“We don’t understand exactly how small they are because we don’t understand the [string] theory perfectly but roughly speaking the proportion of the solar system to an atom is just like the proportion of an atom to a string… that’s pretty small. And it’s very important these strings obey quantum mechanical laws. — Ed Witten
tell me what is the beauty of one single string
well the idea in string theory is that elementary particles instead of being point particles the debate quantum mechanical laws are little loops of vibrating string they also have a quantum mechanical laws and the beauty of that is that it describes many different things all at once if you’ve got for instance a violin string or a piano string they have many different modes or harmonics of vibration if you pluck a string which is at middle C for instance you also see the higher harmonics and that’s responsible for the beauty of music the reason we have symphony orchestras and not just tuning forks is that different instruments excite the higher harmonics in different amounts the pure tone of the tuning fork sounds garish and ugly to the ear the rich sound of a violin comes from the mixture of the different harmonics now in the case of the string you’ve got this one vibrating string it has many different harmonics and we perceive those different harmonics as different elementary particles so for instance the electron the quark the photon the neutrino the graviton all these things are different modes of vibration of a single string and that’s very beautiful at harmonious getting the different particles from different forms of vibration of a string just as a musician gets the richness of the tone from the harmonics of the violin string how small is the string if it will say small means in this case that the super string is looks up at an awesome atom as an atom looks up to the entire solar system something like that we don’t understand exactly how small they are because we don’t understand the theory perfectly but roughly speaking the proportion of the solar system to that I’m just like the proportion of an atom to a string that’s small that’s pretty small and it’s very important that these strings of a quantum mechanical laws make I’ll just take a moment at the blackboard to explain them so classically a point particle as we discussed before traces out an orbit in space which has made a little bit fuzzy and that fuzziness is extremely important that has a lot to do with how quantum mechanics was discovered for instance at the beginning of the century when people discovered that there were atoms and there were electrons and they were atomic nuclei they had the problem that if you’ve got for instance of protons with an electron orbiting endeth and then you use Maxwell’s equations this guy thought the bad electron should the emitting electromagnetic radiation and should spiral into the atom in an extremely short time much faster than the twinkling of an eye what turned out though is that the quantum mechanical fuzziness keeps the electron from spiraling in the notion of spiraling in as a classical concept and that fuzzy electron is smeared out quantum mechanically in such a way that it just can’t fall in so this cured a basic problem in the theory of electricity and gave us our modern theories of atoms molecules and all the microscopic things which are based on this quantum mechanical uncertainty in the case of gravity there is a similar problem if you have one body orbiting another einstein’s theory that says that gravitational radiation should be emitted and again you have this problem of an in spiral and you might think that quantum mechanical fuzziness would cure it but in fact it doesn’t an additional source of fuzziness is needed then you get that in string theory and string theory instead of a point particle which has time of false traces a loop at each time you’ve got a little string and then at a later time that’s maybe somewhere else and as time evolves this fits together into a smooth surface called the world volume a world sheet of the strength but I’ve kind of drawn a classical picture here it’s made fuzzy it’s hard to draw but I won’t really do so but we’ve got a quantum-mechanical string so it’s spread out in two different ways one is that it’s a little stringy instead of a point and secondly it’s quantum mechanical so they both have the effect of smearing out a little bit our familiar concepts and making what we know become a little bit fuzzy adjust this combination solves the problem for gravity the way the quantum mechanical fuzziness did for electricity but at least to a theory whose predictive power is much tighter the arbitrariness that you’ve got in the standard theory is greatly reduced in the case of the string theory and that enables you to make statements that don’t have an analogue in the usual context like the fact that gravity is an inevitable consequence now in talking a little bit about how particles interact I’m not going to try to draw the quantum mechanical fuzziness that’s always there but it would be too complicated to try to keep it automatic so we’re just going to draw a classical pictures but now I want to say something that fine mentor us thought you should think of these particles as they move along in space and time sometimes breaking into two and sometimes rejoining so here one particle broke into two at this moment and two rejoined into one year the overall process is that two came in from the past and two 1000 the future so that was a scattering process and Fineman taught us how to calculate quantum mechanical probability amplitudes for every such picture well the thing about them is that everyone will agree that there were definite space-time events where something happens one particle broke into two or two particles joined into one and those events are what you might call technically singularities in this graph through distinguished events that standard quantum field theory needs special rules for what happens to those singularities which is the basic limitation of its predictive power even after I tell you what the particles are you don’t know how they interact because to know how they interact you would need now they’re allowed to break and join and that’s a separate question in string theory the set up is a little bit different each of these particles is replaced by a little tube which describes the history of a propagating string and where a particle breaks into two discontinuously a string can smoothly that didn’t split apart into two strings and then here’s another one coming in and then they go out so now I’ve drawn a spacetime picture but two strings coming in in the past and two going out in the future and the point of this picture is meant to be that it’s all perfectly smooth unlike this one which has two discrete events at which breaking or joining happens so the result of that is that if you know what the string is you also know how it attracts you know what it’s allowed to do but if you know what the particles are you still needs a separate recipe for how it’s allowed to behave so that sort of is the germ of the fact that string theory is much more predictive than standard quantum field theory you don’t need to separately say what the objects are and how they behave once you’ve said what the objects are how they behave is completely defined the other thing is that technically you run into problems in standard quantum field theory when these interaction events coincide in space-time that’s where you meet infinities that people grappled with for decades for example Freeman Dyson was one of those who discovered the renewals ation of quantum electrodynamics worthy problems for electricity were finally definitively tamed but for gravity that process doesn’t work that’s why gravity doesn’t work with standard quantum field theory but when you go to the string because there aren’t these distinguished events the traditional difficulties disappear and so gravity becomes possible and when you probe more deeply it actually becomes necessary in the light of string theory if you write down an equation or a picture like that the strings what is the beauty write down an equation of string theory yet which is dear to your heart it’s a kind of beauty explain what it’s around I’m talking about duality for instance or we might start here with something more elementary the Nandu go to action is the basic principle that determines how these strings move in space-time and it’s a beautiful equation that also governs the behavior of a soap bubble at ordinary space so if you think of if you’ve ever seen the oscillations of a soap bubble and you’ve ever noticed that they can take curious and graceful shapes that’s one manifestation of what this equation does but it’s other manifestation is that it describes what the strings are but therefore also describes at the same time how they’re allowed to bathe what the interactions are how one string can break into two L’s strings can scatter what reactions can occur how atoms can form it’s the most complete well it’s not the most complete but it does a lot yeah and in standard quantum field theory that means in pre string physics it has no analog over here you do write bits and pieces you can write a very nice piece that goes back sort of to oil at Lagrangian Newton in different aspects and it’s analog which many who study physicists sent us would meet us undergraduate probably looks like that and it’s fairly close analog of the nambu-goto formula but it only describes a piece of the picture and there’s the rest of the truth which is where the particles are interacting or breaking or joining or whatever they’re doing where things are happening rather than just particles propagating freely you need additional laws which can’t be written down neatly in this one it takes another language completely so then going to string theory you replace this one this one sort of describes a rubber bands well now just a little bit misleading this one describes the soap bubble in a sense that this one describes something of lower dimension but when we go from here to here well just mathematically in some ways it’s richer but in some ways it’s quite similar but the physics that it describes is much more harmonious because a formula like this one can never give a complete account of the particles you need separate rules for how they behave how they interact what they’re allowed to do this sort of just says what they are but this formula says what the strings are and also how they behave and the people dreamed for a long time in physics to have something like that were you to automatically know the interactions once you knew what the particles were you could say that in gravity Einstein offered them for the gravitational field but in the rest of physics that’s generally been out of reach bits and pieces of it are achieved something like that is achieved for the W and Z bosons on the electromagnetic field in the standard model of particle physics but for the rest of the particles like the neutrino or the electron you really have got to go to the string picture before you’re able to say that knowing what it is you also know what it can do yeah and there’s fun with it you’ll see what it is and you see what it can do that’s right it’s understand still it’s the movement of the universe so to say yeah let this go it took Cooper why they call well it felt too poetic but it’s not exactly the phrase I would use either yeah well I’d say it’s of course hard to convey it with perfect accuracy but what I would try to say is that in these strange case once you say what the strings are what strings you’re trying to describe then their behavior is uniquely determined whereas for electrons you sort of dial it up so you can say what’s the mass of the electron what’s its electric charge and so on and the standard quantum field theories would still make sense for different values of those numbers in the way I’ve explained it so far the way I’ve said it is that if you know what the string is then you also know what it does and that’s sort of because this picture here is smooth well this other one has those interaction events were breaking and joining happens but that’s kind of not a complete explanation in the particle side you’ve got quite a lot of freedom and saying what the particles are allowed to be in the string side it’s severely restricted what kind of strings you can introduce that’s a long story that took a lot of work in the 70s because finding that there are any possibilities for l2 his six strings was extremely difficult I’ll occupy literally dozens of papers so people by the mid 80s had distilled it to the fact that there seemed to be five string theories that made sense there were five candidates for what kind of string you could have they differed by very general properties for instance in some theories in some cases the string was an insulator in other cases the strings were superconductors in some cases the strings were closed loops like I drew on the blackboard and in one of the five theories the strings were allowed to have endpoints like pieces of string instead of closed loops but anyway when all this had done when you put in all the constraints of relativistic quantum mechanics there were five kinds of strings you could do so there seemed to be five candidates for how you could describe nature in this new framework there was a period in the early 80s when it seemed that there was this very wonderful new framework for physics there were three candidates who hadn’t yet been discovered in this new framework gravity was inevitable well in the pre string framework that was actually impossible and that of course was very attractive and exciting but on the other hand you could also point to things that were wrong these three theories were unified theories of gravity quantum mechanics in matter but some aspects of the matter were wrong what bothered me the most in those days was that you could argue in general than in any of those three theories the weak interactions would have to conserve parody which means that nature would look the same if you looked in a mirror but we’ve known since the 50s that although nature almost looks the same if you look in the mirror if you look very closely at the details of radioactive decays of certain atoms you see that actually nature isn’t symmetrical between left and right if you take a movie and then you put the film in backwards and protect it most things in everyday life would look fine but certain experiments in almond tree particle physics and nuclear physics actually wouldn’t make sense if the film was played backwards yet it seemed that you could prove in string theory that the theory would have to be symmetrical between left and right at least for the realm of the standard experiments that was wrong that was a really important contradiction I thought between string theory in nature and it motivated a lot of work that I mean eventually others did in that period I in 1983 Rosco Mae and I did a calculation involving gravitational anomalies but made very precise why the weak interactions would have to would have to be symmetrical between left and right and then in 1984 there was the breakthrough that greeted Schwartz made where they got a new insight about the anomaly cancellation and suddenly the idea that the weak interactions had to be symmetric between left and right was out the window but then a lot of other things happened so the weak interactions could break the symmetry but then the models of elementary particle physics became a lot more realistic in very short order especially with the discovery of the other two string theories the heterotic strings so this is this of course made a tremendous impression on me because if the theory was wrong the question you asked well how can you avoid left-right symmetry of the theory might not have had an answer and even if you could have conjured up some mathematical answer or not nothing good would have necessarily come out of it the fact that when you solve this problem so many other things popped into place is the kind of thing which in my judgment doesn’t happen if you’re on the wrong track overall so since then I personally haven’t had doubts that it must be on the right track now how many more layers we’ve gotta peel away before we understand that there’s another story and what that legend done I don’t know if you say it will completely change our way of thinking about nature the laws of nature well you see somehow space and time will only be approximations I don’t know exactly how but very very roughly the classical idea of position and velocity of a particle is an approximation in quantum mechanics that you get when you can treat certain operators as if they commute if you don’t care which of two things is done first then you can talk about the classical ideas but if you pay attention to what’s first and what’s last then you’re in this quantum mechanical world where everything is much stranger now in the framework of physics that we have up to now position and varsity have been confounded but space and time still are perfectly sharp but it’s very clear for a lot of reasons that in the future the concepts of space and time are going to be the fuzz up that there will be something new that we’ve got that’s more basic than space and time as we know them and space and time will be approximations that will make sense when the lengths and times involved are bigger when the length sometimes involved are small they won’t make sense that’s why the very notion of time will break down near the Big Bang if you want to understand the Big Bang or black holes or the structure of elementary particles there’s some deeper level about what space and I’m really R which is what string theorists are grappling towards the laws of nature as they’ve been uncovered in the last few centuries and especially as they’ve been uncovered in the last century are very surprising they’re very subtle in the concepts that physicists have needed and many of the details are surprising we’ve mentioned some of them the curvature of space-time others that are equally surprising like antimatter the fact that particle has a similar but opposite anti particle and they can annihilate when they need or conversely they can be created from pure energy there are lots and lots of surprising things here I’m in that case I’m mentioning a surprising phenomenon but the concepts by which the human mind explains or predicts them are also in many cases very surprising very very different from what you might notice just naively in everyday life and looking at things around you they’ve got a great beauty which is a little hard to describe maybe if one hasn’t experienced it it’s an aesthetic beauty there right do you was as we know them are very beautiful mathematically they involve very interesting and subtle concepts yeah we do you may be so subtle well it’s very delicate you see if I gave you the naive idea which is still on the blackboard replace a definite orbit of a point particle by something fuzzy no you could think about it a thousand people walked in the room for a thousand years and you might never come up with something as crazy as the actual answer which involves quantum mechanical Hilbert spaces operators that have commute wave functions that have a strange equations and have peculiar physical interpretations so it’s a rich story and it all hangs together beautifully and accounts resolves many contradictions or apparent contradictions in nature that at first sight look just as strange as the question what was there before the beginning so lots of things that prove to have their analog lots of things that prove to have their explanations in strange mathematical structures that are relevant to nature seem paradoxical just like some of the paradoxes about the beginning of time so I think perhaps some viewers of this program might be customed to thinking about the beauty of music for instance but the beauty of science and I might say also the beauty of pure mathematics are very different but they’re just as real and vivid to those who experience them as the beauty of music it’s not just that in the course of time physicists learned to write more and more accurate equations in writing more and more accurate equations fyssas has learned that the more and more accurate equations are based on new subtle and surprising concepts that fit together just right or resolve all the contradictions to everything they have to do whether it’s going back to Newton’s laws in the regime where Newton was able to study nature or reproducing atomic pager in certain other regimes it fits together perfectly in ways that are really extremely surprising and of course the greatest thing about it is that it works not just fits together logically but it describes the world we live in the best equations and the best theories we’ve got as I’ve mentioned are really quantum mechanics and general relativity and the best theories are tested in so many different ways but at a point so nicely there’s so many different phenomena that they really have remarkable power and describing nature but one thing I’m trying to convey is that the thrill it’s not just from the power of being able to describe many things and put the combination of the beauty of the theory the beauty or harmony of the theory and its power and application to the real world that combination gives a thrill that I think neither ingredient would fully give separately
Edward Witten: On the Shoulders of Giants World Science Festival
Isaac Newton wrote, “If I have seen a little further it was by standing on the shoulders of giants.”
Acknowledging the scientists who blazed intellectual trails before him, Isaac Newton wrote, “If I have seen a little further it was by standing on the shoulders of giants.” In this special annual series, we invite our audience to stand on the shoulders of a modern-day giant. In 2015, we were honored to present an address by a titan of physics, Edward Witten. Professor Witten is a leading light of superstring theory and the only physicist to have won the vaunted Fields Medal, mathematics’ highest honor. Known for advancing a number of novel approaches in mathematics and physics, Witten opened up new vistas in 1995 when he unified five seemingly competing superstring theories into M-theory, which seeks to unify Einstein’s general theory of relativity with quantum mechanics.
“Since quantum mechanics is not deterministic and the principle of least action sounds unnatural in a deterministic theory it’s kind of logical for them to go together”
What if string theory is correct?
“But there’s a much deeper rhyme if string theory is correct then first of all random two dimensional Quantum geometry is key to unifying the forces. The one-dimensional random geometry lets us describe our quantum theories of today but the two-dimensional case forces us to unify the particles and forces because of the many different ways that a string can vibrate. But there’s something more to this which is the deepest rhyme I have to offer you today. It turns out that one of the states of a vibrating string, so remember, for violin string this is the basic way can vibrate and this is the second and there are many, many more. Likewise the string used in my kind of string theory can can vibrate in many different ways but one of the states of the vibrating string turns out to be a graviton, a basic Quantum unit of the gravitational field, analogous to the photon which is a basic Quantum unit of light. To say this differently when we unify the elementary particles and their forces using string theory we get general relativity for free as part of the bargain. So if string theory is correct it basically means that two-dimensional random Quantum geometry, on the string World sheet, which we know how to do although it stretches our understanding. We know how to do this but it’s relatively close to the frontier of what we know how to do. It’s the key to a new kind of four-dimensional random Quantum geometry which we need, but otherwise do not know how to do, and that’s the deepest rhyme, or potential rhyme, that I have to offer you today. Thank you.”
What is it about mathematics that mathematicians employ the language of philosophy to speak about “truth” and the language of art to speak about “beauty”? What makes mathematical propositions true? What makes them beautiful. Conversely, can mathematical propositions be true without being beautiful and/or be beautiful without being true? Edward Witten is a theoretical physicist and professor of mathematical physics at the Institute for Advanced Study in Princeton, New Jersey. Witten is a researcher in string theory, quantum gravity, supersymmetric quantum field theories, and other areas of mathematical physics.
“Calculus [mathematics] is universal… nuclear physics is incredibly complicated but it’s described by extremely simple equations.”
IF Ed Witten is a human genius functioning at the highest level of human intelligence.
THEN when Artificial Super-intelligence (ASI) is 1 billion times more intelligent than Ed Witten.
(1) Is ASI, at that point in space time, still a non-deterministic intelligent machine? In interaction with humans? In mathematics? In physics? In chemistry? In its emergent goals?
(2) IF hard problems in nature like: (1) what is the nature of consciousness? and (2) is string theory correct? can be solved with ASI explanations to humans? If we study Ed Witten’s elegant way of explaining String Theory… which is almost understandable for a layman… how would humans relate to the ASI at that point, in conversation with a god-like intelligence?
Sir Roger Penrose is an English mathematical physicist, recreational mathematician and philosopher. He is the Emeritus Rouse Ball Professor of Mathematics at the Mathematical Institute of the University of Oxford, as well as an Emeritus Fellow of Wadham College.
Sir Roger Penrose is an English mathematical physicist, recreational mathematician and philosopher. He is the Emeritus Rouse Ball Professor of Mathematics at the Mathematical Institute of the University of Oxford, as well as an Emeritus Fellow of Wadham College.
“It seems like nature prefers simplicity… we live in a structure with enormous amounts of symmetry which strikes us is beautiful and elegant.” — Max Tegmark
