Cumrun Vafa: String Theory | Lex Fridman Podcast #204

1. 0:00 – 1:51

   Introduction

   1. LFLex Fridman0:00

      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.

2. 1:51 – 4:34

   Difference between math and physics

   1. LFLex Fridman1:51

      What is the difference between mathematics and physics?

   2. CVCumrun Vafa1:55

      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-

   3. LFLex Fridman4:04

      (laughs)

   4. CVCumrun Vafa4:04

      ... 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

3. 4:34 – 7:52

   Evolution of quantum mechanics

   1. CVCumrun Vafa4:34

      underpinning it.

   2. LFLex Fridman4:35

      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?

   3. CVCumrun Vafa5:02

      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?

   4. LFLex Fridman6:49

      (laughs)

   5. CVCumrun Vafa6:50

      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.

   6. LFLex Fridman7:19

      Yes.

   7. CVCumrun Vafa7:20

      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.

   8. LFLex Fridman7:38

      When we say amplitude, you mean probability?

   9. CVCumrun Vafa7:40

      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

4. 7:52 – 8:51

   Can mathematics lead humanity off track

   1. CVCumrun Vafa7:52

      the other.

   2. LFLex Fridman7:52

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

   3. CVCumrun Vafa8:01

      Yes. I would say that mathematics can lead us astray as much as old physical ideas can lead us astray.

   4. LFLex Fridman8:08

      (laughs) That's true, yeah.

   5. CVCumrun Vafa8:09

      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.

5. 8:51 – 14:10

   Beauty in mathematics

   1. CVCumrun Vafa8:51

   2. LFLex Fridman8:51

      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.

   3. CVCumrun Vafa9:19

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

   4. LFLex Fridman9:27

      So beauty is, uh, fundamental in the universe?

   5. CVCumrun Vafa9:29

      I think beauty is fundamental.

   6. LFLex Fridman9:30

      (laughs)

   7. CVCumrun Vafa9:31

      At least that's the way many of us view it.

   8. LFLex Fridman9:32

      It's not emergent? (laughs)

   9. CVCumrun Vafa9:33

      (laughs) It's not emergent.

   10. LFLex Fridman9:34

       (laughs)

   11. CVCumrun Vafa9:35

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

   12. LFLex Fridman9:40

       (laughs)

   13. CVCumrun Vafa9:40

       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.

   14. LFLex Fridman10:32

       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.

   15. CVCumrun Vafa11:44

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

   16. LFLex Fridman11:49

       Yeah.

   17. CVCumrun Vafa11:49

       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.

   18. LFLex Fridman12:54

       Mm-hmm.

   19. CVCumrun Vafa12:54

       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.

   20. LFLex Fridman13:08

       Mm-hmm.

   21. CVCumrun Vafa13:08

       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

6. 14:10 – 20:04

   Philosophers using symmetry

   1. CVCumrun Vafa14:10

      so today.

   2. LFLex Fridman14:10

      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-

   3. CVCumrun Vafa14:44

      Yes.

   4. LFLex Fridman14:44

      ... 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.

   5. CVCumrun Vafa15:02

      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.

   6. LFLex Fridman15:41

      (laughs)

   7. CVCumrun Vafa15:42

      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.

   8. LFLex Fridman16:12

      That's brilliant, by the way, the fact that they did that as well.

   9. CVCumrun Vafa16:14

      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?"

   10. LFLex Fridman16:24

       (laughs)

   11. CVCumrun Vafa16:25

       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.

   12. LFLex Fridman16:38

       Mm-hmm.

   13. CVCumrun Vafa16:38

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

   14. LFLex Fridman16:45

       Yeah.

   15. CVCumrun Vafa16:45

       So they said the earth is at the center of the universe.

   16. LFLex Fridman16:47

       That makes sense actually.

   17. CVCumrun Vafa16:48

       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-"

   18. LFLex Fridman16:54

       Mm-hmm.

   19. CVCumrun Vafa16:54

       "... because you have to pick a direction."

   20. LFLex Fridman16:56

       Mm-hmm.

   21. CVCumrun Vafa16:57

       "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.

   22. LFLex Fridman17:10

       Mm-hmm.

   23. CVCumrun Vafa17:11

       But they were even smarter than that. Aristotle didn't agree with this argument.

   24. LFLex Fridman17:14

       (laughs) .

   25. CVCumrun Vafa17:16

       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."

   26. LFLex Fridman17:34

       Mm-hmm.

   27. CVCumrun Vafa17:35

       "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."

   28. LFLex Fridman17:49

       Mm-hmm.

   29. CVCumrun Vafa17:49

       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.

   30. LFLex Fridman18:23

       Did they use the language of symmetry and the symmetry breaking-
7. 20:04 – 23:16

   How can ancient geometry be used to understand reality

   1. LFLex Fridman20:04

      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?

   2. CVCumrun Vafa20:17

      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.

   3. LFLex Fridman20:44

      Mm-hmm.

   4. CVCumrun Vafa20:45

      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.

   5. LFLex Fridman21:50

      Mm-hmm.

   6. CVCumrun Vafa21:51

      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.

   7. LFLex Fridman22:57

      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

8. 23:16 – 26:09

   Key ideas in the history of physics

   1. LFLex Fridman23:16

      before we go into that mysterious beautiful world-

   2. CVCumrun Vafa23:18

      (laughs)

   3. LFLex Fridman23:19

      ... 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.

   4. CVCumrun Vafa23:52

      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."

   5. NANarrator24:56

      (laughs)

   6. CVCumrun Vafa24:57

      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,

9. 26:09 – 29:46

   Einstein's special relativity

   1. CVCumrun Vafa26:09

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

   2. NANarrator26:17

      Yeah.

   3. CVCumrun Vafa26:18

      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."

   4. NANarrator26:40

      Yeah.

   5. CVCumrun Vafa26:41

      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.

   6. NANarrator27:59

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

   7. CVCumrun Vafa28:04

      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.

   8. NANarrator28:27

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

   9. CVCumrun Vafa28:31

      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.

   10. NANarrator28:43

       Yeah.

   11. CVCumrun Vafa28:43

       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.

   12. NANarrator29:28

       (laughs)

   13. CVCumrun Vafa29:28

       Like, even when I'm describing it, I feel like a little bit-

   14. NANarrator29:31

       Yeah.

   15. CVCumrun Vafa29:31

       ... like isn't it, you know, funny?

   16. NANarrator29:33

       (laughs)

   17. CVCumrun Vafa29:33

       As you're just feeling the same way. It is.

   18. NANarrator29:35

       Yes.

   19. CVCumrun Vafa29:35

       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,

10. 29:46 – 37:44

    Physicists building intuition

    1. CVCumrun Vafa29:46

       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.

    2. NANarrator30:06

       Mm-hmm. Makes sense.

    3. CVCumrun Vafa30:07

       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?"

    4. LFLex Fridman31:03

       Why? Yes.

    5. CVCumrun Vafa31:04

       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.

    6. LFLex Fridman31:13

       (laughs)

    7. CVCumrun Vafa31:13

       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.

    8. LFLex Fridman31:38

       (laughs)

    9. CVCumrun Vafa31:38

       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."

    10. LFLex Fridman32:07

        Yeah.

    11. CVCumrun Vafa32:07

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

    12. LFLex Fridman32:11

        (laughs)

    13. CVCumrun Vafa32:12

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

    14. LFLex Fridman32:19

        Yeah.

    15. CVCumrun Vafa32:19

        When the intuitions clash, then you, then you side on the ... You replace the intuition.

    16. LFLex Fridman32:25

        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)

    17. CVCumrun Vafa32:55

        (laughs)

    18. LFLex Fridman32:55

        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)

    19. CVCumrun Vafa33:07

        (laughs)

    20. LFLex Fridman33:08

        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)

    21. CVCumrun Vafa34:17

        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.

    22. LFLex Fridman34:25

        Mm-hmm.

    23. CVCumrun Vafa34:26

        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.

    24. LFLex Fridman34:41

        Mm-hmm.

    25. CVCumrun Vafa34:41

        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.

    26. LFLex Fridman34:59

        (laughs) You have to connect the bricks. (laughs)

    27. CVCumrun Vafa35:00

        But, but it ... You have to connect the ... (laughs) Yeah, exactly. You have to connect the bricks.

    28. LFLex Fridman35:03

        (laughs)

    29. CVCumrun Vafa35:03

        Literally.

    30. LFLex Fridman35:04

        Yeah. (laughs)
11. 37:44 – 39:28

    Best work by Einstein

    1. CVCumrun Vafa37:44

       ways.

    2. LFLex Fridman37:44

       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?

    3. CVCumrun Vafa38:13

       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.

    4. LFLex Fridman38:20

       The beginning is the seed.

    5. CVCumrun Vafa38:21

       The beginning is the seed.

    6. LFLex Fridman38:22

       O- once you embrace that weirdness-

    7. CVCumrun Vafa38:24

       Yes, yes.

    8. LFLex Fridman38:24

       ... all the weirdness, all the rest

    9. NANarrator38:25

       (laughs)

    10. CVCumrun Vafa38:25

        I would say that's, that's ... Even though he says the most beautiful moment for him-

    11. LFLex Fridman38:29

        Yes.

    12. CVCumrun Vafa38:29

        ... 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.

    13. LFLex Fridman38:39

        Mm-hmm.

    14. CVCumrun Vafa38:39

        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.

    15. LFLex Fridman38:59

        The general relativity to you is not, like, uh, the c- c- conception of space time.

    16. CVCumrun Vafa39:05

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

    17. LFLex Fridman39:10

        Hmm.

    18. CVCumrun Vafa39:10

        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.

12. 39:28 – 49:30

    Quantum mechanics

    1. CVCumrun Vafa39:28

    2. LFLex Fridman39:28

       Where does, uh, quantum mechanics come into view?

    3. CVCumrun Vafa39:32

       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.

    4. LFLex Fridman40:07

       Can we pause and briefly say what is quantum mechanics?

    5. CVCumrun Vafa40:10

       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.

    6. LFLex Fridman40:49

       Mm-hmm.

    7. CVCumrun Vafa40:49

       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.

    8. LFLex Fridman41:28

       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?

    9. CVCumrun Vafa41:45

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

    10. LFLex Fridman41:51

        Right.

    11. CVCumrun Vafa41:51

        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-

    12. LFLex Fridman42:28

        Mm-hmm.

    13. CVCumrun Vafa42:28

        ... 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-

    14. LFLex Fridman42:35

        This is the end of the story. (laughs)

    15. CVCumrun Vafa42:35

        ... perfectly exactly correct. That doesn't bother me.

    16. LFLex Fridman42:37

        Yes.

    17. CVCumrun Vafa42:38

        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.

    18. LFLex Fridman42:54

        So you were talking about Dirac?

    19. CVCumrun Vafa42:55

        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."

    20. LFLex Fridman44:29

        Mm-hmm.

    21. CVCumrun Vafa44:30

        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.

    22. LFLex Fridman44:48

        (laughs)

    23. CVCumrun Vafa44:49

        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.

    24. LFLex Fridman45:34

        (laughs) Yes.

    25. CVCumrun Vafa45:34

        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...

    26. LFLex Fridman46:20

        Yeah.

    27. CVCumrun Vafa46:20

        ... 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.

    28. LFLex Fridman46:44

        Mm-hmm.

    29. CVCumrun Vafa46:44

        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...

    30. LFLex Fridman47:55

        Mm-hmm.
13. 49:30 – 51:45

    Quantum gravity

    1. LFLex Fridman49:30

       Is there something to be said about quantum gravity?

    2. CVCumrun Vafa49:32

       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?

    3. LFLex Fridman49:55

       (laughs)

    4. CVCumrun Vafa49:55

       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-

    5. LFLex Fridman50:17

       Mm-hmm.

    6. CVCumrun Vafa50:17

       ... 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.

    7. LFLex Fridman50:49

       Mm-hmm.

    8. CVCumrun Vafa50:51

       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.

    9. LFLex Fridman51:19

       Mm-hmm.

    10. CVCumrun Vafa51:19

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

    11. LFLex Fridman51:25

        Yeah.

    12. CVCumrun Vafa51:25

        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.

    13. LFLex Fridman51:41

        So the infinity shows up, what do we do, wh- what do we do with the infinity?

14. 51:45 – 1:07:54

    String theory

    1. LFLex Fridman51:45

       Let's get to the fun part. Let's talk about string theory. (laughs)

    2. CVCumrun Vafa51:48

       Yes.

    3. LFLex Fridman51:50

       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?

    4. CVCumrun Vafa52:02

       (laughs) Yeah.

    5. LFLex Fridman52:02

       How do we represent the elementary particles and, uh, the laws of physics using this new framework?

    6. CVCumrun Vafa52:09

       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-

    7. LFLex Fridman53:12

       Mm-hmm.

    8. CVCumrun Vafa53:12

       ... 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.

    9. LFLex Fridman53:37

       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?

    10. CVCumrun Vafa53:58

        Yes. You should literally think about string, but string with zero thickness.

    11. LFLex Fridman54:02

        With zero thickness.

    12. CVCumrun Vafa54:04

        So now it's, it's a, it's a, it's a loop of energy so to speak.

    13. LFLex Fridman54:07

        Mm-hmm.

    14. CVCumrun Vafa54:07

        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.

    15. LFLex Fridman54:19

        But it is very, very tiny.

    16. CVCumrun Vafa54:21

        Very tiny.

    17. LFLex Fridman54:22

        Much smaller than, uh, elementary particles of physics.

    18. CVCumrun Vafa54:25

        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-

    19. LFLex Fridman54:34

        Mm-hmm.

    20. CVCumrun Vafa54:35

        ... 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-

    21. LFLex Fridman54:45

        Phew.

    22. CVCumrun Vafa54:45

        ... 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-

    23. LFLex Fridman54:54

        Unimaginably small, I would say.

    24. CVCumrun Vafa54:56

        Very small, very small. So we, we basically think from far away, string is like a point particle.

    25. LFLex Fridman55:00

        Yeah.

    26. CVCumrun Vafa55:00

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

    27. LFLex Fridman55:06

        Mm-hmm.

    28. CVCumrun Vafa55:07

        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.

    29. LFLex Fridman55:49

        Mm-hmm.

    30. CVCumrun Vafa55:50

        Now, perhaps it's also useful to recount of how string theory came to be.
15. 1:07:54 – 1:14:32

    10th Dimension

    1. CVCumrun Vafa1:07:54

       nevertheless.

    2. LFLex Fridman1:07:55

       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-

    3. CVCumrun Vafa1:08:13

       Yes, yeah.

    4. LFLex Fridman1:08:14

       ... or becomes powerful when you can connect it to some deep intuition. So how do we intuit-

    5. CVCumrun Vafa1:08:19

       Yes.

    6. LFLex Fridman1:08:19

       ... 10 dimensions?

    7. CVCumrun Vafa1:08:20

       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.

    8. LFLex Fridman1:09:05

       Mm-hmm.

    9. CVCumrun Vafa1:09:05

       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.

    10. LFLex Fridman1:09:49

        Mm-hmm.

    11. CVCumrun Vafa1:09:49

        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.

    12. LFLex Fridman1:10:02

        Mm-hmm.

    13. CVCumrun Vafa1:10:03

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

    14. LFLex Fridman1:10:08

        (sighs) Right.

    15. CVCumrun Vafa1:10:08

        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.

    16. LFLex Fridman1:11:00

        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.

    17. CVCumrun Vafa1:11:10

        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.

    18. LFLex Fridman1:11:31

        Mm-hmm.

    19. CVCumrun Vafa1:11:31

        But not our pictures.

    20. LFLex Fridman1:11:32

        So your sense is we can have a deep understanding of reality by looking at its, uh, uh, slices, lower dimensional slices.

    21. CVCumrun Vafa1:11:40

        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.

    22. LFLex Fridman1:11:53

        Mm-hmm.

    23. CVCumrun Vafa1:11:54

        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.

    24. LFLex Fridman1:12:39

        Mm-hmm.

    25. CVCumrun Vafa1:12:39

        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?

    26. LFLex Fridman1:12:46

        (laughs)

    27. CVCumrun Vafa1:12:47

        Easy. You just take an interval, and it's another interval, that's just gonna be a square.

    28. LFLex Fridman1:12:52

        Yeah.

    29. CVCumrun Vafa1:12:54

        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.

    30. LFLex Fridman1:13:09

        Mm-hmm.
16. 1:14:32 – 1:25:37

    Skepticism regarding string theory

    1. CVCumrun Vafa1:14:32

    2. LFLex Fridman1:14:32

       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.

    3. CVCumrun Vafa1:15:49

       Yes.

    4. LFLex Fridman1:15:50

       Uh, can you do, describe w- why the cyn- cynicism and how do we reverse that trend?

    5. CVCumrun Vafa1:15:56

       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-"

    6. LFLex Fridman1:17:18

       Mm-hmm.

    7. CVCumrun Vafa1:17:18

       "... that this is it because of experiments. That should not prevent my mind not to think about it."

    8. LFLex Fridman1:17:23

       That's right.

    9. CVCumrun Vafa1:17:24

       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.

    10. LFLex Fridman1:18:53

        Mm-hmm.

    11. CVCumrun Vafa1:18:53

        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 different facets of physics, like questions in condensed matter physics, questions of particle physics, questions about this and that has, have come together to find beautiful answers by using ideas from string theory at the same time as a lot of new math has emerged. That's an aspect which I wouldn't emphasize as evidence to physicists, necessarily, because they would say, "Well, okay, great you got some math. But what does it do with reality?" But as I explained, many of the physical principles we know of have beautiful math underpinning them, so it certainly leads further, um, confidence that we may not be going astray, even though that's not the full proof, as we know. So, so there are these aspects that give further evidence for string theory, connections between each other, connection with the real world. But then there are other things that come about and I can try to gi- give examples of that. So, so these are further evidences, and these are certain predictions of string theory. They are not as, as, as detailed as we want.

Episode duration: 2:13:21