent of each other that doesn't seem to map the real world for example if you form a black hole by dumping entangled photons into it you're gonna admit you cannot be the entropy of the black hole would be less than what is calculated houses accounted for yeah so what I what I tried to express was the fact that any such mechanical model of the entropy of the black hole gets the black hole entropy wrong by a huge amount it's way too little so in our model there are these degrees of freedom everywhere in space right now if I wait a second and think about the causal diamond you know that what got formed during that second even though there are no black holes we in our model would say how did the boundary of that causal diamond there's a huge number of of very low energy quantum degrees of freedom that we can't see because they're all out there and they're not they don't correspond to localized excitations here their equilibrium state is one in which there are no localized excitations here a state where there are localized excitations here is a state that's somewhat out of equilibrium because of these constraints that I talked about okay hey I have a question that I hope makes sense in terms here's a theory but might not be if you have some entangled particles that are quantum entangled is it possible to know that they are entangled if they are entangled with something outside of the causal diamond and if so is it possible to infer anything about what is outside the cost causal diamond using entangled particles okay this this depends a lot on the number of quantum states of the system that they're entangled with so there's a the following general and it also depends on your initial conditions so the question is if I think about something outside the causal diamond you know when I start the causal diamond by saying okay now let's start to count right now I could have had things that were entangled because they were together in a larger causal diamond that started further in the past so is that the situation is that is that the situation you want to talk about so let's talk about that situation okay so now if I've got two systems and I've entangled them in and you want to get the most information you can you put them in a maximally entangled quantum state if this if that state is generic and this system is bigger than this system then there's zero information in this system about what's going on over here and vice versa so when you look at a pair of entangled photons if you've entangled them with some apparatus out here okay then the state of those photons doesn't know anything about the apparatus okay this is a this is known as page's theorem and it was actually developed in the context of black hole physics but it's a very general theorem in quantum mechanics and quantum information and and it's a very simple theorem - it's just basically it's it's it's the reason that you know if you take any small system and couple it to a much larger system you get into a state of thermal equilibrium in which the only thing that you can predict is average quantities that you may have constrained because they're conserved like the energy or the total angular momentum or something like that so this is basically the a quantum version of that theorem says that if you entangle two systems in a generic way one is smaller even by a little bit than the other in terms of the number of states then typically this one has no information about this one and this one has all the information there is about the smaller system representation i'm karis multi do in the inflation theory actually space at those rates the galaxies disappear you know over time and you see that I'll be sure that it has not already happened and some galaxies have disappeared that we don't even know okay good so let me first clarify this is not exactly inflation theory inflation theory is what happened very early on in the universe before the formation of the galaxies the current acceleration of the universe so there's a very beautiful galaxy that we've seen called the sombrero galaxy the sombrero galaxy is now out of our causal Dimond and it will disappear as I told you it'll take you know a hundred times the current age of the universe so don't wait around to see it disappear so it's it's we can see life that came from it originally that is in our causal diamond but it itself is outside we can no longer do experiments on things in the sombrero galaxy so there may be other galaxies that are even further away that we never saw okay it's possible so you hear these days that supersymmetry is already almost dead just because of what's already been excluded by the LHC so that's completely wrong right so but I suppose that the supersymmetric partner particles are found in the ranges you predict will that be strong evidence for your models or are there other models out there that also predict those ranges yeah there many other models that also predict those ranges so this is definitely not a definitive test of our models the the stuff we've said about inflation is is not reproducible in any standard model that I know about but it has to do with the non Gaussian fluctuations in the gravitational wave modes of the Cosmic Microwave Background and those we haven't even measured the Gaussian fluctuations yet so the chances that I'm going to live to see that prediction falsified are very small so do you does your theory assume spaces three dimension or do you prove that space is 3-dimensional priori we can make models with various dimensions of space the inflation model I strongly believe will not make sense in any other dimension than three that the reason for that is too technical for me to try to explain here but that that's what we think is correct in that sense the the I'm sorry I even said that wrong it's not the inflation model so much but the dark energy model is is one that I don't think and it can exist in any dimension besides three so in that sense we predict three if you say that this is the only possible explanation for dark energy which of course it isn't thank you let's think Tom again come over here each SETI speaker gets to take home our special SETI talk smug alien robots are talking about what's common to their causal diamonds

Channel: SETI Institute

Views: 44,711

Rating: 4.7083335 out of 5

Keywords: Quantum Mechanics (Field Of Study), space time, Thomas Banks, string theory, Quantum Field Theory (Field Of Study), Black Hole (Celestial Object Category)

Id: XzgLMOQaiLM

Length: 81min 39sec (4899 seconds)

Published: Thu Jul 02 2015