Cumrun Vafa: String Theory | Lex Fridman Podcast #204

Lex Fridman 0:00 The following is a conversation with Comrade Vafa, a theoretical physicist at Harvard, specializing in string theory. He is the winner of the 2017 Breakthrough Prize in Fundamental Physics, which is the most lucrative academic prize in the world. Quick mention of our sponsors: Headspace, Jordan Harmage's Show, Squarespace, and Allform. Check them out in the description to support this podcast. As a side note, let me say that string theory is a theory of quantum gravity that unifies quantum mechanics and general relativity. It says that quarks, electrons, and all other particles are made up of much tinier strings of vibrating energy. They vibrate in 10 or more dimensions, depending on the flavor of the theory. Different vibrating patterns result in different particles. From its origins, for a long time, string theory was seen as, uh, too good not to be true, but has recently fallen out of favor in the physics community, partly because over the past 40 years it has not been able to make any novel predictions that could then be validated through experiment. Nevertheless, to this day, it remains one of our best candidates for a theory of everything, or a theory that unifies the laws of physics. Let me mention that a similar story happened with neural networks in the field of artificial intelligence, where it fell out of favor after decades of promise and research, but found success again in the past decade as part of the deep learning revolution. So, I think it pays to keep an open mind since we don't know which of the ideas in physics may be brought back decades later and be found to solve the biggest mysteries in theoretical physics. String theory still has that promise. This is the Lex Fridman Podcast, and here's my conversation with Comrade Vafa.

Lex Fridman 1:52 What is the difference between mathematics and physics?

Cumrun Vafa 1:55 Well, that's a difficult question, because in many ways, math and physics are unified in many ways. So, to distinguish them is not an easy task. I would say that perhaps the goals are ma- of math and physics are different. Uh, math does not, uh, care to describe reality, physics does. That's the major difference. But a lot of the thoughts, processes, and so on, which goes to understanding the nature and reality are the same things that mathematicians do. So, in many ways, they are similar. Uh, mathematicians care about, uh, deductive reasoning, and, uh, physicists, or physics in general, we care less about that. Uh, we care more about interconnection of ideas, about how ideas support each other, or if there's a puzzle con- uh, discord between ideas, that's more interesting for us. And part of the reason is that we have learned in physics that the ideas are not sequential, and if you think that there's one idea which is more important and we start with there and go to the next idea and next one and deduce things from that like mathematicians do, we have learned that the, like, the third or fourth thing we deduce from that principle turns out later on to be the actual principle. And, uh, from a different perspective starting from there leads to new ideas which the original one didn't lead to, and that's the beginning of a new revolution in science. So, this kind of thing we have seen again and again in the history of science, we have learned to not like deductive reasoning because that gives us a- a bad starting point to think that we actually have the original thought process should be viewed as the primary thought and all these are deductions, like the way mathematicians sometimes does. So, in physics, we have learned to be skeptical of that way of thinking. We have to be a bit open to the possibility that what we thought is a deduction of a hypothesis actually the reason that's true is- is the opposite, and so we- we reverse the order. And so this- this switching back and forth between ideas makes us more fluid about, uh- uh, deductive fashion. Of course, it sometimes gives a wrong impression, like, "Physicists don't care about rigor, they just, you know, they just say random things, you know, they are willing to-

Lex Fridman 4:04 (laughs)

Cumrun Vafa 4:04 ... to say things that are not backed by, you know, th- the logical reasoning." That's not true at all. So des- despite- despite this, uh, fluidity in saying which one is a primary thought, we are very careful about trying to understand what we have really understood in terms of relationship between ideas. So, that's- that's, uh, that's an important ingredient, and in fact, solid math being behind physics is, I think, uh, one of the attractive features of, uh, of a physical law. So, we look for beautiful math

Cumrun Vafa 4:34 underpinning it.

Lex Fridman 4:35 Can we dig into that process of, uh, starting from one place and then the f- uh, ending up at, like, the fourth step and realizing all along that the place you started at was wrong? So does- is that happen when there's a discrepancy between what the math says and what the physical world shows? Is that how you then can go back and do the revolutionary idea for a different starting place altogether?

Cumrun Vafa 5:02 Perhaps I'll give an example to see- to s- see how this goes, and in fact, the historical example is, uh, Newton's work on classical mechanics. So- so Newton formulated the laws of mechanics, uh, you know, the force F equals to MA and- and his other laws, and they look very simple, elegant, and so forth. Later, uh, when we studied more examples of- of mechanics and other similar things, physicists came up with the idea that the notion of potential is interesting. Potential was an abstract idea which kind of came, you could take its gradient and relate it to the force, so you don't really need a theory, but it solved, helped some thoughts. And then later, uh, Euler and Lagrange reformulated Newtonian mechanics in a totally different way in the following fashion. They said if you take... if you want to know where a particle at this point and at this time, how does it get to this point at the later time, is the following. You take all possible paths connecting this particle from going from the initial point to the final point-... and you compute the action. And what is an action? Action is the integral over time of the kinetic term of the particle, minus its potential. So you take this integral, and each path will give you some quantity. And the path it actually takes, the physical path, is the one which minimizes this integral or this action. Now, this sounded like a backward step from Newton's. Newton's s- formulas seemed very simple. F equals to MA, and you can write F as minus the gradient of the potential. So why would anybody start formulating such a simple thing in terms of this complicated looking principle? You have to s- study the space of all paths and all things, and find the minimum, and then you get the same equation, so what's the point?

Lex Fridman 6:49 (laughs)

Cumrun Vafa 6:50 So Euler and Lagrange's formulation of Newton, which is a, which was kind of a ref- uh, recasting in this language, is just a consequence of Newton's law. F equals MA gives you the same fact that this path is a minimum action. Now, what we learned later, last century, was that when we deal with quantum mechanics, Newton's law is only an a- an average correct. And the particle going from one to the other doesn't take exactly one path. It takes all the paths.

Lex Fridman 7:19 Yes.

Cumrun Vafa 7:20 With the, with the amplitude, which is proportional to the exponential of the action times an imaginary number, I. And so this fact turned out to be the reformulation of quantum mechanics. We should start there as the basis of the new law, which is quantum mechanics, and Newton is only an approximation on the average correct.

Lex Fridman 7:38 When we say amplitude, you mean probability?

Cumrun Vafa 7:40 Uh, yes. The amplitude means if you com- sum up all these paths with the exponential I times the action, if you sum this up, you get a number, a complex number. You square the norm of this complex number, it gives you the probability to go from one to

Cumrun Vafa 7:52 the other.

Lex Fridman 7:52 Is there ways in which mathematics can lead us astray when we use it as a tool to understand the physical world?

Cumrun Vafa 8:01 Yes. I would say that mathematics can lead us astray as much as old physical ideas can lead us astray.

Lex Fridman 8:08 (laughs) That's true, yeah.

Cumrun Vafa 8:09 So, it is, if you get stuck in some- something, then you can easily fool yourself that just like, uh, the thought process. We have to free ourselves of that. Sometimes math does that role. Like say, "Oh, this is such a beautiful math. I definitely wanna use this somewhere." And so you just get carried away, and you just get maybe carried too far away. So that is certainly true. But I wouldn't say it's more dangerous than old physical ideas. To me, new math ideas, uh, is as much potential to lead us astray as old physical ideas, which could be long-held principles of physics. So I'm just saying that we should keep an open, uh, mind about the role that math plays. Not to be antagonistic towards it, and not to over, over welcoming it. We should just be open to possibilities.

Lex Fridman 8:51 What about looking at, at a particular characteristics of both physical ideas and mathematical ideas, which is beauty? Do you think beauty leads us astray? Meaning, um, and, and you offline showed me a, uh, a really nice puzzle that illustrates this, uh, this idea a little bit. Uh, maybe you can speak to that or another example where, uh, beauty makes it tempting for us to assume that the, the law and the theory v- we've found is actually one that perfectly describes reality.

Cumrun Vafa 9:19 I think that beauty does not, uh, lead us astray, because I feel that beauty is a requirement for principles of physics.

Lex Fridman 9:27 So beauty is, uh, fundamental in the universe?

Cumrun Vafa 9:29 I think beauty is fundamental.

Lex Fridman 9:30 (laughs)

Cumrun Vafa 9:31 At least that's the way many of us view it.

Lex Fridman 9:32 It's not emergent? (laughs)

Cumrun Vafa 9:33 (laughs) It's not emergent.

Lex Fridman 9:34 (laughs)

Cumrun Vafa 9:35 I think, I think Hardy is the mathematician who said that there's no permanent place for ugly mathematics.

Lex Fridman 9:40 (laughs)

Cumrun Vafa 9:40 And so I think the same is true in physics, uh, that, uh, if we find a principle which looks ugly, uh, we are not going to be, that's not the end stage. So therefore, beauty is going to lead us somewhere. Now, it doesn't mean beauty is enough. It doesn't mean if you just have beauty, if I just look at, uh, something is beautiful, then I'm fine. No, that's not the case. Beauty is certainly a criteria that every good physical theory should pass. That's at least the view we have. Why do we have this view? That's a good question. It is, uh, partly, uh, m- you could say based on exper- experience of science over centuries. Partly is a philosophical view of what, what, what reality is or should be. And, uh, in principle, you know, it could have been ugly, and we might have had to deal with it, but we have gotten maybe, uh, confident through examples after examples in the history of science to look for beauty.

Lex Fridman 10:32 And our sense of beauty seems to incorporate a lot of things that are essential for us (laughs) to solve some difficult problems, like symmetry. We find symmetry beautiful and the breaking of symmetry beautiful. Somehow, symmetry is a, is a fundamental part of how we conceive of beauty at all layers of reality, which is interesting. Like, uh, in, in both the visual space, like w- the way we look at art, we look at each other as human beings, the way we look at creatures in the biological space, the way we look at chemistry, and then to the physics world as, as, as the work you do. It's, it's kinda interesting. It l- it makes you wonder, like, (laughs) which one is the chicken or the egg? Is symmetry the ch- the chicken and our conception of beauty the egg, or the other way around? Or somehow the fact that every, that symmetry is part of reality, is it, it somehow creates the brain that then is able to perceive it? Or maybe that's, this is just 'cause we, uh, m- maybe it's so obvious it's almost trivial that symmetry, of course, will be part of every kind of universe that's possible. Uh, and then our, any kind of organism that's able to observe that universe is going to appreciate, uh, symmetry.

Cumrun Vafa 11:44 Well, these are good questions. Uh, we don't have a deep understanding of why we get attracted to symmetry.

Lex Fridman 11:49 Yeah.

Cumrun Vafa 11:49 Why do laws of nature seem to have symmetries underlying them? And the reasoning or the examples of whether, if there wasn't symmetry, we would have understood it or not. We could have said that, "Yeah, if there were, you know, things which didn't look that great, we could understand them." For example, we know that symmetries get broken, and we have appreciated nature...... in the broken symmetry phase as well. The world we live in has many things which do not look symmetric, but even those have underlying symmetry when you look at it more deeply. So, we have gotten maybe spoiled perhaps by, by the appearance of symmetry all over the place, and we look for it. And, um, I think this is, this is perhaps related to sense of aesthetics that scientists have, and we don't usually talk about it among scientists. Uh, in fact, it's kind of a philosophical view of, why do we look for simplicity or beauty or so forth? And, uh, I think, in a sense, scientists are ma- uh, a lot like philosophers. Sometimes I think, especially modern science, seems to shun aw- shuns philosophers and philosophical views.

Lex Fridman 12:54 Mm-hmm.

Cumrun Vafa 12:54 And I think at their peril. I think, I think in my view, science, uh, owes a lot to philosophy. And in my view, many scientists, in fact, probably all good scientists, are perhaps amateur philosophers.

Lex Fridman 13:08 Mm-hmm.

Cumrun Vafa 13:08 They may not state that they are philosophers or they, they may not like to be labeled philosophers, but in many ways what they do is like what i- is philosophical takes of things. Looking for simplicity or symmetry is an example of that, in my opinion, or seeing patterns. You see, for example, another example of the symmetry is like how you come up with new ideas in science. You see, for example, an idea A is connected with an idea B. Okay, so you, you study this connection very deeply, and then you find the cousin of an idea A, let me call it A prime, and then you immediately look for B prime. If A is like B and if there's an A prime, then you look for B prime. Why? Well, it completes the picture. Why? Well, it's philosophically appealing to have more balance in terms of that. And then you look for B prime, and lo and behold, you find this other phenomena which is a physical phenomena which you call B prime. So this kind of thinking motivates asking questions and looking for things, and it has guided scientists, I think, through many centuries, and I think it continues to do

Cumrun Vafa 14:10 so today.

Lex Fridman 14:10 And I think if you look at the long arc of history, I suspect that the things that will be remembered is the philosophical flavor of the ideas of physics and chemistry and computer science and mathematics. Like, I think the actual details will be shown to be incomplete or maybe wrong, but the philosophical intuitions will carry through much longer. The- there's a sense in which, if it's true that we haven't figured out most of how things work currently-

Cumrun Vafa 14:44 Yes.

Lex Fridman 14:44 ... that, uh, it'll all be shown as wrong and silly. It'd almost be a historical artifact. But the, the human spirit, whatever, like, the, the longing to understand, the, the way we perceive the world, the way we conceive of it, uh, of our place in the world, those, those ideas will carry on.

Cumrun Vafa 15:02 I completely agree. In fact, I believe that, uh, almost ... Well, I believe that none of the principles or, or laws of physics we know today are exactly correct. All of them are approximations to something. They are better than the previous versions that we had, but none of them are exactly correct and none of them are gonna stand forever. So I agree that that's the process we are heading, we are improving. And yes indeed, the thought process and that philosophical take is common. So when we look at, you know, older, uh, uh, scientists, or maybe even all the way back to Greek philosophers, and the things that they way they thought and so on, almost everything they said about, you know, nature was incorrect.

Lex Fridman 15:41 (laughs)

Cumrun Vafa 15:42 But the way they thought about it and many things that they were thinking is still valid today. For example, they thought about symmetry breaking. They were trying to explain the following. They were ... This is a beautiful example, I think. They had figured out that the earth is round, and they said, "Okay, Earth is round." They have, you know, they had seen the length of the shadow of this meter stick, and they had seen that if you go from the equator upwards north, they find that depending on how far away you are that the length of the shadow changes. And from that, they have even, they had even measured the radius of the earth to good accuracy.

Lex Fridman 16:12 That's brilliant, by the way, the fact that they did that as well.

Cumrun Vafa 16:14 Very brilliant. Very brilliant. So these Greek philosophers were v- very smart. And so, uh, they had taken it to the next step. They ask, "Okay, so the earth is round. Why doesn't it move?"

Lex Fridman 16:24 (laughs)

Cumrun Vafa 16:25 They thought it doesn't move. They, they, they were looking around, nothing seemed to move, so, so they said, "Okay, we have to have a good explanation." It wasn't enough for them to, you know, be there. So they were really wanna deeply understand that fact, and they come up with this symmetry argument.

Lex Fridman 16:38 Mm-hmm.

Cumrun Vafa 16:38 And the symmetry argument was, "Oh, if the earth is spherical, it must be at the center of the universe for sure."

Lex Fridman 16:45 Yeah.

Cumrun Vafa 16:45 So they said the earth is at the center of the universe.

Lex Fridman 16:47 That makes sense actually.

Cumrun Vafa 16:48 And they said, you know, "If Earth is going to move, which direction does it pick? Any direction it picks, it breaks that spherical symmetry-"

Lex Fridman 16:54 Mm-hmm.

Cumrun Vafa 16:54 "... because you have to pick a direction."

Lex Fridman 16:56 Mm-hmm.

Cumrun Vafa 16:57 "And that's not good, because it's not symmetrical anymore. So therefore, the earth decides to sit put, because it would break the symmetry." So, so they had the incorrect science, they thought the earth doesn't move, and they, but they had this beautiful idea that symmetry might explain it.

Lex Fridman 17:10 Mm-hmm.

Cumrun Vafa 17:11 But they were even smarter than that. Aristotle didn't agree with this argument.

Lex Fridman 17:14 (laughs) .

Cumrun Vafa 17:16 He said, "Why do you think symmetry prevents it from moving? Because the preferred position? Not so." He gave an example. He said, "Suppose you are a person and you put, we put you at the center of a circle, and we spread food around you on a circle around you, loaves of bread, let's say."

Lex Fridman 17:34 Mm-hmm.

Cumrun Vafa 17:35 "And we say, 'Okay, stay at the center of the circle forever.' Are you going to do that just because it's a symmetric point? No. You are gonna get hungry, you're gonna move towards one of those loaves of bread despite the fact that it breaks the symmetry."

Lex Fridman 17:49 Mm-hmm.

Cumrun Vafa 17:49 So from this way, he tried to argue being at the symmetric point may not be the preferred thing to do. And this idea of spontaneous symmetry breaking is something we just use today to describe many physical phenomena. So spontaneous symmetry breaking is the feature that we now use. But this idea was there, thousands of years ago, but applied incorrectly-... to the physical world, but now we are using it. So these ideas are coming back in different forms. So I agree very much that the thought process is more important, and these ideas are more interesting than the actual applications that people may find today.

Lex Fridman 18:23 Did they use the language of symmetry and the symmetry breaking-

Cumrun Vafa 18:25 Yes.

Lex Fridman 18:25 ... and spontaneous symmetry breaking? That's really interesting-

Cumrun Vafa 18:27 Yes.

Lex Fridman 18:28 ... 'cause like y- I could see, uh, a conception of the universe that kind of tends towards perfect symmetry, and is stuck there, like the idea... not stuck there, but achieves that optimal and stays there. The idea that you spontaneously break out of symmetry, uh, like have these perturbations, j- like jump out of symmetry and back, that's no- that's a really difficult idea to, uh, to load into your head.

Cumrun Vafa 18:55 Right.

Lex Fridman 18:55 Like wh- where, where does that come from? And, and then, and then the idea that you may not be at the center of the universe.

Cumrun Vafa 19:02 Right.

Lex Fridman 19:02 That is a really tough idea.

Cumrun Vafa 19:05 Right. So symmetry's sometimes an explanation of being at the symmetric point is sometimes a simple explanation of-

Lex Fridman 19:10 Yeah.

Cumrun Vafa 19:10 ... many things, like if you have a ball, um, a circular ball, then the bottom of it-

Lex Fridman 19:17 Mm-hmm.

Cumrun Vafa 19:17 ... is the lowest point. So if you put a, you know, pebble or something, it will slide down and go there at the bottom and stays there at the symmetric point, because the preferred point, the lowest energy point. But if that same symmetric circular ball that you had had a bump on the, on the bottom-

Lex Fridman 19:31 Mm-hmm.

Cumrun Vafa 19:32 ... the bottom might not be at the center. It might be on a circle on the table.

Lex Fridman 19:36 Yeah.

Cumrun Vafa 19:37 In which case, the pebble would not end up at the center. It would be at the lower energy point. Symmetrical, but it breaks the symmetry once it takes a point on that circle.

Lex Fridman 19:44 Yeah.

Cumrun Vafa 19:45 So, so we can have symmetry reasoning for where things end up, or symmetry breakings, like this example would suggest.

Lex Fridman 19:52 We talked about beauty. I find geometry to be beautiful. Uh, you have, uh, m- a few examples that are geometric in nature in, in your book.

Lex Fridman 20:04 Uh, how can geometry in ancient times or today be used to understand reality? And maybe how do you think about geometry as a distinct tool in mathematics and physics?

Cumrun Vafa 20:17 Yes, geometry is my favorite part of math as well, and Greeks were enamored by geometry. They tried to describe physical reality using geometry and principles of geometry and symmetry. Platonic solids, the five solids they had, uh, discovered, had these beautiful solids. They thought, "It must be good for some reality. They, they must be explaining something." They attached, you know, one to air, one to fire, and so forth. So they tried to give physical reality to symmetric objects.

Lex Fridman 20:44 Mm-hmm.

Cumrun Vafa 20:45 These symmetric objects or symmetries of rotation, and this great symmetry groups we call today a rotation group in three dimensions. Now, we know now, we kind of laugh at the way they were trying to connect that symmetry to, you know, the laws of the, the, the realities of, of physics. But actually, it turns out mo- in modern days, we use symmetries in not too far away exactly in these kind of thoughts processes in the following way. In the co- in the context of string theory, which is this, The Field I Study, we have these extra dimensions. And these extra dimensions are compact, tiny spaces typically, but they have different shapes and sizes. We have learned that if you, if these extra shapes and sizes have symmetries, which are related to the same rotation symmetries that the Greek were talking about, if they enjoy those discrete symmetries, and if you, if you take that symmetry and caution the space by a- in other words, identify points under these symmetries, you get properties of that space at the singular points which force emanates from them.

Lex Fridman 21:50 Mm-hmm.

Cumrun Vafa 21:51 What forces? Forces like the ones we have seen in nature today, like electric forces, like strong forces, like weak forces. So these same principles that was, were driving them to connect geometry and symmetries to nature is driving today's physics now much more, you know, modern ideas. But nevertheless, the symmetries connecting geometry to physics. In fact, often we s- sometimes we have, we ask the following question. Suppose I want to get this particular, you know, physical reality. I wanna have this particles with these forces and so on. What do I do? It turns out that you can geometrically design the space to give you that. You say, "Oh, I will put the sphere here. I will do this. I will shrink them." So if you have two spheres touching each other, and shrinking to, m- to zero size, that gives you strong forces. If you have one of them, it gives you the weak forces. If you have this, you get that. And if you want to unify forces, do the other thing. So these geometrical translation of physics is, is one of my favorite things that we have discovered in, in modern physics in the context of string theory.

Lex Fridman 22:57 The sad thing is when you go into multiple dimensions, and w- we'll talk about it, is we start to lose our capacity to, uh, visually intuit the world we're discussing, and then we go into the realm of mathematics, and we lose that. Unfortunately, our brains are such that we're limited. But

Lex Fridman 23:16 before we go into that mysterious beautiful world-

Cumrun Vafa 23:18 (laughs)

Lex Fridman 23:19 ... let, let's take a small step back, and you also in your book have this kinda through the space of puzzles, through the space of ideas, have a brief history of physics, of physical ideas. Now, we, we, we talked about Newtonian mechanics, uh, leading all through different, like Lagrangian, Hamiltonian mechanics. Can you describe some of the key ideas in the history of physics? Maybe lingering on each from, uh, electromagnetism, to relativity, to quantum mechanics, and to today as we'll talk about with quantum gravity and string theory.

Cumrun Vafa 23:52 Sure. So, um, I mentioned the classical mechanics and the other Lagrange formulation. Uh, one of the next, uh, important milestones for physics were, uh, the discoveries of laws of electricity and magnetism. So Maxwell put, put the discoveries all together in the context of what we call the Maxwell's equations.... and he noticed that when he put these discoveries that, you know, Faraday and others had made, uh, about electric and magnetic phenomena, the, in terms of mathematical equations, it didn't quite work. There was a mathematical inconsistency. Now, uh, you know, one could have two attitudes. One could say, "Okay, who cares about math? I'm doing nature and electric force, magnetic force. Math, I don't care about." But it bothered him. It was inconsistent. The equations he were writing, the two equations he had written down did not agree with each other, and this bothered him. Uh, but he figured out, you know, if you add this, jiggle this, uh, equation by adding one little term there, it works. At least it's consistent. What is the motivation for that term? He said, "I don't know. Have we seen it in experiments? No."

Narrator 24:56 (laughs)

Cumrun Vafa 24:57 Why did he add it? Well, because of mathematical consistency. So he said, okay, math forced him to this, do this term. He added this term, which we now today call the Maxwell term, and once he added that term, his equations were nice, you know, differential equations, mathematically consistent, beautiful, but he also found a new physical phenomena. He found that because of that term, he could now get electric and magnetic waves moving through space at a speed that he could calculate. So he calculated the speed of the wave, and lo and behold, he found it's the same as the speed of light, which puzzled him, because he didn't think light had anything to do with electricity and magnetism. But then he was courageous enough to say, "Well, maybe light is nothing but these electric and magnetic fields moving around." And he didn't, he, he wasn't alive to see the verification of that prediction, and indeed it was true. So this mathematical inconsistency, which, which we could say, you know, this mathematical beauty, drove him to this physical very important connection between light and electric and magnetic phenomena, which was later confirmed. So then physics progresses,

Cumrun Vafa 26:09 and it comes to Einstein. Einstein looks at Maxwell's equation, says, "Beautiful. These are nice equations, except we get one speed light."

Narrator 26:17 Yeah.

Cumrun Vafa 26:18 Uh, who, who measures this light speed? And he asks the question, "Are you on, are you moving? Are you not moving? If you move, the speed of light changes, but Maxwell's equation has no hint of different speeds of light." It doesn't say, "Oh, only if you're not moving, you get this speed." It's just, you always get this speed. So Einstein was very puzzled, and he, he was daring enough to say, "Well, you know, maybe everybody get the same speed for light."

Narrator 26:40 Yeah.

Cumrun Vafa 26:41 And that motivated his theory of special relativity, and this is an interesting example, because the idea was motivated from physics, from Maxwell's equations, from the fact that people tried to, uh, try to measure the properties of ether, which was supposed to be the medium in which the light travels through. And the idea was that only in that, in that medium, the speed is speed of... if you're at rest with respect to the ether, this speed is speed of light, and if you're moving, the speed changes. And people did not discover it. Michelson and Morley's experiment showed there is no ether. So, uh, then Einstein was courageous enough to say, "You know, light is the same speed for everybody, regardless of whether you're moving or not." And the interesting thing is, about special theory of relativity, is that under, the math underpinning it is very simple. It's linear algebra, nothing terribly deep. You can teach it at a high school level, if not earlier. Okay, is, does that mean Einstein's special relativity is boring? Not at all. So this is an example where simple math, you know, linear algebra, leads to deep physics. Einstein's theory of special relativity, motivated by this inconsistency that Maxwell equation would suggest for the speed of light, depending on who observes it.

Narrator 27:59 What's the most daring idea there? That, that, uh, the speed of light could be the same everywhere.

Cumrun Vafa 28:04 That's the basic, that's the guts of it. That's the core of Einstein's theory. That statement underlies the whole thing. Speed of light is the same for everybody is hard to swallow, and it doesn't sound right. It sounds completely wrong, on the face of it. And it was, it took Einstein to make, to make this, the daring statement. It would, it would be, it would be laughing in some sense. How could possibly, how could anybody make this possibly ridiculous claim? And it turned out to be true.

Narrator 28:27 How does that make you feel? 'Cause it, it, it still sounds ridiculous. (laughs)

Cumrun Vafa 28:31 It, it sounds ridiculous until you learn that our intuition is at fault about the way we conceive of space and time. The way we think about space and time is wrong, because we think about the nature of time as absolute.

Narrator 28:43 Yeah.

Cumrun Vafa 28:43 And part of it is because we live in a situation where we don't go with very high speeds, that our speeds are small compared to the speed of light, and therefore the phenomena we, we observe does not distinguish the relativity of time. The time also depends on who measures it. There's no absolute time. When you say it's noon today now, it depends on who's measuring it, and it, it, not everybody would agree with that statement. And to see that, you would have to have fast observer moving, you know, speeds close to the speed of light. So, so this shows that our intuition is at fault, and a lot of the discoveries in physics precisely is getting rid of the wrong old intuition. And it is funny, because we get rid of it, but it's, always lingers in us in some form.

Narrator 29:28 (laughs)

Cumrun Vafa 29:28 Like, even when I'm describing it, I feel like a little bit-

Narrator 29:31 Yeah.

Cumrun Vafa 29:31 ... like isn't it, you know, funny?

Narrator 29:33 (laughs)

Cumrun Vafa 29:33 As you're just feeling the same way. It is.

Narrator 29:35 Yes.

Cumrun Vafa 29:35 It is. But we kind of replace it by an intuition. And actually, there's a very beautiful example of this, how physicists do this, try to replace their intuition,

Cumrun Vafa 29:46 and I think this is one of my favorite examples about how physicists develop intuition. It goes to the work of Galileo. So, you know, again, uh, let's go back to Greek philosophers, or maybe Aristotle in this case. Now, again, let- let's make a criticism. He thought that objects, uh, the heavier objects fall faster than the lighter objects.

Narrator 30:06 Mm-hmm. Makes sense.

Cumrun Vafa 30:07 It kind of makes sense, and, you know, people say about the feather and so on, but that's because of the air resistance, but you might think, like, if, if you have a heavy stone and a light pebble...... the heavy one will fall first. If you don't, you know, do any experiments, that's the first gut reaction. I would say everybody would say that's the natural thing. Galileo did not believe this, and he kind of, um, uh, did the experiment. Uh, famously it's said he went on the top of Pisa Tower and he dropped, you know, these heavy and light stones, and they fell at the same time when they- he dropped it at the same time, from the same height. Okay, good. So he said, "I'm done." You know? "I've showed that the heavy and lighter objects fall at the same time. I did the experiment." Scientists at that time did not accept it. Why was that? It's because at that time, science was not just experimental. The experiment was not enough. They didn't think that they have to soil their hands in doing experiments to get to the reality. They said, "Why is it the case?"

Lex Fridman 31:03 Why? Yes.

Cumrun Vafa 31:04 So Galileo had to come up with an explanation of why heavier and lighter objects fall at the same rate. This is the way he convinced them, using symmetry.

Lex Fridman 31:13 (laughs)

Cumrun Vafa 31:13 He said, "Suppose you have three bricks, the same shape, the same size, same as everything, and we hold these three bricks at the same height and drop them. Which one will fall to the ground first?" Everybody said, "Of course, we know it's symmetry that tells you. You know, they are all the same shape, same size, same height. Of course, they fall at the same time." Yeah, we know that. Next, next.

Lex Fridman 31:38 (laughs)

Cumrun Vafa 31:38 It's trivial. He said, "Okay, what if we move these bricks around with the same height? Does it change the time they hit the ground?" They said, "If it's the same height," again by the symmetry principle, because the height translation, horizontal translation is a symmetry, "no, it doesn't matter. They all fall at the same rate." Good. "Does it matter how close I bring them together? No, it doesn't." Okay. "So once I to- make the two bricks touch and then let them go, do they fall at the same rate? Yes, they do." But then he says, "Well, the two bricks that touch are twice more mass than this other brick."

Lex Fridman 32:07 Yeah.

Cumrun Vafa 32:07 "And you just agreed that they fall at the same rate." They say, "Yeah, yeah, we just agreed. That's right. That's great."

Lex Fridman 32:11 (laughs)

Cumrun Vafa 32:12 Yes. So he de-confused them by dystrophy reasoning. So this way of repackaging some intuition, a different pa- intuition.

Lex Fridman 32:19 Yeah.

Cumrun Vafa 32:19 When the intuitions clash, then you, then you side on the ... You replace the intuition.

Lex Fridman 32:25 That's brilliant. I, I, in some of these diff- more difficult physical ideas, physics ideas in the 20th century and the 21st century, it starts becoming more and more difficult to then replace the intuition. You know, what, what does the world look like for an object traveling close to the speed of light? Y- you start to think about like the edges of super massive black holes, and you start to think like, "What, what's that look like?" Or, uh, I've been re- uh, into gravitational waves or something. (laughs)

Cumrun Vafa 32:55 (laughs)

Lex Fridman 32:55 It's like when the fabric of space-time is being morphed by gravity, like what's that actually feel like? If I'm riding a gravitational wave, what's that feel like? (laughs)

Cumrun Vafa 33:07 (laughs)

Lex Fridman 33:08 Um, I mean, I think some of those are more sort of hippie, not useful, uh, intuitions to have. But if you're an actual physicist or whatever the particular discipline is, I wonder if it's possible to meditate, to sort of, um, escape through thinking, prolonged thinking and meditation on a wo- on a world. Like, live in a visualized world that's not like our own in order to understand a phenomena deeply. So like replace the intuition, like through rigorous meditation on the idea in order to conceive of it. I mean, if we talk about multiple dimensions, I wonder if there's, um, a way to escape of the three-dimensional world in our mind in order to then start to reason about it. It's, uh ... The more I talk to topologists, (laughs) the more they seem to not operate at a- at all in the visual space. They really trust the mathematics. Like, which is really annoying to me because topology and differential geometry feels like it has a lot of potential for beautiful pictures. (laughs)

Cumrun Vafa 34:17 Yes, I think it, they do. Actually, in, uh, I would not be able to, uh, do my, my research if I don't have an intuitive feel about geometry.

Lex Fridman 34:25 Mm-hmm.

Cumrun Vafa 34:26 And, uh, I will get to it, as you mentioned late- uh, before that, uh, how, for example, in string theory, you deal with these extra dimensions. And I'll be very happy to describe how we do it, because without intuition, we will not get anywhere. And I, I don't think you can just rely on formalism. I don't.

Lex Fridman 34:41 Mm-hmm.

Cumrun Vafa 34:41 I don't think any physicist just relies on formalism. That's not physics. That's not understanding. So we have to intuit it, and that's crucial, and this, there are steps of doing it, and we learn it might not be trivial, but we learn how to do it. Similar to what this Galileo picture I just told you, you have to build these gradually.

Lex Fridman 34:59 (laughs) You have to connect the bricks. (laughs)

Cumrun Vafa 35:00 But, but it ... You have to connect the ... (laughs) Yeah, exactly. You have to connect the bricks.

Lex Fridman 35:03 (laughs)

Cumrun Vafa 35:03 Literally.

Lex Fridman 35:04 Yeah. (laughs)

Cumrun Vafa 35:04 So yeah, so then, uh, so going back to your question about the his- uh, the path of the history of the science. So I was saying about the electricity and magnetism and the special relativity, where simple idea re- led to special relativity. But then he went further, thinking about acceleration in the context of, uh, relativity, and he came up with general relativity, where he talked about, you know, the fabric of space-time being curved and so forth, and matter affecting the, the, the curvature of the space and time. So, so this gradually became a, uh, uh, a connection between geometry and physics. Namely, he replaced Newton's, you know, uh, gravitational force with a very geometrical beau- beautiful picture. It's much more elegant than Newton's, but much more complicated mathematically. So, so when we say simpler, we mean in some form it's simpler, but not in pragmatic terms of equation solving. The equations are much harder to solve in Einstein's theory, and, and in fact so much, so much harder that Einstein himself couldn't solve many of his, many of the cases. He thought, for example, you couldn't solve the equation for a spherical symmetric matter. Uh, like, like if you had a symmetric sun, he didn't think you can actually write the, solve this equation for that. And a year after he, he said that, it was solved by, by Schwarzschild. So it was-

Lex Fridman 36:20 For f-

Cumrun Vafa 36:20 ... it was that hard that-

Lex Fridman 36:21 Yes.

Cumrun Vafa 36:21 ... he didn't think it's gonna be that easy. So yeah, the formalism is hard. But the contrast between the special relativity and general relativity is very interesting, because one of them has almost trivial math-

Lex Fridman 36:31 Mm-hmm.

Cumrun Vafa 36:31 ... and the other one has super complicated math.

Lex Fridman 36:34 Yeah.

Cumrun Vafa 36:34 ... both are physically amazingly important. And so, so we have learned that, you know, the physics, uh, may or may not require complicated math. We should not shy from using complicated math like Einstein did. Nobody ... Einstein wouldn't say, "I'm not gonna touch this math because it's too much, you know, tensors or, you know, curvature and I don't like four-dimensional space time because I can't see four dimension." He wasn't doing that. He was willing to abstract from that because physics drove him in that direction. But his motivation was physics. Physics pushed him. Just like Newton pushed to de- develop calculus because physics pushed him, that he didn't have the tools so he had to develop the tools to answer his physics questions. So his motivation was physics again. So to me, those are examples which show that math and physics have this symbiotic reali- relationship, which, which kind of reinforce each other. Here, I'm using ... I'm giving you examples of both of them, namely Newton's work led to development of mathematics, calculus. And in the case of Einstein, he didn't develop Riemannian geometry, he just used them. So, so it goes both ways. And in the context of modern physics, we see that again and again it goes both

Cumrun Vafa 37:44 ways.

Lex Fridman 37:44 Let me ask a ridiculous question. Uh, you know, you talk about your favorite soccer player at a bar. I- I- I'll ask the same question about Einstein's ideas, which is, um, which one do you think is the biggest leap of genius? Is it the, uh, E=MC2? Is it Brownian motion? Is it special relativity? Is it general relativity? Which, which, uh, of, of the famous set of papers he's written in 1905 and in general his work, was the biggest leap of genius?

Cumrun Vafa 38:13 In my opinion, it's special relativity. The idea that speed of light is the same for everybody is the beginning of everything he did.

Lex Fridman 38:20 The beginning is the seed.

Cumrun Vafa 38:21 The beginning is the seed.

Lex Fridman 38:22 O- once you embrace that weirdness-

Cumrun Vafa 38:24 Yes, yes.

Lex Fridman 38:24 ... all the weirdness, all the rest

Narrator 38:25 (laughs)

Cumrun Vafa 38:25 I would say that's, that's ... Even though he says the most beautiful moment for him-

Lex Fridman 38:29 Yes.

Cumrun Vafa 38:29 ... he says it is when he realized that if you fall in an elevator, you don't know if you're falling or whether you're ... In the ... Whether you're in the falling elevator or whether you're ne- next to the earth's gravitational field.

Lex Fridman 38:39 Mm-hmm.

Cumrun Vafa 38:39 That, that to him was his aha moment, which inertial mass and gravitational mass being identical geometrically and so forth as part of the theory, not because of, uh, you know, some m- some, uh, funny coincidence. Uh, that's for him. But I feel, from outside at least, it feels like the speed of light being the same is the, is the really aha moment.

Lex Fridman 38:59 The general relativity to you is not, like, uh, the c- c- conception of space time.

Cumrun Vafa 39:05 In a sense, the conception of space time already was part of special relativity when you talk about length contraction.

Lex Fridman 39:10 Hmm.

Cumrun Vafa 39:10 So general relativity takes that to the next step. But beginning of it was already space length contracts, time dilates. So once you talk about those, then yeah, you can dilate more or less different places, then it's curvature. So you don't have a choice. So it kind of started, uh, just with that same simple thought, speed of light is the same for all.

Lex Fridman 39:28 Where does, uh, quantum mechanics come into view?

Cumrun Vafa 39:32 Exactly. So this is the next step. So Einstein's, you know, uh, developed general relativity and he's beginning to develop the foundation of quantum mechanics at the same time, the photoelectric effects on others. And, um, so, so quantum mechanics overtakes, in fact, Einstein in many ways, because he doesn't like the probabilistic interpretation of quantum mechanics and the formulas that's emerging. But physicists march on, and, uh, try to, for example, combine Einstein's theory of relativity with quantum mechanics. So, Dirac takes special relativity, tries to see how is it compatible with quantum mechanics.

Lex Fridman 40:07 Can we pause and briefly say what is quantum mechanics?

Cumrun Vafa 40:10 Oh, yes, sure. So quantum mechanics ... Uh, so I, I, I discussed briefly when I talked about the connection b- between Newtonian mechanics and, uh, or the Lagrange reformulation of, of the Newtonian mechanics and interpretation of this or the Lagrange, uh, formalism in terms of the paths that the particle take. So when we say a particle goes from here to here, we usually think it ... Classically, it f- follows a specific trajectory. But actually, in quantum mechanics, it falls, follows every trajectory with different probabilities. And so there's this fuzziness. Now, most probable, it's the path that you actually see.

Lex Fridman 40:49 Mm-hmm.

Cumrun Vafa 40:49 And deviation from that is very, very unlikely and probabilistically very minuscule, so in everyday experience, we don't see anything deviated from what we expect. But quantum mechanics tells us that, that things are more fuzzy, things are, are not as s- precise as the line you draw, things are a bit like cloud. So if you go to microscopic, uh, scales, like atomic scales and lower, these phenomena become more pronounced, you can see it much better. The electron is, is not at a point, but the cloud spread out around the nucleus. And so this fuzziness, this probabilistic aspect of reality is what quantum mechanics, uh, describes.

Lex Fridman 41:28 Can I briefly pause on that, on that idea? Do you think this is, uh, quantum mechanics is just a really damn good approximation, a, a tool for predicting reality, or does it actually describe reality? Do you think reality is fuzzy at that level?

Cumrun Vafa 41:45 Well, I think that reality is fuzzy at that level, but I don't think quantum mechanics is necessarily the end of the story.

Lex Fridman 41:51 Right.

Cumrun Vafa 41:51 So, um, so quantum mechanics is certainly an improvement over classical physics, that much we know by experiments and so forth. Whether I'm happy with quantum mechanics, whether I view quantum mechanics ... For example, the, the thought, the measurement, uh, description of quantum mechanics, am I happy with it? Am I thinking that's the end stage or not? I don't. I don't think we are at the end of that story, and many physicists may or may not view this way. Some do, some don't. But I think that, uh, it's the best we have right now. That's for sure. It's the best approximation for reality we know today. And so far, we don't know what it is, the next thing that-

Lex Fridman 42:28 Mm-hmm.

Cumrun Vafa 42:28 ... improves it or replaces it and so on. So but as I mentioned before, I don't believe any of the laws of physics we know today are-

Lex Fridman 42:35 This is the end of the story. (laughs)

Cumrun Vafa 42:35 ... perfectly exactly correct. That doesn't bother me.

Lex Fridman 42:37 Yes.

Cumrun Vafa 42:38 I'm not like dogmatic and say, "I have figured out this is the law of nature. I know everything." No.No. That's, that's... The, the beauty about science is that we are not dogmatic and we are, we are willing to... In fact, we are encouraged to s- be skeptical of, of what we ourselves do.

Lex Fridman 42:54 So you were talking about Dirac?

Cumrun Vafa 42:55 Yes, I was talking about Dirac, right. So Dirac was trying to now combine this Schrodinger's equations which, which was described in the context of, you know, trying to talk about how these probabilistic waves of electrons move for the atom which was good for i-... for speeds which were not too close to the speed of light, to what happens when you get to the near the speed of light. So then you need relativity, so then Dirac tried to combine Einstein's relativity with quantum mechanics. So he tried to combine them and, uh, he wrote this beautiful equation, the Dirac equation, which roughly speaking take the square root of, of the Einstein's equation in order to connect it to Schrodinger's time evolution operator which is first order in time derivative to get rid of the, the naive thing that Einstein's equation would have given, which is second order, so you have to take a square root. Now square root usually has a plus or minus sign when you take it. And when he did this, he originally didn't notice this pos-... didn't pay attention to this plus or minus sign but later physicists pointed out to Dirac, says, "Look, there's also this minus sign and if you use this minus sign, you get negative energy." In fact, uh, it was very, very annoying that, you know, somebody else tells you this obvious mistake you make. Pauli, famous physicist, told Dirac, "This is nonsense. You're going to get negative energy with your equation, which negative energy without any bottom. You can go all the way down to negative infinite energy, so it doesn't make any sense." Dirac thought about it and then he remembered Pauli's exclusion principle. Bef- just before him, Pauli had said, "You know, there's this principle called the exclusion principle that, you know, two or-... two electrons cannot be on the same orbit."

Lex Fridman 44:29 Mm-hmm.

Cumrun Vafa 44:30 And so Dirac said, "Okay, you know what? All these negative energy states are filled orbits, occupied. So according to you, uh, uh, Mr. Pauli, uh, there's no- no place to go, so therefore they only have to go positive." Sounded like a big cheat.

Lex Fridman 44:48 (laughs)

Cumrun Vafa 44:49 And then Pauli said, "Oh, you know what? We can change orbits from one orbit to another. What if I take one of these negative energy orbits and put it up there? Then it seems to be a new particle which has opposite properties to the electron. It has positive energy but it has positive charge. What is that?" Elec-... uh, Dirac was a bit worried, he said, "Maybe that's proton? Because proton has plus charge." He wasn't sure. But then he said, "Oh, maybe it's proton." But then they said, "No, no, no, no. It has the same mass as the electron. It cannot be proton because proton is heavier." Dirac was stuck. He says, "Well, then may- may- maybe another particle we haven't seen." By that time, Dirac himself was getting a little bit, uh, worried about his own equation and his own crazy interpretation.

Lex Fridman 45:34 (laughs) Yes.

Cumrun Vafa 45:34 Until a few years later, Anderson, in photographic cosmic, uh... I mean, the photographic plates that he had gotten from these cosmic rays, he discovered a, a particle which goes in the opposite direction that the electron goes when there's a magnetic field and with the same mass, exactly like what Dirac had predicted. And this was what we call now positron, and in fact beginning with the work of Dirac, we know that every particle has an antiparticle. And so this idea that there's an antiparticle came from the simple math, you know, there's a plus and a minus from the Dirac's quote-unquote mistake. So again, trying to combine ideas, sometimes the math is smarter than the person who uses it to ap- apply it...

Lex Fridman 46:20 Yeah.

Cumrun Vafa 46:20 ... and you try to resist it and then you, you're kind of confronted by criticism which is the way it should be. So a physicist comes and says, "No, no, that's wrong," and he correct it and so on. So that is a development of the idea there's particle, there's antiparticle and so on. So this is the beginning of development of quantum mechanics and the connection with relativity, but the thing was more challenging because we had to also describe how electric and magnetic fields work with quantum mechanics.

Lex Fridman 46:44 Mm-hmm.

Cumrun Vafa 46:44 This was much more complicated because it's not just one point. Electric and magnetic fields were everywhere, so you had to talk about fluctuating and a fuzziness of electrical field and magnetic fields everywhere, and the math for that was, was, was very difficult to deal with. And this led to a subject called quantum field theory. Fields, and like electric and magnetic fields had to be quantum, had to be described also in a wavy way. Feynman in particular was one of the, uh, pioneers and along with Schwingers and others to try to come up with a formalism to deal with fields, like electric and magnetic fields, interacting with electrons in a consistent quantum fashion and they dis- developed this beautiful theory, quantum electrodynamics from that. And later on that same formalism, quantum field theory, led to the discovery of other forces and other particles all consistent with the idea of quantum mechanics. So that was how, uh, physics progressed and so basically we learned that all particles and all the forces, uh, are, are in some sense related to particle exchanges. And so for example, electromagnetic forces are, are mediated by a particle we call photon...

Lex Fridman 47:55 Mm-hmm.

Cumrun Vafa 47:55 ... and, uh, and so forth, and same for other forces that they discovered, strong forces and the weak forces. So, so we got the sense of what quantum field theory is.

Lex Fridman 48:03 Is that a big leap of, uh, of an idea that, uh, particles are fluctuations in a field? Like, uh, the idea that everything is a field? Is, is the old Einstein light is a wave, both a particle and a wave, kind of idea, is that a huge leap in our understanding of conceiving the universe's fields?

Cumrun Vafa 48:26 I would say so. I would say that on viewing the particles, this duality that Bohr mentioned between particles and waves, that waves can behave sometimes like particles, sometimes like waves, is one of the biggest, uh, leaps of, uh, imagination that quantum mechanics m- made physics do. So I, I agree that that is quite remarkable.

Lex Fridman 48:45 Is duality fundamental to...... to the universe or is it just because we don't understand it fully? Like, will it eventually collapse into a clean explanation that doesn't require duality? Like, the- the- the- that- that a phenomena could be two things at once and both to be true. So, that seems weird.

Cumrun Vafa 49:06 So in fact, I- I- I was going to get to that when we get to string theory, but maybe I can comment on that now.

Lex Fridman 49:10 Mm-hmm.

Cumrun Vafa 49:11 Duality turns out to be running the show today, and it's the whole thing that we are doing in string theory.

Lex Fridman 49:15 (laughs)

Cumrun Vafa 49:15 Duality is the name of the game. So it's a most beautiful subject and I want to talk about it-

Lex Fridman 49:20 Let- let- let's talk about it in the context of string theory then.

Cumrun Vafa 49:22 Let's talk about it in the context of string theory, yes.

Lex Fridman 49:23 So, so we, uh, do we want to take a next step into ... 'cause we mentioned general relativity, we mentioned quantum mechanics.

Lex Fridman 49:30 Is there something to be said about quantum gravity?

Cumrun Vafa 49:32 Yes. That's exactly the right point to talk about. So namely, we have talked about quantum fields, and I talked about electric forces, photon being the particle carrying those forces. So for gravity, quantizing gravitational field, which is this coverage of space time according to Einstein, you get another particle called graviton. So, what about gravitons?

Lex Fridman 49:55 (laughs)

Cumrun Vafa 49:55 Should be there, no problem. So then you start computing it. What do I mean by computing it? Well, you compute scattering of one graviton off another graviton, maybe a graviton with an electron, and so on, see what you get. Feynman had already mastered the- this, uh, quantum electrodynamics. He said, "No problem, let me do it." Even though these are such weak forces-

Lex Fridman 50:17 Mm-hmm.

Cumrun Vafa 50:17 ... the gravity is very weak, so therefore to see them, these quantum effects of gravitational waves is, was impossible. It's even impossible today. So Feynman just did it for fun. He, he usually, you know, had this mindset that I want to do something which I will see an experiment, but this one, let's just see what it does. And he was surprised because the same techniques he was using for doing, uh, the same calculations, quantum electrodynamics, when applied to gravity, failed. The formulas seemed to make sense, but he had to do some integrals and he found that when he does those integrals, he got infinity.

Lex Fridman 50:49 Mm-hmm.

Cumrun Vafa 50:51 And it didn't make any sense. Now, there were similar infinities in the other pieces that, but he had managed to make sense out of those before. This was no way he could make sense out of it. He just didn't know what to do. He didn't feel it's an urgent issue because nobody could do the experiment, uh, so he was kind of said, "Okay, there's this thing but okay, we don't know how to exactly do it, but, but that's the way it is." So in some sense, a natural conclusion from what Feynman did could have been like, gravity cannot be consistent with quantum theory.

Lex Fridman 51:19 Mm-hmm.

Cumrun Vafa 51:19 But that cannot be the case, because gravity is in our universe, quantum mechanics in our universe. They both together somehow should work.

Lex Fridman 51:25 Yeah.

Cumrun Vafa 51:25 So it's, it's not acceptable to say you don't, they don't work together. So, so that was a puzzle. How does it possibly work? It was left open. And then we get to the string theory. So this is the puzzle of quantum gravity. The particle description of quantum gravity failed.

Lex Fridman 51:41 So the infinity shows up, what do we do, wh- what do we do with the infinity?

Lex Fridman 51:45 Let's get to the fun part. Let's talk about string theory. (laughs)

Cumrun Vafa 51:48 Yes.

Lex Fridman 51:50 Uh, let's, uh, discuss some technical basics of, uh, string theory. What is string theory? What is a string? How many dimensions are we talking about? What are the different states?

Cumrun Vafa 52:02 (laughs) Yeah.

Lex Fridman 52:02 How do we represent the elementary particles and, uh, the laws of physics using this new framework?

Cumrun Vafa 52:09 So, string theory, uh, is the idea that the fundamental entities are not particles but extended higher dimensional objects, like one-dimensional strings. Like loops. These loops could be open like, uh, with two ends, like an interval, or a circle without any ends. So, and they're vibrating and moving around in space. So, how big they are? Well, you can of course stretch it and make it big or you can just let it be whatever it wants. It can be as small as a point because the c- circle can shrink to a point and be very light, or you can, you know, stretch it and becomes very massive, or it could oscillate and become massive that way. So depends on which kind of state you have. In fact, the string can have infinitely many modes depending on which kind of oscillation it's doing. Like a guitar has different harmonics, string has different harmonics. But for the string, each harmonic is a particle, so each particle will give you, ah, this is a more massive harmonic, (laughs) this is a less mass. So the lightest harmonics, so to speak, is no harmonics, which means like the string shrunk to a point-

Lex Fridman 53:12 Mm-hmm.

Cumrun Vafa 53:12 ... and then it becomes like a massless particles or light particles like photon and graviton and so forth. So when sh- when you look at tiny strings which are shrunk to a point, the lightest ones, they look like the particles that we, we think, they are like particles. In other words, from far away they look like a point, but of course if you zoom in, there's this tiny little, you know, little circle that's there that's shrunk to almost a point.

Lex Fridman 53:37 Should we be imagining, this is to the visual intuition, should we be imagining literally strings that are potentially connected as a loop or not? When you and when somebody outside of physics is imagining a basic element of string theory which is a string, should we literally be thinking about a string?

Cumrun Vafa 53:58 Yes. You should literally think about string, but string with zero thickness.

Lex Fridman 54:02 With zero thickness.

Cumrun Vafa 54:04 So now it's, it's a, it's a, it's a loop of energy so to speak.

Lex Fridman 54:07 Mm-hmm.

Cumrun Vafa 54:07 If you can think of it that way, and so there's a tension like a regular string, if you pull it there's a, you know, you have to, you have to stretch it. But it's not like a thickness like made of something. It's just energy. It's not made of atoms or something like that.

Lex Fridman 54:19 But it is very, very tiny.

Cumrun Vafa 54:21 Very tiny.

Lex Fridman 54:22 Much smaller than, uh, elementary particles of physics.

Cumrun Vafa 54:25 Much smaller. So we think if you let the string to be by itself, the lower state, there will be like fuzziness or a size of that tiny little circle which is like a point-

Lex Fridman 54:34 Mm-hmm.

Cumrun Vafa 54:35 ... about could be anything between ... We don't know exact size but in different models have different sizes, but something of the order of 10 to the minus, let's say, 30 centimeters. So 10-

Lex Fridman 54:45 Phew.

Cumrun Vafa 54:45 ... to the minus 30 centimeters just to compare with the size of the atom which is 10-8 centimeters is 22 orders of magnitude smaller.... so, so-

Lex Fridman 54:54 Unimaginably small, I would say.

Cumrun Vafa 54:56 Very small, very small. So we, we basically think from far away, string is like a point particle.

Lex Fridman 55:00 Yeah.

Cumrun Vafa 55:00 And that's why a lot of the things that we learned about point particle physics carries over directly to strings.

Lex Fridman 55:06 Mm-hmm.

Cumrun Vafa 55:07 So therefore, there's not, not much of a mystery why particle physics was successful, because a string is like a particle when it's not stretched. But it turns out having this size, being able to oscillate, get bigger, turned out to be resolving these puzzles that Feynman was having in calculating his diagrams, and it gets rid of those infinities. So when you are trying to do those infinities, the regions that give infinities to Feynman, as soon as you get to those regions, then the s- string starts to oscillate, and these oscillation structure of the strings resolves those infinities to finite answer at the end. So, s- the size of the string, the fact that it's one dimensional gives a finite answer at the end, resolves this paradox.

Lex Fridman 55:49 Mm-hmm.

Cumrun Vafa 55:50 Now, perhaps it's also useful to recount of how string theory came to be.

Lex Fridman 55:55 Yes.

Cumrun Vafa 55:56 Because it wasn't like l- somebody said, "Well, let me f- solve the problem of Einstein's, eh, s- solve the problem that Feynman had with unifying Einstein's theory with quantum mechanics by replacing the point by a string." No, that's not the way, the thought process. The thought process was much more random. Physicist, Lencioni in this case, was trying to describe the interactions they were seeing in colliders, in, in accelerators.

Lex Fridman 56:21 Mm-hmm.

Cumrun Vafa 56:22 And they were seeing that some process, in some process when two particles came together and joined together, and when they were separately, in one way, and the opposite way, they behaved the same way. In some way there was a symmetry, a duality, which he didn't understand. The particles didn't seem to have that symmetry. He said, "I don't know what it is, what's the reason that these colliders and experiments were doing seems to have this symmetry, but let me write the mathematical formula which exhibits that symmetry." He used gamma functions, beta functions and all that, you know, complete math, no physics, other than trying to get symmetry out of his equation. He just wrote down a formula as the answer for a process.

Lex Fridman 57:03 Mm-hmm.

Cumrun Vafa 57:03 Not, not a method to compute it. Just say, "Wouldn't it be nice if this was the answer?"

Lex Fridman 57:07 (laughs) Yeah, yes.

Cumrun Vafa 57:09 Physicists looked at this formula, "Hmm, that's intriguing. It has this symmetry, all right, but what is this? Where is this coming from? Which, which kind of physics gives you this?"

Lex Fridman 57:16 Mm-hmm.

Cumrun Vafa 57:17 S- I don't know.

Lex Fridman 57:18 (laughs) Yeah.

Cumrun Vafa 57:19 A few years later, people saw that, oh, the equation that you're write, the process that you're writing in the intermediate channels that particles come together seems to have all the harmonics.

Lex Fridman 57:30 Mm-hmm.

Cumrun Vafa 57:30 Harmonics sounds like a string. Let me see if what you're describing has anything to do with the strings, and people tried to see if what he's doing has to do with the strings. They said, "Oh, yeah, indeed, if I study s- scattering of two strings, I get exactly the formula you wrote down." That was the reinterpretation of what he had written in the formula as the strings. But still had nothing to do with gravity. It had nothing to do with resolving the problems of gravity with quantum mechanics. It was just trying to explain a process that people were seeing in hadronic physics collisions. So it took a few, a few more years to get to that point. They, they, they noticed that, uh, physicists noticed that whenever you try to find the spectrum of strings, you always get a massless particle which has exactly the properties that a graviton is supposed to have. And no particle in hadronic physics that had that property. You are getting a massless graviton as part of the scattering without looking for it. It was forced on you. People were not trying to solve quantum gravity, quantum gravity was pushed on them. I don't want this graviton, get rid of it. They couldn't get rid of it. They gave up trying to get rid of it. Physicists said, Sherik and Schwarz said, "You know what? String theory is a theory of quantum gravity." They changed their perspective altogether. We are not describing the hadronic physics, we're describing this theory of quantum gravity.

Lex Fridman 58:49 And that's when string theory probably got, uh, like, um, exciting, that this could be the unifying theory.

Cumrun Vafa 58:56 Exactly. It got exciting, but at the same time, not so fast. Namely, it should have been fast, but it wasn't, because particle physics, through quantum field theory, were so successful at that time. This is mid '70s. Standard model of physics, electromagnetism and unification of electromagnetic forces with all the other forces were beginning to take place without the gravity part. Everything was working beautifully for particle physics, and so that was the shining golden age of quantum field theory and all the experiments, standard model, this and that, unification, and spontaneous symmetry breaking was taking place, all of them was nice. This was kind of like a side show and nobody was paying so much attention. This exotic string is needed for quantum gravity? Ah, maybe there's other ways, maybe we should do something el- So yeah, it wasn't paid much attention to, and, uh, this took a little bit more effort, to try to actually connect it to, to re- reality. There were t- few more steps. First of all, there was a puzzle that you were getting extra dimensions. String was not working well with three spatial dimensions on one time, it needed extra dimension. Now, uh, there are different versions of strings, but the version that ended up being related to f- to having particles like electron, what we call fermions needed 10 dimensions, what we call superstring. Now, why super? Why the word super? It turns out this, uh, this version of the f- string, which had fermions, had an extra symmetry which we call super symmetry. This is a symmetry between a particle and another particle with exactly the same properties, same mass, same charge, et cetera. The only difference is that one of them has a little different spin than the other one, and one of, and one of them is a boson, one of them is a fermion, because of that shift of spin. Otherwise they're identical, so there was this symmetry. String theory had this symmetry. In fact, super symmetry was discovered through string theory, theoretically. So theoretically, the first place that this was observed when, when you were describing these fermionic strings.So that was the fir- beginning of the study of super symmetry was the Weyl string theory. And then it had remarkable properties that, you know, the symmetry meant and so forth that people began studying super symmetry after that. And that was continuati- that was kind of a tangent direction at the beginning for string theory, but people in particle physics started also thinking, "Oh, super symmetry is great. Let's see if we can have super symmetry in particle physics and so forth, forget about strings." And they developed on a different track as well. Super symmetry in different models became a subject on its own right, understanding super symmetry and what does this mean. Mm-hmm. Because it unified bosons and fermions, it unifies some ideas together. So photon is a boson, electron is a fermion, could things like that be somehow related? Mm-hmm. It was a kind of a natural kind of a question to try to kind of unify, because in physics, we love unification. Now gradually, string theory was beginning to show signs of unification. It had graviton, but people found that you also have things like photons in them. Different excitations of string behave like photons, another one behaves like electron. So a single string was unifying all these particle into one object. That's remarkable. It's in 10 dimensions though. (laughs) It is not our universe because we live in three plus one dimension. Yes. How could that be possibly true? Yes. So this was a conundrum. It was elegant, it was beautiful, but it was very specific about which dimension you're getting, which structure you're getting. It wasn't saying, "Oh, you just put D equals to four, you get your space time dimension that you want." No. It didn't like that. It said, "I want 10 dimensions, and that's the way it is." So it was very specific. Now, so people try to reconcile this by the idea that, you know, maybe these extra dimensions are tiny. So if you take three macroscopic spatial dimensions on one time and six extra tiny spatial dimensions, like tiny spheres or tiny circles, then it avoids contradiction with manifest fact that we haven't seen extra dimensions in experiments today. So that was a way to avoid conflict. Now this was a way to avoid conflict, but it was not observed in experiments. Is string observed in experiments? No, because it's so small. Mm-hmm. So it's beginning to sound a little bit funny. Similar feeling to the way perhaps Dirac had felt about this positron, plus or minus, you know? It was beginning to sound a little bit like, "Oh yeah, not only I have to have 10 dimension, but I have to this, I have to also this and..." And so you s- so conservative physicists would say, "Hmm, you know, I haven't seen these in experiments. I don't know if they are really there. Are you pulling my leg? Uh, do you want me to imagine things that are not there?" So this was an attitude of some physicists to- towards string theory, despite the fact that the puzzle of gravity and quantum mechanics merging together worked- Mm-hmm. ... but still was this skepticism. "You're putting all these things that you want me to imagine there are these extra dimensions that I cannot see, uh-huh, uh-huh, and you want me to believe that string that you have not even seen experiments are real? Uh-huh. Okay, what else do you want me to believe?" (laughs) So it was kind of beginning to sound a little funny. Now I was, I will pass forw- forward a little bit further, um, a few decades later when string theory became the mainstream... Mm-hmm. ... of efforts to unify the forces and particles together, we learned that these extra dimensions actually solve problems. They weren't a nuisance the way they originally appeared. First of all, the properties of these extra dimensions reflected the number of particles we got in four dimensions. If you took these six dimensions to have like six, five holes or four holes, it ten- changed the number of particles that you see in four dimensional space time. Mm-hmm. You get one electron and one muon if you had this, but if you did the other J shape, you get something else. Mm-hmm. So geometrically, you could get different kinds of physics. So it was kind of an, a mirroring of geometry by physics down in the macroscopic space. So these extra dimension were becoming useful. Fine, but we didn't need the extra dimensions to just write an electron in three dimensions. We did, we wrote it, so wha- so what? Was there any other puzzle? Yes, there were. Hawking. Hawking had been studying black holes in mid '70s, uh, following the work of Bekenstein, who had predicted that black holes have entropy. So Bekenstein had tried to attach the entropy to the black hole. If you throw something into the black hole, the entropy seems to go down because you had something entropy in, outside the black hole and you throw it. Entropy was un- a black hole was unique, so the entropy did not have any... black hole had no entropy. So you seem, the entropy seemed to go down. And so that's against the laws of thermodynamics, so Bekenstein was trying to say, "No, no, therefore black hole must have an entropy." So he was trying to understand that he found that if you assign entropy to the, uh, to be proportional to the area of the black hole, it seems to work. And then Hawking found not only that's correct, he found the correct proportionality factor of, factor of a one quarter of the area in Planck units is the correct amount of entropy, and he gave an argument using quantum m- semi-classical arguments, which barely, which means basically using a little bit of quantum mechanics, because he didn't have the full quantum mechanics of string theory, he could do some aspects of approximate quantum arguments. Mm-hmm. So heuristic quantum arguments led to this entropy form- formula. But then he didn't answer the following question. He was getting a big entropy for the black hole, the black hole with the size of a horizon of a black hole is huge, has a huge amount of entropy. What are the microstates of this entropy? When you say, for example, a gas's entropy, you count where the atoms are, you count this, this pocket or that pocket, there's information about there and so on, you count them. For the black hole, the way Hawking was thinking, there was no degree of freedom. You throw them in and there was just one solution. So where are these entropy? What is, what are these microscopic states? They were hidden somewhere. So later in string theory, uh, the work that, uh, we did with my colleague, Strominger, in particular, showed that these ingredients in string theory-... of black hole arise from the extra dimensions. So the degrees of freedom are, are hidden in terms of things like strings, wrapping these extra circles in these hidden dimensions. And then we started counting how many ways, like, the strings can wrap around this circle and the h- extra dimension or that circle, and counted the microscopic degrees of freedom. And lo and behold, we got the microscopic degrees of freedom that Hawking was predicting four dimensions. So the extra dimensions became useful-

Lex Fridman 1:07:29 (laughs)

Cumrun Vafa 1:07:30 ... for resolving a puzzle in four dimensions. The puzzle was, where are the degrees of freedom of the black hole hidden? The answer, hidden in the extra dimensions, the tiny extra dimensions. So then by this time, it was beginning to s- s- we see aspects-

Lex Fridman 1:07:45 Mm-hmm.

Cumrun Vafa 1:07:45 ... that extra dimensions are useful for many things, not a nuisance. It wasn't to be kind of, you know, be ashamed of. It was actually in the welcome features. New feature,

Cumrun Vafa 1:07:54 nevertheless.

Lex Fridman 1:07:55 How do you intuit the 10 dimensional world? So yes, it's a feature for describing certain phenomena like the, the entropy in black holes, but what, um, you said that to you a, a theory becomes real-

Cumrun Vafa 1:08:13 Yes, yeah.

Lex Fridman 1:08:14 ... or becomes powerful when you can connect it to some deep intuition. So how do we intuit-

Cumrun Vafa 1:08:19 Yes.

Lex Fridman 1:08:19 ... 10 dimensions?

Cumrun Vafa 1:08:20 Yes. Um, so I will, I will explain, uh, how, how some of the analogies work. First of all, we do a lot of analogies. And by analogies, we build intuition. So I will, I will start with this example. I will try to explain that if we are in 10 dimensional space, if we have a seven dimensional plane and an eight dimensional plane, we ask typically in what space do they intersect each other, in what dimension? That might sound like how do you possibly give an answer to this? So we start with lower dimensions. We start with two dimensions. We say if you have one dimension and a point, do they intersect between a, on a plane? The answer is no. So a, a line, one dimensional, a point, zero dimension, and a two dimensional plane, they don't typically meet.

Lex Fridman 1:09:05 Mm-hmm.

Cumrun Vafa 1:09:05 But if you have a one dimensional line and another w- line, which is one plus one, and a plane, they typically intersect at a point. Typically means if you are not parallel, typically they intersect at a point. So one plus one is two, and in two dimension, they intersect at the zero dimensional point. So you see two dimension, one and one, two, two minus two is zero, so you get point out of intersection. Okay? Let's go to three dimension. You have a plane, two dimensional plane and a point. Do they intersect? No. Two and zero. How about a plane and a line? A plane is two dimensional, and a line is one. Two plus one is three. In three dimension, a plane and a line meet at points, which is zero dimensional. Three minus three is zero.

Lex Fridman 1:09:49 Mm-hmm.

Cumrun Vafa 1:09:49 Okay? So plane and a line intersect at a point in three dimension. How about a plane and a plane in 3D? A plane is two and this is two, two plus two is four. In 3D, four minus three is one, they intersect on a one dimensional line.

Lex Fridman 1:10:02 Mm-hmm.

Cumrun Vafa 1:10:03 Okay, we're beginning to see a pattern. Okay, now come to question. We're in 10 dimensions, now we have the intuition.

Lex Fridman 1:10:08 (sighs) Right.

Cumrun Vafa 1:10:08 We have a seven dimensional plane and an eight dimensional plane in 10 dimension. They intersect on a plane, what's the dimension? Well, 7 plus 8 is 15 minus 10 is 5. We draw the same picture as two planes, and we write seven dimension, eight dimension, but we have gotten the intuition from the lower dimensional one what to expect. It doesn't scare us anymore. So we draw this picture, we cannot see all the seven dimensions by looking at this w- two dimensional visualization of it, but it has all the features we want. It has, so I, we draw this picture, which is seven, seven on the, they, they meet at the five dimensional plane, which is five. So we have, we have built this intuition. Now, this is a, an example of how we come up with intuition. Let me give you more examples of it, because I think this will show you that people have to come up with intuitions to visualize it. Otherwise, we will, we'll be a little bit, uh, lost.

Lex Fridman 1:11:00 So, so what you just d- described is kind of, uh, in these high dimensional spaces focus on the meeting place of, uh, two planes in high dimensional spaces.

Cumrun Vafa 1:11:10 Exactly. How the planes meet, for example. What's the dimension of their intersection and so on. So how do we come up with intuition? We, we borrow examples from lower dimensions, build up intuition, and draw the same pictures as if we are talking about, uh, 10 dimensions, but we are drawing the same as a two dimensional plane, because we cannot do any better. But our, our, our, our words change.

Lex Fridman 1:11:31 Mm-hmm.

Cumrun Vafa 1:11:31 But not our pictures.

Lex Fridman 1:11:32 So your sense is we can have a deep understanding of reality by looking at its, uh, uh, slices, lower dimensional slices.

Cumrun Vafa 1:11:40 Exactly. Exactly. And this, this is, comes, brings me to the next example I want to mention, which is sphere. Let's think about how do we think about a sphere? Well, the sphere is a sphere, you know, the round nice thing. But sphere has a circular symmetry.

Lex Fridman 1:11:53 Mm-hmm.

Cumrun Vafa 1:11:54 Now, I can describe the sphere in the following way. I can describe it by an interval, which is think about this going from the north of the sphere to the south. And at each point, I have a circle attached to it. So you can think about the sphere as a line with a circle attached with each point, the circle shrinks to a, the circle shrinks to a point at end points of the interval. So I can say, "Oh, one way to think about the sphere is an interval, where at each point on that interval, there's another circle I'm not drawing." But if you like, you can just draw it. Say, "Okay, I want draw it." So from now on, there's this mnemonic. I draw an interval when I want to talk about the sphere, and you remember that the end points of the interval mean a strong circle. That's all.

Lex Fridman 1:12:39 Mm-hmm.

Cumrun Vafa 1:12:39 And then you say, "Yeah, I see. That's a sphere." Good. Now, we want to talk about the product of two spheres. That's four dimensional. How can I visualize it?

Lex Fridman 1:12:46 (laughs)

Cumrun Vafa 1:12:47 Easy. You just take an interval, and it's another interval, that's just gonna be a square.

Lex Fridman 1:12:52 Yeah.

Cumrun Vafa 1:12:54 A square is a four dimensional space. Yeah. Why is that? Well, at each point on the square, there's two circles, one for each of those directions you drew.... and when you get to the boundaries of each direction, one of the circles shrink on each edge of that square.

Lex Fridman 1:13:09 Mm-hmm.

Cumrun Vafa 1:13:10 And when you get to the corners of the square, all, both circles shrink. This is a sphere times a sphere. I have defined interval.

Lex Fridman 1:13:17 Mm-hmm.

Cumrun Vafa 1:13:17 I just described for you a four-dimensional space.

Lex Fridman 1:13:19 Mm-hmm.

Cumrun Vafa 1:13:20 Do you want a six-dimensional space? No problem. Take the, take a corner of a room. In fact, if you want to have a sphere times a s- ... Take a sphere times a sphere times a sphere.

Lex Fridman 1:13:29 Mm-hmm.

Cumrun Vafa 1:13:30 Take a cube. A cube is a rendition of this six-dimensional space. It's two, a sphere times another sphere times another sphere, where three of the circles I'm not drawing for you. For each one of those directions, there's another circle. But each time you get to the boundary of the cube, one circle shrinks. When the boundaries meet, two circle shrinks. When three boundaries meet, all the three circle shrink. So, I just give you a picture. Now, mathematicians come up with amazing things, like, you know what? I wanna take your point in space and blow it up. You know, these concepts like topology and geometry are complicated. How do you do? In this picture, it's very easy. Blow it up in this picture means the following. You think about this cube, you go to the corner and you chop off a corner.

Lex Fridman 1:14:12 (laughs)

Cumrun Vafa 1:14:12 Chopping off the corner replaces the point-

Lex Fridman 1:14:15 Yeah.

Cumrun Vafa 1:14:15 ... replaces the point by a triangle.

Lex Fridman 1:14:17 Yes.

Cumrun Vafa 1:14:17 That's called blowing up a point, and then this triangle is what they call P2, projective two-space. But these pictures are very physical and you feel it. There's nothing amazing. I'm now talking about six dimension. Four plus six is 10, the dimension of string theory. So, we can visualize it, no problem.

Lex Fridman 1:14:32 Okay, so that's building the intuition to a complicated world of string theory. Nevertheless, these objects are really small. And just like you said, experimental validation is very difficult because the objects are way smaller than anything that we currently have the tools and accelerators and so on to, um, to reveal through experiment. So, there's a kind of skepticism that's not just about the nature of the theory because of the 10 dimensions, as you've explained, but in that we can't experimentally validate it, and it doesn't necessarily, to date, maybe you can correct me, predict something fundamentally new. So, it's, it's beautiful as an explaining theory, which means that it's very possible that it is a fundamental theory that describes reality and unifies the laws. But there's still a kind of skepticism. And, uh, me from a sort of an outside observer perspective have been observing a little bit of a s- growing cynicism about string theory in the, in the recent few years. Can you describe the cynicism about sort of ... By cynicism, I mean, a cynicism about the hope for this theory of pushing theoretical physics forward.

Cumrun Vafa 1:15:49 Yes.

Lex Fridman 1:15:50 Uh, can you do, describe w- why the cyn- cynicism and how do we reverse that trend?

Cumrun Vafa 1:15:56 Yes. First of all, the criticism, uh, for string theory, uh, is healthy in some, in a sense that in science, we, we have to have different viewpoints, and that's good. So, I, I don't ... I welcome criticism. Uh, and the, the, the reason for criticism, and I think that is a valid reason, is that there has been zero experimental evidence for string theory. That is, no experiment has been done to show that there's, you know, there's this l- loop of energy moving around. And so that's a valid, valid, uh, objection, and valid worry. And if I were to say, "You know what? String theory can never be verified or experimentally checked, that's the way it is," they would have every right to say, "What you're talking about is not science." Because in science, we will have to have experimental consequences and checks. The difference between s- string theory and something which is not scientific is that string theory has predictions. The problem is that the predictions we have today of string theory is hard to access by experiments available with the energies we can achieve with the colliders today. It doesn't mean there's a problem with string theory, it just means technologically we're not that far ahead. Now, we can have two attitudes. You say, "Well, if that's the case, why are you studying this subject?" Because we can't do experiment today. Now, this is becoming a little bit more like mathematics in that sense. You say, "Well, I want to learn. I want to know w- how the nature works even though I cannot prove it today-"

Lex Fridman 1:17:18 Mm-hmm.

Cumrun Vafa 1:17:18 "... that this is it because of experiments. That should not prevent my mind not to think about it."

Lex Fridman 1:17:23 That's right.

Cumrun Vafa 1:17:24 So, that's the attitude many string theorists follow. That, that, that it should be like this. Now, so that's the, that's the a- an answer to the criticism, but there's actually a better answer to the criticism, I would say. We don't have experimental evidence for string theory, but we have theoretical evidence for string theory. And what do I mean by theoretical evidence for string theory? String theory has connected different parts of physics together. It didn't have to. It has brought connections between particle physics all the w- Suppose you're just interested in particle physics. Suppose you're not even interested in, in, in gravity at all. It turns out there are product- properties of certain particle physics models that string theory has been able to solve using gravity, using ideas from string theory, ideas known as holography, which is relating something which has to do with particles to something having to do with gravity. Why did it have to be this rich? This subject is very rich. It's not something we were smart enough to develop. It came at us. As I explained to you, the development of string theory came from accidental discovery. It wasn't because we were smart enough to come up with the idea that, "Oh, yeah, string, of course, has gravity in it." No, it was accidental discovery. So, some people say it's not fair to say we have no e- evidence for string theory. Graviton, gravity is an evidence for string theory. It's predicted by string theory. We didn't put it by hand. We got it. So, there's a qualitative check that, okay, gravity is a prediction of string theory, it's a post-diction because we know gravity existed.

Lex Fridman 1:18:53 Mm-hmm.

Cumrun Vafa 1:18:53 But still, th- uh, logically, it is a prediction because w- uh, really, we didn't know it had, it had graviton and we later learned that, oh, that's the same as gravity. So, it literally, that's the way it was discovered. It wasn't put in by hand.So, so the, there, there are many things like that, that there are, there are