Juan Maldacena Public Lecture: The Meaning of Spacetime

foreign [Music] [Applause] hello everyone I'm Lauren Hayward a teaching faculty member here at Perimeter Institute and I am so happy to welcome you back to perimeter for a special summer lecture perimeter Institute was created to be a place where people ask big questions about the universe perimeter is just over two decades old but people on this land have been asking big questions about the universe for thousands of years looking at the night sky and understanding our place in the cosmos is a human constant throughout the ages perimeter is situated on the traditional territory of the anishinobe hoden Ashani and neutral peoples The Institute is located on the Haldeman tract we are thankful to those who preceded us and we will strive to act responsibly and collaboratively to carry forward the Quest for knowledge for the betterment of all now for those watching our live webcast online we hope you'll join the conversation we are at Perimeter on Twitter and perimeter scientists are online to answer your questions if you have a question for tonight's speaker you can ask it with the hashtag pilive that's hashtag p-i-l-i-v-e now this week perimeter is proud to be hosting the 33rd annual strings conference which brings together the extended String Theory Community The Institute is truly buzzing with 200 in-person attendees and many more joining virtually from around the world and at this time I would like to welcome one of the organizers of the strings conference Sabrina pastorski a faculty member here at Pi who will introduce tonight's speaker [Applause] I'm very happy to have the honor to introduce tonight's speaker Juan malosena is one of the Giants of the strings community and theoretical physics more generally his proposal of the adsc Ft correspondence was a groundbreaking discovery that has served as a catalyst for countless research Endeavors over the past 25 years attempting to understand the Deep connections between gravity and Quantum field Theory born in Argentina Professor malisena received his PhD from Princeton University and is currently the Carl P Feinberg professor at The Institute for advanced study he's a member of the American physical Society the American Academy of Arts and Sciences and the World Academy of Sciences he's received many awards throughout his distinguished career including being one of the inaugural laureates of the prestigious breakthrough prize in fundamental physics in 2012. tonight he will discuss ideas that arose from the study of quantum aspects of black holes and will also delve into how wormholes are related to quantum entanglement join me in welcoming Juan melisena to the stage [Applause] thank you very much okay thank you very much for the very kind introduction it's a real pleasure to be here I've had a wonderful week during the strings conference and I'll try to transmit some of the enthusiasm that we have with string theories have for our field so I'll be talking about the meaning of space-time black holes wormholes and quantum entanglement so Galileo said that the book of nature is written in the language of mathematics and geometry so let's talk a bit about geometry don't worry I will not talk to you about mathematics so we'll talk about geometry let's start with euclidean geometry so it's based on very simple Concepts such as points uh lines mainly straight lines circles Etc and out of these Concepts we can use it to do many things for example we could use it to describe images in fact many software programs use this type of geometrical concepts to store the images and so on there's just an example now geometry arose from technological necessities of the time like measuring Fields leveling taxes Etc the Greeks formalize and abstracted the rules of geometry and they summarize them starting from some axioms and they had a list of axioms so Euclid had a list of axioms and one of them was for example just to give you an example that if you give two points any two distinct points then there is a unique line that unique straight line passing through it through them okay that's I guess something we all I think it's obvious that's a starting point and if you assume this then you can prove many other things process of formalizing geometry this geometrical constructions has continued to this day and in fact now we can imagine curved geometries and higher dimensional geometries and so on and we have similar principles to describe all of these cases now geometry is a very basic notion um it is possible even to find it in unexpected places and so I'm going to give you an example of how we can find it even in children's games so there is this game called spotted that consists of has many different cards with different images and when you play you have to match an image that is in your car to the image that's been played to the image in a car that's been played and by the way I'm not getting any AD money but so for example these are the cards and for example you have these two different cards and then you can find the image that is in common between these two cards can you find it yeah there it is so for example between these two other cards there is also an image in common can you find it okay good good you're you're getting good okay so we're not going to continue um so what we see is that given any two cards there is a unique image in common now there is a kind of geometry behind this game uh so I just said that given any two different cards there is a unique image in common and this sounds similar to that postulate of geometry if we reflect replace the word cards by points and image by lines so we can from this little game and this little system of cards we can abstract this notion of geometry and um in fact so we defining replacing the the names in this way there is a geometry behind this game in fact something called finite geometry which is something that was developed in the 17th and 18th centuries um there is also higher dimensional geometry behind language models such as chat GPT and well a lot of software programs for example in that case words are represented as points in some higher dimensional space that's another example um now this concept of geometry were used to measure the geometry of our real world our world the the Earth sorryness uh developed the simple observation where he noticed that if you have a vertical stick at some time of the year it has no Shadow but if you move some distance away it will have some Shadow and then by measuring this angle and this distance we could estimate the size the size of the Earth in particular he showed that the surface of the Earth is not flat but it's a curved space geometry so this shows for example that euclidean geometry was wrong for measuring Fields so you have to use a different geometry the geometry of a sphere of course it's that that little mistake that you make is small for small Fields it only gets big if you were to measure fields which are the size of a continent so the the notion of euclidean geometry continues to be good for relatively small objects such as small fields uh but this one one of our first examples where we go from this this flat geometry to the curve geometry still at the time and till the beginning of the 20th century it was believed that euclidean geometry was a good description for describing the three-dimensional geometry of let's say outer space or the space in which the Earth sits um okay now let's make a small break from geometry and go back to physics um there is an important physics principle from the beginning of the 20th century which is the principle of special relativity the principle of Relativity itself is older it goes back to the days of Galileo and it says that observers move in with constant relative velocity observe the same laws of physics so if you are in a moving cart and someone is in a stationary cart they both make the same observations um now special relativity has one extra postulate which says that the speed of light is the maximal speed of propagation of signals and also it's the same for all observers so all observers measure the same speed of light so this is an additional law of physics and in accordance to the first uh postulate is the same for all of them so this is a little graph and here we have the red Observer is stationary since the light traveling at a certain speed and then we have the moment of server Observer and your intuition would say that what speed would he measure would he measure the lower speed or the same speed lower exactly that's what your intuition would say but the idea in physics in reality this person actually sees exactly the same speed and the only way this can work is if time flows differently for the two observers so two the two observers have a different notion of time and that's a consequence of this principle of special relativity so what this implies is that we can join space and time into a new kind of geometry so we can play a game somewhat similar to the game we were playing this children's game we were discussing we were going to discuss a new kind of geometry where we are going to define a point in a slightly different way so we're going to define a point as an event something that happens at some place in time so for example a point would be the beginning of the lecture that happened here in this room okay um and we can draw that for example in if space was just one dimensional we have this is the direction of space and for us it in still this would be the direction of time and then uh after a while uh at the end of the lecture we'll have another event which will be the end of the lecture that's this other point um and so those are two points now lines will be trajectories of particles or observers so for example if you are sitting in your chair you are not moving anywhere so you are sitting hopefully during the whole lecture hopefully we won't leave during the middle of the election um then we can have a particle let's say a neutrino that came from the Sun and went through us and crossed us at the beginning of the lecture by the end of the lecture it will be very that neutrino will be very far away okay we can have one that is traveling a little further further faster and finally we can have a light Ray which travels as fast as possible and that's the maximal propagation so anything any straight line of an observer will an observer moving with constant velocity will be within that well we'll have it to travel at within this range um if it's traveling let's say to the right um now so the light ray goes at the maximum velocity now something interesting is that this uh so if we are the static Observer we divide space and time according to this let's say access so this is space and this is time if we are a moving Observer like let's say this one um we would call our time Direction so we are just sitting here for us as we move forwards in time and not moving in space that will correspond to let's say this axis that's this axis an axis of equal time would correspond to actually it turns out to correspond to a line like this so what they call Space and Time Each of this observers how they divide space and time depends on the velocity they are moving at but they are all seeing the same let's say combined space time so the conclusion is that out of space and time we can make a geometry in the way that we just mentioned and that's the geometry used to describe physics in accordance to the principles principles of relativity now we'll make a small apparent detour from geometry and we'll talk about the force of gravity um so the force of gravity you probably remember from your high school days so you have two bodies let's say a big mass and a little body small mass and with the force of gravity says that the acceleration that this Mass feels is um first of all independent of this mass and proportional to the other mass in the distance and the Newton constant now there are two things I want to draw your attention to is that the acceleration of this Mass so how far how how this mass will move is actually independent of its mass and the second aspect is that the force is instantaneous so that it only depends on where these masses are so for example if I were to move this Mass uh if I suddenly move this Mass immediately this other mass will feel the force changing um now this is bad for relativity so the Newton the Newton's law has to be changed so as to make it consistent with the principle that no information can travel faster on the speed of light however this first fact will be something that will be retained in fact is based that observation is something that Einstein called his happiest thought and this is the idea that that if you are falling freely in a gravitational field your weight disappears so in other words the main effect of gravity is appears so for example if you are sitting in an elevator you are standing in an elevator on top of let's say a scale you will see your weight but then if the wires break and you are falling freely then you're you're falling at the same rate as the elevator and the scale and so on and your scale will Mark we will show zero weight weight has disappeared now I don't recommend doing this experiment in an elevator but I'm told that it's very very fun to do this experiment in outer space I haven't done it myself but the astronaut and the um the spaceship are both falling in the gravitational field of the Earth or within the Earth and both moving in exactly the same way and they feel the the astronauts feel they are floating okay so based on that observation Einstein developed the idea of general relativity and it's a general relativity is Einstein's theory of gravity and the basic concept the basic idea is that the geometry of space-time is not flat but this curved so and the idea is that if you are a particle moving freely falling freely that particle will move along uh that space time along the shortest trajectory so the analog of a straight line is the in some sense shortest trajectory and then he had the idea that this curvature is produced by the presence of matter so he had an equation which basically says that the curvature of space-time is uh is proportional to the amount of matter that you have so our conclusion is that so space time is really described by this curve geometry and again as we said before points are events and straight lines are the trajectories of observers falling freely and for our everyday experience uh of course that space time is pretty close to uh to Flat space now in some cases you can really see very clearly the curvature of space-time so this is an example where um we are here at the Earth and we are looking back at the universe and this is called gravitational lensing so here we have a cluster of galaxies which is just a big Mass um that curves the space-time geometry and then the light Ray that comes from an even Galaxy that is even further away will follow the line so let's say straight lines and here we see that we have two uh straight lines that initially are moving apart from each other and then they meet again so that's something that could not happen in flat space where two lines that are initially moving away from each other would continue moving away from each other but here we they come back to the Earth and in the earth we see two images of the same galaxy so a very clear demonstration of the curvature of SpaceTime and it is somewhat uh in some sense similar in spirit to how Aristotle shows that the curvature of the Earth was that the Earth was not flat by looking at the trajectories or the the properties of light rays um now this Theory makes one interesting prediction which is the existence of gravity waves which was detected a few years ago and where researchers here at the perimeter played uh and it made interesting contributions to this discovery now in addition there were two very surprising predictions black holes and the expansion of the universe and I call them very surprising because Einstein himself didn't quite believe these predictions so when people started talking about these things he he was so surprised he said now this can't be you must be doing something wrong in fact there is this famous phrase uh your math is great that your physics is this much this is what Einstein told the metro and I I like this phrase very much because that's sometimes what other physicists is the last string theories now we now have great observational evidence for both we have this picture of a close-up of the black hole at the center of the Milky Way that I'm sure you've seen black hole is roughly there and this is uh taken by the Event Horizon telescope and again researchers who work here at the Institute participate in this wonderful experiment and we also have a lot of evidence of the expanding Universe I'm sure you've seen this picture I want to explain it in detail only just to mention that we have a lot of evidence from the cosmic microwave background of course the whole history of the formation of galaxies and so on um and now uh we'll turn to a new topic we'll make a slide slight change and then we'll try to go back to gravity and the new topic is the other revolution of the earliest the early 20s 20 20th century which was the development of quantum mechanics so classical physics was changed in two ways one was the development of special relativity the relativity of time and the discovery of space-time and then the idea of the curve space-time or general relativity and now we're going to discuss a few words about quantum mechanics I'm sure you've heard something about quantum mechanics before and quantum mechanics is a new type of description of physical systems that the main point the main point is that it is intrinsically probabilistic so things are not completely determined but there is a certain probabilistic element and then there are a few other properties of quantum mechanics such as the uncertainty principle there are some things you cannot know at the same time like the position and momentum of a particle and also there are other features such as the so-called sum overpass that sometimes if a particle can go through either through one slit or another slit there is a sense in which the particle goes through both lead and then um there is some interference effect similar to a wave for the probability of finding the the particle at this point um okay but what's important something that's important for us is that quantum mechanics explains many things it explains chemistry that explains atoms it explains matter Etc now it's a pretty weird explanation of matter where atoms are mostly empty space so the size of the nucleus is much much smaller than the size of the atom and in fact it requires a lot of work to explain simple obvious things so there are some things that we take for granted but in this quantum mechanical description of atoms and matter are actually very interesting in fact the physical appearance of most substances are what we call immersion properties so if we if we say well why it's the screen white um well and why is uh well this because of how it reflects uh the light and perhaps we have the our my computer is shiny so why is the computer shiny well it has to do with particular properties of the arrangements of many atoms and so they arise from a large number of quantum particles and their interactions so many of these properties so for example a mountain can appear very solid uh also the water can appear very solid to the insect the water will not appear solid to us and in fact the mountain also would not appear solid if uh you wear a neutrino or a dark matter particle that can just pass through the whole Mountain without interacting with anything so in both cases the mounting or the water consists mostly of native space and this solid properties that we we take for granted come out of the interactions between these different particles now let's uh so that's an important concept this idea of immersions and now we'll we'll introduce yet another concept so in the history of the 20th century people put together the idea of quantum mechanics with the idea of special relativity so the idea that uh signals can propagate at most with the speed of light and this lead to the modern description of particle physics which is called Quantum field Theory so that's so great is you could call it relativistic quantum mechanics it describes the behavior of Elementary particles the interactions between Elementary particles so in this this description each light for example is described in terms of the Quantum of Light which is a kind of particle and it can be exchanged between charged particles and that leads to the attraction between the charged particles and in the same way that we can describe pictures using geometrical concepts we can describe the evolution of particles in in our universe by a set of lines uh that there are geometrical concepts which exist in space-time so now this picture here is in space-time and there are particles and there are interactions and this type of diagrams represent so that they can represent the propagation of these particles and there is a way to calculate the probabilities for each of these diagrams so quantum mechanics is probabilistic and so there are formulas Behind these pictures which we can use to describe particle collisions and Integris very well with what we see in particle collisions okay and in this way we can describe all the matter we see at the very fundamental level we describe with this type of pictures so particles moving in the space-time geometry now there is an important question which is whether we can include gravity can we finish uh the developments of the 20th century and put together a general relativity with quantum mechanics so we know nature is just one it's not divided into gravity and electromagnetism or or matter this this is just a division in our mind uh nature is just one and we should have a way to describe quantum gravity but we should have a consistent way of discussing general relativity together with quantum mechanics now there are there are two approaches to this problem and one is an approximate approach which is similar to the quantum filter approach and it's an approach as I'll review works well for some problems but not for others and then there is a more precise approach and is what we would call a full Phantom theory of gravity and I will start with the approximate approach so in the approximate approach the idea is very similar to the idea that one had in for ordinary particle physics we will just now have all these particles moving instead of them moving in a flat geometry they are moving in a curved space-time geometry and again you can create particles and you have to add one particle which is the graviton the the Quantum of gravity and in this way you can you can describe various things and when the radius of the curvature of the universe is very much larger than the so-called plank distance this works very well and in particular so let me just say what the Planck distance is so plug distance is a combination of the various fundamental constants of nature G Newton H bar and C so these are basic constants and out of them we can make a quantity which has dimensions of length and Planck made this combination when he discovered the Planck constant and he said this distance must play an important role in physics it's a very very tiny distance so it's not the distance we can see with a microscope in fact our best microscopes today can explain can explore a distance of order 10 to the minus 18 meters so the distance much much bigger than 10 to the minus 35 meters um just to give you an idea of the size of the blank scale let's imagine that we grow to the size of the Galaxy okay now we are the size of the Galaxy the minimal size we can see today with our accelerators would be our size okay so it's a big difference the plank scale would be the minimal size we measure today with accelerator so another factor of 10 to 18. anyway this is a very tiny distance but it was recognized as a basic length scale of general relativity and it's basically the length scale at which the quantum effects of gravity become very important so if you were to look at space time at this very tiny distance space time would be highly fluctuating and so on um very would be very probabilistic space time at long distance is very very sharp and clearly defined very classical so this approximation this simple approximation to um to Quantum gravities is good enough for most circumstances of daily life in fact it's also good enough for almost all places in our universe now there is a there is a situation where there is a complete failure of this approximate description and this happens uh at two places so the the most interesting one where it happens is at the beginning of the Big Bang so at this very uh first instance the we think the curvature of uh space time became very large and the words the word Singularity means uh if you don't know what it means you get the right meaning because we don't know what happens there so you know um just means we don't have any idea what happens there and according at least to this Theory and the other case is singularity there are similar singularities in the interior of black holes as I'll explain in a little while in more detail so these are places where the approximate Theory fails so it fails in this extreme circumstances um and this circumstance here is of course very important for us because that we would like to understand what happens there we like to understand the beginning of the universe so that's the main motivation to study quantum gravity is to understand what happened at the beginning so for that we need a full theory of quantum gravity the full Theory but before we start talking about the full Theory uh let me continue uh we will come back to the full Theory later but let me discuss some important successes of the approximate approach so now we go back take a step back again and discuss we'll discuss in more detail some important successes of that approximate approach so the first one is that it leads to a big surprise for black holes um and this is the fact discovered by Hawking that makes Hawking very famous the idea that black holes the loss of quantum mechanics in the context of black holes implies that black holes can emit thermal radiation they need some radiation and this radiation is such that the temperature of the radiation increases as the black hole size decreases so if you make have a smaller black hole it will look hotter it would be like a hot let's say it could become red and if it shrinks enough it could even become white so it could be so hot that it could have the temperature of the Sun and it will look white to our eyes so it would be a white black hole it looks like a contradiction in terms right black holes were supposed to be black but now they're black they're white so big surprise um now this effect is uh almost Irrelevant for astrophysical black holes with atrophysical black holes well they're completely relevant for astrophysical black holes because after physical black holes are very massive they have very low temperature so low that it's even lower than the temperature of the cosmic microwave background so you have no hope of seeing this tiny temperature for astrophysical black holes if you had smaller black holes the effect can become bigger for example a black hole of a mass of a continent would have the size of the bacterium that's the size of the wavelength of typical wavelength of white light and then that black hole would look would really look white now this type of black holes are not readily made in our universe but in theory this is what you would find um now let me just explain why that effect happens so I'll explain it with some kind of cartoons and the point is the basic point is that the quantum vacuum is somewhat complicated State um so the quantum vacuum is such that if you looked at the small region of the vacuum what you measure is quite unpredictable so you you have so the the measurements at that point could change from measurement to measurement and there is a kind of lack of information that you have if you only look at the little portion of the vacuum and this is a computer simulation for a particular Quantum field Theory the whole vacuum is simpler so if you look at the whole vacuum then you see for example that you have no particles if you look at the small portion of the vacuum and you look there it might be that you see something like a particle but if you look at the whole vacuum you don't and the reason is essentially that you have some ignorance in some parts but uh that ignorance is correlated with some other ignorance you have in the other part if you look only at the other part but if you look at the hole you have a complete picture with which produces a more predictable and precise state now this might have looked a little abstract so since it was a bit abstract let me just describe it with an analogy because it's an important point for the rest of the lecture and imagine that somebody tells you a portion of a sentence so let's say Mary stepped out of hair and then you can decide how to complete the sentence any volunteer to complete the sentence want to complete the sentence what good so that's one possibility okay so you can complete and we'll all perhaps come with different ways of completing this sentence um and and so we have a certain lack of information of what the sentence is there are many possibilities for what lies outside the sentence so we cannot say what the sentence means it doesn't have a definite meaning definite clear crisp meaning now we know it impulse very well we don't know the full meaning because then in different ways but if someone told you the full sentence let's say Mary stepped out of her Comfort Zone by explaining quantum physics to a group of investors then you have the full meaning um now it's clear what the whole thing is so if you have the whole picture clear meaning you have only a small picture so that's similar to looking at the portion of the vacuum versus the full vacuum okay so uh in that case you get a world form sentence you have a portion we lack some information and in fact there is a way to quantify the information we lack so in the case of the sentence we could imagine listing all the possible ways to complete it some will be very improbable some will be more probable and and we can quantify there is a well-defined way to quantify the entropy or the lack of information that we have using so-called information Theory we can assign a number to uh roughly speaking counting the number of different ways in which it can end so I said the vacuum is then in this analogy like a well-formed sentence um so now let's uh return uh back to black holes and so this is a picture of the space-time geometry around the black hole um remember roughly time is roughly like this and space is roughly like horizontally exactly how what do you call space and time depending on how you're moving but roughly speaking is that so each point here is an event that happens in a space time light rays are moving at 45 degrees and this region here is the outside of the black hole and if you are here is the region that looks like flat space far away so you have a light Ray that is coming out it will go out like this so here the the this direction you can think of it as the direction that comes out of the black hole so um and then there is a if you if you're at some event here and you shoot the light Ray going outwards that light Ray uh will will go up um but then eventually it will collapse into a singularity so we have here a singularity in the future so this is a bit like a big crunch so the interior of a black hole looks like a big crunch geometry where the universe collapses at some finite time so if you're traveling here as an observer you find that your Universe collapses and you die when you get to the singularity so I'm sorry that's what general relativity says um okay so and not only do you die but there is no way to escape from this uh according to General activity what was the question yeah that's right you can't escape because that would require you to travel faster than the speed of light so speed of light moves here at 45 degrees if you wanted to escape you would have indeed to travel faster than the speed of light absolutely correct um okay so that's uh that's that's the space-time geometry and there is a particular light Ray which is the one that divides the region from which you can escape from the region where you so the direction where you can escape which is this one outside from the region where you cannot escape and we call that the Horizon so this is some light Ray and so if you are an outside Observer you can see only a portion of the geometry so the portion that is outside because the the points here the events that are inside can never send you a signal so you ignore what happened here in the interior you can only measure what happens here in the exterior so we had the vacuum of space-time the the whole space-time vacuum and split by The Horizon into two pieces the piece outside and some piece inside and so we have a phenomenon similar to we had with the sentence in this sentence analogy where we get only a portion and because we get this portion it leads to some ignorance some Randomness and in physics this ignorance or Randomness translate it translates into temperature so whenever you have something at finite temperature we have this feature and we got the quantification of this lack of information is sometimes called entropy or disorder is what what the lack of information of what's inside now from the black hole we can calculate the central pure amount of disorder using the loss of thermodynamics so Hawking gave us the formula for the temperature of the black hole as a function of its mass or its energy and then we use the Lotus thermodynamics and we can get an entropy and it turns out that the entropy has a very simple formula which is just the area of this Horizon so this is like a sphere um is the the trajectory of those light rays um and it's the area um so the area has some dimensions of length and divided by that plank length the same quantity that Planck had originally thought that it might play an important role here indeed plays an important role and appears in this formula of course since this distance is very tiny for if you have a macroscopic area this is a huge future huge entropy in fact if you were to calculate the entropy of the universe the most of the entropy of the universe comes from the entropy of the big black holes at the center of galaxies that is more important than any other entry and then the second of thermodynamics um with would imply that the area should increase and indeed the loss of general relativity say that the area always increases so Hawking had shown even before this formula was developed that if you have a horizon the area of the Horizon always increases that this just comes from solving Einstein's equations those equations that we discussed before that have nothing to do with thermodynamics so it's an interesting consistency picture okay so black holes emit radiation they lose Mass We call we call that the evaporation now this as I said was Irrelevant for astrophysical black hole but let's imagine someone made let's say someone came and had some way of making a very small black hole let's say one kilogram black hole and so someone gives you this one kilogram black hole and you you would say well what what one kilogram black hole cannot attract me very much it's probably not a big problem okay however due to this effect the one kilogram black hole using the formula e equal to MC square will will evaporate and will emit an energy which is equal to its mass and that energy if you work out what it is it's just like a 20 Megatron nuclear bomb so don't accept the one kilogram black hole from anyone fortunately there are no such black holes around and we have described some results for black holes used from this approximate method remember all these results are derived by this approximate monetization method for Gravity um but there are some questions about black holes which we cannot answer using this approximate method so for example what precisely comes out of a black hole so if you throw in some matter into a black hole you can throw water you can throw a I don't know gold and what comes out seems to be just radiation can we recover the information of the matter that formed the black hole and in other words is the process of black hole formation and evaporation consistent with the loss of quantum mechanics which says that this information cannot be destroyed now to answer this type of questions we need the full Theory so now we'll return to the discussion of the full Theory and we really don't have a full Theory but we have a theory under construction which we call string theory and now we are having this conference on string theory and the goal of this conference is to make progress in the construction of this Theory understanding this Theory better and extending its range of validity of the things that we understand now to understand more things about this Theory maybe one way to say this is that our picture of the theory is something like this picture okay so you can see there is a building there and uh you're pretty sure there is a building but we don't have the sharp outlines we don't know everything about the theory we know we have some idea about the theory now my attempt today will be to try to give you an idea without formulas without mathematics it will be more impressionistic hopefully you will get the idea that there is some picture but that will remain to be seen so well what we're going to try to see now is that um well I'm not going to describe this theory in detail uh we're only I'm going to describe discuss one aspect which is that we are learning some interesting interesting things about the quantum aspects of black holes and so we'll focus on one particular aspect and the aspect that we will focus on is the idea of space-time as an immersion concept now we can we can motivate this as the following let's say question these are the type of questions you have in the University entrance exams in the US I don't know if you have those in Canada but so these are questions about analysis so what there is two atoms a space time is two so what you know see we use atoms to describe water what are the things we use to describe space time so space-time atoms you would say are there some something like this and the area is similar so we will we'll talk about an idea that is somewhat similar but these Elementary atoms or sometimes we call them qubits so qubits is the basic amount of quantum information or the basic degree of freedom in quantum mechanics these atoms are not local in our space but they are really sitting far away um and so this is the idea of holography and the idea is that so we understand this in some special cases so some universes with a constant negative curvature and in this universes they have in some sense some boundaries some region very far away and in this universes we can describe everything that is happening in an interior in terms of some qubits some degrees of quantum degrees of freedom that live on the boundary and this degrees of freedom are interacting a lot with each other but not with they don't have any gravity so gravity only exists in the interior this is a kind of a little picture for this so we the idea is that we have two separate descriptions two different descriptions one is we could have a particle moving in the interior so in this space times there is a kind of gravitational potential well that keeps particles moving in the interior and um then you have other particles that this this funny motion that is represented here tries to give you the idea that these particles are strongly interacting with each other um now you can ask well how how you would describe a black hole in this way so in this space times you could imagine that you have a black hole in the interior and the idea is the black hole would correspond to a large number of particles that are strongly interacting and live at the boundary okay and the temperature and entropy of the black hole would come from the temperature and entropy of these particles that live at the boundary so the idea of this description is that the theory on the boundary obeys the rules of quantum mechanics and so therefore so does the black hole in the interior and then the black holes are consistent with quantum mechanics but for that you need to accept this holographic conjecture that space time and the boundary Theory related in this way so we'll come to the discussion of immersion geometry so in this description geometry is emergent in the following sense so we have some space time and the qubits live far away at the boundary and but the gravitational space time has one more dimension um so let me try to explain how that happens using an analogy so imagine a sentence so we come back to this idea of a sentence and the sentence says if a man does not give Pace with his companions Perhaps it is because he hears A Different Drummer now when you heard this sentence you probably in your mind divided into various words and then you probably group the words in some way analyzing the grammar of the sentence and so on and the meaning of the sentence you found the various substance sub sentences or subclauses and so on and until you got the the full sentence so in fact there were also long distance correlations for example between the word man his and he or between the concept of keeping pace and drummer okay that's a kind of deeper level correlation as we include more words in our analysis we get to a deeper meaning of a sentence okay so we have a in some sense an extra Dimension which is the depth of meaning or the direction of meaning in the sentence How Deeply encoded is a particular concept within this sentence so in this analogy the idea is that the state of the quantum system is analogous to a very long sentence that lives at the boundary and the bulk geometry is doing some analysis of the meaning of this particular sentence so that's in the analysis reflecting the correlations that you have between the various words of the sentence and their correlations that are encoded that involve short distances along the sentence and some involve words that are very far away in the sentence and for example particles in the space time could be particular words that are either repeated or have some correlated meaning in the sentence and a bulk Observer so someone who lives in this bulk is a bit like a character in a novel whose text is living at the boundary okay so someone who lives in this phase time that's what it would be he's also some kind of immersion concept or a merchant object in this description and it's interacting with other immersion Concepts and so on so perhaps a slightly more accurate way to describe this is that the boundary is a superposition of many possible sentences that has to do with the quantum mechanical aspect that involves probabilities and the bug space time represents those statistical correlations now you can ask what is a black hole in the space time so let me make an let's make an analogy for that so we go back to the sentence and now uh we change some words so here we change the word he is to it's and he to she and so on and we change these words so once we change this word uh we lose the full meaning of the sentence of the rational sentence we keep somehow a little bit sum of the meaning but not we we lose the meaning at a certain depth so beyond that depth we have a kind of horizon we don't know what this speaker is talking about okay and then if we continue changing uh change in words then this Horizon of meaning gets closer to the individual words and the sentence makes less sense okay and that grows of inner ignorance has to do with the it's represented in the balcas the area growth okay and we could imagine the situation where we completely change all the letters in the sentence now the the black hole grows as much as it can grow and we just don't know what we don't know anything there is no information in this sentence um and now imagine that the changes in the sentence came from a reversible process so for example an encryption algorithm so in that case it is possible to uh to reverse the process and recover the original sentence so that the loss of physics at the boundary change the state of the boundary similar to changing the sentence and it's analogous to an encryption process in the sense that it is reversible and so we can in principle and do the formation of the black hole and recover the information so that that's what it would mean to recover the information okay now let's let me just go back and discuss again this idea of portions of a sentence um so if I show you again this sentence Mary little lamp you might have different guesses for what the block word might mean so there is one that probably you first thought about but there could be many other ones Mary killed a little lamb okay that would be a cruel Mary but maybe she was hungrier um so you're you're missing part of the meaning um and so in the same way we can consider this very long sentence that lives at the boundary or this very long very complex Quantum state that lives at the boundary and block of a portion should decide not to look at that portion and when you do not look at that portion you get you you have some ignorance and you there is an interesting formula characterizing the ignorance that you have in this case of a Quantum systems that give rise to Geometry and this formula says that the ignorance that you have is proportional to the area of a minimal area surface so you consider a surface that ends at the tips of the region you blocked and you you can let it move so it can be anywhere but you find the surface that has the maximal area and we're in a curved geometry so if you're wearing a flat geometry the the surface with the minimal area sorry would be a straight line but in the curve geometry the in this in this particular curve geometry the minimal area is this surface so that's the one that has least number of angels and demons and and you can calculate this minimal area and you divide by L plank the plank length in the interior and that gives you the entropy so it's very similar to the formula for black olentropy except that we're not talking about the Horizon we are talking about this minimal area and this is a very important form what's a very important formula because it related geometric concept like area to Quantum information concept as this entropy or amount of information of a blocked region now we can also ask whether we can recover a portion of the bulk if we miss uh what we can recover about the bulk if we miss a portion of the boundary and then the idea is that if you're missing this portion of the boundary um you will miss uh also this portion of the bulk space time in other words when you have a very long sentence and you're missing this mission you could imagine that you can recover meaning the meaning of the sentence or let's say it's a novel that is in the region is very far away from let's say the pages you lost but you but there will be some part that you would certainly not know and depending on the structure of the novel you might or might not figure out what's going on but you certainly will miss something and you tell you the part of the meaning of the novel that you missed this would be this ritual insight so that's an allergy um so this this idea that the bulk is encoded in the boundary is encoding a boundary in a way that also similar to how Quantum information can be stored in a quantum computer so in order to remove errors in quantum computers you store information also in some kind of distributed way where information is encoded in correlations between different degrees of freedom and that's called a Quantum error correcting code that was developed in the 90s by Peter Shore and is how quantum computers are supposed to work and almeridan Harlow found more recently that actually we should think about the merchants of the space-time using this type of ideas so all these developments have shown that space-time immersions in some way from quantum entanglement or in other words that SpaceTime emerges from correlations in this Quantum system or another way of saying this is that geometry is related to patterns of entanglements or correlations so it's somehow similar to how meaning emerges from the correlations between words when we have sentences um so in fact people use ways to describe so I'm not going to explain this picture but this picture appears in papers of tensor networks and so this is some way to encode Quantum correlations in a system so and gifabidal was one of the developers of these ideas he was here at the perimeter Institute and he I think he recently left and worked to work in artificial intelligence so he went from the quantum world to the world of sentences but what you can see is that the pictures are kind of a similar structure so this analogy is actually conceptually well it's kind of big but it's awesome sense now let me make a comment so this idea that you can the space time can be immersioned from Quantum degrees of freedom implies in principle that you could make a little Quantum if you have a Quantum system and you can manipulate it as as much as you wish then you could make a little tiny small universe that is governed by Einstein's equations so if you if you just to make the tiniest Universe we can imagine that is governed by Einstein's equations we will need about 10 000 qubits okay so quantum computers today have about 50 100 so there is some way to go but well maybe we'll get there sometime uh in contrast our big universe the universe we live in we think we would need a further 10 to the 120 qubits and in addition our universe is expanding and we don't really know how to describe it using these methods so now I'm going to discuss uh an interesting case of uh the relationship between entanglement and geometry is a little more dramatic case of how geometric and emerge from entanglement and this is just going back to a funny feature of the simplest black hole solution and it is the fact that the simplest solution of vacuum Einstein equations describes actually two black holes so these are two black holes that are very far away but they are sharing a simple simple single interior so in some sense there is a geometry which at some Moment In Time looks a bit like this so they are far away so this is the far away distance but they are really connected uh through the interior now the the interior is time dependent so the distance between the two through the interior changes and let's say at time equal to series like this and then as time progresses it becomes uh thinner and more distant in such a way that if you were a traveler trying to go from one side to the other you wouldn't be able to go you will fall into the black hole you will get crashed at the black hole Singularity and you will not be able to Traverse this one but the space time that it describes has these connections and the interpretation is that this this geometry corresponds to two entangled black holes so each black hole has some entropy some degrees of freedom some qubits that if you look at one of them they are thermal they have some Randomness but if you look at two of them together that Randomness is correlated in such a way as to make a pure coherent whole and and that pure coherent whole of course give strikes to a geometry which is connected through the interior so let me give you another analogy for this connection through the interior so let's imagine we have two sentences so we have the same sentence we had before and now we have the same sentence here in the bottom is the same sentence but in Spanish okay and so if you analyze the sentences the words are quite different so you the grouping of letters is different but if you start analyzing it you get to a point where the two sentences have the same common meaning so you would have the description of the geometry is doing the analysis of the English sentence and this region of the geometry is there and given the analysis of the Spanish sentence and at some point you get to the meaning of a sentence and which is common to both cases so this is a bit like um analogous to that wormhole so they have this common meaning now there's a small variation of this process where you bring the worm the two black holes closer together and you allow some simple form of interaction between them and in that case then the Wormhole can become traversable in that case you can you can indeed travel between one side so you first of all the black hole ceases to be a black hole there is no Horizon anymore and then you um you can go through this uh Wormhole I want to explain all the details um but this in quantum mechanics this process of allowing some interaction and then You're Going Through the Wormhole is related to quantum teleportation so let me uh what time I'm supposed to end okay what a few more minutes so some analogy for this uh business of quantum teleportation through Wormhole so this this this process has three elements entanglement communication and this idea of wormhole so let me just make a little bit some classical analogy so imagine that Bob and Alice has been married for many years so they share many common memories so that means that um Alice can sandbox let's say a look or just simply a few words and Bob will know what she means okay okay so in some sense there was an idea which is a much more complex well an idea that got transferred from Alice's mind this is kind of representation of her mind with all the meaning and so on inside and Bob's mind so when the idea went from Alice to Bob and it managed to go thanks to the fact that they shared all these common memories and just some simple look so if a person from the outside that only hears the word or so the look would not be able to guess what the idea was because they don't have their common experience now I'm not talking about this but there was a recent uh mini revolution in our field about similar wormholes that were important for understanding how information is encoded in Hawking radiation and the black hole interior so I'll I won't discuss that so in conclusions uh I emphasize the fact that Quantum systems can give rise to a geometry this emerging geometry and that the geometry of ours on space time could be immersion in a similar way we really understand this for universes that are a bit different from ours that have let's say mostly negative curvature our universe is a bit different because it has positive curvature um now an interesting consequence is that we could make these little tiny universes in the laboratory very very tiny and in the future we hope that this will lead to an understanding of the singularity inside of black holes we don't have that yet and after understanding that Singularity inside the black holes which has to do with the Big Crunch hopefully we'll then understand the singularity at the beginning of the universe which is really the biggest question in our field and the thing we that really drives us forward to keep investigating this Theory further to to understand how the universe really began and with that begin we'll just end thank you [Applause] [Applause] thank you so much Professor Imelda Cena for your fascinating talk we will now open the floor to questions so for those here in person there's a microphone set up in the stairs to the audience's right we'll ask that you limit yourself to just one question relevant to the talk just to ensure that everyone has a chance to ask their questions so please form a line here we have someone already please go ahead thank you Professor for your Whirlwind tour of the recent developments in quantum mechanics I have one ten part question but um so uh as a swing series you're obviously partial to uh you know like a unification uh of quantum mechanics and uh general relativity you know identification based on string theory but what are other leading candidates for unification of these two understandings that are not responding Theory well I mean the question is the idea that quantum mechanics and string theory sorry quantum mechanics and general activity should be put together is very old people had various approaches um strength here I think is the one that is further along but there are ideas for example of triangulating your space time and then integrating overall or some in overall possible ways of doing that defining a quantum theory in that way there's something called Loop quantum gravity there are there are various other ideas that that capture some aspects of this story but I would say that if you want to get to the point where you really derive Einstein's equations and a Continuum geometry as to a string theory is the only one that can do that hi thank you for the talk Professor so my question is in approximate Theory you mentioned that entropy is proportional to the area but if entropy is increasing shouldn't the size of black hole should keep on increasing and not evaporate very good question yeah very good question so um I the the entropy is equal to the area in the classical Theory so so actually when you do this approximate approach the entropy gets an additional term which is the entropy of the quantum fields that live outside the geometry um and so the full entropy of the system outside is the area plus the entropy of the fields outside now when the black hole evaporates the um the black hole becomes smaller the area becomes smaller but there is Hocking radiation and because cocaine radiation is thermal the entropy outside has also increased and in fact it increases more than the decrease of the area so that the total entropy actually increases this is something that was proven by Aaron wall in about a decade ago so it's relatively recent yeah sure sure no one knows how to make a black hole it was said in the meeting here uh 2020 February but 20 years before in Scientific American it more or less had the same argument you describe traversable wormholes and the warp drive is sort of a transformation of that in illusion of gravity which you didn't mention they just turned on the rhicic and he said at the end it may be it was too soon to tell but it may be generating tiny black holes from the areas correspondence do you still think that in the more recent Scientific American they described sort of the low viscosity of but they attributed to the strong force but the strong force is made of luans and you also mentioned Lawns do you think you could uh in The Fifth Dimension as he described generates some sort of chain reaction to create this bubble what are your thoughts okay well your question contained various different elements let me see if I can say well first of all before the LHC turned on people discussed that perhaps it could make black holes the LHC has turned on and has not produced any black holes as far as we have seen that that was possible in some scenarios so that's one point at least not four-dimensional black holes um you can I I didn't I wasn't some other parts of your question refer to the type of quantum system that has known gravity descriptions and there is one example of a Quantum system that involves a particles similar to gluon so similar to the particles that govern strong interactions in nature it's a it's a theory which is let's say a casino of the theory that describes strong interaction so it has gluons and also some other particles that we don't have in nature but when you put all those particles together they give rise to this uh five extra dimensional space time and in that description when you have a collision of these particles you can make a black hole in the Fifth Dimension so in the extra dimensional space from the point of view of the boundary theory that black hole is viewed as a gas of particles similar to what we had in manual transparencies where we had the particles moving at the boundary so it's uh described as a ball of gluons or Quark glue on plasma is called um and so this correspondence that this this relationship can then be used to calculate or acetoic model for trying to understand that those processes in qcd so I'm not saying qcd because it is the theory of strong interactions so for this zero strong interactions in nature we don't know what this five dimensional description would be but for similar theories we do know and for those they can be used as a toy model um could would we be able to harness talking radiation or any other energy from a black hole yeah that's uh that's a good question so if we look at the black holes that we have in nature that we are that are known to exist no because they are first of all they are very far away and they emit very little hook in radiation there is more matter falling into the black hole than there is radiation coming out for those black holes that exist in nature now if you ask me what's theoretically possible Right the best possibility is to have magnetic black magnetically charged black holes so if you had um I told you that black holes that have one kilogram would explode like a nuclear bomb now if uh you had a magnetically Charged black hole so that's very difficult to make we think we think they they can exist theoretically but they would be super difficult to make but if you could make them well if they existed for some reason then those uh with with emit Hawking radiation will settled into a kind of black hole at zero temperature that's not emitting hook in radiation then you can take some matter and drop it into this black hole and that matter that you're dropping in with almost instantly we converted in hooking radiation and would be a source of energy so that's uh that's one uh scenario you could have it's it's very science fiction like very unlikely to be realized for many reasons in particular because we don't think nature naturally produces this magnetically charged Black Codes and making them artificially which seems exceedingly difficult The View that um time here had a beginning so I was wondering um what your thoughts are on these theories of time didn't have a beginning like if yes yes yes yes yes yes yes I um yeah we we draw this picture with something that somehow starts here and what you're asking is could there be something before before this point some other Universe time existed before the Big Bang and then something happens here and um well we don't know maybe maybe we could have it maybe we could not have it but the point is that we don't understand until we understand what happens here we cannot really know for sure so people sometimes say oh perhaps there existed I mean there are some people who speculate and say well maybe there was a time before the Big Bang and then they make some theory of what will happen but that that's not really a well-defined theory it's one of these theories where you say well something existed before then a miracle happens here and then I you know we don't have a well-defined theory that allows us to go from before to after and part of the the question of understanding what happens here is to be able to answer the to answer that your question which is a very good question thank you so much Professor maldistina that's all the time that we have tonight for Q a so I want to thank everyone for joining us both here at Perimeter and online and let's all thank Professor Imelda Cena again for his wonderful lecture [Applause] [Music] thank you [Music] thank you

Channel: Perimeter Institute for Theoretical Physics

Views: 146,057

Keywords: physics, theoretical, perimeter, institute, canada, ontario, science, stem

Id: DODp-ajPuU8

Length: 74min 7sec (4447 seconds)

Published: Fri Jul 28 2023