Nima Arkani-Hamed: The End of Space-Time

good evening everyone it's a pleasure to welcome you here to this uh for me really exciting event my name is Johannes hen I'm a director at the max plan Institute for physics in Munich um so this evening we have a pleasure of hearing first a talk of the mysterious title the end of space time uh then there'll be Refreshments at a reception just outside and then in the second part we'll have a moderated discussion which involves uh various people so there's a Nima Kani Hamed a theoretical physicist from Princeton there's professor also Professor Nemo there's Professor Amina C here from LMU Munich and the discussion will be moderated by Jean rubner who is vice president of communication at Tom University so this uh this event is part of a workshop that's organized at the through the cluster of Excellence Origins which is shared between LMU University Tom University and the max plan Institute for physics among other institutions and it's a pleasure to see many colleagues from these institutions here among others managing director did the list of The oxbang Institute of physics and and many other colleagues I'd like to say a special thanks to the many people who helped organizing making possible this event uh there's a lot of them so let me just uh mention in particular Baba ravenkel who's head of communication at Max Planck and our colleague sorana schultes and also our secretary veracen without whom three of them I think it's fair to say this event would not have taken place so I think I think it's it's worthwhile to give a big hand of Applause to the three of them thank you I'd also like to say welcome to people who are following this event online I see we have a full house here so so uh it's also being streamed through the Max Planck uh the institute's uh YouTube channel and I think also through the institute for advanced studies channel uh at Princeton so whoever's online also welcome to all of you so now without further Ado I'd like to just briefly introduce the speaker so uh Nema is a theoretical physicist from Princeton as I said works at the institute for advanced study his work is is trying to connect uh Theory and experiment and I think he's particularly interested in in different experiments ranging from collisions of particles of Elementary particles like like at the LHC at CERN but also at the same time ranging to experiments uh to do with cosmological observations so that's really a span a broad span of different uh different kinds of physics um so so I'm very excited now to uh to hand over to Nema and to hear about the end of space-time uh there'll be a 30-minute talk uh after the talk will also be a chance to ask questions to Nema so let's have a big kind of Applause for Nema thank you all right is this thing on am I too loud is it okay all right very good okay well it's really a fantastic pleasure uh to um be here uh and indeed I'm talking about the sort of a rather dramatic sounding uh title about the uh end of space time um but it's it's not really uh hyperbole uh we are at a at a point in our in the development of fundamental physics I I feel I think a lot of people feel um which is the kind of thing that that happens on the sort of once a century time scale in this business uh where the the fundamental principles that by now are spectacularly successful at describing everything we see in the real world from the tiniest distances we're probing at accelerators like the Large Hadron Collider a thousand times small in the nucleus of the atom all the way out to the size of the observable universe 10 15 billion light years across there's a set of ideas and principles that were handed To Us by the Revolutions in the first part of the 20th century uh which were these revolutionary developments of the prince principles of space-time and of quantum mechanics both of which of course have uh huge contributions from German physics and physicists and these twin principles turn out to be astonishingly restrictive in uh how they allow us to talk about consistent laws of nature on the one hand and astonishingly powerful on the other and it's indeed essentially these principles and not much else that uh that goes into giving us a menu of possibilities for what the world could possibly look like and a particular combination uh that the the sort of theoretical framework that Lots us talk about laws of physics that are compatible with quantum mechanics the principles of quantum mechanics and space-time is known as Quantum field Theory so that's a sort of a large theoretical framework that lets us talk about possible laws of physics and there's a particular Quantum field Theory um it's a famous standard model of particle physics and cosmology that describes everything we see in the world around us over the the huge range of distances that we just talked about so we're in a situation where our existing principle tended us to these from these revolutions are astonishingly powerful and they work but we have strong suspicions that the next step in physics has got to pull the rug out from under us and has to remove some of these principles from their primary um role in our in the description of physics and uh maybe this statement is a statement which um uh most theoretical physicists who have thought about this problem would agree with um that's certainly the notion of space-time is likely an approximate one and won't survive in a more uh complete the next complete description of physics and this is because of some very simple thought experiments that we can do that have to do with the presence of both gravity and quantum mechanics so the slogan is that because of gravity and quantum mechanics and notion of space-time is doomed so why is that so let's imagine doing a few simple thought experiments I'm a terrible artist so you're going to have to tolerate my terrible art in this talk this is supposed to be a magnifying glass okay but let's say I'm going to use this magnifying glass to try to look at some small region of space and time just to see what's there just in the vacuum now because of quantum mechanics and Heisenberg's uncertainty principle in order to look at shorter and shorter distances literally to look at have to look at it with light with shorter and shorter wavelengths that would have higher and higher frequencies and in quantum mechanics that would tell us that the minimum energy that I would need to probe very short distances has got to actually get larger and larger so in order to probe shorter and shorter distances we need to put more and more energy into a smaller and smaller region of space that's the explanation for the huge irony why gigantic particle accelerators like the Large Hadron Collider which are 27 kilometers around are what we have to use to study nature at the tiniest distances we've ever probed we need the biggest machine to probe the tiniest distances ever precisely because of this business about the uncertainty principle but anyway in a world without gravity and infinite funds you just ask governments for more and more and more money and you can probe arbitrarily short distances by going to arbitrarily High energies but in the actual world we have gravity and something very bad happens at some point you put so much energy into such a tiny region of space that Einstein tells us it equals mc squared so it's like putting an enormous amount of mass into a tiny region of space and you know what happens when you put a huge amount of mass into a tiny region of space you collapse the region you're looking at into a black hole and no information can possibly get out of it so your act of trying to look at very tiny distances instead produces a black hole that makes it impossible to see what's going on in there and if you try to do this with an even more powerful microscope and even higher energies what happens you make an even larger black hole so your attempt to probe shorter and shorter distances stymies itself and it's simply impossible to give operational meaning to distances and times that are small enough now the relevant distances and times involved here are tiny 10 to the minus 33 centimeters times of order 10 to the minus 43 seconds that's how long it takes light to Traverse a distance of 10 to the minus 33 centimeters and the fact that just to compare the size of the atom is 10 to the minus eight centimeters the size that we're probing at the Large Hadron Collider is 10 to the minus 17 18 centimeters so we're a long long way from probing this directly experimentally nonetheless we can do the thought experiment and we see that something new has to happen and every time it's happened to us before in physics that we can't even in principle give operational meaning to some Concept in this case we're trying to give operational meaning to space and time it's not that that concept doesn't actually exist and then the more complete definition of physics it won't be there and somehow it will arise as an approximate emergent phenomenon for more primitive building blocks now where do these questions become important well there's a there's a few obvious places where this kind of question becomes important for example uh we know the universe is expanding so if we run the picture of the expanding Universe back in time uh it's Contracting getting us uh uh hotter and hot hotter denser and denser and there's the moment that we colloquially refer to as a big bang um uh where the curvatures are of the universe and the temperatures and everything is at this ridiculous scale we're just talking about on the previous slide now sometimes people ask what happened at the Big Bang or before the Big Bang and we don't know because what's going on is that the whole notion of before is breaking down the whole notion of time is breaking down around the Big Bang so so it's not even clear if the words make sense what happened before um uh similar things happen if you throw yourself into a black hole if you cross the Event Horizon of a black hole then what happens inside isn't like you hit a point that's sitting there but it's like being on the inside of a collapsing universe and it's like running this picture of the expanding Universe in reverse and you get sort of crunched in in your future at some point again we don't know what happens there so these are just places where our theories simply break down we don't there are well posed questions that we can't give answers to um and they break down when quantum mechanics and gravity both become dominantly strong now uh there's lots of bit there's been a lots of work uh over the past 30 40 years thinking about this problem from various points of view um one of the remarkable developments that uh would be a whole series of colloquiao on its own that I won't uh say anything about in uh in detail today um but just to show you the sort of unity of uh of um of uh Concepts and ideas in physics um uh is that around uh a little over 20 years ago uh string theorists realized that uh that uh we could think about uh this idea of space-time emerging from more primitive building blocks at least in the First toy setting where you can see that space can emerge from building blocks that don't have space in it and physicists love to put systems in boxes and so what you want to do if you're setting this kind of fundamental question is is considered a whole universe in a box and there's a way to talk about a universe in a box where the inside of the box is a very curved space so you can really think of this uh as a tin can the way it looks like in this picture but the geometry on the inside of the tin can is curved in an unusual way so that the distance from any point on the inside to the walls of the tin can is infinite but it takes light a finite amount of time to bounce off of the walls so that's kind of unusual geometry is known as anti-decider space and physicists realize that if they could imagine experiments that were done on beginning and ending on the walls of the space just pinging the walls of the box then you would imagine what's going on you ping the walls some waves come crashing in they go crashing back out you measure what happens out as a function of what you threw in but they realized that they could uh they could give a description of of what happened here without ever mentioning the existence of the Interior only talking about uh ordinary interactions of particles that live on the walls of this box and in a very concrete sense the inside of the box kind of emerges out of the Dynamics of thinking about the very strong interactions of particles that only live on the walls of the box when the interactions between these particles are very strong and you can't follow what each one of them is doing individually there's an effective description of what's going on that makes it look as if there's an interior with space in the interior gravity in the interior even strings in the interior but fundamentally there's just sort of particles interacting very very strongly on the walls so this is a first example where out of of a quantum mechanical system with very very strong interactions with particles emerges a space and gravity in the interior and there's uh that the whole general idea is known as holography it's something like uh the colloquial picture of a hologram um where which is a fundamentally two-dimensional thing which encodes three-dimensional information and there's many aspects of this dictionary I'll just mention one of them one of the most basic ones if someone told you look this interior space here really doesn't exist everything is sort of living on on a screen uh out there you would say what the heck are you talking about I could have this purple ball and the green ball and one of them is here and the other one's further out so what could it possibly mean that they're in different positions here if this space isn't really there and the answer is that the purple dot in this in this in this description is described by some kind of fuzz of energy of some size in the wall description and as you move the purple dot to the Green Dot that corresponds to changing the size of the ball so somehow the position in this extra space is encoded by the size of excitations in this hologram so that just gives you some idea how the information which is sort of lower dimensional can encode in it properties that we ascribe to the presence of space and when you study it further gravity and lots of other things uh uh coming out as well okay so this is a huge a huge subject that's being studied intensively continues to be studied intensively um but the the world in a tin can is not our world okay we don't we don't live in a tin can very important about this Tin Can is that it's infinitely old it's a tin can that lived forever it will live forever into the future and most of the interesting questions about our universe most of the literally existential questions about our universe are cosmological ones they have to do with the fact that our universe was born at some point we'd like to know how our universe was born what it means that our universe was born we want to know something about the fate of the universe in the future all of these questions involve the notion of time in a crucial way and I probably don't have time to talk about this in uh in a detail but there are some questions about the birth of the universe or the Big Bang that are mysterious um there is a whole Pandora's box of questions that perhaps in a question session I'll say something more about if people ask um about something that astronomers discovered in the late 1990s that the the universe is not only expanding but the rate at which is expanding is accelerating it's doubling in size at a constant rate every 10 billion years or so and this fact that the universe is accelerating opens a huge number of conceptual uh uh mysteries on us in physics um and all of these ideas are both the notion of time plays a really crucial role and for a variety of reasons it looks like especially at the notion of time uh goes goes away somehow a lot has to change about our understanding in physics but especially the things that are uh crucially tied into or just uh to our descriptions of quantum mechanics also have to be modified in some way so uh so so that's a kind of a clue from far in the future that we have to eventually understand the emergence of time um and uh very likely not just the emergence of space-time but very plausibly some kind of uh deeper rubric out of with both space-time and quantum mechanics emerge so we were led to ask this question then is there some deeper structure underlying space-time and quantum mechanics and if so it's clear that it must involve new physical and mathematical ideas and um and uh we can take some inspiration for what this uh might look like so that I hope it's clear this is a huge challenge okay we're trying to understand what replaces space-time maybe even what uh extends our Notions of quantum mechanics this is one of those questions that it sounds like uh it sounds like a fascinating question to to sort of think about but not to get up in the morning and work on and uh one of the I think most uh remarkable things about the period of our in the development of our field that we're in is that we're essentially at a point you can get up in the morning and work on problems like this or at least work on problems that are heading in this in this direction um and uh there's many strategies for attacking these problems but the one that I want to focus on for the rest of this talk and the one that's most closely connected to the themes of this wonderful Workshop that's being run here has to do with this sort of uh take some inspiration from this historical fact that in the past when similarly huge conceptual leaps were needed um uh and we did have a similar conceptual leap that was needed when we transitioned from the Newtonian classical Universe to the discovery of quantum mechanics and the principles of space-time quantum mechanics even more revolutionary um there were Clues to what was coming that were hiding in plain sight as funny features of the existing theoretical framework um and uh again I'll be happy to give some historical examples of that if people ask later but I want to just move to at least some of the funny features of the existing theoretical framework that seemed to be related to the question of what replaces uh the notion of uh space time so let's talk about uh from all of these uh highfalutin Airy fairy philosophical discussion to something very concrete and directly relevant to observations in physics we we talk about the collisions of particles like uh protons at the Large Hadron Collider and when the protons Collide protons are big messy bags of they're not Elementary particles themselves they're big messy bags well not big they're 10 to the minus 14 centimeters but that's big on the scale that we're talking about here okay so the messy bags of particles they're made out of these really point-like Elementary constituents the quarks that are held together with gluons so really what happens when the these two protons Collide at ridiculously high energies is that we care about the sort of head-on collisions between the quarks and the gluons the elementary constituents that are inside the proton um and so we want to figure out what happens when the gluons hit each other when the quartz and the gluons hit each other quarks and quartz hit each other and so on okay so there's this big mess of stuff that's happening with these Elementary particles smashing into each other and uh for example you need to be able to calculate what happens when two of the gluons and the proton hit each other and two gluons come out three gluons come out four gluons come out uh these are just ordinary processes that are happening tens of thousands or hundreds of thousands of times a second depending on what exactly you're talking about and you and this is just a known stuff the standard stuff so you have to be able to calculate this ordinary stuff that's going on and accurately enough to subtract it and look for something new right so so uh so there's a there's a there's a motivation for just trying to understand how to do these bread and butter ordinary seaming calculations this does not seem to be the glamor part of theoretical physics okay so this looks like an engineering problem with apologies to any engineers in the in the audience okay it looks like a complicated problem and in fact if you look at it it's definitely complicated looking um Richard Feynman one of the things that made him famous is he taught us how to think about these processes in the late 1940s 67 years ago by imagining that here are the pictures of all the possible ways two gluons can come in and hit each other in various ways and turn into four gluons going out and there's some basic interactions that can happen these little sort of stick blobs with the four things uh and and three uh things meeting at a vertex and there are some rules that you're supposed to mathematical rules you're supposed to associate to each one of these pictures but each one of them is supposed to represent some particular way that the process could happen in space-time and you're supposed to add up all the different ways that the process could happen because of feynman's way of thinking about quantum mechanics Feynman taught us to think that quantum mechanics arises by thinking that that that particles take every conceivable path from one point to the other and you're supposed to imagine adding up all the possible histories that something could happen in order to get uh the uh the so-called quantum mechanical amplitude for a process um uh maybe the the most Salient feature about quantum mechanics is that we can't predict the future uh with exactly the same initial State something different can happen every time you do the experiment over and over again but you can predict the probability for any given final State and in order to calculate that probability you're supposed to sum up all these pictures uh and um and take the the the the square of the answer at the end to get the probability um and it just looks complicated and if you do it it is complicated okay so there's like 100 pages of very complicated looking algebra if you actually just do it from textbook ways of doing physics okay so um and that's fine not every question has a simple answer and part of the chauvinism of fundamental physics is to declare as interesting only those questions that have simple answers and as engineering those questions that don't however physics also has a wonderful way of rewarding morally good behavior and uh and people actually needed to do this calculation in order to you know connect with the experimental program at colliders like the LHC and a little over 30 years ago they found something astonishing that these hundreds and hundreds of pages of algebra in some cases actually collapsed to a single term okay so this is completely nuts that uh that naively you would think well it's complicated two things come in four things go out can happen in zillions of ways they've got to add them all up of course it's complicated I'm asking a complicated question get a complicated answer but when you actually do it and get to the bottom line you find the sort of one term formula I'm not going to explain what these symbols mean now or maybe ever uh but um but uh I it should make you clear there it should make it clear there's something going on you see feynman's way of doing this physics makes the usual rules of space-time and quantum mechanics as Manifest as possible that's a result okay that's what made him justifiably famous so you want to make the rules of space-time and quantum mechanics as manifested impossible you'll get feynman's pictures and you will think that the answer looks like hundreds of pages of algebra and yet it doesn't it isn't okay so uh so there's some kind of new extraordinary structures that are lurking there just hiding in plain sight under our noses not in some exotic speculative place but in the behavior of completely conventional ordinary physics it's just that we're being invited to think about completely conventional ordinary physics from a new point of view and presumably from this point of view the principles of space-time and quantum mechanics will not be the stars of the show some other ideas will be the stars of the show that will make the fact that these formulas are incredibly simple obvious and perhaps if we understand what those principles are in a general enough setting we'll begin to understand where space Simon quantum mechanics might actually come from uh so that's the that's the uh that's the logic uh that's that's motivating this um line of work and uh again there's lots of Clues to this structure going back 30 years 20 years um but uh there's a particular point of view an angle on it that's been pursued over the past decade or so um that has begun to see the emergence of new structures in mathematics that seemed to be deeply connected to uh these uh very basic physical questions again I want to stress these things they're not just relevant to the large adron collider right they're happen all the time in the world around us when you look out the window right essentially everything that happens in the world is a concatenation over and over again of these basic Elementary scattering processes happening over and over and over so it's the most basic process in nature and it's astonishing that the most basic process in nature seems to be governed by ridiculously complicated answers which however have incredible Simplicity and hidden structures underneath them and what is it that makes it look complicated forcing it to look like it respects quantum mechanics and space-time so what are we invited to do find some way of thinking about what the objects are from a different point of view um and and and so clearly uh that as I mentioned there have to be some uh some new physical and mathematical ideas involved and and the mathematical structures that are in that are emerging are in very sort of uh uh interesting parts of mathematics that have not typically had any connection with physics never mind connection with physics is such a basic level in areas like combinatorics number Theory and various aspects of algebraic geometry and in in various concrete examples uh we can begin to see how the rules of space-time and quantum mechanics can actually come out of some more primitive structures and uh so um what I'm uh uh at least my own point of view about what's going on is that uh the the string theorists have started telling us uh 20 years ago and are continuing to intensively study the sort of fascinating fact that quantum mechanical systems can in some cases give us uh space emergent from uh from the strong quantum mechanical interactions of particles but uh my own suspicion is that further in the future uh we need to instead be looking like something like this you see here there's an asymmetry quantum mechanics is sort of on top as king and space and gravity and so on emerge from it whereas at least my own thought is that there are some more abstract set of ideas and that we'll see quantum mechanics in space time not just emerging space but space time uh emerge together joined at the hip uh inexorably and one of the sociologically interesting things about it is that uh far-flung physics and mathematicians have been uh brought together in a fruitful and active uh collaboration now I think I have around 10 minutes uh all right five uh so I want to at least give you a flavor and this is just meant to be a flavor of what uh of what some of these uh mathematical ideas look like um and uh to also give you a flavor of what some of the physical ideas are so let's go back and talk about the interactions between gluons and the very very simplest interaction you could think of is when three gluons meet at a point in space-time not really two because uh that that just is a glue on moving on the straight line okay so that that's no interaction at all but we the simplest interaction that we can have is three gluons meeting at a point in space time now I didn't tell you but the the the the the gluons also are sort of spinning particles so they're moving along at the speed of light but they're either spinning in the direction of motion or opposite to the direction of motion so that's the plus and the minus sign here and it turns out that while those uh other amplitudes were two to four gluons and so on are very complicated these very simple plus amplitudes are incredibly simple again I'm not explaining what these symbols mean but just so you see that there are some extremely simple things that goes into the very basic most basic uh interactions we're talking about so what are all the complicated things uh happen all the complicated things happen when we draw these pictures of Feynman and in these pictures and all the stuff that's going on in the inside the particles that are moving around on the inside there they're not real there are what we call virtual particles even if you read sort of popular descriptions of physics they're called virtual um and that's because they don't actually propagate a long place from one one place uh to the other in principle from Infinity on one side to Infinity on uh from minus infinity on one side sort of plus infinity on the other they propagate over finite distances they're produced and absorbed they're not real particles they're sort of uh they're as their name suggests they're they're a convenient fiction that we introduce as sort of theoretical physicist to give a rational description of what happened inside here but you know an experimentalist who just throws the particles in and sees them come out they don't see all this stuff happen it's a theorist who tells them no no what's going on in there is you made these virtual particles and you sum over all these ways that are happening and in fact it's exactly the existence of these virtual particles that's the origin of all this horrible complexity in these uh in these calculations these sort of hundreds of pages of algebra bra are a consequence of demanding and thinking that all these virtual particles are in there so there's something else that you could do you could go back and say forget about virtual particles well there's a physical idea is we're going to eliminate virtual particles on the other hand we want to somehow keep the idea that we're going to build more complicated interactions by piecing together simpler ones but what we can do is take these exactly physical processes where every particle there is an ordinary is a physical particle not a virtual particle and we could see what happens when we glue them together so these pictures are not feynman's pictures everything here would correspond to sort of a a a a non-virtual gluon but we can just experiment and see what happens when we glue these building blocks together and then we discover some very interesting things so for instance if if you're talking about a process with two gluons in and three out this single picture where what you're gluing together or the real process is that actually gives you the total answer for the process with two gluons in and three gluons out that single picture where everything here is physical not virtual this single picture is what we get instead of the 30 pages of algebra if we do the two in four out that's a little more complicated but it's this funny picture plus two more that look just like it just sort of cycling these indices uh uh forward by by two um so it's three terms that add up to the correct answer instead of 100 pages of uh algebra so that's very interesting that once we decide we banish this notion of uh that we banish the notion of uh a virtual particle if we only allow ourselves to glue things together in this physical way then um uh we find these extremely simple representations of the actual answer but we also discover that the individual building blocks uh cannot be given a description as an actual space-time process okay so these are not meeting at points in space time these are not uh these are not sort of local processes in in space-time so we can write the answer in this incredibly simple way but the individual pieces do not look like they come from local space-time physics nor are they individually compatible the principles of quantum mechanics and yet there's some kind of world of ideas that spits out these basic building blocks that doesn't care about space-time and quantum mechanics but somehow manifests the Simplicity of the answer and also um after you play around with us for a while you understand there's a huge array of different ways of expressing the answer in this form and so you start to wonder what sort of new world of uh ideas do these objects come from and uh so that was the physical idea to eliminate the notion of a virtual particle and now I want to give you a flavor of the kind of mathematical ideas that end up uh being behind where these things come from and to do that we're going to uh strip off almost all the complexity of the scattering of particles instead of thinking about the energies and the directions they're coming from where I'm going to imagine scattering them only by scattering their labels so I have particles one two three four five let's say coming in and their scattering is just going to scatter around their labels okay so it's one two three four five and I'm just gonna scatter them quote unquote by turning it into three five two one four it's one of the most basic things that you could talk about in mathematics is to permutation okay I just take one two three four five and I permute them what in the world could permutations have to do with the scatterings of gluons blah blah blah well we'll see in just a second with a few pictures in fact there's an old relationship between uh this very basic Notions and combinatorics permutations and scattering that goes by the by the following thing so uh let me imagine just graphically denoting the permutation by writing one two three four five down here and a one two three four five up there and I'm just going to draw a line for where everyone goes so one goes to four two goes to three three goes to one and so on right so I've just graphically denoted the uh the permutation right I haven't done done anything but all of a sudden that looks like a scattering process it looks like I have a bunch of particles in one dimension of space one two three four five and they move up in time so two and three are moving up in time they hit each other then this hits one you see this picture of a this way of graphically representing a permutation also represents a picture of a scattering process in one dimension of space and one dimension of time uh and in fact there's a there's a very beautiful and by now classic story in mathematical physics that can that uh connects uh permutations to a scattering in one dimension of space uh in this way but this is clearly a very special one dimension of space we don't live in one dimensional space and uh it's very important that the basic scattering processes here involve two particles in and two particles out there's no creation or destruction of particles and that's the most fundamental thing that we saw before was the basic interactions were three gluons meeting at a point so you can two can create one or one can create two Okay so all right but maybe around 15 years ago now uh 17 years ago mathematicians discovered another graphical way of presenting permutations okay and it goes like this you draw if you want to let's say permute one to three two to one and three to two you don't draw one two three down here and one two three up there you draw them around a big circle and you put a little black dot in the middle and the rule is to see what happens is you walk in to see where does like one go you walk in from one and if you hit a black vertex you make a right turn okay so you see if you do that in this example you get one to three two to one three to two uh you could get the opposite way to do the permutation by using a white vertex okay and so then I can now glue them together in more interesting ways and if you just follow your nose left right left right as you hit uh white and black vertices this also produces a permutation one to three two to four or three to one four to two and so on now what's remarkable is that every permutation can be represented like this okay so there's a reason purely within combinatorics another graphical way of representing the most basic scattering process imaginable just permuting things there's a graphical way of representing it by exactly the kind of pictures that we saw uh were associated with the most basic physical processes that we are talking about okay so that's just gives you a flavor of why combinatorics has to do with the subject and I don't have any time to talk about the rest of the story in detail but just just to say that the sort of big big picture is that uh that that the that there's a there's a there's a mathematical structure uh that where if you give me the energies and the directions of the particles are coming from and and their and their their spins whether they're spinning in or opposite to the direction of motion you build a certain geometric shape associated with that and the volume of that shape gives you the amplitude for the scattering process and if you want to sort of calculate the volume you might want to break up the shape into simple pieces there are lots of different ways of breaking it up into simple pieces like building a jigsaw puzzle uh in in or cutting this object up in uh different ways and each one of these pieces is represented with one of these sort of physical only processes that we talked about that were fundamentally associated with permutations the pieces don't have a space-time or quantum mechanical interpretation but the full volume does and in a very precise sense the no the the rules of space-time and quantum mechanics arise as derivative Notions from this more abstract mathematical structure so um that's really all I wanted to uh to to to say about the the kind of things that we've been seeing maybe I'll make um one uh sort of technical comment and one General comment before ending the technical comment is that what we've been seeing in these examples is not just that space time can come out of more primitive principles but it's really that the principles of space-time and quantum mechanics are tied together they both come out of the same kind of uh more abstract underlying rubric um and but the more in general comment I I want to make uh that I sometimes talk about in a public talks is this has been uh especially this last part of the talk very abstract very theoretical what the heck could this possibly have to do with what anyone in the world might might care about and um you know often when people in basic science are asked this question we point back to famous examples from history um you know famously Michael Faraday was asked by some uh by some British politician what good is the experiments he's doing in his lab and he said I don't know sir but one day you will tax it okay and it ended up being true but ended up being true 50 years later and you know quantum mechanics when it was being developed by sort of 20 people studying seemingly abstruse questions 50 years later led to the less than that led to the amongst other things the invention of the transistor that completely revolutionized everything about our daily our our daily life so why does this happen over and over over again is it is it an accident you could say over and over again it's just it's just an accident and it won't keep keep happening but I think there's a reason it keeps happening and it's because in this part of science we're asking very basic questions about things in the world that we take for granted around us you know a hundred years ago it was not obvious to people that the question why is grass green and why is water wet were good questions about the world right they might have had random answers but it turned out that the ordinary properties of completely ordinary seemingly nothing exciting about it going on matter around us needed quantum mechanics in order to understand and having control of what that matter looks like that was offered by this deep understanding that ultimately was a deep theoretical understanding that came from theoretical physics was what was eventually needed to harness this enormous magic that was hugely beyond the reach of any individual or even large collection of the human beings today uh I think the analogy is there's something that we take massively for granted about us which is the very existence of the space and time around us okay uh that's uh that's even more obviously something to take for granted that just exists that there's nothing to do about but and I'm not guaranteeing that if we understand what space time is more fundamentally that in 100 or 200 years we'll have some major technological breakthrough but I am guaranteeing that the only access we have to power and magic and mystery in awe that's vastly beyond the reach of any individual human being is out there in the universe and the only way that we can access it is by studying it thank you very much [Applause] thank you very much I'm glad that space-time is still working here so you're here to answer questions if not everybody is totally flashed yes please yeah hey thanks for the great talk um I have a question about the emergence of space from quantum mechanics so as you nicely explained this in Ado CFT there's this way where one dimension emerges from like a notion of scale on the boundary so I was wondering whether you know of any concrete example or whether you can think that any especially with this slide in mind whether you think that any concrete example can exist with more than one dimension emerges from hardwired quantum mechanics well since since you already mentioned uh since you're probably part of the cognizanti already for at least part of this question already in classic adsc ft more than one dimension emerges we normally say there's a sort of one holographic direction that emerges but in classic ads there's a whole extra five Dimensions that emerge as well it's just not infinitely large it's a but it's a it can be very large a compact sort of spherical spaces so I don't think there's anything very deep about the number of Dimensions that emerge and there are examples with a large number of Dimensions emerge but but the emergence of time is a totally different thing so that's the that's the real that's the real uh difference and that's the real uh basic difference between the world and a box and our world okay I see a question in the back um sort of sort of force row back there yes um hi uh thanks for the great talk um so at the very end when you were talking about how you are composing these um scattering processes out of permutations it reminded me um of Applied category Theory and especially when you mentioned the the amplitohedron I guess that so so am I correct in assuming that and if so could you maybe elaborate a bit more in that uh well um I should say that uh I think um I'm not a mathematical physicist I'm a I'm a normal physicist I guess I don't know uh What uh but uh um uh I mean I love math but that's not the same thing uh the fact that that a bumpkin like me is uh driven into stuff like this is just an example of the power of physics uh and the power of these ideas out there is that they're out there they have nothing to do with how crappy you are um you know they even take crappy old me and you know force you to follow your nose and get into this crazy uh mathematical territory and I say all of this because even six months ago if you said the word category Theory to me I would have laughed in your face and said a useless formal nonsense and yet it's somehow turned into something very important in my intellectual life in the last six six months or so so I don't know the answer to your question but um but uh it is it is a startling thing that that that mathematicians find structures that end up being of some some deep use to physicists one of the interesting things about this subject though is that it's novel in the sense that um I mean there are some examples like it in history before but not as many as the more classic connection between physics and math the more classic connection between physics and math is either math is 50 years ahead and it's all sitting there and the mathematician moves on to something else and the nine sign is like oh thank you Riemann for giving me differential geometry so I can use it for GR uh or a similarly with group theories mathematicians were 150 years ahead in that in that case and more recently in the past 30 or 40 years a Quantum field theorists and string theorists have gotten intuition physical intuition for objects uh physical objects that make mathematical predictions that are astonishing to the mathematicians but that's a case where you know the it's a physicist in the lead and they know all the right answers and the mathematicians are desperately trying to catch up and uh and understand this is an interesting subject in that for very mysterious reasons the physicist and Mathematics are running into the same very large strange animal around the same time and so it's not that one group is ahead of the other and so we're sort of talking to each other and have very different intuitions for what these uh beasts are about but they're being gradually explored uh together so it's not an example of the sort of category Theory it's all just sitting there and it just has to be applied there's some there's some particular aspects of categorical thinking that turn out to be very relevant not for literally what I talked about but for things in this neighborhood okay we can afford one more question and I know there's a lot of brain power in this room yes please we have a question in the first row right here oh right well thank you again for for the interesting talk one simple question which type of measurements you would wish to have I mean you have a collider picture on your T-shirt you have shown some of these so so among everything we are measuring in the universe on the small scale large scale on the low energy high energy on the vacuum which which one you would pick up to make some progress this is a this is a very very large question on which I have many interesting things to say but um but I I would say that um uh at least I think they're they're interesting but um but I I would say that uh but the the quick answer is that I'm personally most interested in measurements at the extremes uh so I'm interested in very high energy collisions and I'm measure interested in cosmological observations in the largest possible scales and and um and what's what's truly amazing is that these two sets of ideas are related to each other and not just sort of vaguely related but actually very concretely even technically related to each other there's a sort of famous fact that to understand the early history of the universe you see the universe is huge today but it was expanding so early on it's very small it's very small very hot very high energy so that's one reason why there's a connection between very high energy physics and the universe because the early history of the universe had very high energy collisions in it but they're actually deeper and more subtle reasons if you go way back to at least to a picture of the very early universe that many people believe and has lots of indirect experimental evidence called inflation there's a there's a remarkable picture of this early inflationary period where the universe was expanding inside doubling in size you know every 10 to the minus 36 seconds or something like that and and that grew a teeny tiny initial spec into the entire observable universe that we see and one of the most amazing stories in in science in the 21st century I think is that is that there's a picture that very tiny quantum mechanical fluctuations in the early Universe are stretched out by this inflationary Epoch to give us hotter and colder spots on the sky that eventually turn into places with more and less mass that eventually turn into places with denser and less dense matter that eventually turn into you and I okay so all the clumping and all the structure that we see around us comes from these quantum mechanical fluctuations very early on the mathematics and the physics and the mathematics that involved in those quantum mechanical fluctuations of the vacuum are technically and conceptually very very similar to those of particle scattering processes and so that's why questions about very high energy scattering as well as questions about observations on the sky at enormously large distances turn out to be very closely connected to each other but anyway that's that's kind of a theorist fact observationally as far as learning about the universe nothing beats in my mind going to the extremes and seeing what's there and it takes a long time and you know but people have been doing this for thousands of years will be doing it for thousands of years to come maybe machines will be doing it at some point but but we can't stop up doing it okay thank you very much for this great talk for answering the questions now we have a break and time to discuss all the food for thought that you gave us and please be back at a quarter past eight for the second round here and we'll talk we'll have the physicist talk with the sociologist about the consequences of all that I'm sure you're looking forward to it [Applause]

Channel: Max-Planck-Institut für Physik

Views: 146,842

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Id: GL77oOnrPzY

Length: 49min 42sec (2982 seconds)

Published: Thu Sep 08 2022