The Doom of Space Time (Dinner at the University of Oxford) - Nima Arkani-Hamed

okay it's my great pleasure to introduce professor Nima Arkady Hamed as our after dinner speaker I've known Nima for a long time since he was a graduate student at Berkeley in fact after that he went on to slack and Stanford as a postdoc and then I was rather rapidly snapped up by Harvard where he became a full professor and then moved on to paradise as it were the Institute fraud study and princeton worries now so his one of our most renowned theoretical physicists in particle theory and cosmology he's visited here for the past couple of days and in two days he will have given I think it's five or is it six talks six talks which is this is the sixth one now it's quite amazing anyway so today he successfully persuaded us that quantum gravity strengthen and so forth where was on very large scales could be reasonably well understood with the anti-de sitter universe in that framework and just to provoke him slightly let me mention that the one prediction then of string theory as exists from anti-de sitter space is that of a negative because we're constant which is I think we all know is probably slightly far from reality anyway with that as a as a beginning is going to tell us something different I'm sure so Nima thank you so ok so um it's been a terrific terrific visit and a lovely dinner and you'll all be I think I was asked to talk about emergent time and and I assure you right away that emergent time here does not mean extra emergent time for me to talk so but but perhaps you will not be happy to know that at least a good chunk of the remarks that I'm making here are going to be virtually identical to some marked to some remarks that I made at the beginning of the very first talk I gave here over in the maths Institute on relations between algebraic geometry and quantum field theory but believe it or not that the remarks that I made the beginning of that talk will actually be relevant to the remarks to the tutu to the subject that I'm talking about here so emergent time what is there to say about emergent time the idea of emergent time that the first thing to say about is we have absolutely no idea what it should mean if it even makes sense and and so that should make my job very easy so it's hard to say something manifestly wrong because the whole question might be manifestly wrong but uh but contemplating the idea that it might be something like emergent time is one of those good tough questions it's a good tough question because it's it's not quite sharply articulated right I mean if questions in science that are perfectly sharply articulated or 99.99% of the questions there are and the basic job is that the question is easy to define and we just don't know what the answer is you can go about getting it and you get the answer you can know and check that you got the answer very good then there are the questions which are the questions that we tend to think about more in fundamental physics or to be drawn to in fundamental physics that are just on the edge of being articulated both in a sharp way they clearly involve things we don't quite understand there's clearly something going on there's some issue at stake but they're not so sharply formulated and part of the jobs that try to sharply formulate them or more sharply formulate them or find baby versions of the prop that we can actually do something about and start working on there are some questions that are so far away from being at that stage it's not particularly fruitful to think about them even as a physicist but the question of emergent time if it makes sense is probably not one of those questions it's something that that's just on the edge of being articulated bole interestingly enough that we might be able to do something about it and that's what I want to tell you about so Joe just reminded us of this wonderful fact that was learned by string theorists in the last 10-15 years that not that it's a prediction of string theory but that if you have universes with a negative cosmological constant in anti-de sitter spacetime x' if we go out to very very large scales we can talk about the we can talk about the precise kinds of observations that can be made in space signs like that at the boundary in a beautiful way in a beautiful way where all of the interior of the space and the gravity and indeed the strings and all the extra dimensions and all the jazz of the bulk theory is completely reproduced by good old-fashioned theory of particles and fields that live on the boundary ordinary theory without gravity that lives on the boundary so universes like that that have a boundary with time running from the infinite pass to the infinite future in universes like that we have a very good understanding of how to think about what quantum gravity is and we have a good first baby example of what emergent space should look like so it's a great example of how space can emerge from no space in this case the interior of this of the space and gravity and strings and all the rest of it is just some is a consequence of the strong interactions of ordinary particles that live on the boundary so what about emergent time since this is a so on the one hand it sounds like a big mysterious thing what could it possibly mean but of course very often it's a good idea very often happens to us in physics that we have the right equations long before we have the right words in the right interpretation so following Dirac's maxim the point is to find the right equations first so let's let's see if we if we can get anywhere just playing around and space and time don't seem all that different at the level of equations just change flip a few signs here and there and tada you go from let's say Minkowski space to Euclidean space in fact that whooping science you were there the going from in Cal State to Euclidean space is a deep aspect of quantum field theory in a sense our best way of thinking about what ordinary quantum field theory is without gravity involves formulating the theory first in Euclidean space and defining the results that we get in the Minkowski space that we care about by an analytic continuation so this flipping of signs is actually not just the stupid exercise it's actually something important it's it's it's it's important and deep that we can think about about quantum field theory in that way so if we kept the same kind of game with space and time let's take this anti de sitter space that we understand so well it'll just flip some signs okay if we flip some signs we can change the sign of the cosmological constant we changed some space and time and we take a space that has a spatial boundary and we convert it to a space that has a temporal boundary in the infinite future if you just do the same trivial plus minus sign flips you go from anti-de sitter space to disinter space fantastic right this is a space that's so confusing that I spent so long a pontificating about earlier today that's so deep and mysterious but no big deal switcheroo some signs and all of a sudden there it is it's a de sitter space where the analog of the boundaries and space are now at infinite future time but this is where the analogies begin to break down because there really is a difference between time and space in the case of anti-de sitter space the kinds of questions we talked about or correlations between what happens when we ping the system at early times and see what comes out at late times the analog of those correlation functions in de sitter space are things that no observer can measure okay there are correlations between things that are going on at widely separated points at infinite future time and only some putative God's eye picture of the entire universe would have access to those observables they're not they don't deserve to be called observables in any operational sense of the word and actually associated with that likely associated with that fact is that we strongly suspect that the sitter space isn't stable and that in fact the only way we know how to get de sitter space involves these possibilities for it to decay out to other vacuum and so the probability that if you start with one de sitter space you end up in that de sitter space everywhere should be zero and yet in this picture that that's not true so it seems that simply switching time and space in this case something that's so successful elsewhere just gives us something that we don't know how to interpret so and other similar attempts to do something simple-minded like that lead to similar difficulties so it's not the situation where you just do something something something naive and it works you do something naive and it's confusing right so what can we do what what can we do in this when we're confronted with this kind of question trying to figure out what emergent time might mean sounds on the face of it to be almost impossible right because physics has changed a lot in the last 400 years but one thing that has always been about is talking about how things move around in space as they evolve in time and if we don't even have time to talk about it's not even clear what physics is supposed to be about so how can we possibly make some some progress on on this question well there's one obvious way of making progress which is to try to confront questions where issues involving time it's beginning or its end or some confusing aspect of it show up okay but not to choose the hardest versions of questions like that but the easiest versions of questions like that that are as closely as possible continuously connected to other things that we understand okay so that's the most obvious way to go so for instance one obvious place where emergent time is got to play a role whatever it means is near the Big Bang singularity similarly if we have universes with a Big Crunch we need to figure out what emergent time might mean as we go there to understand the end of time but a way that we can perhaps approach the question of under standing merchants I'm close to big Crunch's is to exploit the fact that the inside of a black hole is very much like a collapsing universe and if you jump into a black hole the reason you eventually get sucked into a singularity and die is very similar to what would happen to you in a crunching universe the geometry is in fact almost identical to a crunching universe it isn't homogeneous but apart from that it's very very similar so trying to understand the fate of the observer that throws themselves into a black hole and eventually gets crunched at a singularity trying to figure out what happens there is is a question that on the one hand brings up the issue of what the end of time is supposed to mean but on the other hand it's connected this to something the formation of a black hole and its ultimate evaporation is it's physics that can be measured with observations that start at an end at infinity okay so the entire scattering process the process of forming the black hole and watching it evaporate is something that is attached to a precise observable that we can talk about so one obvious program is to try to figure out how from the information of all the radiation that comes out ultimately all the hawking radiation that comes out how can you reconstruct the inside of the black hole how can you reconstruct information about what was going on in the black hole and that has been a long-standing problem we now believe that all the information does come out of the black hole but how precisely to figure out the experience of someone who falls in from that data is something which has been a long-standing problem there's been a recent controversy over the last one or two years about crazy things happening near the horizons of black holes called firewalls and things like that there I would be stunned if there was such a thing as a firewall but it spurred people to think more carefully about how to do that and there's actually been some really some very nice recent technical work on figuring out how to embed and talk about the physics not close to the singularity but at least as you cross the horizon on the other side of the horizon how you get to talk about the other side of the horizon of the black hole in the language of something you can measure out at infinity okay so there's a very long way to go but that's that's an example of a way we can start making progress on the of what emergent time might mean to start by connecting it to something else that we understand okay okay so that's that's one kind of strategy there's another kind of strategy which doesn't involve actually thinking about black holes or singularities or cosmology directly at all this is this is what I'll end with and this is the part which is identical to what I told my mathematician friends on on Monday you see this is a very big step if it's really true that we have to figure out emergent time if there's some way of thinking about physics where space and time are going to be emergent it sounds like it's it's it's a big deal even these remarkable equivalences and dualities that we found have not forced us to make such such a radical step okay so it's obviously going to be a radical step and how can we possibly make a step like this perhaps without input from experiment because the relevant questions are cosmological or they're down to the Planck scale we're unlikely to get subtle cosmological questions or down at the plot see we're unlikely going to get direct hints from experiment about them well we can take some inspiration from a previous time when we've had to take a similarly radical step and I think part of the reason I'm mentioning this here is that I think this is the sort of thinking we're clearly about some of the some of the philosophical aspects of these of these questions might actually spur research and might might might spur research about the actual physics but so let's so the example that I want to talk about this Oracle example is the development of quantum mechanics so quantum mechanics is the most radical thing that we've we've ever seen in physics is the biggest transition from classical to quantum we lost classical determinism and I want you to imagine as a little thought experiment that you're a classical physicist in the year 1770 in the middle of the night by the ghost of theoretical physicist future okay who says I have a message to you from the year in 1930 determinism is gone and they vanish into the night as ghosts of theorists future I want to do yeah and and that's that's all they tell you right so you obviously can't sleep what are you going to do with this what you're going to do with this information what if they go tell someone else you know they write the paper first right not you you have to you have to do something about this information and you could try to do things you could try to randomly modify Newton's laws by making them non-deterministic and you're never going to get anywhere doing that okay that that's an example adding stochastic terms and Newton's laws is an example of conservative radicalism as opposed to radical conservatism it's an idiot thing to do it's never going to work and that's because it's totally arbitrary anyway in this case we also know it wasn't the answer the rear the right answer wasn't anything like that ah and you might quickly convince yourself that you're not going to sit there and just guess what the correct theory is right that leap is enormous you're not going to sit there in 1770 and guess about wave functions and hilbert spaces and the entire picture of decoherence and all the crazy stuff that has to happen to get the classical world to emerge out of quantum mechanics you're not going to do that so what could you do you could just say ah screw it and wait for experiments but now then you waste this ghost coming it's a big deal right they don't make the trip often so what can you do what's something that you can do is is say look if there is no determinism fundamentally then it must be that the determinism we appear to see in Newton's laws it's somehow also not fundamental there must be some way of talking about classical physics you would argue which isn't manifestly deterministic why because the underlying theory isn't deterministic and whatever the correspondence limit of that theory is to the theory you have under your feet now it can't bring out of nowhere a principle that wasn't there to begin with you can't be a little non-deterministic like being a little pregnant right or if you were will be like these idiot things like adding stochastic terms to Newton's laws but if it's not like that so the right correspondence principle limit can't be manifestly deterministic it has to reproduce classical physics but it can't reproduce classical physics in the way that's handed to you by Newton it has to reproduce classical physics in a different way in a new way where determinism isn't manifest but somehow comes out of some principles and you could then take some inspiration from this visit of the ghost to look for such a reformulation of classical physics is there such a reformulation of classical physics there is it's a principle of least action and it's a way of thinking about classical physics it when we all learn it as undergraduates it's very it's very striking it's very strange how does it seem the particles sniffs out every path you can take from A to B and it picks the one that minimizes the action why is it possible to talk about and and then of course it turns out that it is deterministic right the kind of variations you allow and what you do the sorts of actions you pick make it equivalent to Newton's laws but uh but why is it possible why does such a totally different philosophical starting point lead to exactly the same equations and as I'm sure many of you know the people who discovered the principle Lee section the most between Euler Lagrange they were mystified that there was this very very different way of thinking about classical physics today we know why that different way of thinking about classical physics exists the world is not deterministic it's quantum mechanical and but the classical limit of quantum mechanics must land you on the nose not on Newton's laws but on some way of talking about classical physics that isn't manifestly deterministic which is a principle of least action that's why it had to exist it exists and when you find that second way of talking about classical physics you are in a much better position in a sense you've taken 90% of the step toward quantum mechanics by managing to talk about something that is deterministic without having determinism hardwired into the description okay so now that's not the way the history actually unfolded experiments did help historically but I believe that even without any experiments people would have eventually discovered quantum mechanics following these kinds of following this kind of logic it would have taken a lot longer because you would think about why the principle of least action exists and you would eventually think in terms of some stationary phase argument in fact Hamilton was playing games like this writing down formulas that looked vaguely like the path integral exponentiating the action of the phase and so on okay so I think people would have invented the path integral fairly quickly uh it would have taken a long time obviously is to realize that you should interpret it as an amplitude that's a probabilistic interpretation and all the rest of it but but but the important point here is that even big revolutions in physics never never just of course they never crash the old order that we all know they'll have to reduce to the old stuff in some limit that we know but something that we talk about which is equally equally true but we talked about a little less as not only don't they reduce to the old to the old physics they explained mysterious features of the old physics when you understand the deeper structure better of course it's the most famous in the context of GR with the principle of equivalence and so on but but for the example that I want I think this quantum mechanical case is even more striking so back then it was the Terman ism that had to be lost today it's space-time that has to be lost we have to figure out how to make do without space-time and so what we can do is cast around under our feet not just in these extreme situations involving black holes and cosmology and other things there it must show up but there are the problems must show but we can take some inspiration from the doom eventual doom of space-time to try to figure out some way of talking about good old-fashioned ordinary physics tying our hands behind our back and refusing to use space-time as a crutch to describe to describe what is going on now so that's that's a sort of a that's a highfalutin strategy for trying to cope with what emergent space-time might be and I'll just end by by saying that that while this is a very abstract kind of argument a really fascinating thing that people have discovered by studying good old-fashioned quantum field theory okay a subject in principle handed down to us by Bohr and Dirac and Heisenberg the basic structure hand does already noun by back that just understood and refine better and better in the intervening times but the structures has handed us then we've understood especially in the last twenty years that this structure has just absolutely miraculous properties that are not manifest in the in the way it's handed to us at first people started noticing this in in situations where when the interactions between the particles are weak we think we understand what's going on okay and particles bang into each other and and and everything is fine and people like Fineman even gave us these visual ways of thinking about how all the interactions happen but when the interaction between the particles get strong our usual analytic methods break down and so something new happens in principle we could simulate things on a computer in practice we can't even do that except without except with it with a great deal of work we've done it for the usual strong interactions but but for many other theories we don't know what happens and so people would like to know what happens when the couplings become strong and what was discovered 20 years ago is that so there there be monsters we don't know what's going on with a coupling become strong but what people discovered start discovering twenty years ago is that when the couplings become strong remarkably many quantum field theories have a totally equivalent description in terms of other quantum field theories okay these other quantum field theories might have a completely different seemingly if you believe that things like gauge symmetries are fundamental you would be shocked to discover that these dual quantum field theories have totally different gate symmetries totally different particle contents but when the interactions of one theory is weak the interaction of the other theory are strong and so so it's not manifestly inconsistent and the end result for the observables of the two theories are identical the most dramatic example of this is the correspondence that we've alluded to many times today that a gravitational theory and a gauge theory can be identical that's that's that's another miracle that is not manifest at all you stare at the diagrams of fine men what more in Heisenberg etc handed us in Dirac and powie if you told them hey your theory in some regime is identical with the theory of gravity in one higher dimension they would think you're nuts but it's true so when it's one or two miracles that happened you think oh those are miraculous things but at some point the number of miracles start becoming comparable to the number of ordinary things going on and if that happens it strongly suggests that you're thinking about it wrong even this standard physics not new even the standard physics we're thinking about perhaps not quite right and in the last 10 years or so it's become obvious that even when the interactions are weak even in a place where we principle understand what's going on thanks to fine men and Friends even there uh there's the usual space-time picture for what's going on tremendously complicates the computation for what actually happens when you throw a bunch of particles in together and watch them come back out and the final answers are shockingly simpler than what you would expect from from these space-time descriptions of what's going on so both when the couplings are strong and when the couplings are weak by insisting on describing the physics in a way that makes space-time front and center we hide things we obscure things we make things that are simple complicated we appear complicated we completely obfuscate the fundamental similarities between what look like different physical theories the only reason they look different is that if you insist on giving them a spacetime description we have to use different words to describe them but they're in fact identical okay so all of these arguments suggest that sitting here in the structure of good old-fashioned ordinary physics many of these things are been sitting around for the last 50 60 years they could have been observed at any time in that period okay and the structure of standard physics are clues to a new way of thinking about physics without space-time and uh and and I suspect that and that's another example of very concrete thing that that we can do it's nice when these highfalutin things and concrete things line up the highfalutin things tell us to be suspicious of space-time and perhaps look for a different formulation of physics where we get rid of them the concrete things tell us space-time is complicating the calculations and we should try to get rid of it and so this is something that many of us are starting to try and do is to find new ways of thinking about quantum field theory is where space-time is eviscerated in fact even the usual Hilbert space quantum mechanical picture of what's going on is sometimes eviscerated and we are and we start trying to find new underlying principles that that are going to reproduce the same physics from a different starting point there is some limited success for very a toy theories along these lines in the last number of years but the underlying principles even in these toys are still not clear but I think it's something that may bear fruit so we have a number of ways that we can that that we can proceed to attack this question but it does have this character as I hope I've convinced you it's a question that seems like a big grand question but you can find sub questions related to it that go roughly in the direction of the big one where you can just get enough of a foothold to be able to start scaling this mountain and and hopefully figuring out what it all might mean Thanks

Channel: PhilosophyCosmology

Views: 43,950

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Keywords: Philosophy of Cosmology, University of Oxford, University of Cambridge, Nima Arkani-Hamed

Id: KyRO8Wv4BaY

Length: 27min 38sec (1658 seconds)

Published: Wed May 07 2014