Knots and Quantum Theory - Edward Witten

good evening it's my pleasure to welcome you to another exciting friend's talk my name is Ronald gehbert and I'm a friend of the Institute in fact I'm a rare breed of friend because I've been on the other side I was a theoretical physicist and member in the school of Natural Science 14 years ago I was very excited and deeply moved when Pamela asked me whether I'd like to announce today's speaker edward witten Eddie's the reason I came to America and he's also one of the key reasons why my wife and I are so passionate about the friends and the Institute I will never forget the day I received the invitation letter from Ed the undisputed lord of the strings to come to come to the Institute to use a comparison it's as if the late Michael Jackson the King of Pop had invited me to join him for concert I cannot possibly list all of its accomplishments and prizes however it's particularly noteworthy that he's the only physicist who's been awarded the Fields Medal which is the equivalent of the Nobel Prize in mathematics it is also the most cited physicists living today with more than 350 published scientific papers he has established mathematical physics as a subject in its own right today ed will talk to us about knots and quantum theory while it's obvious to me that tangled strings can form knots I'm curious to hear what this has to do with quantum theory so ed please twist our brains well thanks thanks to the friends for inviting me and thanks very much Reinhart for the kind introduction so actually the talk I'm going to give today is a little bit different from any I've given in the past I decided that it wouldn't be that exciting for me to give an overview of anything since I've done it before so instead I was going to give a talk in which I actually would try to explain to you what I've been working on in the last year but the trouble is that I can't quite do that I'll really spend most of the time trying to orient to you about the background and then we'll just say a few words about what I've been doing now first of all I'm not is more or less what you think it is it's a possibly tangled loop in ordinary space so that's an example of not the only thing is that this is kind of useless not because it doesn't tie anything to anything usually we think of knots as having a reason for example you're tying something together possibly but from a mathematical point of view that's an excess baggage so the essence of a knot is a loop in three-dimensional space a loop such as the one I've drawn here so it's confusing to look at and that's one of the basic truths about knots knots are perplexing to try to comprehend even though in principle they seem like simple things in concept so the example probably reminds us of something we know from everyday life which is that well it's very easy to generate a messy knot and once you've done so it could be pretty hard to understand what you've got so in particular if you've got a knot it can be pretty hard to know if it can be untangled and I think it's even harder if you're given two different tangles to decide whether they're equivalent so we kind of feel given a messy piece of string especially if we have some reason to know that from the way it was made that it can be undone that we can undo it but if you're given two pictures like this and he has to decide if they're equivalent that's really messy now this might not sound like a question in math if your concept of math is that it has to do with adding subtracting multiplying and dividing but in fact there's a lot more to math and that in the 20th century mathematicians developed a rather deep theory of knots knots turned out to be rather deep mathematical objects and mathematical knot theory gave surprisingly surprising ways to answer questions like whether a given knot can be untangled or whether do different tangles are actually equivalents okay so that's what mathematicians did and I'll tell you a little bit more about it in a bit but before going farther I'd like to address the question of why I am interested as a physicist now knots are things that can exist in three-dimensional space but personally I'm only interested in them because of something surprising that emerged in the last three decades much of the theory of knots is best understood in the framework of 20th and 21st century developments in quantum physics in other words what I care about personally are not the knots per se but their relations to a quantum physics now okay I was actually asked while we were chatting before the Sun or when not Theory got started and okay people wrote about knots in the 19th century but by 1923 James Alexander defines an invariant of knots that mathematicians still study today and an important refinement was made later by our former colleague here at the Institute John Conway but the story has Otto it begins with something called the Jones polynomial which was discovered by von Jones in 1983 so he discovered a new property of knots called the Jones polynomial it's led to a lot of new discoveries continuing to the present day so it's very modern close to the frontier of contemporary mathematics but it's also surprisingly Elementary in the base of concept you could go into a high school class at least a high school class of kids who like math and explain what the Jones polynomial is without compromising very much there are not many things at the frontiers of modern mathematics where one would say that for instance nobody would claim that you could explain Andrew Wiles was proof of fair Mao's Last Theorem two high school students not even close not even the concepts that he used or the tools or techniques it's layer upon layer from the proof of Fermat's Last Theorem as many layers removed from what you could explain to high school students but the Jones polynomial even though it is near the frontiers of modern mathematics there's also soil on entry that you can actually can explain it to high school students so what Jones discovered basically was a way to compute a number for any not so we'll call R naught K and we'll write J sub K for the number Jones calculates for this knot so there's going to be a definite rule to calculate JK so no matter how messy the knot might be such as the one I showed you a picture of little Waldo you can calculate the number JK attached to that knot if your enough and what Jones discovered is that if this magic number JK is not equal to one the knot K can never be untangled now moreover if two different knots have different numbers then they're not equivalent to each other you can't bend and stretch one into the other without cutting the strands now if we take this knot here you could think about trying to unravel it and you probably won't make much progress but how could you prove that that particular messy tangle tangle blue post ring cannot be unknotted cannot be turned into a a simple circle that isn't tangled up well Jones won't gave a way to answer a question like that calculate this number J attached to the knot and if it isn't one it means the knot can't be untied and more generally if two knots have different numbers then they're not equivalent to each other you can't transform one into the other without cutting and tearing the string so finding the method by which Jones count calculates J sub K was clever but once it was discovered in principle you can use it without any cleverness there's just a set of instructions that you're supposed to follow and you use them to calculate J K so how do we calculate j k well one important fact one important rule is that it's 1 in the case of the unlock which I probably should have drawn before untangling a knot means moving around the strings so as to transform it into the unknown without breaking or tearing anything for all the up and knots we have to play a little game so to play the game we pick three favorite numbers for example 2 3 & 5 but any numbers will do I'm going to do something that might seem to make life more complicated instead of a single not K we're going to consider three knots KK Prime and K double Prime and if the three knots that we pick are related in a certain way there's going to be a relationship what mathematicians call an identity the twice J of one knot plus three times J of the second knot plus five times J of the third note is going to be zero remember there's nothing special about the numbers two three and five we just picked them John says you can take your favorite numbers in fact this identity is so powerful that it will enable us to calculate the J's so this identity isn't going to be true for every three set of knots I have to tell you how the three knots should be related to make the identity true to explain that I've drawn something which isn't a knot it's not enough because something is missing so out here we've drawn a bit of a knot but the blue dotted line inside the blue dotted line I've left a gap represented by the question mark to make it not out of this thing we would have to there are four strands that end on the blue dotted line and to complete the picture we need to somehow connect those fans by the way if we connect them what we arrive at might be either connected or not connected although I use the term not I we're not going to worry about whether it's actually a single piece of string or more than one piece of string more than one piece of string would make what mathematicians call a link so to explain what KK Prime and K double prime were going to be I'll give you three different ways to fill in what's missing here so as to make a knot we pick three different ways if you glue any one of these three little pictures in here you'd complete the picture and make a knot so that gives you K okay Prime and K double Ranma and then we declare that the numbers unfortunately wrote here functions I was trying to get rid of such mathematical terminology so it should say the numbers JK JK Prime and JK double prime associated to these knots should obey this relation two times J of the first knot plus three times J of the second knot plus five times J of the third knot should be zero so that's a relationship that Jones is not numbers obey and you say anytime the two strands crossed each other we could draw a circle around it and call that K and then we would make K Prime and K double prime by replacing the picture inside the circle so this is an operation that we can do whenever we look at or not and we see two strands that look like they're on top of each other so if we've got a picture like this so we're one strand crosses another gives what not there is call a crossing so in this picture you see roughly a dozen crossings one two three four five and so on it looks like it's more than a dozen we could draw a little circle around the any crossing and then we could add in the two other pictures so we get a relation the two times the J number of this knot plus three times the J number of some other knot and so on five times the J number of the third knot would add up to zero so there are a lot of different ways to apply the rule to a given thought such as this one it's not very hard to see that if you are given this rule you can actually calculate J for any knot so that's definitely what we would prove to our audience our hypothetical audience of high school students interested in math so if you were faced with the problem of untangling the snot you might notice well if I could pass this through that one it would be easier so the identity tells us passing through this strand through this one it's like replacing K by K double Prime if we didn't have to worry about the third knot it would tell us that one J number is just minus five-halves times the other but the third term in the identity is simple in a different way because the lines don't cross at all anyway if you work at it a bit I won't take the time right now but if you work at it a bit this identity is so strong that it tells you what happens if you either cross a knot through another or not or else remove a crossing and after a little while you find that you can calculate the J number for every not actually the easy part is to show that you can calculate J for any not given our rule the hard part is to show that there's never a contradiction there might be a contradiction because there are many ways to apply the rule this particular knot had about 15 crossings and so we could apply our rule at any crossing and then at any other crossing and so on there are many ways we could proceed and you might run into a contradiction but Jones and other knot theorists shown showed in the 1980s that there's never a contradiction one always arrives at the same number same answer for the Jones number JK of a knot K no matter how you calculate it so the proof showed that Jones's recipe is correct but it left a why question why it works what it means if you wish the trouble is that although that's sort of one of the most basic questions in math or physics it's hard to explain if you don't work in mathematics or in allied field if you're not accustomed to mathematical work you might have only a hazy idea that there is a difference from understanding what's true and understanding why it's true but the beauty of the Y answers is actually a lot of the reason that people do mathematics in the first place now in this case as people worked on the Jones polynomial they discovered more and more remarkable formulas with less and less understanding of what they meant but there was a clue in fact there were lots of clues as the subject developed it had many ties with mathematical physics in fact Jones in his original work had one relationship to mathematical physics and many others were discovered a lot of things the wildering Lee many ties between the Jones polynomial and mathematical physics if anything there were too many links between the Jones polynomial and mathematical physics if you're trying to solve a mystery it's much better to have a good clue than a large assortment of clues of dubious merit so I won't try to tell in detail how this story unfolded in the 80s but I will mention those who influenced me the most were three members of the IAS one of whom is now my colleague on the faculty and former Institute professor Michael attea the distinguished mathematician who's now in Edinburgh so there were all kinds of links between the Jones polynomial and mathematical physics of different kinds but it turned out that the natural explanation has to do with quantum theory so now I need to tell you a little bit about quantum theory and how it differs from pre twentieth century physics so imagine a classical particle for example it could be the planet Venus it starts somewhere it ends somewhere else in between it will travel on a nice reasonable orbit that you can find by solving Newton's laws by solving Newton's equations of motion here inside is a quantum particle it can follow any path at all a fairly typical path might be quite irregular like this one if you look in detail at the path followed by a quantum particle it might look like it lacks rhyme or reason now for the quantum particle we have to allow all possible paths I drew one here but I drew three more over here so these are paths of particle could follow and going from here to here according to Fineman it could do whatever it wants so to speak it can go on any path at all I've drawn this path this one in this one and since the lectures about knots I couldn't resist that two of my three pairs are knotted although to make it easily drawable I'll use the same knot in each case this particular knot is called the truffle by the way this knot is a little bit that's drawn here it's a little bit more like a knot in real life it starts somewhere and it ends somewhere else it's tied down at the end and it's not it in between it's thought of freely floating not in empty space like the mathematicians usually think about and like I drew reason earlier now one important thing is that we're doing quantum physics but it's going to be relativistic quantum physics because after all the 20th century gave us relativity along with quantum mechanics so when I draw a path it's not a path in space it's a path in space-time so it's true that a path can be knotted but that's special to three dimensions if you had a fourth dimension you could always slip the loops across each other and in two dimensions you couldn't even draw a knot the lines would cross rather than avoiding each other in three space three is the right dimension four knots so if you're going to interpret your knots as the paths followed by a particle in space and time it'll have to be a spacetime of the right dimension when we count time as one of the space-time dimensions and the real world has four dimensions three space dimensions and one dimension of time but to understand knot theory at least in the approach I'll be explaining for the next little bit we're going to imagine living in a world of only three space-time dimensions not for a world of two space dimensions in one time so this is actually what I drew the world of three space-time dimensions where you can think of time as running from left to right and yes we're letting our particles zigzag back and forth burden time since we allow that relativistically so now after on a knotted path so a quantum physicist doesn't a classical physicist finds the right orbit by solving Newton's laws but a quantum physicist doesn't know what the right orbit was the quantum particle could travel on any possible orbit and a quantum physicist has to sum over all possible paths by which the particle might reach his destination now to do this sum well this is a very schematic history of physics in one sentence but roughly speaking how to do this psalmist what physicists learned in developing quantum theory and ultimately constructing what's now the standard model of particle physics quantum mechanically any path is possible but if the particle did travel on a particular path which I'll call K then there's what's called a probability amplitude for the particle to arrive at its destination via this path and that amplitude depends on K the way that the probability amplitude depends on K is very important it's the reason that there's some order even in a quantum universe all paths are possible but peculiar paths with a lot of zigzags are not very likely the particle could do anything but when you do the sum over all possible paths you get an answer that mostly at least under familiar conditions where our ordinary intuition applies the sum over all possible paths mostly corresponds to paths that are pretty close to the classical path that Newton would have favored now so but even to try to do this to do the somme overpass and find out that Newton's result is a good approximation you need to be able to calculate the quantum mechanical amplitude that the particle did travel on a given path K that amplitude is given by something which is called the Wilson operator I'll call it W sub K for today we don't really need to know exactly how its defined all we need to know is that it's a basic ingredient in quantum physics and for instance if you want to calculate the force between two quarks in an atomic nucleus what you use is the Wilson operator so once you start thinking about the sum over quantum paths and the Wilson operator it turns out that there's a very simple connection between the Jones polynomial and quantum physics the connection is simply the following we've regarded knot K as the space-time orbit of a charged particle then the Jones polynomial in other words Jones's number is the average value of the Wilson operator here's the formula in its simplest terms the number J sub K that Jones attached to a naught is the average value of the Wilson operator where the averaging is a process of quantum averaging you might wonder what are the numbers 2 3 & 5 that we use when we played the game well they're determined by the charge of the particle and Planck's constant loosely speaking now one point I perhaps should add is that technically when we carry out this program well we don't use the standard model of particle physics for one reason we need a three-dimensional model not a four-dimensional model the model we have to use is developed using something called the turn Simon's function for gauge fields where sine Chernus was one of the most famous mathematicians of the 20th century Simon's is also a very distinguished mathematician as well as businessman and is trusty now why if why have I been telling you these things well one reason is that I like them and it's fun to relive my early days at the IAS but that's not the only reason there's actually a more contemporary twist in the story I've been working on it this year and I want to tell you at least a few words about it although it is a little bit harder to explain properly than the story we've just been talking about so we took what you might have thought was around about interpretation of knots in everyday life the simplest interpretation of a knot is an object that exists in space a Norden an object in real space that we can see but to interpret the Jones polynomial in quantum theory we instead has a viewer not as a path in space-time so interpreting and not as a path in space telling this may be less obvious than interpreting and not as a physical object in space around 1990 when he was a member at the is my colleague Igor Frankel started to develop pieces of what he hoped with the ANU mathematical theory in which the knot would be seen as a physical object rather than a panthan space-time I wish that I talked him a lot he was about us ideas when he was here and I wish I could claim that I encouraged him and made useful comments but I didn't I only gave him reasons it wouldn't work anyway if it was going to work it was supposed to involve a more powerful version of the Jones polynomial in a theory that would have one dimension more technically the reason I thought it wouldn't work actually was that the chern-simons function is special to three dimensions it can't be related classically to anything in one dimension work so I thought that would mean that there wouldn't be a four dimensional theory related to the Jones polynomial but with the not as a physical object rather than a path in space-time but frankly didn't listen and he continued developing the ideas with colleagues such as Lou crane who's now at the University of Kansas and a student Michael covin off and finally by 2000 Kove enough created what's now known as Co fond of homology which is a refinement of the Jones polynomial in which the knot is a physical object rather than the path of the point particle now in a couple of ways it's like the Jones polynomial it's very clever to invent it but once it's invented it can be computed by an explicit set of rules the only trouble is that I won't tell you the rules for defining qivana for multi for the Jones polynomial I basically explained the rules but maybe I went through it too fast but for Covent ophthalmology you really wouldn't want to go into a high school class until it tried to explain the rules for defining kovin or homology in principle they're elementary but it would take a pretty unusual high school student to who would have the patience to try to understand it you don't need quantum physics to define and calculate koval Ophthalmology and in fact most people working on it don't think in terms of quantum physics at all but just like I told you earlier about the Jones polynomial the literature on kovin ophthalmology is full of what answers and it's kind of short on my answers so there are amazing discoveries of what's true they generated more and more mr. as formulas and the possibility is open or given history with the Jones polynomial and the way that the Kovan our theory was invented as a more refines contemporary counterpart you would at least wonder that maybe the quantum dimension is needed to get a better explanation of what the formulas mean you think I told you this already we can define Covell phonology by an explicit recipe so so I mean if you it's hard it's a much more sophisticated recipe but once you learn the recipe you can friendly given not just calculate its covin or phonology but it's not a recipe you try to explain in high school now qivana phonology has had a lot of impact mathematically for example our math school here at the is had a special program uncover an ophthalmology a few years ago so a few years ago a group of three physicists actually proposed a quantum interpretation of : ophthalmology based on some earlier work Vava was my student actually ends actually vafan off for my students the other two were former IES members so their story used plenty of avant-garde ideas about quantum fields and strings and all that but as beautiful and powerful as it was I always suspected well always means always since 2004 that there might be a more direct route what really troubled me a little bit was that okay the Jones polynomial was interpreted in quantum theory and then it was generalized to cover enough and these authors interpreted Covanta phonology in quantum theory but the way they did it look like it had nothing in common with the way the Jones polynomial was interpreted in quantum theory and that just didn't feel like it should be the end of the story so I thought there should be another dimension to the answer and I spent the last year trying to construct a more direct route from quantum theory to covilhã phonology honestly even though in a sense I found what I was looking for I don't know whether to say I found the more direct route or just a somewhat different one then now I gave you a very schematic picture of how quantum theory is related to the Jones polynomial and I'll have to be even less detailed for covin ophthalmology but I will say a word or two the main difference between Covanta phonology and the Jones polynomial is that the goal of the theory is more abstract so what Jones defined forgiven not is a number but what coven I've described forgiving lot is a space of quantum states except you didn't call them quantum states he just called it a space a vector space if you wish so if you think of the knot as a physical object in three-dimensional space then it's kovin ophthalmology is the space of possible quantum states so the problem that presents itself given covin AUVs crazy algebraic recipe for computing coven or phonology is to find a quantum theory in which it's true that it makes sense to consider or not as a physical object and the space of quantum states are not will turn out to be what coven I've just defined so that's what the problem is but it might have sounds like a mouthful whereas in the case of the Jones polynomial the problem is just to calculate a number which I more or less explained the Jones calculated the number now because the theory is in four space-time dimensions instead of three for space-time is the right dimension for the real world at least microscopically so the theory involves ideas and methods that are even closer to real particle physics than those that go into understanding the Jones polynomial so okay they're closer to real particle physics but well one could have tried to give a lecture just about some of those ideas but I thought I'd have to be very schematic here since we've already gone into quite a bit I'll mention though very briefly two of the main ideas that are important in making sense of covin ophthalmology and quantum theory but weren't needed for the Jones polynomial for the Jones polynomial in a sense we only needed the basics of quantum mechanics and relativistic quantum theory and how we do gauge theory but for Kove enough Theory we need a lot more avant-garde ideas one important idea is symmetry between electric and magnetic fields you probably learned about electric and magnetic fields in high school if you wants a little bit deeper into it at the university you would have run into Maxwell's equations in which the electric or magnetic fields play very similar roles but symmetry between electricity and magnetism quantum mechanically is a very subtle idea that's only been important in theoretical physics relatively recently so electric magnetic duality was pioneered by Goddard notes and olive among others in the mid 70s and it was proposed in the myths in the 70s by a tufts Mandelstam and others Polyakov I should mention in connection with the problem of how quarks are buying bound together in nucleons but really electric magnetic duality only came to be well understood in the mid 90s and if I were giving an overview talk today rather than trying to tell you what I've been doing in the last year I might have devoted the whole hour just to trying to explain to you what electromagnetic duality is since the mid 90s it's been one of the main ingredients inside ease of quantum fields and strings at the IAS and elsewhere another ingredient of string theory also turns out to be important that's extra dimensions what we want to supposed to be theory in for space-time dimensions but it turns out that understanding it properly involves relating it to theories in five and six dimensions but the biggest surprise of all is that even though it can be defined by an explicit recipe with no reference to quantum physics normally it can be defined but that's what happened Kove enough defined his theory by an explicit recipe with no reference to quantum physics but actually coronal homology can be understood perhaps much better using the most newfangled tools in the quantum theorists toolkit so I've tried today at least to give you a little bit of hint not about any big picture but about my picture of last year and I think maybe we've left some time for questions too yes I don't know about Calvin ophthalmology but for the Jones polynomial there's a glimmering of an application because people trying to develop quantum computers it's a different direction I could have gone on in the talk to explain that but people trying to develop quantum computers have the problem of what they call decoherence interaction of a material with the outside world where the subtle quantum effects that you need for quantum computer get lost and one of the one of the most seriously discussed ideas for making a quantum computer involves quantum Hall systems at very low temperatures very strong magnetic fields where the quantum theory relevant to the Jones polynomial comes in so there actually is in condensed matter physics it's not completely proved experimentally but there are experimental studied systems which are believed to be described by the Jones polynomial more exactly the the the the quantum interference effects that you got when quasi particles move around are believed to be described by the Jones polynomial so it's early days so no one has an idea if that method or any other will be used to make a quantum computer but that's any a partial answer to your question there's also a much more recent development involving what are called topological insulators discovered just in the last couple years the topic is called topological insulators it might take us to far afield if I would try to describe what they are now but it's actually a look a little bit closer to Cove and ophthalmology it's okay it's imaginable that a further extension could lead to carve an ophthalmology but certainly it uses the Jones polynomial in an interesting way by rights your question shouldn't have had an answer it's a miracle that it does yes I'm trying to think if I know anything at all like that the question was whether tangles that occur in biology it could be usefully started using the Jones polynomial I think I could state it that way my guess is well I was surprised about the condensed matter physicists found but I haven't heard of anything like that in biology yes it really strongly suggest that they should exist and there's a sad fact of the matter which is that the theory of cosmic inflation was invented around 1980 by Alan Guth and others to explain why mono poles are very scarce the inflationary universe is supposed to have made them dilute and since there's a decent amount of experimental evidence since then supporting the inflationary universe they might actually be correct that interpretation of what's happened might be correct it's got a very sad corollary which is that Guth overdid it he was trying to make monopole scarce enough but yes the inflationary universe dilutes the mono poles by the exponential of a large number and the exponential of a large number is a very very large number yes so that may be the answer to where the mono balls went but I'll tell you that I spend my time studying theories that really only make sense if monopoles exist well the hardest part of research is exactly to decide what questions you're going to work on you need to if you ask a too big a question you won't be able to answer it and if you ask two little questions it's not worth answering so you try to find the sweet spot of something that's worth doing that you actually can do and you spend a large fraction of your time not able to find the sweet spot so a very large fraction of your days actually even if you are working on a good problem a very large fraction of the days at the end of the day it seems like you've done nothing you might have spent most of the day staring at a sheet of paper and I really mean it more or less literally or finding excuses for wasting time because you can't think of what else to do since I'm telling you what I worked on in the last year I might as well tell you how I work yes it is sometimes but this thing I've told you about probably seems like a strange passion to most of my colleagues but it is my passion unfortunately I may have succeeded in explaining the Jones polynomial but I think it was too hard to explain Cove and ophthalmology properly but it's something I really care about regardless of who else does and once I started working on it it made it a little bit easier to in this particular year I'm not describing every year in my work but in this last year it made it a little bit easier to resist distractions possibly to my own detriment because I believe there are some of the distractions that I shouldn't have been that I should have followed more closely than I have yes yes yes I really think that what is significant both mathematically and physically is that not an whole related cluster of things in low dimensional geometry but I've stressed nots today or best understood in terms of quantum theory so I'm not giving everybody's answer but I'm giving you my answer but I really find fascinating it's not the nuts per se but the fact that the way to study the knots is quantum theory yes well I know two problems that I've been postponing the only question is what to tell you about them well one is kind of fortuitous but some of my colleagues younger colleagues here at the Institute they made a surprising discovery in mathematical physics a couple years ago all day tachikoma and Kyoto unfortunately there isn't really time to explain it because it involves superficially ideas that are what miles away from the knots but I can plead accident but I think that this story about Cove and ophthalmology is probably a couple applicable to their stuff as well so that's one thing I want to do there's a second thing I want to do it's something that's been nagging at me for about 25 years really in around 1986 some Russian colleagues actually one of them was one of these guys I mentioned who worked on covilhã phonology Albert Schwartz he's now in the US but at the time they were Russian colleagues they pointed out a very interesting property of superstring perturbation theory which I was sure at the time would have an impact on the field but it didn't I recently did a citation search for there paper and it has very few citations and nobody did anything significant with it and the authors of the paper are probably well at the cost of being a little bit melodramatic I feel that the authors of the paper on me might be the only ones who paid attention to it so I think would be a shame if we all retire and the paper gets forgotten so I kind of would like to do something with it yes well I'm worried that that isn't the right question for this audience the answer is not on purpose but once a colleague levers and I discovered a new way to construct a quantum theory some people thought rozanski Witten theory that generates some of the facility of invariance well I can't think of anything to say about it for a general audience so I think I'll stop anything any questions yes it's it's definitely our best shot it's our only real shot and we've definitely discovered a lot of exciting ideas that go way beyond what we'd understand today if we hadn't had string theory for example the kind of mathematical physics related to cover off multi that's miles away from physics but it's an illustration of the power of the ideas we wouldn't have that except because of the way they show up in string theory personally I think string theory is on the right track but a much younger people will have to decide that later on yes yes I was asked okay the answer to a question I was asked about magnetic monopoles is that I spend my time working on theories that only makes sense if monopoles exist but they haven't been discovered so you could ask let me you can ask your question in a moment but I just want since my answer apparently was unclear I want to elaborate on it slightly the answer to the previous question I perhaps extrapolate it slightly from the question David asked before but a semi compelling explanation of why the monopoles haven't been seen if they're there is the inflationary universe which in fact was invented precisely to reduce the abundance of mono Bowls in the real world that might be the right interpretation although it's a frustrating one it would have been better if Alan Guth had reduced the abundance of monopoles to a manageable amount but unfortunately he overdid it anyway what's your question all big theories have their skeptics yes well I can't comment very usefully because I haven't really looked at it but as I said a moment ago all big theories have their critics yes yes yes well they can pass through the same point and then you run into a phenomenon okay if example Newton had the one over R squared force law so if particles got close there's a strong force you have to calculate that force it changes the answer so two strands can pass through each other but when they do the quantum answer changes there's a simpler theory when they don't pass through each other but it makes sense your question makes perfect sense it has an answer which the quantum theory will give they're not usually called not polynomials but there's a more general thing you can define when they did cross each other you get a different answer something a spacetime history that is self crossing is different from a knot so it can have a different answer and it does I haven't wrote a paper about it once any other questions

Channel: Institute for Advanced Study

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Length: 50min 57sec (3057 seconds)

Published: Tue Aug 30 2016