#204 – Cumrun Vafa: String Theory

Cumrun Vafa is a theoretical physicist at Harvard. Please support this podcast by checking out our sponsors: – Headspace: https://headspace.com/lex to get free 1 month trial – The Jordan Harbinger Show: https://www.youtube.com/thejordanharbingershow – Squarespace: https://lexfridman.com/squarespace and use code LEX to get 10% off – Allform: https://allform.com/lex to get 20% off EPISODE LINKS: Cumrun’s Twitter: https://twitter.com/cumrunv Cumrun’s Website: https://www.cumrunvafa.org Puzzles to Unravel the Universe (book): https://amzn.to/3BFk5ms PODCAST INFO: Podcast website: https://lexfridman.com/podcast Apple Podcasts: https://apple.co/2lwqZIr Spotify: https://spoti.fi/2nEwCF8 RSS: https://lexfridman.com/feed/podcast/ YouTube Full Episodes: https://youtube.com/lexfridman YouTube Clips: https://youtube.com/lexclips SUPPORT & CONNECT: – Check out the sponsors above, it’s the best way to support this podcast – Support on Patreon: https://www.patreon.com/lexfridman – Twitter: https://twitter.com/lexfridman – Instagram: https://www.instagram.com/lexfridman – LinkedIn: https://www.linkedin.com/in/lexfridman – Facebook: https://www.facebook.com/lexfridman – Medium: https://medium.com/@lexfridman OUTLINE: Here’s the timestamps for the episode. On some podcast players you should be able to click the timestamp to jump to that time. (00:00) – Introduction (07:08) – Difference between math and physics (09:51) – Evolution of quantum mechanics (13:09) – Can mathematics lead humanity off track (14:07) – Beauty in mathematics (19:27) – Philosophers using symmetry (25:20) – How can ancient geometry be used to understand reality (28:32) – Key ideas in the history of physics (31:26) – Einstein’s special relativity (35:03) – Physicists building intuition (43:01) – Best work by Einstein (44:45) – Quantum mechanics (54:47) – Quantum gravity (57:02) – String theory (1:13:11) – 10th Dimension (1:19:48) – Skepticism regarding string theory (1:30:53) – Key figures in string theory (1:35:13) – String Theory’s Nobel Prize (1:38:18) – Edward Witten (1:46:56) – String Theory Landscape & Swamplands (1:55:46) – Theories of everything (2:10:12) – Advice for young people (2:13:14) – Death

Speaker names marked ? are inferred from speaking time and the show’s known hosts — they are not voice-verified.

• 0:00Lex Fridman?

  The following is a conversation with Cameron 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 Harbridge 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.

• 0:45Lex Fridman?

  Different vibrating patterns result in different particles. From its origins, for a long time, string theory was seen as 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.

• 1:30Lex Fridman?

  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. As usual, I'll do a few minutes of ads now. No ads in the middle. I think those get in the way of the conversation, so I avoid those. I try to make these interesting, but I give you timestamps, so if you skip, please still check out the sponsors by clicking the links in the description. It's the best way to support this podcast. I'm very fortunate to be able to be very picky about the sponsors we take on, so hopefully, if you buy their stuff, you'll find value in it, just as I have.

• 2:12Lex Fridman?

  This show is sponsored by a new sponsor, Headspace. It's a meditation app. It's a new sponsor, but it's an app that I've had in my life for many years. I've used it off and on since, I think, 2015 or even earlier than that, maybe even 2013. Anyway, for many years, I've used it both for structured, like guided meditation sessions, and less structured meditation sessions. People, friends of mine, have told me that they love using it for, quote unquote, "emergency meditation sessions." Like, if there's a drama at work or a fight with a significant other, you can do like this emergency session to calm your mind, to breathe. Anyway, Headspace is meditation made simple.

• 2:56Lex Fridman?

  Go to headspace.com/lex. That's headspace.com/lex for a free one-month trial with access to Headspace's full library of meditations for every situation. Like I said, they're a new sponsor, so now's the time to go sign up so that they partner with this podcast for the long term. Again, that's headspace.com/lex. Go there to support them and to support this podcast. This episode is also sponsored by The Jordan Harbinger Show. Search for it on YouTube and everywhere else podcasts are available. Subscribe, listen, you won't regret it. Jordan has some great recent conversations with Michio Kaku,

• 3:38Lex Fridman?

  Neil deGrasse Tyson, and our friend, Cal Newport. He has, I think, many conversations with Cal Newport, actually. And I really enjoy how they get into sort of, into the weeds. They're both, obviously, productivity junkies, masters, experts. They study what makes for an effective life, for productive life. And it's kind of interesting to have a push and pull discussion between them of what makes for productive life. So I really enjoy listening to those two together. But overall, Jordan is just a good interviewer. I enjoy listening to him to study what makes for a fun conversation, interesting conversation to listen to. Again, search for Jordan Harbridge's show on YouTube,

• 4:20Lex Fridman?

  but you can also listen to it everywhere podcasts are available. This show is also sponsored by Squarespace. They make it easy for you to make your own website. Like I mentioned recently, I used them to build gogginschallenge.com for the four by four by 48 challenge that David Goggins recently hosted. I was on the phone with David and I suggested that I can quickly make the website for him. And he got excited at the possibility and we put together a site in just a couple of hours. It was super easy and the site was just a single page that described what the challenge was about, when it was happening, what David was doing. It also had a form that you could submit where you could tell the story

• 5:03Lex Fridman?

  about how you participate in a challenge, sort of a story after you complete the challenge of what you had to go through to complete the challenge. Anyway, go to lexfridman.com/squarespace for a free trial. And when you're ready to launch, use the offer code Lex to save 10% off your first purchase of a website or domain. Again, that's lexfridman.com/squarespace. This show is also sponsored by Allform, a furniture company. They ship to your home quickly, take it back for free if you don't like it in the first 100 days. It's easy to assemble, looks beautiful, classy and sexy, feels amazing. I love it.

• 5:44Lex Fridman?

  It's a, has like a modular design that you can assemble all kinds of small and large furniture together. Like I said, it looks beautiful. I have a black leather couch. Back in Boston, I have a love seat that I shared with a great and powerful Mr. Michael Malice as we partook in many hours of conversation together and also other substances that I cannot mention. But it was an amazing experience sitting in a love seat with Michael Malice. No, we did not make love, but we did make a lot of amazing conversation. This was for the episode where I wore, obviously, the black suit and tie and he wore the white suit and the white tie.

• 6:29Lex Fridman?

  I really like the way their furniture looks and the way it feels. It's very fast delivery. Anyway, go to allform.com/lex to pick out your own furniture. That's allform.com/lex. This is the Lex Fridman Podcast and here's my conversation with Kamran Bafa.

• 7:08Lex Fridman?

  What is the difference between mathematics and physics?

• 7:12Speaker 01

  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 of math and physics are different. Math does not 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. Mathematicians care about deductive reasoning and physicists or physics in general, we care less about that.

• 7:54Speaker 01

  We care more about interconnection of ideas, about how ideas support each other or if there's a puzzle, 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 we 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 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

• 8:37Speaker 01

  learned to not like deductive reasoning because that gives us 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 mathematics 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 is actually the reason that's true is the opposite. And so we reverse the order. And so this this switching back and forth between ideas makes us more fluid about 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 to say things

• 9:21Speaker 01

  that are not backed by, you know, the logical reasoning, that's not true at all. So despite despite this fluidity in seeing 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 that's an important ingredient. And in fact, solid math being behind physics is, I think, one of the attractive features of a of a physical law. So we look for beautiful math underpinning it.

• 9:51Lex Fridman?

  Can we dig into that process of starting from one place and then the ending up at like the fourth step and realizing all along that the place you started at was wrong? So 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 different starting place altogether?

• 10:18Speaker 01

  Perhaps I'll give an example to see to see how it goes. And in fact, the historical example is Newton's work on classical mechanics. So so Newton formulated the laws of mechanics, you know, the force F equals to ma and his other laws, and they look very simple, elegant, and so forth. Later, when we studied more examples 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 it a priori, but it solved, helps some thoughts.

• 10:57Speaker 01

  And then later, 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.

• 11:43Speaker 01

  Now, this sounded like a backwards step from Newton's. Newton's formula seemed very simple. F equals to ma and you can write F is 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 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? So Euler and Lagrange's formulation of Newton, which is a, which was kind of a 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 minimal action. Now, what we learned later, last century, was that when we deal with quantum mechanics, Newton's law is only an average correct.

• 12:29Speaker 01

  And the particle going from one to the other doesn't take exactly one path. It takes all the paths.

• 12:36Lex Fridman?

  Yes.

• 12:36Speaker 01

  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?

• 12:54Lex Fridman?

  When we say amplitude, you mean probability?

• 12:56Speaker 01

  But yes, the amplitude means if you sum up all these paths with exponential i times the action. If you sum this up, you get the number, complex number. You square the norm of this complex number gives you a probability to go from one to the other.

• 13:09Lex Fridman?

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

• 13:18Speaker 01

  Yes, I would say that mathematics can lead us astray as much as old physical ideas can lead us astray. So it is if you get stuck in some something, then you can easily fool yourself that just like the thought process, we have to free ourselves of that. Sometimes math does that role, like say, oh, this is such a beautiful map. I definitely want to use it 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 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 mind about

• 13:59Speaker 01

  the role that math plays, not to be antagonistic towards it and not to over welcoming it. We should just be open to possibilities.

• 14:07Lex Fridman?

  What about looking at a particular characteristics of both physical ideas and mathematical ideas, which is beauty? You think beauty leads us astray, meaning and you offline showed me a really nice puzzle that illustrates this idea a little bit. Now, maybe you can speak to that or another example where beauty. Makes it tempting for us to assume that the law and the theory we found is actually one that perfectly describes reality.

• 14:36Speaker 01

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

• 14:44Lex Fridman?

  So beauty is fundamental in the universe?

• 14:46Speaker 01

  I think beauty is fundamental, at least that's the way many of us view it.

• 14:49Lex Fridman?

  It's not emergent?

• 14:50Speaker 01

  It's not emergent. I think Hardy is the mathematician who said that there's no permanent place for ugly mathematics. And so I think the same is true in physics, that if we find a principle which looks ugly, 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 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 partly, you could say, based on experience of science over centuries, partly is philosophical

• 15:33Speaker 01

  view of what reality is or should be. And in principle, you know, it could have been ugly and we might have had to deal with it, but we have gotten maybe confident through examples after examples in the history of science to look for beauty.

• 15:49Lex Fridman?

  And our sense of beauty seems to incorporate a lot of things that are essential for us to solve some difficult problems like symmetry. We find symmetry beautiful and the breaking of symmetry beautiful. Somehow symmetry is a fundamental part of how we conceive of beauty at all layers of reality, which is interesting. Like in both the visual space, like where 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 the work you do. It's kind of interesting. It makes you wonder like.

• 16:25Lex Fridman?

  Which one is the chicken or the egg? Is symmetry the chicken in our conception of beauty, the egg? Or the other way around? Or somehow the fact that every the symmetry is is part of reality is it somehow creates the brain that then is able to perceive it? Or maybe that's this is just because we maybe it's so obvious, it's almost trivial that symmetry, of course, will be part of every kind of universe that's possible.

• 16:54Lex Fridman?

  And then are any kind of organism that's able to observe that universe is going to appreciate symmetry?

• 17:01Speaker 01

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

• 17:06Lex Fridman?

  Yeah.

• 17:06Speaker 01

  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 I think this is this is perhaps related to sense of aesthetics that scientists have.

• 17:50Speaker 01

  And we don't usually talk about it among scientists. In fact, it's kind of a philosophical view of why do we look for simplicity or beauty or so forth? And I think in a sense, scientists are a lot like philosophers. Sometimes I think especially modern science seems to shun philosophers and philosophical views. And I think at their peril. I think I think in my view, science owes a lot to philosophy. And in my view, many scientists, in fact, probably all good scientists are perhaps amateur philosophers. They may not state that they are philosophers or they may not like to be labeled philosophers. But in many ways, what they do is like what is philosophical takes of things.

• 18:35Speaker 01

  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 no 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 phenomenon, which is a physical phenomenon, which you call B prime.

• 19:17Speaker 01

  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 so today.

• 19:27Lex Fridman?

  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. There's a sense in which, if it's true, that we haven't figured out most of how things work currently, that 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

• 20:12Lex Fridman?

  the the way we perceive the world, the way we conceive of it, of our place in the world, those those ideas will carry on.

• 20:19Speaker 01

  I completely agree. In fact, I believe that almost, well, I believe that none of the principles or laws of physics we know today are exactly correct. All of them are approximations to something. They are better than the previous versions of what 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 scientists or maybe even all the way back to Greek philosophers and the things that the way they thought and so on, almost everything they said about, you know, nature was incorrect. But the way they thought about it and many things that they were thinking is still valid today.

• 21:03Speaker 01

  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 have seen the length of the shadow of a 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.

• 21:28Lex Fridman?

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

• 21:31Speaker 01

  Very brilliant, very brilliant. So these Greek philosophers are very smart. And so they had taken it to the next step. They asked, okay, so the earth is round. Why doesn't it move? 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 really wanna deeply understand that fact. And they come up with a symmetry argument. And the symmetry argument was, oh, if the earth is a spherical, it must be at the center of the universe for sure. So they said the earth is at the center of the universe.

• 22:04Lex Fridman?

  That makes sense.

• 22:04Speaker 01

  And they said, you know, if the earth is going to move, which direction does it pick? Any direction it picks, it breaks that spherical symmetry because you have to pick a direction. 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 earth doesn't move. And they, but they had this beautiful idea that symmetry might explain it. But they were even smarter than that. Aristotle didn't agree with this argument. 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.

• 22:46Speaker 01

  And we spread food around you on a circle around you, loaves of bread, let's say. 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're going to get hungry, you're going to move towards one of those loaves of bread, despite the fact that it breaks the symmetry. 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.

• 23:31Speaker 01

  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.

• 23:39Lex Fridman?

  Did they use the language of symmetry and symmetry breaking and spontaneous symmetry breaking? That's really interesting. Cause like, I could see a conception of the universe that kind of tends towards perfect symmetry and is stuck there, like they, not stuck there, but achieves that optimal and stays there. The idea that you would spontaneously break out of symmetry, like have these perturbations, jump out of symmetry and back. That's not, that's a really difficult idea to, to load into your head. Like where, where does that come from? And then, and then the idea that you may not be at the center of the universe.

• 24:18Speaker 01

  Right.

• 24:19Lex Fridman?

  That is a really tough idea.

• 24:21Speaker 01

  Right. So symmetry sometimes an explanation of being at the symmetric point is sometimes a simple explanation of many things. Like if you have a bowl, a circular bowl, then the bottom of it 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 it's the preferred point, the lowest energy point. But if that same symmetric circular bowl that you had had a bump on the, on the bottom. The bottom might not be at the center. It might be on a circle on the table.

• 24:52Lex Fridman?

  Yeah.

• 24:53Speaker 01

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

• 25:01Lex Fridman?

  Yeah.

• 25:01Speaker 01

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

• 25:09Lex Fridman?

  We talked about beauty. I find geometry to be beautiful. You have a few examples that are geometric in nature in your book. 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?

• 25:34Speaker 01

  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 discovered, had these beautiful solids. They thought it must be good for some reality. They must be explaining something. They attached, you know, one to air, one to fire, and so forth. They tried to give physical reality to symmetric objects.

• 26:02Speaker 01

  These symmetric objects are symmetries of rotation and discrete symmetry groups, we call today, of 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 realities of physics. But actually, it turns out, in modern days, we use symmetries in not-too-far-away exactly in these kind of thoughts, processes, in the following way. In the, in the context of string theory, which is this, the Feelley 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,

• 26:47Speaker 01

  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 quotient the space by it, in other words, identify points under these symmetries, you get properties of that space at the singular points which force emanates from them. 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.

• 27:29Speaker 01

  But nevertheless, the symmetry is connecting geometry to physics. In fact, often we sometimes we have we ask the following question. Suppose I want to get this particular, you know, physical reality. I want to have these 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 put this sphere here. I would do this. I will shrink them. So if you have two spheres touching each other and shrinking to 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.

• 28:14Lex Fridman?

  The sad thing is when you go into multiple dimensions, and we'll talk about it, is we start to lose our capacity to 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 before we go into that mysterious, beautiful world, let's take a small step back. And you also in your book have this kind of. Through the space of puzzles, through the space of ideas, have a brief history of physics, of physical ideas. Now, we talked about Newtonian mechanics, leading all through different Lagrangian, Hamiltonian mechanics. Can you describe some of the key ideas in

• 28:57Lex Fridman?

  the history of physics, maybe lingering on each, from electromagnetism to relativity to quantum mechanics and to today, as we'll talk about with quantum gravity and string theory?

• 29:09Speaker 01

  Sure. So I mentioned the classical mechanics and the old Lagrangian formulation. One of the next important milestones for physics were the discoveries of laws of electrician magnetism. So Maxwell 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 Faraday's and others had made about electric and magnetic phenomena, in terms of mathematical equations, it didn't quite work. There was a mathematical inconsistency. Now, you know, one could have had two attitudes. One say, okay, who cares about math? I'm doing nature, electric force, magnetic force, math I don't care about. But it bothered

• 29:54Speaker 01

  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. But he figured out, if you add this jiggle, this 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. Why did he add it? Well, because of mathematical consistency. So he said, okay, math forced him to 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, differential equations, mathematically consistent, beautiful. But he also found a new physical phenomenon. He found that because of that term, he could now get electric and magnetic waves moving

• 30:41Speaker 01

  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 wasn't alive to see the verification of that prediction, and indeed 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 electrical magnetic phenomena, which was later confirmed.

• 31:24Speaker 01

  So then physics progresses and it comes to Einstein. Einstein looks at Maxwell's equation, says, beautiful, these are nice equation, except we get one speed light. Yeah. Who, who measures this light speed? And he asked the question, are you, 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 the speed. It's just you always get the speed. So Einstein was very puzzled and he, he was daring enough to say, well, you know, maybe everybody gets the same speed for light. Yeah. And that motivated this theory of special relativity. And this is an interesting example because the idea was motivated from physics, from Maxwell's equations,

• 32:06Speaker 01

  from the fact that people tried to, tried 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, the speed of, if you're at rest with respect to the ether, the 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 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 the math underpinning it is very simple.

• 32:48Speaker 01

  It's linear algebra, nothing terribly deep. You can teach it at a high school level, if not earlier. Okay, 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.

• 33:15Lex Fridman?

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

• 33:20Speaker 01

  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. It's hard to swallow. It doesn't sound right. It sounds completely wrong on the face of it. And it was took Einstein to make to make this daring statement. 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.

• 33:44Lex Fridman?

  How does that make you feel? Because it it still sounds ridiculous.

• 33:48Speaker 01

  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. And part of it is because we live in a situation where we don't go with very high speeds. There are 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 is no absolute time. When you say it's noon today now, it depends on who's measuring it. And it not everybody would agree with that statement. And to see that, you will 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.

• 34:32Speaker 01

  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. Like even when I'm describing it, I feel like a little bit like, isn't it not funny? As you're just feeling the same way. It is.

• 34:51Lex Fridman?

  Yes.

• 34:52Speaker 01

  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. 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, let's go back to Greek philosophers or maybe Aristotle in this case. Now again, let's make a criticism. He thought that objects, the heavier objects fall faster than the lighter objects. Makes sense. It kind of makes sense and, you know, people say about feather and so on, but that's because of the air resistance. But you might think like if you have a heavy stone and a light pebble, the heavy one will fall first.

• 35:35Speaker 01

  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 did the experiment. Famously, it 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 he dropped it at the same time from the same height. Okay, good. So he said, I'm done, you know, I've shown that the heavy and lighter objects fought at the same time. I did the experiment. Scientists at that time did not accept it. Why was that? 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? Why?

• 36:20Speaker 01

  So Galileo had to come up with an explanation of why heavier and lighter objects fought the same rate. This is the way he convinced them, using symmetry. 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 tells you, you know, they're all the same shape, same size, same height. Of course, they fall at the same time. Yeah, we know that. Next, next. 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,

• 37:04Speaker 01

  because the height translation, horizontal translation is a symmetry. No, it doesn't matter. They all fall the same rate. Good. Doesn't matter how close I bring them together. No, it doesn't. Okay, suppose I make the two bricks touch and then let them go. Do they fall at the same rate? Yes, they do. But they said, well, the two bricks that touch are twice more mass than this other brick. And you just agreed that they fall at the same rate. They say, yeah, yeah, we just agreed. That's right. That's strange. Yes. So he deconfused them by this symmetry reasoning. So this way of repackaging some intuition, a different intuition. When the intuitions clash, then you then you side on the you replace the intuition.

• 37:41Lex Fridman?

  That's brilliant. I in some of these 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? You you start to think about like the edges of supermassive black holes. And you start to think like, what? What's that look like? Or I've been into gravitational waves recently. It's like when the fabric of spacetime is being morphed by gravity. Like, what's that actually feel like? If I'm riding a gravitational wave, what's that feel like?

• 38:25Lex Fridman?

  I mean, I think some of those are more sort of hippie, not useful 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 escape through thinking, prolonged thinking and meditation on a world, like live in a visualized world that's not like our own in order to understand a phenomenon 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 a way to escape with a three dimensional world

• 39:09Lex Fridman?

  in our mind in order to then start to reason about it. It's the more I talk to topologists.

• 39:17Lex Fridman?

  The more they seem to not operate at all in the visual space. They really trust the mathematics, which is really annoying to me because topology and differential geometry feels like it has a lot of potential for beautiful pictures.

• 39:34Speaker 01

  Yes, I think they do. Actually, I would not be able to do my research if I don't have an intuitive feel about geometry. And we'll get to it, as you mentioned before, that's 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 don't think you can just rely on formalism. I don't. I don't think any physicist just relies on formalism. That's not physics. That's not understanding. So we have to intuit. And that's crucial. And there are steps of doing it, and we learned, it might not be trivial, but we learned how to do it. Similar to this Galileo picture I just told you, you have to build these gradually.

• 40:16Lex Fridman?

  But to connect the bricks.

• 40:17Speaker 01

  You have to connect the bricks. Exactly. You have to connect the bricks. Literally. So, yeah. So then, so going back to your question about the path of the history of the science. So I was saying about the electromagnetic magnetism and the special relativity, where simple idea led to special relativity. But then he went further, thinking about acceleration in the context of relativity, and he came up with general relativity, where he talked about, you know, the fabric of spacetime being curved and so forth, and matter affecting the curvature of the space and time. So this gradually became a connection between geometry and physics, namely, he replaced Newton's gravitational force with a very geometrical

• 41:01Speaker 01

  beautiful picture. It's much more elegant than Newton's, but much more complicated mathematically. So when we say it's simpler, we mean, in some form, it's simpler, but not in pragmatic terms of equation solving. The equations are much harder to solve than Einstein's. 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, like if you had a symmetric sun. He didn't think you can actually write the, solve his equation for that. And a year after, he said that it was solved by Shorchild. So it was, it was that hard that he didn't think it's going to be that easy. So, yeah, the formalism is hard. But the contrast between the special relativity and general relativity is very interesting

• 41:45Speaker 01

  because one of them has almost trivial math and the other one has super complicated math. Both are physically amazingly important. And so, so we have learned that, you know, the physics 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 going to touch this math because it's too much, you know, tensors or, you know, curvature and I don't like the four dimensional spacetime 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 develop calculus because physics pushed him, that he didn't have the tools.

• 42:29Speaker 01

  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 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 ways.

• 43:01Lex Fridman?

  Let me ask a ridiculous question. You know, you talk about your favorite soccer player, DeBarr. I'll ask the same question about Einstein's ideas, which is, which one do you think is the biggest leap of genius? Is it the E equals MC squared? Is it Brownian motion? Is it special relativity? Is it general relativity? Which, which of, of the famous set of papers he's written in 1905 and in general, his work was the biggest leap of genius?

• 43:30Speaker 01

  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.

• 43:37Lex Fridman?

  The beginning is the seed.

• 43:38Speaker 01

  The beginning is the seed.

• 43:38Lex Fridman?

  Once you embrace that weirdness, all the weirdness.

• 43:41Speaker 01

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

• 43:46Lex Fridman?

  Yes.

• 43:46Speaker 01

  He says that 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 next to the earth gravitational. 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, you know, some, some funny coincidence. 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.

• 44:15Lex Fridman?

  The general relativity to you is not like the conception of spacetime.

• 44:21Speaker 01

  In a sense, the conception of spacetime already was part of special relativity when you talk about length contraction. 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 than its curvature. So you don't have a choice. So it's kind of started just with that same simple thought. Speed of light is the same for all.

• 44:45Lex Fridman?

  Where does quantum mechanics come into view?

• 44:48Speaker 01

  Exactly. So this is the next step. So Einstein's, you know, developed general relativity and he's beginning to develop the foundation of quantum mechanics at the same time, the photoelectric effects and others. And 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 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.

• 45:24Lex Fridman?

  Can we pause and briefly say what is quantum mechanics?

• 45:27Speaker 01

  Oh yes, sure. So quantum mechanics, so I, I discussed briefly when I talked about the connection with, between Newtonian mechanics and the Euler-Lagrange re-formulation of, of the Newtonian mechanics and interpretation of this Euler-Lagrange 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 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. And deviation from that is very, very unlikely and probabilistically very miniscule.

• 46:10Speaker 01

  So in everyday experiment, 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 precise as the line you draw. Things are a bit like cloud. So if you go to microscopic scales, like atomic scales and lower, these phenomena become more pronounced. You can see it much better. The electron is is not at the point, but the cloud spread out around the nucleus. And so this fuzziness, this probabilistic aspect of reality is what quantum mechanics describes.

• 46:45Lex Fridman?

  Can I briefly pause on that on that idea? Do you think this is quantum mechanics is just a really damn good approximation? A tool for predicting reality? Or does it actually describe reality? Do you think reality is fuzzy at that level?

• 47:02Speaker 01

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

• 47:08Lex Fridman?

  Right.

• 47:08Speaker 01

  So 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 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're 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 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 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

• 47:51Lex Fridman?

  This is the end of the story.

• 47:52Speaker 01

  Exactly correct. It doesn't bother me.

• 47:54Lex Fridman?

  Yeah.

• 47:54Speaker 01

  I'm not like dogmatic, say, I have figured out this is the law of nature. I know everything. No, no, that's that's the beauty about science that we are not dogmatic. And we are we are willing to, in fact, we are encouraged to be skeptical of what we ourselves do.

• 48:10Lex Fridman?

  So you were talking about Dirac.

• 48:12Speaker 01

  Yes, I was talking about Dirac, right. So Dirac was trying to now combine this Schrodinger's equations, 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 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 he wrote this beautiful equation, the Dirac equation, which roughly speaking, take the square root of 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 naive thing that Einstein's equation would have given,

• 48:57Speaker 01

  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, 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, 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 is 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. Just before him, Pauli had said, you know,

• 49:41Speaker 01

  there's this principle called the exclusion principle, that, you know, two electrons cannot be on the same orbit. And so Dirac said, okay, you know what? All these negative energy states are filled orbits, occupied. So according to you, Mr. Pauli, there's no place to go. So therefore, they only have to go positive. Sounded like a big cheat. 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?

• 50:25Speaker 01

  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, cannot be proton, because proton is heavier." Dirac was stuck, he says, "Well, then maybe another particle we haven't seen."

• 50:44Speaker 01

  By that time, Dirac himself was getting a little bit worried about his own equation and his own crazy interpretation. Until a few years later, Anderson, in photographic cosmic, in the photographic place that he had gotten from these cosmic rays, he discovered 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 this simple math, you know, there's a plus and a minus from the Dirac's quote-unquote mistake.

• 51:29Speaker 01

  So again, trying to combine ideas, sometimes the math is smarter than the person who uses it to apply it, and we try to resist it, and then you you're kind of confronted by criticism, which is the way it should be. So physicist comes and says, "No, no, that's wrong," and you 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. 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 fields and magnetic fields everywhere, and the math for that

• 52:14Speaker 01

  was was was very difficult to deal with. And this led to a subject called quantum field theory. Fields, 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 pioneers, along with Schröinger 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 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 physics progressed. And so, basically,

• 52:58Speaker 01

  we learned that all particles and all the forces are, in some sense, related to particle exchanges. And so, for example, electromagnetic forces are mediated by a particle we call photon, and so forth. And the same for other forces that they discovered, strong forces and the weak forces. So we got a sense of what quantum field theory is.

• 53:20Lex Fridman?

  Is that a big leap of an idea that particles are fluctuations in a field, like the idea that everything is a field? 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 as fields?

• 53:42Speaker 01

  I would say so. I would say that 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 leaps of imagination that quantum mechanics made physicists do. So I agree that that is quite remarkable.

• 54:02Lex Fridman?

  Is duality fundamental to the universe, or is it just because we don't understand it fully? Like, we'll eventually collapse into a clean explanation that doesn't require duality, like that a phenomenon could be two things at once, and both to be true?

• 54:21Lex Fridman?

  So that seems weird.

• 54:22Speaker 01

  So in fact, I was going to get to that when we get to string theory, but maybe I can comment on it now. Duality turns out to be running the show today is the whole thing that we are doing is string theory. Duality is the name of the game. So it's the most beautiful subject and I want to talk about it.

• 54:37Lex Fridman?

  Let's talk about it in the context of string theory. So we, do you want to take a next step into, because we mentioned general relativity, we mentioned quantum mechanics. Is there something to be said about quantum gravity?

• 54:49Speaker 01

  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 curvature of spacetime according to Einstein, you get another particle called graviton. So what about gravitons? 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 with graviton with an electron and so on, see what you get. Feynman had already mastered this quantum electrodynamics. He said, no problem, let me do it.

• 55:31Speaker 01

  Even though these are such weak forces, the gravity is very weak. So therefore, to see them, these quantum effects of gravitational waves was impossible. It's even impossible today. So Feynman just did it for fun. He usually 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 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. And it didn't make any sense. Now, there were similar infinities in the other pieces, but he had managed to make sense out of those before. This was no way he could make sense out of it.

• 56:16Speaker 01

  He just didn't know what to do. He didn't feel it's an urgent issue because nobody could do the experiment. 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. But that cannot be the case because gravity is in our universe. Quantum mechanics in our universe, they both together somehow should work. So 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.

• 56:58Lex Fridman?

  So the infinity shows up. What do we do? What do we do with infinity? Let's get to the fun part. Let's talk about string theory.

• 57:05Speaker 01

  Yes.

• 57:07Lex Fridman?

  Let's discuss some technical basics of string theory. What is string theory? What is a string? How many dimensions are we talking about? What are the different states? How do we represent the elementary particles and the laws of physics using this new framework?

• 57:26Speaker 01

  So string theory 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 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 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.

• 58:09Speaker 01

  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. This is a less massive. So the lightest harmonic, so to speak, is no harmonics, which means like the string shrunk to a point. And then it becomes like a massless particles or light particles like photon and graviton and so forth. So when when you look at Tiny strings, which are shrunk to a point, the lightest ones, they look like the particles that 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.

• 58:53Lex Fridman?

  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?

• 59:15Speaker 01

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

• 59:19Lex Fridman?

  With zero thickness.

• 59:20Speaker 01

  So notice, it's a, it's a, it's a loop of energy, so to speak. If you can think of it that way. And so there's a tension like a regular string. If you pull it, there's, you know, you have to, you have to stretch it. But it's not like a thickness, like you're made of something. It's just energy. It's not made of atoms or something like that.

• 59:36Lex Fridman?

  But and it is very, very tiny.

• 59:38Speaker 01

  Very tiny.

• 59:38Lex Fridman?

  Much smaller than elementary particles of physics.

• 59:42Speaker 01

  Much smaller. So we think if you let the string to be by itself, the lowest state, there will be like fuzziness or a size of that tiny little circle, which is like a point about, could be anything between, we don't know the 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 to the minus 30 centimeters, just to compare with the size of the atom, which is 10 to the minus eight centimeters, is 22 orders of magnitude smaller. So.

• 1:00:10Lex Fridman?

  Unimaginably small, I would say.

• 1:00:12Speaker 01

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

• 1:00:17Lex Fridman?

  Yeah.

• 1:00:17Speaker 01

  And that's why a lot of the things that we learned about point particle physics carries over directly to strings. So therefore, there's not, not much of a mystery why particle physics was successful, because 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 this puzzles that Feynman was having in calculating his diagrams. And it gets rid of those infinities. So when you're trying to do those infinities, the regions that give infinities to Feynman, as soon as you get to those regions, then this string starts to oscillate. And this oscillation structure of the strings resolves those infinities to finite answer at the end.

• 1:00:59Speaker 01

  So the size of the string, the fact that it's one dimensional, gives a finite answer at the end, resolves this paradox. Now, perhaps it's also useful to recount of how string theory came to be. Yes. Because it wasn't like somebody say, well, let me solve the problem of Einstein'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, Vennettiano in this case, was trying to describe the interactions they were seeing in colliders, in accelerators. And they were seeing that some process, in some process, when two particles came together

• 1:01:43Speaker 01

  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 we're 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, not a method to compute it, just say, wouldn't it be nice if this was the answer? Yes. Physicist looked at this one, hmm, that's intriguing.

• 1:02:27Speaker 01

  It has this symmetry all right, but what is this? Where is this coming from? Which, which kind of physics gives you this? So I don't know. A few years later, people saw that, oh, the equation that you're writing, the process that you're writing in the intermediate channels that particles come together seems to have all the harmonics. Harmonic 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 anything to do with the strings. Oh, yeah, indeed. If I study scattering of two strings, I get exactly the formula you wrote down. That was the reinterpretation of what he had written and the formula as a string. But it still had nothing to do with gravity. It had nothing to do with resolving the problems of gravity with quantum mechanics.

• 1:03:11Speaker 01

  It was just trying to explain a process that people were seeing in hadronic physics collisions. So it took a few more years to get to that point. They noticed that, physicists noticed that whenever you try to find the spectrum of strings, you always get a massless particle, which has exactly the properties that the graviton is supposed to have. And no particle in hadronic physics that had that property. You are getting a massless graviton as part of this 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.

• 1:03:55Speaker 01

  Physicists, Shirkhan Shor said, you know what? String theory is theory of quantum gravity. They changed their perspective altogether. We are not describing the hadronic physics. We're describing the theory of quantum gravity.

• 1:04:06Lex Fridman?

  And that's when string theory probably got like exciting, that this could be the unifying theory.

• 1:04:13Speaker 01

  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.

• 1:04:34Speaker 01

  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, 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 else. So anyhow, it wasn't paid much attention to. And this took a little bit more effort to try to actually connect it to, to reality. There were a 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.

• 1:05:16Speaker 01

  Now, there are different versions of strings, but the version that ended up being related 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, this version of the string which had fermions, had an extra symmetry,

• 1:05:38Speaker 01

  which we call supersymmetry. 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 them is a boson, one of them is a fermion because of that shift of spin. Otherwise, they are identical. So there was this symmetry. String theory had this symmetry. In fact, supersymmetry was discovered through string theory theoretically.

• 1:06:08Speaker 01

  So theoretically, the first place that this was observed, when, when you were describing these fermionic strings. So that was the beginning of the study of supersymmetry was via string theory. And then it had remarkable properties that, you know, the symmetry meant and so forth, that people began studying supersymmetry after that. And that was continuation, that was a kind of a tangent direction at the beginning for string theory. But people in particle physics started also thinking, oh, supersymmetry is great. Let's see if we can have supersymmetry in particle physics and so forth. Forget about strings and they developed on a different track as well. Supersymmetry in different models became a subject on its own right. Understanding supersymmetry and what does this mean? Because it unified bosons and fermions, unified some ideas together.

• 1:06:52Speaker 01

  So photon is a boson, electron is a fermion. Could things like that be somehow related? 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. It is not our universe because we live in three plus one dimension. How could that be possibly true? So this was a conundrum.

• 1:07:34Speaker 01

  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'll 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 tried 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.

• 1:08:19Speaker 01

  Now, this was a way to avoid conflict, but it was not observed in experiments. A string observed in experiments? No, because it's so small. 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 the dimension, but I also have to this, I have to also this. And so you, so conservative physicists would say, hmm, you know, I haven't seen these experiments. I don't know if they are really there. Are you pulling my leg? Do you want me to imagine things that are not there? So this was an attitude of some physicists towards string theory, despite the fact that

• 1:09:02Speaker 01

  the puzzle of gravity and quantum mechanics merging together work, but still was this skepticism. You're putting all these things like 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? So this kind of beginning to sound a little funny. Now, I was, I would pass forward, forward a little bit further. A few decades later, when string theory became the mainstream of efforts to unify the forces and particles together, we learned that these extra dimensions actually solved problems. They weren't a nuisance the, the way they originally appeared. First of all, the properties of these extra dimensions reflected the number of particles

• 1:09:46Speaker 01

  we got in four dimensions. If you took these six dimensions to have like six, five holes or four holes, it can change the number of particles that you see in four dimensional space time. You get one electron and one muon if you had this, but if you did the other J shape, you get something else. So geometrically, you could get different kinds of physics. So it was kind of a, a mirroring of geometry by physics down in the macroscopic space. So these extra dimensions 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 what? Was there any other puzzle? Yes, there were. Hawking. Hawking had been studying black holes in mid seventies, following the work of Bechenstein, who had predicted that black holes.

• 1:10:33Speaker 01

  Have entropy. So Beckenstein had tried to attach entropy to the black hole. If you throw something into the black hole, the entropy seems to go down because you had something entropy outside the black hole and you throw it. Entropy was, the black hole was unique, so the entropy did not have any, the black hole had no entropy. So you seem, the entropy seemed to go down. And so that's against the laws of thermodynamics. So Beckenstein 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, 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, a factor of a one quarter of the area in Planck units is the correct amount of entropy.

• 1:11:16Speaker 01

  And he gave an argument using quantum 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. So heuristic quantum arguments led to this entropy 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 the horizon of a black hole is huge. That's a huge amount of entropy. What are the microstates of this entropy? When you say, for example, the gas's entropy, you count where the atoms are. You can't see this bucket or that bucket. There's that 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.

• 1:12:01Speaker 01

  So where are these entropy? What are, what are these microscopic states? They were hidden somewhere. So later in string theory, the work that 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 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 in four dimensions. So the extra dimensions became useful

• 1:12:46Speaker 01

  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, we see aspects that extra dimensions are useful for many things. It's not a nuisance. It wasn't to be kind of, you know, be ashamed of. It was actually in the welcome features, new feature nevertheless.

• 1:13:11Lex Fridman?

  How do you intuit the 10 dimensional world? So yes, it's a feature for describing certain phenomena like the entropy in black holes. But what you said that to you, a theory becomes real or becomes powerful when you can connect it to some deep intuition. So how do we intuit 10 dimensions?

• 1:13:37Speaker 01

  Yes, so I will, I will explain 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 eight dimensional plane, we ask typically in what space do they intersect each other and 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 typically on a plane? The answer is no. So a line one dimensional, a point zero dimension on a two dimensional plane, they don't typically meet.

• 1:14:22Speaker 01

  But if you have a one dimensional line and another line, which is one plus one on 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 a 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.

• 1:14:54Speaker 01

  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. 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. Okay, we're beginning to see the pattern. Okay, now come to the question. We're in 10 dimension. Now we have the intuition. We have a seven dimensional plane and an eight dimensional plane in 10 dimension. They intersect on a plane. What's the dimension? Well, seven plus eight is 15, minus 10 is 5. We draw the same picture as two planes, and we write seven dimension, eight dimension,

• 1:15:39Speaker 01

  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 two dimensional visualization of it, but it has all the features we want. It has, so we draw this picture, it says seven, seven, and they they they meet at a five dimensional plane. It says five. So we have, we have built this intuition. Now, this is 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 be a little bit lost.

• 1:16:17Lex Fridman?

  So what you just described is kind of in these high dimensional spaces, focus on the meeting place of two planes in high dimensional spaces.

• 1:16:26Speaker 01

  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 10 dimensions, but we are drawing the same as a two dimensional plane, because we cannot do any better. But our our our words change, but not our pictures.

• 1:16:49Lex Fridman?

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

• 1:16:57Speaker 01

  Exactly, exactly. And this this is the comes, brings me to the next example I want to mention, which is sphere. Let's think about, how do we think about the sphere? Well, the sphere is a sphere, you know, the round, nice thing. But sphere has a circular symmetry. 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 endpoints of the interval. So I can say, oh, one way to think about the sphere is an interval,

• 1:17:40Speaker 01

  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 won't 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 endpoints of the interval mean a strong circle. That's all. And they 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? Easy. You just take an interval and another interval. That's just going to be a square. Yeah. 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,

• 1:18:23Speaker 01

  one of the circles shrink on each edge of that square. And when you get to the corners of the square, all both circles shrink. This is a sphere times a sphere. I have defined an interval. I just described for you a four dimensional space. 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 stick, take sphere times a sphere times a sphere. Take a cube. A cube is a rendition of this six dimensional space. Two 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 circles shrinks. When three boundaries meet, all the three circles shrink.

• 1:19:08Speaker 01

  So I just give you a picture. Now, mathematicians come up with amazing things. Like, you know what? I want to take a point in space and blow it up. You know, these concepts like topology and geometry, 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. Chopping off the corner replaces a point.

• 1:19:31Lex Fridman?

  Yeah.

• 1:19:32Speaker 01

  It replaces a point by a triangle.

• 1:19:33Lex Fridman?

  Yes.

• 1:19:34Speaker 01

  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 not talking about six dimension. Four plus six is 10, the dimension of string theory. So we can visualize it, no problem.

• 1:19:48Lex Fridman?

  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 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,

• 1:20:32Lex Fridman?

  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 me, from a sort of an outside observer perspective, have been observing a little bit of a 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?

• 1:21:06Speaker 01

  Yes.

• 1:21:07Lex Fridman?

  Can you do describe why this cynicism and how do we reverse that trend?

• 1:21:12Speaker 01

  Yes. First of all, the criticism for string theory is healthy in some in a sense that in science, we we have to have different viewpoints and that's good. So I don't I welcome criticism. And 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 little loop of energy moving around. And so that's a valid, valid 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.

• 1:21:54Speaker 01

  Because in science, we will have to have experimental consequences and checks. The difference between 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 are 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 you 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 how the nature works, even though I cannot prove it today that this is it because of experiments.

• 1:22:37Speaker 01

  That should not prevent my mind not to think about it. That's right. So that's the attitude many string theorists follow, that it should be like this. Now, so that's the 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 part of physics all the... Suppose you're just interested in particle physics. Suppose you're not even interested in gravity at all. It turns out there are properties of certain particle physics models that string theory has been able to solve using gravity,

• 1:23:22Speaker 01

  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? The 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, 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 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. Okay, gravity is a prediction of string theory.

• 1:24:07Speaker 01

  It's a post-diction because we know gravity existed. But still, logically, it is a prediction because really, we didn't know it had a graviton. We later learned that, oh, that's the same as gravity. So literally, that's the way it was discovered. It wasn't put in by hand. So there are many things like that, that there are different facets of physics. Like questions in condensed matter physics, questions of particle physics, questions about this and that 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, okay, great, you got some math, but what's it do with reality?

• 1:24:52Speaker 01

  But as I explained, many of the physical principles we know of have beautiful math underpinning them. So it certainly leads further confidence that we may not be going astray, even though that's not the foodproof, as we know. 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 give examples of that. So these are further evidences, and these are certain predictions of string theory. They are not as detailed as we want, but they are still predictions.

• 1:25:28Speaker 01

  Why is the dimension of space and time three plus one?

• 1:25:33Speaker 01

  Say, I don't know, just deal with it, three plus one. But in physics, we want to know why. Well, take a random dimension from one to infinity. What's your random dimension?

• 1:25:46Speaker 01

  A random dimension from one to infinity would not be four. Eight would most likely be a humongous number, if not infinity. I mean, if you choose any reasonable distribution which goes from one to infinity, three or four would not be your pick. The fact that we are in three or four dimension is already strange.

• 1:26:05Speaker 01

  The fact that strings is sorry, I cannot go beyond 10 or maybe 11 or something. The fact that there's just upper bound. The range is not from 1 to infinity, it's from 1 to 10 or 11 or whatnot. It already brings a natural prior, oh yeah, 3 or 4 is, you know, it's just on the average. If you pick some of the compactifications, then it could easily be that. So in other words, it makes it much more possible that it could be three of our universe. So the fact that the dimension already is so small, it should be surprising. We don't ask that question. We should be surprised because we could have conceived of universes with our pre-dimension. Why is it that we have such a small dimension? That's number one.

• 1:26:42Lex Fridman?

  So, oh, so, so a good theory of the universe should give you an intuition of the why it's 4 or 3 plus 1. And it's not obvious that it should be, that that should be explained. We take that as a, as an assumption, but that's a thing that should be explained.

• 1:27:00Speaker 01

  Yeah, so we haven't explained that in string theory. Actually, I did write a model within string theory to try to describe why we end up with 3 plus 1 space-time dimensions, which are big compared to the rest of them. And even though this has not been, the technical difficulty is to prove it is, is, is still not there. But I will explain the idea because the idea connects to some other piece of elegant math, which is the following. Consider a, a universe made of a box, three-dimensional box. Or in fact, if we start in string theory, nine-dimensional box, because we have nine spatial dimension on one time. So imagine a nine-dimensional box. So we should imagine the box of a typical size of the string, which is small.

• 1:27:42Speaker 01

  So the universe would naturally small, start with a very tiny nine-dimensional box. What do strings do? Well, strings go, you know, go, go around the box and move around and vibrate and all that. But also, they can wrap around one side of the box to the other because I'm imagining a box with periodic boundary conditions, so what we call the torus. So the, the string can go from one side to the other. This is what we call a winding string. The string can wind around the box. Now suppose you have, you now evolve the universe. Because there's energy, the universe starts to expand.

• 1:28:15Speaker 01

  But it doesn't it doesn't expand too far. Why is it? Well, because there are these strings which are wrapped around from one side of the wall to the other. When the universe, the walls of the universe are growing, it is stretching the string and the strings are becoming very, very massive. So it becomes difficult to expand. It kind of puts a halt on it. In order to not put a halt, a string which is going this way and a string which is going that way should should intersect each other and disconnect each other and unwind. So a string which winds this way and the string which finds the opposite way should find each other to reconnect and this way disappear. So if they find each other and they disappear. But how can strings find each other?

• 1:29:00Speaker 01

  Well, the string moves and another string moves. A string is one dimensional. One plus one is two and one plus one is two and two plus two is four. In four dimensional spacetime, they will find each other. In a higher dimensional spacetime, they typically miss each other.

• 1:29:17Lex Fridman?

  Oh, interesting.

• 1:29:18Speaker 01

  So if the dimension were too big, they would miss each other. They wouldn't be able to expand. So in order to expand, they have to find each other and three of them can find each other and those can expand and the other one will be stuck.

• 1:29:29Lex Fridman?

  So that that explains why within string theory, these particular dimensions are really big and full of exciting stuff.

• 1:29:34Speaker 01

  That could be an explanation. That's the model we suggested with my colleague Brandenberger. But it turns out to be related to a deep piece of math. You see, for mathematicians, manifolds of dimension bigger than four are simple. Four dimension is the hardest dimension for math. It turns out. And it turns out the reason it's difficult is the following. It turns out that in higher dimension, you use what's called surgery in mathematical terminology, where you use these two dimensional tubes to maneuver them off of each other. So you have two plus two becoming four. In higher than four dimension, you can pass them through each other without them intersecting. In four dimension, two plus two.

• 1:30:19Speaker 01

  Doesn't allow you to pass them through each other. So the same techniques that work in higher dimension don't work in four dimension. Because two plus two is four. The same reasoning I was just telling you about strings finding each other in four ends up to be the reason why four is much more complicated to classify for mathematicians as well. So so there might be these these things. So I cannot say that this is the reason that string theory is is giving you three plus one, but it could be a model for it. And so so there are these kind of ideas that could underlie why we have three extra dimensions, which are large and the rest of them are small. Because absolutely, we have to have a good reason. We cannot leave it like that.

• 1:30:53Lex Fridman?

  Can I ask a tricky human question? So you are one of the seminal figures in string theory. You got the breakthrough prize. You've worked with Edward Witten. There's no Nobel Prize that has been given on string theory. You know, credit assignment is tricky in science. It makes you quite sad, especially big like LIGO, big experimental projects, when so many incredible people have been involved. And yet, the Nobel Prize is annoying in that it's only given to three people. Who do you think gets the Nobel Prize for string theory at first?

• 1:31:31Lex Fridman?

  If it turns out that it, if not in full, then in part, is is a good model of the way the physics of the universe works. Who are the key figures? Maybe let's put Nobel Prize aside. Who are the key figures?

• 1:31:48Speaker 01

  I like the second version of the question. Because I think to try to give a prize to one person in string theory doesn't do justice to the diversity of the subject. That to me is.

• 1:31:57Lex Fridman?

  So there was quite a lot of incredible people in the history of string theory.

• 1:32:00Speaker 01

  Quite a lot of people. I mean, starting with Veneziano, who wasn't talking about strings. I mean, he wrote down the the beginning of the strings. We cannot ignore that for sure. And so so you start with that and you go on with various other figures and so on. So there are different epochs in string theory. And different people have been pushing it. And so, for example, the early epoch, we just told you, people like like Veneziano and Nambu and the Soskin and others were pushing it. Green and Shor's were pushing it and so forth. So this was or Sherrick and so on. So these were the initial periods of.

• 1:32:31Speaker 01

  Pioneers, I would say, of string theory. And then there were, there were the mid eighties that Edward Witten was the major proponent of string theory and he really changed the landscape of string theory in terms of what people do and how we view it. And I think his efforts brought a lot of attention to the community about, high energy community to focus on this effort as the correct theory of unification of forces. So he brought a lot of research, as well as, of course, the first rate work he himself did to this area. So that's in mid eighties and onwards, and also in mid nineties where he was one of the proponents of the duality revolution in string theory. And with that came a lot of these other ideas that, you know, led to breakthroughs involving,

• 1:33:13Speaker 01

  for example, the example I told you about black holes and holography and the work that was later done by Malda Sena about the properties of duality between particle physics and quantum gravity and the connections, deeper connections of holography, and it continues. And there are many people within this range, which I haven't even mentioned, that have done fantastic important things. How it gets recognized, I think, is secondary, in my opinion, than the appreciation that the effort is collective, that in fact, that to me is the more important part of science that gets forgotten. For some reason, humanity likes heroes and science is no exception. We like heroes, but I personally try to avoid that trap.

• 1:33:57Speaker 01

  I feel, and in my work, most of my work is with colleagues. I have much more collaborations than solo author papers and I enjoy it. And I think that that's to me, one of the most satisfying aspects of science is to interact and learn and debate ideas with colleagues because that in flux of ideas enriches it. And that's why I find it interesting. To me, science, if I was in an island. And if I was developing string theory by myself and had nothing to do with anybody, it would be much less satisfying, in my opinion. Even if I could take credit, I did it.

• 1:34:33Lex Fridman?

  Yeah.

• 1:34:33Speaker 01

  It won't be as satisfying.

• 1:34:35Lex Fridman?

  Sitting alone with the with the big metal drinking champagne, no.

• 1:34:39Speaker 01

  I think I think to me, the collective work is more exciting. And you mentioned my getting the breakthrough. When I was getting it, I made sure to mention that it is because of the joint work that I've done with colleagues. At that time, it was around 180 or so collaborators, and I acknowledged them in the in the webpage for them. I write all of their names and the collaborations that led to this. So to me, science is fun when it's collaboration. And yes, there are more important and less important figures, as in any field. And that's true. That's true in string theory as well. But I think that I would like to view this as a collective effort.

• 1:35:13Lex Fridman?

  So, setting the heroes aside, the Nobel Prize is a celebration of, what's the right way to put it? That this idea turned out to be right. So like, you look at Einstein didn't believe in black holes.

• 1:35:29Speaker 01

  Right.

• 1:35:30Lex Fridman?

  And then black holes got their Nobel Prize.

• 1:35:33Speaker 01

  Right.

• 1:35:34Lex Fridman?

  Do you think string theory will get its Nobel Prize Nobel Prizes? If you were to bet money, if this was like, if this was an investment meeting and we had to bet all our money, do you think he gets the Nobel Prizes?

• 1:35:48Speaker 01

  I think it's possible that none of the living physicists will get the Nobel Prize in string theory, but somebody will. Because because unfortunately, the technology available today is not very encouraging in terms of seeing directly evidence for string theory.

• 1:36:03Lex Fridman?

  Do you think it ultimately boils down to the Nobel Prize will be given when there is some direct or indirect evidence?

• 1:36:09Speaker 01

  There would be, but but I think that part of this breakthrough prize was precisely the appreciation that when we have sufficient evidence, theoretical as it is, not experiment, because of this technology lag, you appreciate what what you think is the correct path. So there are many people who have been have been recognized precisely because they may not be around when it actually gets experimented, even though they discovered it. So so there are there are many things like that that's going on in in science. So I think that I would I would want to attach less significance to the recognitions of people. And I have I have a I have a second review on this, which is. There are people who, you know, who look at these works that people have done and put them

• 1:36:53Speaker 01

  together and, you know, make the next big breakthrough. And they get identified with, you know, perhaps rightly with many of these, you know, new visions. But they are on the shoulders of these little scientists.

• 1:37:07Lex Fridman?

  Yes.

• 1:37:08Speaker 01

  Which don't get any recognition, you know, yeah, you did this little work. Oh, yeah, you did this little work. Oh, yeah, yeah, five of you. Oh, yeah, this showed this pattern and then somebody else. It's not fair.

• 1:37:18Lex Fridman?

  Yeah.

• 1:37:18Speaker 01

  To me, to me, those little guys, which, which kind of like, like seem to do a little calculation here, a little thing there, which is not, doesn't, doesn't rise to the occasion of this grandiose kind of thing, doesn't make it to the New York Times headlines and so on, deserve a lot of recognition. And I think they don't get enough. I would say that there should be this Nobel Prize for, you know, they have these Doctors Without Borders, a huge group, they should do similar thing, and the string theories without borders, kind of, everybody is doing a lot of work. And I think that I, I would like to see that effort recognized.

• 1:37:49Lex Fridman?

  I think in the long arc of history, we're all little guys and, and girls standing on the shoulders of each other. I mean, it's all going to look tiny in retrospect. If we celebrate, in New York Times, uh, it, you know, as a newspaper, or the idea of a newspaper in a few centuries from now will be long forgotten.

• 1:38:12Speaker 01

  Yes, I agree with that. Especially in the context of string theory, we should have very long term view.

• 1:38:17Lex Fridman?

  Yes, exactly. Just as a tiny tangent, we, we mentioned Edward Witten, and he, in a bunch of walks of life, for me, as an outsider, comes up as a person who is widely considered as like one of the most brilliant people in the history of physics, just as a powerhouse of a human, like, the, uh, the exceptional places that a human mind can rise to.

• 1:38:43Speaker 01

  Yes.

• 1:38:44Lex Fridman?

  Uh, you've gotten a chance to work with him. What's he like?

• 1:38:46Speaker 01

  Yes, more than that, he was my advisor, PhD advisor. So I, I got to know him very well and I benefited from his insights. In fact, What you said about him is accurate. He is not only brilliant, but you know, he is also multifaceted in terms of the impact he has had in not only physics, but also mathematics. You know, he's gotten a Fields Medal because of his work in mathematics and rightly so. You know, he has used his knowledge of physics in a way which impacted deep ideas in modern mathematics. And that's an example of the power of these ideas in modern high-energy physics and string theory, that the applicability of it to modern mathematics.

• 1:39:28Speaker 01

  So he's quite an exceptional individual. We don't come across such people a lot in history. So I think, yes, indeed, he's one of the rare figures in this history of the subject. He has had great impact on a lot of aspects of not just string theory, a lot of different areas in physics, and also, yes, in mathematics as well. So I think what you said about him is accurate. I had the pleasure of interacting with him as a student and later on as colleagues writing papers together and so on.

• 1:39:58Lex Fridman?

  What impact did he have on your life? Like, what have you learned from him? If you were to look at the trajectory of your mind, of the way you approach science and physics and mathematics, how did he perturb that trajectory?

• 1:40:10Speaker 01

  Yes, he did, actually. So I can explain it because when I was a student, I had the biggest impact by him, clearly as a grad student at Princeton. So I think that was a time where I was a little bit confused about the relation between math and physics. I got a double major in mathematics and physics at MIT, and because I really enjoyed both. And I liked the elegance and the rigor of mathematics, and I liked the power of ideas in physics and its applicability to reality and what it teaches about the real world around us. But I saw this tension between rigorous thinking in mathematics and lack thereof in physics, and this troubled me to no end. I was troubled by that.

• 1:40:54Speaker 01

  So I was at crossroads when I decided to go to graduate school in physics because I did not like some of the lack of rigors I was seeing in physics. On the other hand, to me, mathematics, even though it was rigorous and think it it's sometimes where I didn't see the point of it. In other words, when I see, when I, you know, the math theorem by itself could be beautiful, but I really wanted more than that. I want to say, okay, what does it teach us about something else, something more than just math. So I wasn't, I wasn't that enamored with just math, but physics was a little bit bothersome. Nevertheless, I decided to go to physics and I decided to go to Princeton. And I started working with Edward Witten as my thesis advisor. And at that time, I

• 1:41:34Speaker 01

  was trying to put physics in rigorous mathematical terms. I took one of field theory, I tried to make rigorous out of it and so on. And no matter how hard I was trying, I was not being able to do that. And I was falling behind from my classes. I was not learning much physics and I was not making it rigorous. And to me, it was this dichotomy between math and physics. What am I doing? I like math, but this is not exactly this. There comes Edward Witten as my advisor, and I see him in action, thinking about math and physics. He was amazing in math. He knew all about the math. It was no problem with him. But he thought about physics in a way which did not find this tension between the

• 1:42:18Speaker 01

  two. It was much more harmonious. For him, he would draw the Feynman diagrams, but he wouldn't view it as a formalism. He was viewed, oh yeah, the particle goes over there and this is what's going on. And so wait, you're thinking really, is this particle, this is really electron going there? Oh, yeah, yeah, this not, it's not the formal perturbation thing. No, no, you just feel like the electron, you're moving with this guy and do that and so on. And you're thinking invariably about physics. Or the way he thought about relativity, like, you know, I was thinking, you know, this momentum, he was thinking invariably about physics, just like the way you think about invariant concepts in relativity, which don't depend on the frame of reference. He was thinking about the physics in invariant ways, that the way that doesn't, that gives you a bigger perspective. So this gradually

• 1:43:01Speaker 01

  helped me appreciate that interconnections between ideas and physics replaces mathematical rigor. The different facets reinforce each other. You say, oh, I cannot rigorously define what I mean by this. But this thing connects with this other physics I have seen and this other thing. And they together form an elegant story. And that replaced for me what I believed as a solidness, which I found in math as a rigor. You know, solid. I found that replaced the rigor and solidness in physics. So I found, OK, that's the way you can hang on to. It is not wishy washy. It's not like somebody is just not being able to prove it, just making up a story. It was more than that. And it was no tension with mathematics.

• 1:43:45Speaker 01

  In fact, mathematics was helping it like friends. And so much more harmonious and gives insights to physics. So that's, I think, one of the main things I learned from interactions with Witten. And I think that now perhaps I have taken that to a far extreme. Maybe he wouldn't go this far as I have. Namely, I use physics to define new mathematics Yes. in a way which would be far less rigorous than a physicist might necessarily believe. Because I take the physical intuition, perhaps literally in many ways, that could teach us math. So now I've gained so much confidence in physical intuition that I make bold statements that sometimes, you know, takes math friends off guard. So an example of it is mirror symmetry.

• 1:44:27Speaker 01

  So we were studying these compactification of string geometry. This is after my PhD now. By the time I'd come to Harvard, we're studying these aspects of string compactification on these complicated manifolds, six dimensional spaces called Calabi-Yau manifolds. Very complicated. And I noticed with a couple of other colleagues that there was a symmetry in physics suggested between different Calabi-Yaus. It suggested that you couldn't actually compute the Euler characteristic of a Calabi-Yau. Euler characteristic is counting the number of points minus the number of edges plus the number of faces minus. So you can count the alternating sequence of properties of the space, which is a topological property of a space.

• 1:45:11Speaker 01

  So Euler characteristic of the Calabi-Yau was a property of the space. And so we noticed that from the physics formalism, if string moves in a Calabi-Yau, you cannot distinguish, we cannot compute the Euler characteristic. You can only compute the absolute value of it. Now, this bothered us because how could it not compute the actual sign?

• 1:45:32Speaker 01

  Unless the both signs were the same.

• 1:45:35Speaker 01

  So I conjectured, maybe for every Kalabia with the Oide characteristic is positive, there's one with negative. I told this to my colleague Yao, who was, whose namesake is Kalabia.

• 1:45:47Speaker 01

  That I'm making this conjecture, is it possible that for every Kalabia, there's one with the opposite Oide characteristic? Sounds not reasonable. I said, why? He said, well, we know more Kalabias with negative Oide characteristic than positive.

• 1:46:01Speaker 01

  I said, but physics says we cannot distinguish them, at least I don't see how. So we conjectured that for every Kalabia with one sign, there's the other one, despite the mathematical evidence. Despite the mathematical evidence, despite the expert telling us this is not the right idea. A few years later, this symmetry, mirror symmetry between the sign with the opposite sign was later confirmed by mathematicians. So this is actually the opposite view, that is, physics is so sure about it that you're going against the mathematical wisdom, telling them they better look for it.

• 1:46:32Lex Fridman?

  So taking the, the, the, the, the physical intuition literally, and then having that drive the, the mathematics.

• 1:46:38Speaker 01

  Exactly. And by now, we are so confident about many such examples that has affected modern mathematics in ways like this, that we are much more confident about our understanding of what string theory is. These are other aspects, other aspects of why we feel string theory is correct, is doing these kind of things.

• 1:46:56Lex Fridman?

  I've been hearing you talk quite a bit about string theory landscape and the swampland. What the heck are those two concepts?

• 1:47:04Speaker 01

  Okay, very good question. So let's go back to what I was describing about Feynman.

• 1:47:08Lex Fridman?

  Yes.

• 1:47:08Speaker 01

  Feynman was trying to do these diagrams for graviton and electrons and all that. He found that he's getting infinities he cannot resolve. Okay, the natural conclusion is that field theories and gravity and quantum theory don't go together, and you cannot have it. So in other words, field theories and gravity are inconsistent with quantum mechanics, period. String theory came up with examples, but didn't address the question more broadly that is it true that every field theory can be coupled to gravity in a quantum mechanical way?

• 1:47:44Speaker 01

  It turns out that Feynman was essentially right. Almost all particle physics theories, no matter what you add to it, when you put gravity in it, doesn't work. Only rare exceptions work. So string theory are those rare exceptions. So therefore, the general principle that Feynman found was correct. Quantum field theory and gravity and quantum mechanics don't go together. Except for Jewels, exceptional cases. There are exceptional cases. Okay. The total vastness of quantum field theories that are there, we call the set of quantum field theories, possible things. Which ones can be consistently coupled to gravity? We call that subspace the landscape.

• 1:48:29Speaker 01

  The rest of them, we call the swampland. It doesn't mean they are bad quantum field theories. They are perfectly fine. But when you couple them to gravity, they don't make sense, unfortunately. And it turns out that the ratio of them, the number of theories which are consistent with gravity to the ones without, the ratio of the area of the landscape to the swampland, in other words, is measure zero. And so the swampland is infinitely large? The swampland is infinitely large. So let me give you one example. Take a theory in four dimension with matter, with maximal amount of supersymmetry. Can you get? It turns out a theory in four dimension with maximal amount of supersymmetry is characterized just by one thing, a group. What we call the gauge group.

• 1:49:15Speaker 01

  Once you pick a group, you have to find the theory. Okay, so does every group make sense? Yeah. As far as quantum field theory, every group makes sense. There are infinitely many groups. There are infinitely many quantum field theories. But it turns out there are only finite number of them which are consistent with gravity out of that same list. So you can take any group, but only finite number of them. The ones whose, what we call the rank of the group, the ones whose rank is less than 23. Anyone bigger than rank 23 belongs to the swampland. There are infinitely many of them. They're beautiful field theories, but not when you include gravity. So then this becomes a hopeful thing. So in other words, in our universe, we have gravity.

• 1:49:58Speaker 01

  Therefore, we are part of that Jewels subset. Now, is this dual subset small or large? Yeah. It turns out that subset is humongous, but we believe still finite.

• 1:50:14Speaker 01

  The set of possibilities is infinite, but the set of consistent ones, I mean, the set of quantum features are infinite, but the consistent ones are finite, but humongous. The fact that they're humongous is the problem we are facing in string theory, because we do not know which one of these possibilities is the universe we live in. If we knew, we could make more specific predictions about our universe. We don't know. And that is one of the challenges with string theory. Which point on the landscape, which corner of this landscape do we live in? We don't know. So what do we do? Well, there are, there are principles that are beginning to emerge. So I will give you one example of it. You look at the patterns of what you're getting in terms of these good ones,

• 1:50:58Speaker 01

  the ones which are in the landscape compared to the ones which are not. You find certain patterns. I'll give you one pattern. You find in the all the ones that you get from string theory, gravitational force is always there, but it's always, always the weakest force.

• 1:51:17Speaker 01

  However, you could easily imagine field theories for which gravity is not the weakest force. For example, take our universe. If you take mass of the electron, if you increase the mass of electron by a huge factor, the gravitational attraction of the electrons will be bigger than the electric repulsion between two electrons. And the gravity will be stronger, that's all. It happens that it's not the case in our universe, because electron is very tiny in mass compared to that. Just like our universe, gravity is the weakest force. We find in all these other ones, which are part of the good ones, the gravity is the weakest force. This is called the weak gravity conjecture. We conjecture that all the points in the landscape have this property.

• 1:52:02Speaker 01

  Our universe being just an example of it. So there are these qualitative features that we are beginning to see. But how do we argue for this? Just by looking patterns? Just by looking string theory has this? No, that's not enough. We need more reason, more better reasoning, and it turns out there is. The reasoning for this turns out to be studying black holes. Ideas of black holes turn out to put certain restrictions of what a good quantum filter should be. It turns out, using black hole, the fact that the black holes evaporate, the fact that the black holes evaporate, gives you a way to to check the relation between the mass and the charge of elementary particle. Because what you can do, you can take a charged particle and throw it into a charged black hole

• 1:52:47Speaker 01

  and wait it to evaporate. And by looking at the properties of evaporation, you find that if it cannot evaporate particles whose mass is less than their charge, then it will never evaporate. You will be stuck. And so the possibility of a black hole evaporation forces you to have particles whose mass is sufficiently small so that the gravity is weaker. So you connect this fact to the other fact. So we begin to find different facts that reinforce each other. So different parts of the physics reinforce each other. And once they all kind of come together, you believe that you're getting the principle correct. So weak gravity conjecture is one of the principles we believe in, has a necessity of these conditions. So these are the predictions string theory are making. Is that enough? Well, it's qualitative. It's a semi-quantitative.

• 1:53:32Speaker 01

  It's just the mass of the electron should be less than some number. But that number is, if I call that number one, the mass of the electron turns out to be 10 to the minus 20, actually. So it's much less than one, it's not one. But on the other hand, there's a similar reasoning for a big black hole in our universe. And if that evaporation should take place, gives you another restriction, tells you the mass of the electron is bigger than 10 to the, now in this case, is bigger than something. It shows bigger than 10 to the minus 30 in the Planck unit. So you find, aha, the mass of the electron should be less than one, but bigger than 10 to the minus 30. In our universe, the mass of the electron is 10 to the minus 20. Okay, now this kind of you could call post-diction,

• 1:54:13Speaker 01

  but I would say it follows from principles that we now understand from string theory, first principle. So we are making, beginning to make these kinds of predictions, which are very much connected to aspects of particle physics that we didn't think are related to gravity. We thought, just take any electron mass you want. What's the problem? It has a problem with gravity.

• 1:54:34Lex Fridman?

  And so that conjecture. Has also a happy consequence that it explains that our universe, like, why the heck is gravity so weak? There's a force, and it's not only an accident, but almost a necessity if these forces are to coexist effectively.

• 1:54:51Speaker 01

  Exactly. So that's the reinforcement of what we know in our universe. But we are finding that as a general principle. So we want to know what aspects of our universe is forced on us? Like the weak gravity conjecture and other aspects. How much of them do we understand? Can we have particles lighter than neutrinos? Or maybe that's not possible. You see, the neutrino mass, it turns out to be related to dark energy in a mysterious way. Naively, there's no relation between dark energy and the mass of a particle. We have found arguments from within the swamp land kind of ideas, why it has to be related. And so there are beginning to be these connections between consistency of quantum gravity

• 1:55:34Speaker 01

  and aspects of our universe gradually being sharpened. But we are still far from a precise quantitative prediction, like, we have to have such and such. But that's the hope, that we are going in that direction.

• 1:55:46Lex Fridman?

  Coming up with a theory of everything that unifies general relativity and quantum field theory is one of the big dreams of human civilization, us descendants of apes wondering about how this world works. So a lot of people dream. What are your thoughts about sort of other out there ideas on theories of everything? Or unifying theories? So there's quantum looped gravity. There's also more sort of, like a friend of mine, Eric Weinstein, beginning to propose something called geometric unity. So these kinds of attempts, whether it's through mathematical physics or through other avenues,

• 1:56:29Lex Fridman?

  or with Stephen Wolfram, a more computational view of the universe. Again, in his case, it's these hypographs that are very tiny objects as well. Similarly, a string theory in trying to grapple with this world. What do you think? Is there any of these theories that are compelling to you? They're interesting, that may turn out to be true? Or at least may turn out to contain ideas that are useful?

• 1:56:52Speaker 01

  Yes, I think the latter. I would say that the containing ideas that are true, is my opinion, was what some of these ideas might be. For example, loop quantum gravity. It's to me not a complete theory of gravity in any sense, but they have some nuggets of truth in them. And typically, what I expect to happen, and I have seen examples of this within string theory, aspects which we didn't think are part of string theory come to be part of it. For example, I'll give you one example. String was believed to be 10 dimensional. And then there was this 11 dimensional supergravity. And nobody knew what the heck is that? Why are we getting 11 dimensional supergravity, whereas string is saying it should be 10 dimensional? 11 was the maximal dimension you can have a supergravity. But string was saying, sorry, we're 10 dimensional.

• 1:57:34Speaker 01

  So for a while, we thought that theory is wrong, because how could it be? Because string theory is definitely a theory of everything. We later learned that one of the circles of string theory itself was tiny. That we had not appreciated that fact. And we discovered by doing thought experiments in string theory, that there's got to be an extra circle. And that circle is connected to an 11 dimensional perspective. And that's what later on got called M theory. So there are these kind of things that, you know, we do not know what exactly string theory is, we're still learning. So we do not have a final formulation of string theory. It very well could be that different facets of different ideas come together, like loop quantum gravity or whatnot. But I wouldn't put them on par, namely, loop quantum gravity is a scatter of ideas

• 1:58:17Speaker 01

  about what happens to space when they get very tiny. For example, you replace things by discrete data and try to quantize it and so on. And, you know, it sounds like a natural idea to quantize space. You know, if you were naively trying to do quantum space, you might think about trying to take points and put them together in some discrete fashion, in some way that is reminiscent of loop quantum gravity.

• 1:58:41Speaker 01

  String theory is more subtle than that. For example, I will just give you an example. And this is the kind of thing that we didn't put in by hand, we got it out. And so it's more subtle than, so what happens if you squeeze the space to be smaller and smaller? Well, you think that after a certain distance, the notion of distance should break down. You know, when the ghost smaller than Planck scale should break down. What happens in string theory? We do not know the full answer to that, but we know the following. Namely, if you take a space and bring it smaller and smaller, if the box gets smaller than the Planck scale by a factor of 10, it is equivalent by the duality transformation to a space which is 10 times bigger.

• 1:59:24Speaker 01

  So there's a symmetry called T-duality, which takes L to 1 over L. Well, L is measured in Planck units, or more precisely, string units. This inversion is a very subtle effect. And I would not have been, or any physicist would not have been able to design a theory which has this property, that when you make the space smaller, it is as if you're making it bigger. That means there is no, there is no experiment you can do to distinguish the size of the space. This is remarkable. For example, Einstein would have said, of course, I can't measure the size of the space. What do I do? Well, I take a flashlight, I send the light around, measure how long it takes for the light to go around the space and bring back and find the radius or circumference of the universe. What's the problem? I said, well, suppose you do that and you shrink it.

• 2:00:09Speaker 01

  He said, well, they get smaller and smaller. So what? I said, well, it turns out in string theory, there are two different kinds of photons. One photon measures 1 over L, the other one measures L. And so this duality reformulates. And when the space gets smaller, it says, oh, no, you better use the bigger perspective because the smaller one is harder to deal with. So you do this one. So, so these examples of loop quantum gravity have none of these features. These features that I'm telling you about, we have learned from string theory. But they nevertheless have some of these ideas, like topological gravity aspects, are emphasized in the context of loop quantum gravity in some form. And so these ideas might be there in some kernel, in some corners of string theory. In fact, I wrote a paper about topological string theory and some connections

• 2:00:53Speaker 01

  potentially loop quantum gravity, which could be part of that. So there are little facets of connections. I wouldn't say they're complete, but I would say most probably what will happen to some of these ideas, the good ones at least, they will be absorbed within two string theory if they are correct.

• 2:01:08Lex Fridman?

  Let me ask a crazy out there question. Can physics help us understand life? So we spoke so confidently about the laws of physics being able to explain reality. But, and we even said words like theory of everything, implying that the word everything is actually describing everything. Is it possible that the four Laws we've been talking about are actually missing. They are accurate in describing what they're describing, but they're missing the description of a lot of other things like emergence of life and emergence of perhaps consciousness.

• 2:01:51Lex Fridman?

  So is there, do you ever think about this kind of stuff? Where we would need to understand extra physics to try to explain the emergence of these complex pockets of interesting weird stuff that we call life and consciousness in this big homogeneous universe that's mostly boring and nothing is happening in.

• 2:02:17Speaker 01

  So first of all, we don't claim that string theory is the theory of everything in a sense that we know enough what this theory is. We don't know enough about string theory itself. We are learning it. So I wouldn't say, okay, give me whatever. I will tell you what it, how it works. No. However, I would say by definition, by definition, to me, physics is checking all reality. Any form of reality, I call it physics. That's my definition. I mean, I may not know a lot of it, like maybe the origin of life and so on, maybe a piece of that. But I would call that as part of physics. To me, reality is what we're after. I don't claim I know everything about reality. I don't claim string theory necessarily has the tools right now to describe all the reality either. But we are learning what it is. So I would say that I would not put a border to say,

• 2:03:01Speaker 01

  no, you know, from this point onwards, it's not my territory. Somebody else's. But whether we need new ideas in string theory to describe other reality, reality features, for sure, I believe, as I mentioned, I don't believe anything's, any of the laws we know today is final. So therefore, yes, we will need new ideas.

• 2:03:17Lex Fridman?

  This is a very tricky thing for us to understand and be precise about. But just because you understand the physics doesn't necessarily mean that you understand the emergence of chemistry, biology.

• 2:03:37Lex Fridman?

  Life, intelligence, consciousness. So those are built. It's like you might understand the way bricks work.

• 2:03:46Speaker 01

  Yes.

• 2:03:47Lex Fridman?

  But to understand what it means to have a happy family.

• 2:03:51Speaker 01

  Right.

• 2:03:51Lex Fridman?

  You don't construct, you don't get from the bricks. So directly, you, in theory, you could. If you ran the universe over again. But just understanding the rules of the universe doesn't necessarily give you a sense of the weird, beautiful things that emerge.

• 2:04:08Speaker 01

  Right. No, so let me, let me describe what you just said. So there are two questions. One is whether or not the techniques I use in, let's say, quantum field theory and so on, will describe how the society works.

• 2:04:19Lex Fridman?

  Yes.

• 2:04:19Speaker 01

  Okay. That's far distance, far, far different scales of questions that we're asking here. The question is, is there a change of, is there a new law which takes over that cannot be connected to the older laws that we know, or more fundamental laws that we know? Do you need new laws to describe it? I don't think that's necessarily the case in many of these phenomena like chemistry or so on you mentioned. So we do expect, you know, in principle, chemistry can be described by quantum mechanics. We don't think there's going to be a magical thing. But chemistry is complicated. Yeah, indeed, there are rules of chemistry that, you know, chemists have put down, which has not been explained yet using quantum mechanics. Do I believe that they will be something described by quantum mechanics? Yes, I do. I don't think they are going to be sitting there in the show forever.

• 2:05:02Speaker 01

  But maybe it's too complicated and maybe, you know, we will wait for very powerful quantum computers or whatnot to solve those problems. I don't know. But I don't think, in that context, we have new principles to be added to fix those. So by, by, I'm perfectly fine in the intermediate situation to have rules of thumb or, you know, principles that chemists have found which are working, which are not founded on the basis of quantum mechanical laws, which does the job. Similarly, as biologists do not found everything in terms of chemistry, but they think, you know, there's no reason why chemistry cannot. They don't think necessarily they're doing something amazingly not possible with chemistry. Coming back to your question, does consciousness, for example, bring this new ingredient? If indeed it needs a new ingredient, I would call that new ingredient part of

• 2:05:46Speaker 01

  physical law. We have to understand it. To me, that so I wouldn't put a line to say, okay, from this point onwards, you cannot, it's disconnected, it's totally disconnected from string theory or whatever, we have to do something else.

• 2:05:57Lex Fridman?

  It's not a line. What I'm referring to is can physics of a few centuries from now that doesn't understand consciousness be much bigger than the physics of today, where the textbook grows?

• 2:06:10Speaker 01

  It definitely will. I would say it will grow. I would not, I don't know if it grows because of consciousness being part of it, or we have different view of consciousness. I do not know where the consciousness will fit. I'm not, it's going to be hard for me to, to, to, to guess. I mean, I can make random guesses now, which probably most likely is wrong, but let me just do just for the sake of discussion. You know, I could say, you know, you know, brain could be their quantum computer, classical computer, there are arguments against it being a quantum thing, so it's probably classical, and if it's classical, it could be like what we are doing in machine learning, slightly more fancy and so on. Okay, people can go to this argument to no end and to whether consciousness exists or not, or life, does it have any meaning? Or is there, is there a phase transition where you can say, does electron have a life or not, at what level does a particle become

• 2:06:55Speaker 01

  life? Maybe there's no definite definition of life in that same way that, you know, we cannot say electron, if you, you know, a good, I like this example quite a bit. You know, we distinguish between liquid and a gas phase, like water is liquid or vapor is gas. We say they're different, you can distinguish them. Actually, that's not true. It's not true because we know from physics that you can change temperatures and pressure to go from liquid to the gas without making any phase transition. So there is no point that you can say this was a liquid and this was a gas. You can continuously change the parameters to go from one to the other. So at the end, it's very different looking like, you know, I know that water is different from vapor, but you know, there is no precise point this happens.

• 2:07:37Speaker 01

  I feel many of these things that we think like consciousness, clearly that person is not conscious and the other one is. So there's a difference like water and vapor. But there's no point you could say that this is conscious, there's no sharp transition. So it could very well be that what we call heuristically in daily life, consciousness is similar or life is similar to that. I don't know if it's like that or not, I'm just hypothesizing it's possible, like there's no.

• 2:08:04Lex Fridman?

  There's no discrete phases.

• 2:08:05Speaker 01

  There's no discrete phase transition like that.

• 2:08:07Lex Fridman?

  Yeah, yeah, but this you might, there might be, you know, concepts of temperature and pressure that we need to understand to describe what the heck consciousness in life is that that we're totally missing. I think that's not a useless question, even those questions that is back to our original discussion of philosophy. I would say consciousness and free will, for example, are topics that are very much so in the realm of philosophy currently. But I don't think they will always be.

• 2:08:39Speaker 01

  I agree with you, I agree with you, and I think I am, I'm fine with some topics being part of a different realm than physics today. Because we don't have the right tools, just like biology was. I mean, before we had DNA and all that genetics and all that gradually began to take hold. I mean, at the, when Mandela, when people were beginning with face experiments with biology and chemistry and so on, they gradually they came together. So it wasn't like together, so yeah, I'm, I'll be perfectly understanding of a situation where we don't have the tools. So do the experiments that you think as defines the consciousness in different form and gradually will build it and connect it. And yes, we might discover new principles of nature that we didn't know. I don't know, but I would say that if they are, they will be deeply connected with the else. We don't, we have never, we have seen in physics, we don't have things in isolation.

• 2:09:24Speaker 01

  You cannot, you cannot compartmentalize, you know, this is gravity, this is electricity, this is that. We have learned they all talk to each other. There's no way to make them, you know, in one corner and don't talk. So the same thing with anything, anything which is real. So consciousness is real, so therefore we have to connect it to everything else. So to me, once you connect it, you cannot say it's not reality and once it's reality is physics. I call it physics, it may not be the physics I know today, for sure it's not, but, but I wouldn't, I would, I would be surprised if there's disconnected realities that, you know, you cannot, you cannot imagine them as a part of the same soup.

• 2:09:57Lex Fridman?

  So I guess God doesn't have a biology or chemistry textbook and mostly, or maybe he or she reads it for fun, biology and chemistry. But when you're trying to get some work done, it'll be going to the physics textbook. Okay, what advice? Let's put on your wise visionary hat. What advice do you have for young people today? You've dedicated your book, actually, to your kids, to your family. What advice would you give to them? What advice would you give to young people today thinking about their career? Thinking about life of how to live a successful life, how to live a good life?

• 2:10:36Speaker 01

  Yes. Yes, I have three sons. And in fact, to them, I have, I have tried not to give too much advice. So even though I've tried to kind of not give advice, maybe indirectly it has been some impact. My oldest one is doing biophysics, for example, and the second one is doing machine learning. And the third one is doing theoretical computer science. So there are, there are these facets of interest which are not too far from my area. But I have not tried to, to impact them in that way. But, and they have followed their own interests. And I think that's the advice I would give to any young person. Follow your own interests and let it that take you wherever it takes you.

• 2:11:15Speaker 01

  And this I did in my own case, that I was planning to study economics and electrical engineering when I started at MIT. And, you know, I discovered that I'm more passionate about mathematics. And at that time, I didn't feel mathematics would make a good career. And so I was kind of hesitant to go in that direction, but I did because I kind of felt that that's what I'm driven to do. So I didn't, I don't regret it. And I'm lucky in the sense that, you know, society supports people like me who are doing, you know, these abstract stuff, which, which may or may not be experimentally verified, even let alone applied to the daily technology in our lifetime. I'm lucky I'm doing that and I feel that if people follow their interests, they will find the niche that they're good at.

• 2:12:00Speaker 01

  And this coincidence of hopefully their interests and and abilities are kind of aligned, at least some extent, to be able to drive them to something which is successful. And not to be driven by things like, you know, this doesn't make a good career, or this doesn't do that, and my parents expect that, or what about this? And I think ultimately you have to live with yourself and you only have one life, and it's short, very short, I can tell you, I'm getting, I'm getting there. So I know it's short, so you really want not to, not to, not to do things that you don't want to do. So I think following your interests is my strongest advice to young people.

• 2:12:35Lex Fridman?

  Yeah, it's scary when your interest doesn't directly map to a career of the past or of today. So you're almost anticipating future careers that could be created. It's scary.

• 2:12:49Lex Fridman?

  But yeah, there's something to that, especially when the interest and the ability align, that you will pave, you will pave a path that will find a way to make money. Especially in this society, in, in, in the capitalistic United States society, it feels like ability and passion paves the way.

• 2:13:08Speaker 01

  Yes.

• 2:13:11Lex Fridman?

  At the very least, you can sell funny T-shirts.

• 2:13:13Speaker 01

  Yes.

• 2:13:14Lex Fridman?

  You've mentioned, uh, life is short. Do you think about, um, your mortality? Are you afraid of death?

• 2:13:22Speaker 01

  I don't think about my mortality.

• 2:13:26Speaker 01

  I think that I don't think about my death. Uh, I don't think about death in general too much. First of all, it's something that I can't do much about. And I think it's something that doesn't, it doesn't drive my everyday action. It is natural to expect that it's somewhat like the time reversal situation. So we believe that we have this approximate symmetry in nature, time reversal. Going forward, we die, going backwards, we get born.

• 2:13:48Lex Fridman?

  Yeah.

• 2:13:48Speaker 01

  So what was it to get born? It wasn't such a good or bad feeling, I have no feeling of it. So, you know, who knows what the death will feel like, uh, the moment of death or whatnot. So I don't know. It is not known, but, uh, in what form do we exist before or after? Again, it's something that it's partly philosophical, maybe?

• 2:14:10Lex Fridman?

  I like how you draw comfort from symmetry. It does seem that there is something asymmetric here, breaking of symmetry, because there's something to the creative force of the human spirit that goes only one way.

• 2:14:26Speaker 01

  Right.

• 2:14:27Lex Fridman?

  That it seems the finiteness of life is the thing that drives the creativity. And so it does seem that, at least, the contemplation of the finiteness of life, of mortality, is the thing that helps you get your stuff together.

• 2:14:43Speaker 01

  Yes, I think that's true, but actually I have a different perspective on that a little bit.

• 2:14:47Lex Fridman?

  Yes.

• 2:14:47Speaker 01

  Namely, suppose I told you you're immortal.

• 2:14:51Lex Fridman?

  Yes.

• 2:14:53Speaker 01

  I think your life will be totally boring after that, because you will not... There's... I think part of the reason we have enjoyment in life is the finiteness of it.

• 2:15:03Lex Fridman?

  Yes.

• 2:15:04Speaker 01

  And so I think mortality might be a blessing, and immortality may not. So I think that we value things because we have that finite life. We appreciate things, we want to do this, we want to do that, we have motivation. If I told you, you know, you have infinite life, "Oh, I don't need to do this today. I have another billion or trillion or infinite lives, so why do I do now?" There is no motivation. A lot of the things that we do are driven by that finiteness, the finiteness of these resources. So I think it's a blessing in disguise. I don't regret it, that we have a more finite life. And I think that the process of being part of this thing, that, you know, the reality...

• 2:15:49Speaker 01

  To me, part of what attracts me to science is to connect to that immortality, kind of. Namely, the laws, the reality beyond us. To me, I'm resigned to the fact that not only me, everybody's going to die. So this gives a little bit of a consolation, none of us are going to be around. So therefore, okay, and none of the people before me are around. So therefore, yeah, okay, this is something everybody goes through. So taking that minuscule version of, okay, how tiny we are and how short time it is and so on, to connect to the deeper truth beyond us, the reality beyond us, is what sense of...

• 2:16:31Speaker 01

  Quote unquote immortality I would get, namely, I at least I can hang on to this little piece of truth, even though I know, I know it's not complete, I know it's going to be imperfect, I know it's going to change and it's going to be improved. But having a little bit deeper insight than than just the naive thing around us, little Earth here and little galaxy and so on, makes me feel a little bit more, more pleasure to to live this life. So I think that's the way I view my my role as a scientist.

• 2:16:59Lex Fridman?

  Yeah, the scarcity of this life helps us appreciate the beauty of the immortal, the universal truths of that physics present us. And maybe, maybe one day physics will, will have something to say about that, that beauty in itself, explaining why the heck it's so beautiful to appreciate the laws of physics and yet, why it's so tragic that we, we die so quickly.

• 2:17:30Speaker 01

  Yes, we die so quickly, so that can be a bit longer, that's for sure.

• 2:17:34Lex Fridman?

  It would be very nice. Maybe physics will help out. Well, Kamran, it was an incredible conversation. Thank you so much once again for painting a beautiful picture of the history of physics. And it kind of presents a hopeful view of the future of physics. So I really, really appreciate that. It's a huge honor that you would talk to me and waste all your valuable time with me. I really appreciate it.

• 2:17:56Speaker 01

  Thanks, Lex. It was a pleasure and I loved talking with you and this is wonderful set of discussions. I really enjoyed my time with this discussion. Thank you.

• 2:18:04Lex Fridman?

  Thanks for listening to this conversation with Kamran Vafa. And thank you to Headspace, Jordan Homridge's show, Squarespace, and Allform. Check them out in the description to support this podcast. And now let me leave you with some words from the great Richard Feynman. Physics isn't the most important thing, love is. Thank you for listening and hope to see you next time.