WSU: Fundamental Lessons from String Theory with Cumrun Vafa

[Applause] thank you so i'm going to talk about fundamental lessons that we have learned about string theory so the first part of my talk is going to be introducing the basic ideas so string theory as you may have heard is a theory which has been being pursued for about 45 years now uh as a fundamental fear of everything now that's a big big undertaking so clearly we cannot achieve everything uh even even if we limit ourselves just to the fundamental questions very in in a complete detailed form and that's the case for us today for string theory we have learned a lot of things about string theory in the past 45 years but a lot we haven't understood it is the most promising candidate we have for unifying einstein's theory of relativity which is the theory of gravity with quantum mechanics so these two particular important pillars of modern physics and the basic idea in it is that you have to replace basic particles point particles elementary particles like cork by extended objects like strings that's why it's called string theory and but these happens at a very very tiny scales in other words from far away distance this loop might look just like this point but if you zoom in to about a scale of about 10 to the minus 30 centimeters then these particles might have some extended features like this string or membrane or some such things and this is why we call the string theory the importance of replacing elementary particles by these string like excitations or string like configurations so for example here is depicted a cork inside the nucleus which can be viewed as a string if we kind of have a magnifying glass and look at it and the basic process is for the strings in terms of producing new strings or interacting the strings combining coming along and combining into another string in a very nice nice form in this in this way you see two strings joining and the opposite process would have given you a string splitting to two strings and this underlines all possible interactions that we could in principle envision and in some sense it's a very nice way to unify all these particles and forces into one object if particles are unified just to strings and all its vibrational modes and the interaction is all captured by the simple process of strings coming and joining and forming new strings but it's too early to present the final formulation of string theory its work in progress and work in progress implies working in this context behind computers sometimes blackboards and experiments unfortunately can't help at least not yet and the problem is that the string the size of the string is about trillion times a trillion times too small to be measured or to be experimentally measured by the energies that we have available in the colliders today so it's very difficult to actually zoom in and give the pictures i was drawing so so therefore we don't have the luxury of using experiments to guide us in building our theory so and in particular as i said we have no experimental evidence of string theory to date however it turns out that even the incomplete knowledge of string theory gives us a lot of new principles of physics it revolutionizes a lot of things we know about physics even though we are far from the complete theory and my aim is to try to give some sense of these new principles by by guiding through some examples so um it's going to be of course difficult to describe all the things we have learned in string theory in one talk but i'll try to at least take take you through the tour of some highlights of some of the important ones that we have learned and so if you this picture is just to uh illustrate that i'm going to be talking about the parts under the the lamppost clearly i'm not going to talk about far away in the dark which we still don't know but even what i'm going to tell you even under the lamppost there's a huge amount we have learned and that's what i want to convey but before i even start with string theory i want to go back step back and talk about some historical lessons we have learned through the history of physics itself and in particular i want to see i want to emphasize the fact that the development of physics and the new idea of physics comes always by giving up something we thought was fundamental and absolutely correct something which we did not suspect can be false this has happened again and again in physics and as i will illustrate string theory continues that tradition in giving in that we have to give up a number of principles that we thought are sacred for example let's go back and remind ourselves that at some point earth was viewed as the center of the universe now in fact uh the greeks were uh very very smart in recognizing the first of all the fact that earth was round there's a globe and they they viewed nevertheless that the earth is at the center of the universe okay they didn't question that fact it's why not it should be at the center of the universe uh you know looks they didn't probably have this picture but anyhow they had the picture of some kind of a globe and in fact not only they they had this idea that earth as the center of the universe they used it to argue why earth is not moving they thought earth is not moving so they wanted to explain why the earth was stationary and they had a very clever idea they said look this is at the center of the universe and if it were to move in any direction it would break the fact that it's symmetric it's right at the center so if it goes that way say oh no no it's not center anymore you have lost the center so it's not going to move that was the argument for the greek that the center the universe that not only were at the center but we are stationary so they use the symmetry principle to argue why we are not going to be moving the earth is stationary now of course we recognize that this is a false statement because we know earth is moving and so on but what i wanted to point out here is the clever use of symmetry argument they used to try to convey a physical fact that they thought was true but actually they were really smart in fact aristotle disagreed with this reasoning and in fact he said yes of course earth is at the center but this does not necessarily mean that because of symmetry it can can cannot go anywhere because symmetry can be broken spontaneously and he illustrated this by a very simple idea he said well suppose you have a circle and you have somebody at the center of the circle symmetric like earth or whatever and you distribute food equally along that circle now he said are you going to tell me that the guy is not going to move to the circle to get food after a while and he's going to starve to death okay so he was he was saying that symmetry is not enough to say that preferred position is at the center you will break symmetry to gain food in this example you go some direction and therefore you break the symmetry so at any rate the idea that the idea here illustrates that the combination of the symmetries symmetry breaking and so on was already being discussed by the greek all the way back then and but nevertheless they thought earth was at the center of the universe today we know that's one of the principles that's not true we have given up that a while long ago by now there are other notions like this for example the absolute notion of time you know there's a time clicks everywhere the same way we thought uh and of course this gentleman showed us we are wrong einstein showed that time is relative we don't have an absolute notion of of of time and it could depends on which observer is measuring it so the absolute notion of time also we gave up how about the absolute notion of the state of a system now what do i mean by a state of a system well where things are i mean you say there's a particle there there's this that can you actually describe describe where things are in an absolute way in other words does it make sense to say where things aren't and in fact quantum fuzziness the fact that if you try to describe the state of electrons in an atom they look fuzzy you cannot say exactly where they are when they have a given energy they're kind of spread out says the absolute state of a system is also a little bit fuzzy it's not quite possible to describe it that precisely there's some fuzziness so even that we had to give up so these sounded at the time before these amazing revolutions in physics sounded obviously correct earth was at the center of the universe there was an absolute notion of time and of course you could say where everything is and all of these by now have fallen down these are not principles of physics anymore similarly string theory calls for radical changes of our understanding of the fundamentals of physics and as i said even though we don't know the full theory we know enough to know that this has to come about and we have to have very different new ideas in physics it is in some way reminiscent of early days of quantum mechanics when they had discovered that things are wavy but they hadn't quite written down the correct precise equations that later was described by heiszem against schrodinger so we are in that stage in the development of strength there we have understood that things are wavy but we don't have a precise formulation of how that works so this was of the way of a basic introduction to to where we are heading but i have to do the setting of the of the stage of what it is that uh what kind of elements come into these new principles and the most important thing that we have learned in string theory is duality almost everything we know everything interesting we know in string theory is in some way captured by this concept of duality what that means is the general statement that two very different looking things can never the less be the same thing okay two things which look completely different can be manifestations of the same thing this is the general general meaning i i want to use as duality that two things are the same despite the appearances so here i have described i have drawn a picture here that you should imagine like every point here describes a physical theory so you pick a point in this and this every point you pick in this space corresponds to a solution in physics of of some shape or some something describing the physical theory so you think about a particular point as fixing your theory in that point for example the electrons have this and that property and and our universe looks this and that way and so forth that corresponds to a point so it's a summary of the details of the physical theory is this point but you can have different kinds of physical theories this point can move around in this space so this is the parameter space in which you can choose different kinds of physical theories you can change the mass of the electron you can add more particles and this and that so this is kind of motion in the space is changing the theory and it turns out that there are some special corners in these theories where the physics looks very very special these corner theories one two three four five six in this case i have denoted describe physical systems in which description simplifies so you have an easy description in the middle the description of physics is very complicated but in these corner theories things will become very simple so these corner theories these easy theories that we can access where we can actually describe the theory are analogous to reference frames and einstein's theory which are useful reference frames so as you may recall in the context of einstein's theory physics might look different depending on how fast you are moving so there's physics can be described relative to a particular reference frame these corner theories should be viewed as particularly preferred reference frame that the description is easier for example if i'm in this room the easier description is for me to stand here and describe the objects around me of course i could make a funny motion go around in loops and so on and describe the physics that i would see that way of course that would not be very convenient so similarly these six chord these kind of corner theories are useful descriptions of the same system but it's easier to describe it so so you could think about them that there are these easier versions of this theory that are are somewhat analogous to reference frames for which this physics description simplifies and i'm going to call these corner theories duality frames just an analogy with reference frame of einstein which corresponds to choosing a particular speed that you're going with i'm going to call about these as if they are going with particular speeds you can think about these these particular frames analogous to those so that's the word duality frames but mind you they're describing the same kind of physics it's just different corners so then just as in einstein theory in special theory of relativity what was important was not what particular observer sees because if you think about this object the fact that station relative to me is only relative to me is stationary if somebody is going with the speed that way it will this object would be looking going the other way so to talk about the velocity of this particles an absolutely important concept is a bad idea that's relative to me it has a given speed so the invariant concept in this case is the mass of the object for example or the rest mass of this object that's invariant so there are these kind of concepts that we want to understand as what it is that distinguishes physics which for which all of these guys agree in other words what is an invariant concept we have to understand so what is in the context that we are dealing in the context of string theory what are duality frame invariants so that's the question that that that is posed that we need to understand there's a nice there's a familiar analogy so if you look at the the phase what this is called the phase diagram of some some liquid let's say some object i mean and they have different phases like a liquid solid or gas depending on the pressure and temperature you could be in any of these phases at low temperatures you might get solid if you increase temperature you can get liquid and if you increase it further you could get a gas so these are different phases and of course even though there are different uh phases what is not changing here is the object itself it's made of particular atoms of course the details about how close they are or how far they are from each other and what kind of situation they are in are changing so the different phases but the invariant concept in this case is the the molecules that's made of and in fact uh for example in this particular case there is no easy characterization of liquid versus gas you might think there's an absolute way to say this is liquid versus this is gas but actually there's a continuous way you can change going from being liquid to being a gas and there is no phase transition anywhere if you go around this critical point b and so therefore this idea that you can have a indistinguishable theory indistinguishable phase is clear in this example that the only way to describe it invariantly is in terms of these molecules because there is no particular place that this liquid became gas and vice versa so this is the way we are going to be having it in the context of duality and string theory it's somewhat analogous to this beautiful drawing of azure where if you look at this frame there are these there are these different corners of this the of this drawing for which different things are going on so for example in this corner you have these black birds flying in this white sky and over here is the night sky and the white birds are flying and down here it's day and then there's there's the city and so the same same situation here except it's night and everything here is kind of flip from from one side to the other from left to the right goes from day to night from up to the down goes from birds to this to the ground but as you can see it kind of seamlessly goes from one side to the other so these are the corner theories i'm talking about these four corners in this case the description simplifies you can say oh yeah it's just a day and the birds are flying or oh it's night and some white birds are flying or something else is going on here and here so these are easier description but of course if you go from one of them to the other one it gradually changes completely to something else seamlessly and this is what happens in the context of these dualities and string theory so this is a picture to keep in mind okay so so that was uh the basic beginning of our setting of the stage and we begin to ask our questions the first question are particles basic building blocks of matter are point particles basic building blocks of matter this was a principle that was uh originally suggested actually by the greek again the idea of atom as some indivisible thing that can be can that every matter is made of and it was extended in modern days to the notion of the elementary particles but as we as i already discussed in the context of string theory we know that particles are replaced by extended objects like strings or even like membranes so we already know one principle had to go the basic building blocks of matter are not point particles that's the first absolute thing which is gone in fact more generally you can get different dimensional objects playing the role of particles you can have i said about talked about membranes we like sheets or you can have higher dimensional objects like cubes and this and that so you can have completely different kind of zoo of particles not just elementary point like particles and in fact you can have more interesting things like particles the analog of the particles stretching between each other for example you can have a a sheet here described here by this blue plane and then you have another particle which is this yellow one which ends on it it's kind of different kind of configuration of these guys and these are you could think of them as elementary ingredients in this theory so the existence of these extra object extended object is what is the one hallmark of string theory you can have very interesting structures and in fact it dovetails beautifully with pieces of mathematics so you can have for example a bunch of planes let's say n planes next to each other stack them up next to each other and then you can have these strings which are ending on pairs of them on either side one from one to the other one so you can have different kinds of strings depending on where they end from the left to the right of course there are n choices they can start and n choices that they can end in and this gives you an n by n matrix of strings so this maps the possibilities of a string to an n by n matrix of where they start and where they end and this turns out to be related to the fact that n by n matrices sometimes can describe forces in physics gage forces have a symmetry principle which is captured by an n by n matrix and this is a geometric way that string theory captures it so now i want to move on to the next topic which is the basics of space so we have now set the stage for what are the basics of particles we said particles are now replaced by excellent objects what about where the particles or these membranes or strings live in the space itself what can we say about that for example the very basic thing about the space is that you can put a ruler so you can start measuring it right you can start measuring it is the notion of distance a well-defined concept in einstein's theory it is in einstein's theory you can come and measure the distance from one point to another it's perfectly well-defined question so for example if you have a circle and you want to measure it one way of doing it for for which the for which you can get the radius is that you can send the light around it and measure how long it takes to come back for example this gives you a notion of the diameter of the space so the more precisely the radius is the speed of light times the time it takes so you can you can find out what's the diameter of the space so there's a natural notion of the diameter of the space which makes sense but it turns out that the length is not a duality invariant concept in string theory and in particular you can imagine having a circle of some radius r and another circle of radius one over r so when this circle is big this circle will be small and this is small then they're same size and this is small and this is big so we can reverse the roles they look very different in einstein's theory and one of them if you you send the light around it takes a long time to come back and hear the light takes a short time to come back however it turns out that there is a duality which maps this theory to this theory in the sense that when you start taking a light around here that i have drawn here as you're trying to send the light around the circle and measure how long it takes to come back over here instead of this light you end up sending a round string instead of this the light to be at the given point i'm taking around over here you have a string which is wound around the whole circle and sending it around looks very strange but you can and the time it takes here will give you the same time over there in other words there are two kinds of lights what we call these lights of this type which is sometimes called the momentum state and these kind of lights which are called winding states so there are two different lights depending on which laser pointer you use of the winding type or the momentum type you get different answers for the radius you get either r or one over r so the notion of distance is not an absolutely invariant concept similarly over this side if you send the regular light you get the measure of the distance which is one over r but which corresponds to the winding of this other string so they have a completely different notions and you measure different distances so we learned that the notion of distance is not an absolute concept is topology of a space an invariant concept now what does topology of a space mean it sounds like a very high level math but really i i don't mean anything that fancy it's something very simple it's something which distinguishes spaces from each other without even paying attention to distances we know distance was not an invalid concept in string theory how about some more gross features of this space like say how many handles a space has how many holes does it have or some gross features without actually measuring them now that that that should be you would think a naturally invariant concept that if you have a space you should be able to say well this has two holes this has five holes this has nine holes etcetera it turns out that even this is not invariant the notion of topology the way we usually think about it is not an invariant concept and different frames view the same space with different topologies even though they are identical physics so for example you can have two spaces which look very different topologically different number of holes and handles nevertheless they can have yield identical physics denoting here by w and m these spaces okay so we learned the distance is not an invariant concept the handles and the holes are not the environment concept how about the dimension of this space that's the growth is one of the grossest thing you can say in terms of the gross characterization of the space you can say in terms of it name dimension this is one dimension two dimension three dimension is that an invariant concept is the dimension of space three plus one well actually there are two questions one is whether the dimensions invariant concept and the other one is whether the actual space on time dimensions three plus one first of all in the context of string theory when we have an we have learned that you cannot have space and time to just be three space on one time you need extra dimensions but these extra dimensions are should be viewed as tiny otherwise where are they we only see three spatial directions where are the other spatial directions so we have some other extra dimensions which are kind of wrapped like a circle if you think about this hose as our as our space one one dimension or in this case three dimensions of it are long but the other directions like this one circle that i'm drawing here are tiny so from far away it looks just like this line so so our three-dimensional space it can fool us to think we are in city three-dimensional space but there are these other internal internal directions that are tiny so in fact we have learned in the context of string theory that the dimensional space time is not three plus one but is how about this dimension itself whatever the dimension you want to choose let's say string theory says this ten dimension nine space at one time is that number nine and one it does does everybody agree that that's the number or different frames give you different numbers it turns out that even that's duality frame dependent statement even the dimension of the space is not an invariant concept so that's the most basic thing you cannot even count how many dimensions we live and that can that depends on who is measuring it analogous to einstein's relativity saying somebody's going with which velocity namely an example of it is that you can have for example the 10-dimensional space looks perfectly 10-dimensional but if you change one of the parameters and string theory in this case what we call the coupling constant an extra dimension emerges and looks 11 dimensional now but you could say okay well you could say that this is this is a trick because you know after it was 11 dimensional you're just looking far away so that's that's a cheat but actually there are even more dramatic examples of this but before i get to it i just want to give an example of how this 10 going to 11 does to string so if you have a string which starts going from one side of the space to the other as you increase that parameter g i was drawing in the previous slide the dimension goes up by one and the string itself goes up in one dimension becomes a membrane so even the objects change dimensionality when this happens so it looks like a string becomes a sheet and the space grows but the more dramatic example of the change of dimension comes in the following example you imagine the space and time to be 11 dimensional 10 10 space and one dimension this is the corner of string theory known as m theory and imagine taking out of those ten dimensions of space two of them to be a what we call a taurus which looks like a donut shape object a tiny donut and the rest of it keep it big but take two of them to look like a donut a tiny donut and take the doughnut shaped object this torus shrink it to zero size basically when you shrink it to zero size it's like getting rid of it so your space should look like nine dimensional space when you look at a tiny tiny tiny so the eleven dimensional theory should become nine dimensional right that's that would be no trickier you just change the shape if you put the magnifiers 11 dimensional well it turns out when you do this the theory becomes 10 dimensional not nine dimensional bizarre that's the kind of statement i mean the notion of dimension is not an invariant concept in string theory distance is not invariant topology is not invariant the dimension is not invariant we have to radically change the way we think about space and time so even though these aspects of string theory are quite amazing but the main aspect of string theory is understanding quantum geometry quantum geometry refers to trying to unify geometry with quantum mechanics this was after all one of the triumphs of strength theory you try to combine these two pillars of physics quantum theory and einstein's theory of gravity or which is geometrically based theory so what do we learn about the quantum geometric aspects of string theory so the very first thing is that we want to understand is the notion of fundamental is the notion of fundamentalness invariant namely when we talk about fundamental constitutes like fundamental particles whether that notion is something that everybody agrees you say there's an electron this is a fundamental particle there's a photon that's a fundamental particle is that notion a duality frame invariant concept so in fact in particle physics we divide the particles into two types elementary and composite by looking at this picture you can imagine that i'm thinking of this like for example the nucleus of an atom made of different constituents each one of those constituents perhaps could be elementary if maybe they are made of something else too but you wouldn't think that there's at some point you will have a basic object an elementary object so the question is does the notion of fundamental particle fundamental entity something that everybody agrees on or there could be some disagreement that was fundamental or not it turns out that the notion of what is fundamental even depends on the frame of reference the duality frame some people might think this is fundamental and the other one is composite and some other person will think opposite so in fact a nice example of this in the context of monopoles versus electrically charged matter so magnetic monopoles like these these objects which are just a single pole of a magnet for example have been seen in theoretical examples of of quantum systems to exist but they are typically very massive and so they're very they should be viewed as kind of being made up of these more elementary constituents involving electrically charged fields so you can have some composite combination of these electrically charged fields which behave as if they have magnetic charge and they are these are the analog of the monopoles the magnetically charged objects so we be we usually view monopoles as composite made up of these more elementary ingredients which is why we we kind of don't think we see them in experiments because they're so massive and so big they're hard to make but if you change your parameters they can shrink the center of these monopoles to begin to look like point and in fact from their perspective you can actually have a complete reversal of a description as you shrink them as you change your parameters so the magnetic monopoles become light the electrically charged object becomes massive and heavy and so when you want to describe the electrically charged objects they can themselves be viewed as composites of these magnetically charged objects very bizarre so the notion of what is fundamental or not gradually changes as you change the parameter as this monopole shrinks to a point it behaves like an elementary particle and the electron which was looking elementary becomes fatter and fatter and looks like not an elementary particle anymore you could say well at some point it was and now it's not well but there's no exact dividing line where do you divide it there is no dividing line therefore the notion of fundamental particle is not fundamental itself we cannot have the notion of what is fundamental another example happens for strings i i told you that in the context of string theory point particles are replaced by strings or higher dimensional objects well what about those well it turns out that in string theory also we have a notion of a light string here i'm drawing it by a thin red string and a and a very heavy string analog of these monopoles which are really fat heavy guys so by this thick yellow line but as you change some of the parameters in the theory the light one becomes gradually heavier and the heavier one becomes gradually lighter which i'm denoting here by changing the width of the string and as we change it change the parameter a lot the light one becomes really heavy and the heavy one becomes really light and in this corner you can think about this other string as being composite and the other one being elementary okay so there is no fundamental notion of elementary string in this sense they actually change so there's no notion of fundamentalness here in fact this actually poses a big big challenge for understanding quantum mechanics you see feynman had a very beautiful description of quantum theory in the very geometric way of saying if you want to talk about the the probability of a particle going from a particular point at a given time denoted here by spacetime event a going to a particular point b at a later time what you need to do is to sum over all possible paths that can go but in order to formulate quantum mechanics in this way as feynman does you have to say what is the notion of fundamental particles because this formulation of quantum theory relies on summing over only fundamental particles not composites otherwise it will be redundant you will have to choose the fundamental particles so you say okay i would just choose fundamental particles and i show up calculate all possible ways i can go from one to the other to describe my physics but if you don't know what is fundamental what you replace this picture with we do not have that picture yet this is on the on the border of what we have under student string theory we have known that there is no notion of fundamental particle but we don't know what replaces finance formulation of quantum theory this must be replaced by something else so this has to go too famous pathnagal has to be replaced by some other thing and we don't know yet now we're getting to even more basic things is the notion of quantum itself what is quantum is that notion duality invariant concept do everybody agree that this this thing is a quantum effect or this thing is not a quantum effect is that notion duality environment statement so i told you quantum mechanics basically comes about by starting with something which we call the classical system the usual system that we usually think about but we quantize it which means that it basically introduces a fuzziness so for example when i was describing the electron inside the atom the position of the electron became fuzzy so there's this fuzziness which is quantum so you could say aha if i look at the inside the atom that fuzziness is a quantum effect right just it's not point like it was just fuzzy so you can distinguish the fact that there is some quantum effect so in that case it looks like an invariant concept what is this fuzziness is the quantum effect so i draw this by this picture so you can have i'm just drawing a shape of something like say the path of the electron or something so classically it could have some particular shape a very specific point going the very specific trajectory quantum theory says no no it's not exactly one point it's actually fuzzy so we can say aha this fuzz around the straight line or or very sharp line is because of quantum phenomena which is this here i have denoted by the parameter the famous planck's constant which denotes how much effect of quantum mechanics you have you can dial that to make the quantum effect bigger or smaller so so you can say okay there's a classical piece and then there's a quantum part okay this looks like an environment concept turns out that even that the notion of what is a quantum effect is not an invariant concept how could that be so obvious you know you have this thing that gets fuzzy how could that not be an invariant concept well what happens is roughly like this you start with something which is without this classical and it becomes fuzzy but if you take it extreme fuzziness it becomes again looking classical but a different classical system so the quantum mechanics is a way to go from one quantum mechanics dials from one classical picture to another one as you dial this fuzziness so which one is more fundamental this classical that one you pick you pick so the notion of quantum effect is not fundamental so the pillars of physics are falling one by one down i'm telling you what is not going to stay the notion of quantum versus classical is not fundamental does quantum matter exist in higher dimensions well we know that in three dimensional space and one time there is there is matter you know electron quarks this and that do they exist in higher dimensions of course i have to clarify the question i have already told you string theory lives in higher dimensions so of course since string theory is made of things it's so there's some matter in higher dimensions so what i mean here more precisely is whether they're interesting quantum systems interesting interesting interactions like the kind of things we see inside the nuclei with the confining corks through these strong forces inside the nuclei are there interesting quantum matter systems in higher dimension that's not obvious and in fact there are heuristic arguments that says that in three plus one dimensions the only way you can have interesting matter systems made of particles and that's in other words sorry if you want to have things made of particles you only can go up to three plus one no higher but in string theory it turns out you can go higher and it turns out you can go all the way up to six dimensions and we have discovered theories of matter interesting matter similar to things that could be very exciting like like the the nuclei and so on we are familiar with if you go all the way up to six dimensions so up to six dimension we have interesting matter what kind of matter can you get from them what kind of nuclei or things can there be what kind of periodic tables would that give rise to very interesting so these are the new things we have learned but we have also learned these are the basic entities for these theories will be these uh instead of particles they're made of tensionless strings the strings which are very light so these are new theories that physicists are intensely working on to try to unravel the analog of these new kinds of matter systems in these higher dimensions very enigmatic theories and we are we're in the early days of understanding these theories we have very little computational tools and we are building up computational tools to try to address and address some of the questions we would like to answer the next questions again a fundamental question do black holes have microstates now you have heard about this in previous talks that black holes are black and they apparently behave according to beckenstein and hawking as if there is some degrees of freedom in it associated to the boundary of it the horizon of it and this is surprising that there is such a degree of freedom because if you solve einstein's equation with a given mass and charge and this and that the solution has only you find only one solution exactly one solution with those properties and this means there is no disorder there's complete order the entropy the number of degrees of freedom is just one there's only one possibility our entropy is zero but through some arguments beckenstein and hawking show that the number of degrees of freedom for a black hole should be huge and basically exponential of the area of this horizon surrounding the black hole and the fundamental unique units planck units divided by four so this is a huge number of states but the problem was for breaking cyan hawking they could not account for where they come from where are these degrees of freedom because einstein's equation doesn't show it you solve the einstein's equation in three plus one dimension there's a unique solution there's where these other solutions correspond to and this also suggests an amazing new principle what's what's called holography that the number of degrees of freedom usually in physics goes like the log of the number of degrees of freedom goes like volume that is if you look at the degrees of freedom they are situated in different points of space and so the bigger the volume you have proportionally the bigger entropy you get here we're having a situation which instead of volume goes like area that's bizarre and this is sometimes called holography that they somehow the degrees of freedom behave as if they're in one lower dimension like hologram and so of in three dimensions like in two dimensions there's there's something there's some uh something strange about this relation and it's called holography so the question will be what are these states where are they hidden and string theory answers these questions in an elegant way so here i'm denoting as i mentioned to you the space of the space has let's say three macroscopic dimensions the ones that we see and then there are some hidden dimensions or tiny dimensions which i'm drawing here by this red uh doughnut shape object taurus so you can think about this as internal degrees of freedom of the of the geometry of string and then you can take you can take one of these strings or membranes and wrap it around these cycles of this of this donut at a given point in space so you take this point in space and over that point you take this guy and wrap it around the space in this way this will give you a tiny mass if you just wrap it once but what can you do if you want to make it more like a black hole the black hole is very massive object constantly in a small region what you can do is you take the string and wrap it more and more or this membrane wrap it more and more around the cycles and what you find is that if you do that the geometry changes and you create in this way a black hole and as you can see the degrees of freedom here there are no it's not manifest here what are the degrees of freedom but they are up here so you count how many ways are there and of course there's going to be something related to this size of this hole because they're creating that hole so you count whether the number of states that you did by counting how many ways this string or membrane can wrap around these cycles count all these possibilities and lo and behold you find that's given by exponential of the area over four of this black hole so this is a confirmation that the idea that dickinson hawking had is correct but it also says that this the states that they were looking for the microstates of the black hole were hidden in the internal dimensions of string theory the ones that are tiny that we couldn't see in these examples that's how they arise so this is accounting for the microstates of a black hole as as membranes or what we call generally brains in the internal dimensions of string theory is electromagnetic forces distinguishable from gravitational forces or can they arise from one another in other words how fundamental are electromagnetic forces and gravity forces are they distinguishable you know you would think that gravity and electromagnetic force are completely different things it turns out that even that's not fundamental whether you call the force gravitational or non-gravitational turns out also to be not a duality framing variant concept that gravity can be mimicked by by by extra forces by by electromagnetic type forces so in fact let me explain um let me just go back here a second so so there are two sides to this question one is whether the electromagnetic forces can mimic gravity or whether gravity can mimic electromagnetic forces and both get happen as it turns out so for example if you have a cone-like object gravity can create these cone-like deficits and of course it's behave as if there is a particle there there is and so it affects the degrees of freedom passing through it and it turns out that at these points these conical points they themselves will have some kind of forces living there so having these kind of conical shaped object in the context of gravity leads to forces living on these singularities of this like tip of this cone or more generally if there's a geometry where the tip of the cone is along the line along those lines or along these shapes you'll get new degrees of freedom which play the role of forces fundamental forces it turns out so like the kind of forces we involved in between quarks the gluons and so on so those forces can be mimicked by pure geometry so geometry can mimic forces and the reverse is also true that is gravity can be mimicked by electromagnetic forces as well more precisely there are generalization of electromagnetic forces where instead of one photon you have a huge number of photons interacting with each other in a complicated way and if you take a large enough number of these photons interacting with each other let's say in three plus one dimension it actually behave as if a four plus one dimensional gravity theory so you can kind of holographically develop one extra direction that's part of the statement that the dimension is not an invariant concept that shows there but moreover gravity is not distinguishable from fundamental form element from gauge forces or electromagnetic type forces so so even that is not a duality invariant concept so this is here i'm drawing thinking about the space as a fourth dimensional sphere if you can imagine a four dimensional sphere as being the boundary of a five-dimensional gravitational theory so so you can describe what's going on inside here by properties of electromagnetic type forces on this boundary and this is called holography it's quite a remarkable phenomena so you can have exchanges of gravitons etc being described by properties of the theory on the boundary and this can be visualized geometrically by saying that there is some phase transition in the context of string theory you can have membranes stretched between two sides of the universe and if you take a large number of them so these membranes give you the analog of the n by n matrices the way i was telling you and so give you n square type degrees of freedom on these matrices if they end to be very large it turns out to change the geometry of space itself and the space undergoes a transition where they disappear and they replace these brains by fluxes and this actually is the is is the geometrical underpinning of this holography that i was just describing the next question is is the universe unique now this is surprising units of course is unique that's the word universe i mean it sounds like it's obvious the answer to that question and in fact that is not even true the universe or the potential universes or logically consistent universes are not unique in string theory and we have a huge number of allowed consistent solutions and strength there's there's no uniqueness there's a huge landscape of possible universes which are consistent in string theory and this is sometimes called multiverse and each one have their own properties and we seem to be living in one of these very exceptional corners of this landscape with very exceptional forces with very special properties of dark energy and this and that but nevertheless the potential vast possibilities of all possible string landscape is enormous so that's also strange the uniqueness of the universe is also not true so let me conclude by telling you that string theory has been leading to a revolutionary revision of many fundamental and long-held principles of physics there are many hints for a new principle new principle of physics to take hold and where duality frames play the same role as einstein's reference frames but we have not come up with that overarching principle that combines all these into one fundamental law of nature and so it's clear nevertheless that by the time the dust settles physics would look very different thank [Applause] you you

Channel: World Science U

Views: 1,810

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Keywords: Cumrun Vafa, Lessons from String Theory, calculate black hole entropy, Puzzles to Unravel the Universe, black hole, string theory, Harvard University, Dirac Medal, Eisenbud Prize, Breakthrough Prize in Fundamental Physics, World Science U, University, science unplugged, New York City, NYC, Physics, Stephen Hawking, Albert Einstein, Quantum Mechanics, General Relativity, WSU, World, Science, Festival, Brian Greene

Id: pE9Sg6LZXhM

Length: 53min 16sec (3196 seconds)

Published: Wed Aug 12 2020