Peter Woit: Theories of Everything & Why String Theory is Not Even Wrong | Lex Fridman Podcast #246

1. 0:00 – 0:23

   Introduction

   1. LFLex Fridman0:00

      The following is a conversation with Peter Woit, a theoretical physicist at Columbia, outspoken critic of string theory, and the author of the popular physics and mathematics blog called Not Even Wrong. This is the Lex Fridman Podcast. To support it, please check out our sponsors in the description. And now, here's my conversation with Peter Woit.

2. 0:23 – 14:52

   Physics vs mathematics

   1. LFLex Fridman0:23

      You're both a physicist and a mathematician. So let me ask, what is the difference between physics and mathematics?

   2. PWPeter Woit0:31

      Well, there's kind of a conventional understanding of the subject that they're two, you know, quite different things, so that mathematics is about, you know, making rigorous statements about these abstract, you know, abstract things, things of mathematics, and- and prov- proving them rigorously. And physics is about, you know, doing experiments and testing various models and that. But I think, uh, the more interesting thing is that the- there's a- (laughs) there's a wide variety of what people do as mathematics, what they do as physics, and there's a significant overlap. And that, I- I think is actually the much, much- very, very interesting area. And if you go back kind of far enough to- in- in- in history, and look at figures like Newton or something, I mean, they're- at that point, you can't really tell, you know, was Newton a physicist or a mathematician? The, uh, mathematicians will tell you he was a mathematician, the physicists will tell you he was a physicist. But-

   3. LFLex Fridman1:24

      He would say he's a philosopher. (laughs)

   4. PWPeter Woit1:27

      Yeah. (laughs) That's- that's interesting. But, uh, yeah, anyway, there- there- there was kind of no such distinction then, that's more of a modern thing. And but anyway, I think these days, there's a very interesting space in between the two.

   5. LFLex Fridman1:38

      So, in the story of the 20th century and the early 21st century, what is the overlap between mathematics and physics, would you say?

   6. PWPeter Woit1:46

      Well, I think (clears throat) it's actually become very, very complicated. I think it- it's really interesting to see a lot of what my colleagues in the math department are doing. They- most of what they're doing, they're doing all sorts of different things, but, um, most of them have some kind of overlap with physics or other. Um, so I mean, I'm personally interested in- in one spec- one particular aspect of this overlap, which I think has a lot to do with the most fundamental ideas about physics and about mathematics. But, um, there's just- it- it- you- you kind of see this- this, uh, re- really everywhere at this point.

   7. LFLex Fridman2:18

      Which particular overlap are you looking at? Group theory?

   8. PWPeter Woit2:22

      Yeah. So the, um, at least what- the way it seems to me that if you look at physics and look at the- our most successful, um, laws of fundamental physics, they're really, you know, they have a certain kind of mathematical structure. It's based upon certain kind of mathematical objects and geometry, connections, and curvature of the spinors, the Dirac equation. And, uh, that- these- this very deep mathematics provides kind of a unifying set of math- of ways of thinking that allow you to- to make a unified theory of physics. But the interesting thing is that if you go to mathematics and- and look at what's been going on in mathematics the last 50, 100 years, and even especially recently, there's a- similarly some kind of unifying ideas which bring together different areas of mathematics, and which have been especially powerful in number theory recently. And there's a book, for instance, by, um, Edward Frenkel about love and math, and-

   9. LFLex Fridman3:19

      Oh, yeah, that book's great. I recommend it highly. It's, uh, partially accessible. But it is a nice audiobook, s- uh, that I listened to while running an exceptionally long distance, uh, like across the, uh, San Francisco, uh, Bridge. And, uh, there's something magic about the way he writes about it. But s- some of the group theory in there is a little bit difficult.

   10. PWPeter Woit3:42

       Uh, yeah. That's the problem with- with any of these things, to kind of really say what's going on and- is- and make it accessible is very hard. He, in this book and elsewhere, I think, you know, takes the attitude that kinds of mathematics he's interested in and that he's talking about are- provide kind of a grand unified theory of mathematics. They, um, they bring together geometry and number theory and representation theory, a lot of different ideas in- in a really unexpected way. But I think to- to me, the most fascinating thing is if you look at the kind of grand unified theory of mathematics he's talking about, and you look at the physicist's kind of ideas about unification, it's more or less the same mathematical objects are appearing in both. So it's this, um, I think there's a really- we're seeing a really strong indication that, you know, the deepest ideas that we're discovering about physics and some of the deepest ideas that mathematicians are learning about are really- are, you know, intimately connected.

   11. LFLex Fridman4:36

       Is there something, like if I was five years old and you were trying to explain this to me-

   12. PWPeter Woit4:40

       (laughs) .

   13. LFLex Fridman4:40

       ... is there ways to try to sneak up to this- to- to what this unified world of mathematics looks like? You said number theory, you said geometry, words like topology. What does this universe begin to look like? Are these- what should we imagine in our mind? Is it a- a three-dimensional surface? And we're s- trying to say something about it. Is it, uh, triangles and squares and cubes?

   14. PWPeter Woit5:07

       (laughs) .

   15. LFLex Fridman5:07

       Like what- what are we supposed to imagine in our minds? Is this natural number? What- what's a good thing to try to- for people that don't know any of these tools except maybe some basic calculus and geometry from high school, that they should keep in their minds as to the unified world of mathematics that also allows us to explore the unified world of physics?

   16. PWPeter Woit5:30

       The (laughs) I mean, what- what I (laughs) find kind of remarkable about this is the way in which these- we've discovered these ideas but they're- they're actually quite alien to our everyday understanding. You know, we grow up in this three spatial dimensional world, and we have intimate understanding of certain kinds of geometry and certain kinds of things. But, um, these things that we've discovered in both math and physics are- that they're not at all close in- have any obvious connection to kind of human everyday experience. They're- they're really quite different. And I can say some of my initial fascination with this when I was, uh-... young and starting to learn about it was actually exactly this, um, th- this kind of arcane nature of these things. It was a little bit like being- being told, "Well, there are these kind of s- sem- semi-mystical experience that you can acquire by a long study," and whatever, except that it w- that it was actually true. I mean, there's actually evidence that this actually works. So, you know, I'm a l- a little bit wary of- of trying to give people that kind of thing, 'cause I think it's mostly misleading. But one thing to say is that, you know, that geometry is- is a large part of it, and, um, maybe one interesting thing to say very- that's about more recent- some of the most recent ideas is that it, um... When we think about the geometry of our space and time, it's kind of three spatial and one time dimension. It- it's a, um... Physics is, in some sense, about something that's kind of four-dimensional in a way.

   17. LFLex Fridman7:00

       Mm-hmm.

   18. PWPeter Woit7:00

       And the... A- a really interesting thing about, um, some of the recent developments in number theory have been to realize that the, um, these ideas that we were looking at, you know, naturally fit into a context where your- your theory is four- is kind of four-dimensional, so... So- so- so geom- I mean, geometry is a big part of this, and- and- and we know a lot and feel a lot about, you know, two, one, two, three-dimensional geometry.

   19. LFLex Fridman7:24

       So wa- wait a minute. So we can at least rely on, uh, the four dimensions of space and time and say that we can get pretty far by working in that- in those four dimensions? I thought you were gonna scare me that we're gonna have to go to many, many, many, many more dimensions than that.

   20. PWPeter Woit7:40

       My- my- my point of view which is- w- which goes against a lot of these ideas about unification is that, no, this is really... Everything we s- we know about really is about four dimensions that, um... And- and that you can actually understand a lot of these structures that we've been seeing in fundamental physics and in- in number theory just in terms of four dimensions, that it's kind of... It's in some sense I would claim has been a really, um... Has been kind of a mistake that- that physicists have made in- for decades and decades to try to- to tr- try to go to higher dimensions, to try to- to formulate a theory in higher dimensions, and then- then you're stuck with the problem of how do you get rid of all these extra dimensions that you've created, and... 'C- 'cause we only ever see anything in four dimensions.

   21. LFLex Fridman8:27

       That kind of thing leads us astray, you think? So- so creating all these extra dimensions just to get, uh, give yourself extra degrees of freedom.

   22. PWPeter Woit8:35

       Yeah.

   23. LFLex Fridman8:36

       I- isn't that... I mean, isn't that the process of mathematics is to create all these trajectories for yourself but eventually you have to end up at the, uh, at the- at a, like a final place, but it's okay to... It's- it's okay to sort of, um, create abstract objects on your path to, uh, proving something?

   24. PWPeter Woit8:56

       Yeah. S- yeah, certainly, but... And from- from mathematicians' point of view, I mean, the kinds of... Mathematicians also are very different than physicists in that we like to develop very general theories. We like to... If we have an idea, we want to, um, see what's the greatest generality in which you can talk about it.

   25. LFLex Fridman9:10

       Mm-hmm.

   26. PWPeter Woit9:11

       So from the point of view of most of the ways geometry is formulated, um, by mathematicians, it- it really doesn't ma- it works in any dimension. We can do one, two, three, four, any- any number. There's no particular... For most of geometry there's no particular special thing about four. But, um... And s- anyway, but- but what physicists have- have found- have been trying to do over the years is try to understand these fundamental theories in a geometrical way, and it's very tempting to kind of just start bringing in extra dimensions to- and- and using them to explain the structure, but it, um... Typ- typically this- this attempt kind of founders because you just don't know... You- you end up not being able to explain why we only see four. (laughs) and anyway...

   27. LFLex Fridman9:59

       It i- it is nice in the space of physics that, uh, like if you look at Fermat's Last Theorem, it's much easier to prove that there's no solution for N equals three than it is for the general case.

   28. PWPeter Woit10:11

       Right.

   29. LFLex Fridman10:11

       And- and so I guess that's the nice benefit of being a physicist is you don't have to worry about the general case 'cause we live in a universe with N equals four in this case.

   30. PWPeter Woit10:23

       Yeah, yeah. Physi- physicists are very interested in saying something about specific examples, and I find that interesting e- even when- when I'm trying to do things, uh, in mathematics and I'm trying... Even teaching courses to mathematics students, I find that I'm teaching them in a different way than, um, most mathematicians because I'm very often f- very focused on examples, on- on what's-
3. 14:52 – 36:43

   Beauty of mathematics

   1. LFLex Fridman14:52

      we only have, uh, a few hours, maybe a few days together here on this podcast.

   2. PWPeter Woit14:56

      Yeah. (laughs)

   3. LFLex Fridman14:57

      Uh, let me ask you the question of, um, amongst many of the ideas that you work on in mathematics and physics, what to you is the most beautiful idea or one of the most beautiful ideas, maybe a surprising idea? And once again, unfortunately, the way life works, we only have a limited time together-

   4. PWPeter Woit15:15

      (laughs)

   5. LFLex Fridman15:15

      ... to try to convey such an idea.

   6. PWPeter Woit15:18

      Okay. Well, actually, le- let me just te- tell you something, which I, I, I'm tempted to kind of ex- start trying to explain what I think is this most powerful idea that brings together math and physics, ideas about groups and representations and how it fits quantum mechanics, and... but i- in some sense, I wrote a whole textbook about that, and I don't think we really have time to get very far into it, so.

   7. LFLex Fridman15:39

      Well, can I actually... on a small tangent, you, you did write a paper Towards A Grand Unified Theory Of Mathematics And Physics. Um, maybe you could step there first. What is the key idea in that paper?

   8. PWPeter Woit15:49

      Well, I think we, we've kind of gone, gone over that. I think the, the key idea is what we were talking about earlier, that, um, that just kind of a claim that if you look and see what's the... have been successful ideas unification in physics in the... over the last, um, 50 years or so and what, um, has been happening in mathematics and the kind of thing that Frankl's book is about, that these are very much the same kind of mathematics. And so it's kind of an argument that there really is... you shouldn't be looking to unify just math or just fundamental physics, but taking inspiration for... looking for new ideas in fundamental physics, that they are gonna be in the same direction of, um, uh, getting deeper into mathematics and looking for more inspiration in mathematics from these successful ideas about fundamental physics.

   9. LFLex Fridman16:37

      Could you put words to sort of the disciplines we're trying to unify? So you said number theory. Are we literally talking about all the major fields of mathematics? So it's like, uh, the number theory geometry, uh, so the... like, differential geometry, topology, like...

   10. PWPeter Woit16:51

       Yeah. So the... I mean, one, one name for this, uh, that this is acquired in, in mathematics is the so-called Langlands program.

   11. LFLex Fridman16:59

       Mm-hmm.

   12. PWPeter Woit16:59

       And, uh, so this started out in mathematics. It's the... you know, Robert Langlands kind of realized that a lot of what people were doing and, um... that was starting to be really successful in, in number theory in the '60s, and so th- that this actually was... anyway, that, that this could be, could be thought of in terms of, um, these ideas about symmetry in groups and representations and, and in a way that was also close to some ideas about, about geometry. And, um, then, uh, more later on in the '80s and '90s, there was something called, um, geometric Langlands, that people realized that you could take what people have been doing in number theory in Langlands and, and, and get re-... just forget about the number theory and ask, "What is this telling you about geometry?"

   13. LFLex Fridman17:47

       Mm-hmm.

   14. PWPeter Woit17:48

       And you get a whole... some new insights into certain kinds of geometry that way. So it's... anyway, that, that's kind of the name for this area, is Langlands and geometric Langlands. And, and just recently in the last few months, there's been, um... there's kind of a really major paper that, uh, appeared by, uh, Peter Schulze and Laurent Fargue, where they, you know, made, you know, some, some... a serious advance in trying to understand a very much, uh-... kind of a local problem of what happens i- in number theory near a certain prime number, and they turned this into a problem of exactly the- the kind that geometric Langlands people had been doing, these kind of pure, uh, pure geometry problem. And they found by generalizing the mathematics, they could actually reformulate it in that way, and it- it worked perfectly well, so.

   15. LFLex Fridman18:36

       W- one of the things that makes me sad is, you know, I'm a pretty knowledgeable person in, uh, what is it? At least I'm in the neighborhood-

   16. PWPeter Woit18:48

       (laughs)

   17. LFLex Fridman18:48

       ... of, like, theoretical computer science, right? And it's still way out of my reach. And s- so many people talk about like Langlands, for example, is one of the most brilliant people in mathematics-

   18. PWPeter Woit18:57

       Yeah.

   19. LFLex Fridman18:57

       ... and just really admire his work. And I can't... It's like almost I can't hear the music that he composed, and it makes me sad.

   20. PWPeter Woit19:05

       Yeah.

   21. LFLex Fridman19:06

       You know?

   22. PWPeter Woit19:06

       Well, I mean, I- I think that (laughs) unfortunately, it's not just you, it's I- I- I think even most mathematicians have no... Really don't actually understand what this is about. I mean, the group of people who really understand all these ideas. And so for instance this paper of Lo- of Scholze and Fargue that I was talking about, the number of people who really actually understand how that works is, anyway,

   23. NANarrator19:28

       (laughs)

   24. PWPeter Woit19:29

       ... very, very small. And so it's, uh, so, uh, I think even you find if you talk to mathematicians and physicists, even they will often feel that, uh, you know, there's this really interesting-sounding stuff going on, and which I should be able to understand, it's kind of in my own field I have a PhD in, but it still seems-

   25. LFLex Fridman19:46

       (laughs)

   26. PWPeter Woit19:46

       ... pretty clearly far beyond me right now.

   27. LFLex Fridman19:49

       Well, if we can step into the, back to the question of beauty. Uh, is- is there an idea that maybe is a little bit smaller-

   28. PWPeter Woit19:58

       Yeah.

   29. LFLex Fridman19:58

       ... that you find beautiful in the space of mathematics or physics?

   30. PWPeter Woit20:01

       There's- there's an idea that, uh, you know, I kind of went and got a physics PhD and spent a lot of time learning about mathematics, and I guess it- it was embarrassing that I- I hadn't really actually understood this very simple idea, um, until... And kind of lear- learned it when I actually started teaching math classes, which is that maybe that- that there- there maybe... There's a simple way to explain kind of the fundamental way in which algebra and geometry are connected. So you normally think of geometry as about these spaces and these points, and- and you think of algebra as this very abstract thing about these abstract objects that satisfy certain kinds of relations. You can multiply them and add them and do stuff, but it's- it's completely abstract, it has nothing geometric about it. But the, um, the kind of really fundamental idea is, uh, that unifies algebra and geometry is to th- is to reali- is to think whenev- whenever anybody gives you what you call an algebra, some abstract thing of things that you can multiply and add, that you should ask yourself is that algebra the space of functions on some geometry? So one of the most surprising examples of this, for instance, is, uh, I mean, a standard kind of thing that seems to have nothing to do with geometry is the, um, is the- the- the integers. Uh, then there you can- you can multiply them and add them, it's a- it's- it's an algebra. But the, um, it has- seems to have nothing to do with geometry. But what you can... It turns out... But if you ask yourself this question and ask, you know, is... Are integers... Can you think... If somebody gives you an integer, can you think of it as a function on some space, on some geometry? And it turns out that yes, you can, and the space is the space of prime numbers. And so what you do is you just, if somebody gives you an integer, you can make a function on the prime numbers by just, you know, at each prime number taking that- that integer modulo, that prime. So if, uh, as you say, I don't know, if you're gi- given 10, you know, 10 and you ask what is its value at two, well, it's- it's five times two, so mod two, it's zero, so it has (01:00:55) . What i- what is- what is its value at three? Well, it's nine plus one, so it's- it's one mod three. So it- it's v- it's- it's zero at two, it's one at three, and you can kind of keep going. And so this is really kind of a- a truly fundamental idea. It's at the basis of what's called algebraic geometry, and it just links these two parts of mathematics that look completely different, and it- it's just an incredibly powerful idea, and- and so much of mathematics emerges from this kind of simple relation.
4. 36:43 – 1:05:16

   String theory

   1. LFLex Fridman36:43

      okay. Let's talk a little bit about string theory. You've been a- a bit of an outspoken critic-

   2. PWPeter Woit36:50

      (laughs)

   3. LFLex Fridman36:50

      ... of string theory. Maybe one question first to ask is what is string theory, and, uh, beyond that, why is it wrong, or rather as the title of your blog says, Not Even Wrong?

   4. PWPeter Woit37:06

      Okay. (laughs) Well, one interesting thing about the current state of string theory is that (laughs) I- I think it, I'd argue it's actually very, very difficult to, at this point, to say what string theory means. If people say they're a string theorists, what they mean and what they're doing is a- it's kind of hard t- it's hard to pin down the meaning of the term. But the- but the initial meaning I think goes back to, um ... there was kind of a- a series of developments starting in 1984 in which people felt that they had found a unified theory of- of a so-called standard model of- of- of all the standard, uh, well- well-known kind of particle interactions and gravity, and it all fit together in a quantum theory, and that you could do this in a very specific way by instead of thinking about having a quantum theory of particles moving around in spacetime, think about, uh, a quantum theory of kind of one-dimensional loops moving around in spacetime, so-called strings. And so, um, instead of one degree of freedom, these have an infinite number of degree of freedom. It's a much more complicated theory, but you can imagine, okay, we're gonna quantize this theory of loops moving around in spacetime, and what they found is that they, is that you could make ... you could do this and you could fairly relatively straightforwardly make sense of- of- of such a quantum theory, but only if s- space and time together were 10 dimensional. And so then you had this problem, again, the problem I referred to at the beginning of, okay, now once you make that move, you gotta get rid of six dimensions. And so the hope was that you could get rid of the six dimensions by making them very small and that consistency of the theory would require these, that these six dimensions, um, satisfy a very specific condition called being a Calabi-Yau manifold, and that we knew very, very few examples of this, so what got a lot of people very excited back in '84, '85 was the hope that you could just take this, um, 10-dimensional string theory and find one of a limited number of possible ways of- of getting rid of six dimensions by making them small, and then you would end up with a- an effective four-dimensional theory which looked like the real world. This was the hope. So then there's the- (laughs) a very long story about what happened to that hope over the years. I mean, I- I would argue and pro- part of the te- point of the book and its title was that, um, you know, that this- this ultimately wa- wa- was a failure, that you ended up ... that this idea just didn't, um ... there ended up being just too many ways of doing this, and you didn't know how to do this consistently, um, that it was kind of n- not even wrong in the sense that you couldn't even pin ... you- you never could pin it down well enough to actually get a real falsifiable prediction out of it that would tell you it was wrong, but it was, um ... it was kind of in the i- in- in the realm of ideas which initially look good but the more you look at them, they just, um, they don't work out the way- the way you want and they- they don't actually end up carrying the power or the ... that you originally had this vision of.

   5. LFLex Fridman40:11

      And yes, the- the book title is Not Even Wrong, your blog, your excellent blog title, Is Not Even Wrong. Okay. But there has nevertheless been a lot of excitement about string theory through the decades as you've mentioned. Uh, what are the different flavors of ideas that came, uh, like that branched out? You mentioned 10 dimensions, you mentioned loops with i- infinite degrees of freedom. What- what other interesting ideas to you that kind of emerged from this world?

   6. PWPeter Woit40:41

      Well, yeah, I mean, th- the problem with talking about the whole subject and, well, partly one of the reasons I wrote the book is that it ... it gets very, very complicated. I mean, there's a- a huge amount ... you know, hu- a lot of people got very interested in this, a lot of people worked on it, and in- and in some sense I think what happened is exactly because the idea didn't really work, that this caused people to, you know, instead of focusing on this one idea and digging in and working on that, they just kind of kept trying new things, and so people I think ended up wandering around in a very, very rich space of ideas about mathematics and physics and discovering all, you know, all sorts of really interesting things. It's just the problem is there tended to be an inverse relationship between how interesting and beautiful and fruitful this new idea that they were trying to pursue was and how much it looked like the real world (laughs) . So there's a lot of beautiful mathematics came out of it. I think one of the most spectacular is what the, um, physicists call two-dimensional conformal field theory, and so these are basically quantum field theories and kind of think of it as one space and one time dimension which, you know, have just this huge amount of symmetry and- and, um, a huge amount of structure which ... yeah, and just some totally fantastic mathematics behind it, and, um ... and again, and- and some of that mathematics is exactly also what appears in the Langlands program.

   7. LFLex Fridman42:03

      Mm-hmm.

   8. PWPeter Woit42:03

      So a lot of the, um ... first interaction between math and physics around the Langlands program has been around these two-dimensional conformal field theories.

   9. LFLex Fridman42:12

      Is there, um, something you could say about what the major problems are with string theory? So th- well, like, um ... besides th- that there's no experimental validation, you've, uh, written that a big hole in string theory has been its perturbative definition.

   10. PWPeter Woit42:33

       Yeah.

   11. LFLex Fridman42:34

       Perhaps that's one. Can you explain what that means?

   12. PWPeter Woit42:36

       Well, th- maybe to begin with, I mean, I- I think the, I mean, the simplest thing to- to say is, you know, the- the initial idea really was that ...... "Okay, we're- we have this..." Instead of... What's great is we have this thing that only works, that's very structured and has to work in a certain way for it to make sense. And, um, but- but then you ended up, you ended up in 10 space time dimensions. And so to get back to physics, you had to get rid of five of the dimens- six of the dimensions. And the bottom line, I would say, in some sense, it's very simple. That what people just discovered is just there- there's kind of no particularly nice way of doing this. There's an infinite number of ways of doing it, and you can get whatever you want depending on how you do it. So the- you- you end up the whole program of starting at 10 dimensions and getting to four just kind of collapses out of a- a lack of any way to kind of get to where you want because you can get anything. The be- the hope around that problem has always been that the standard formulation that we have of string theory, which is you can go by the name perturbative, but it- it's kind of... Um, there's a standard way we know of giving a classical theory of constructing a quantum theory and- and working with it, which is this- the so-called perturbation theory. That, um, that we know how to do, and that- that by itself just- just doesn't- doesn't give you any hint as to what to do about the six dimensions. So actual perturbed with string theory by itself really only works in ten dimensions. So you have to start making some kinds of assumptions about how I'm going to go beyond this formulation that we really understand of string theory and get rid of these six- six dimensions. So kind of the simplest one was the, um, Cladial postulate. But, um, when that didn't really work out, people tried more and more different things. And- and the hope has always been that the solution to this problem would be that you would find a deeper and better understanding of what string theory is that would actually go beyond this perturbative expansion, and which- which would generalize this. And- and that once you had that, it would, um- it would solve this problem of... It would pick out what to do with the six dimensions.

   13. LFLex Fridman44:59

       How difficult is- is this problem so... (sighs) If I could restate the problem, it seems like there's a very consistent physical world operating in four dimensions. And, uh, how do you map a consistent physical world in ten dimensions to a consistent physical world in four dimensions?

   14. PWPeter Woit45:20

       Right.

   15. LFLex Fridman45:21

       And how- how difficult is this problem? Is it- is that something you can even answer, um, just in terms of physics intuition, in terms of mathematics mapping from ten dimensions to four dimensions?

   16. PWPeter Woit45:35

       Well, basically, I mean, you have to get rid of the six of the dimensions. So- so there's... There- there's kind of two ways of doing it. One is what we call compactification. You say that there really are ten dimensions, but for whatever reason, six of them are really, are so, so small we can't see them. So you basically start out with ten dimensions and what we call... You know, make- make- make six of them not go out to infinity, but just kind of a finite extent, and then make that size go down so small it's unobservable.

   17. LFLex Fridman46:05

       That's like, that's a math trick. So c- c- can you also help me build an intuition about how rich and interesting the world in those six dimensions is? So compactification seems to imply (laughs) it's not very interesting.

   18. PWPeter Woit46:22

       Well, no, but- but the problem is that what you learn if you start doing math- mathematics and looking at geometry and topology in- in more and more dimensions is that, I mean, asking the question like, "What are all possible six dimensional spaces?" is just, it's kind of an unanswerable question. It's just, uh, I mean, there- it's even kind of technically undecidable in some way. There's just, there's just too, too... There are too many things you can do with all these. If you start trying to make- if you start trying to make one dimensional spaces, it's like, well, you got a line, you can make a circle, you can make graphs. You can kind of see what you can do. But as you go to higher and higher dimensions, there are just so many ways you can put things together of, and get something of that dimensionality. And so it- it- it... Um, unless you have some very, very strong principle which is going to pick out some very specific ones of these six dimensional spaces, and they're just too many of them and you can get anything you want, but, um...

   19. LFLex Fridman47:19

       So if you have ten dimensions, the kind of things that happen, or say that's actually the way, that's actually the fabric of our reality is ten dimensions, there's a limited set of behaviors of objects. I don't know, even know what the right terminology to use, that can occur within those dimensions, like in reality.

   20. PWPeter Woit47:40

       Yeah.

   21. LFLex Fridman47:41

       And so, like, what I'm getting at is like, is there some consistent constraints? So if you have some constraints that map to reality, then you can start saying like, "Dimension number seven is kind of boring. All the excitement happens in the spatial dimensions one, two, three."

   22. PWPeter Woit48:00

       Yeah.

   23. LFLex Fridman48:00

       And time is also kind of boring.

   24. PWPeter Woit48:02

       Yeah.

   25. LFLex Fridman48:03

       And like, some are more exciting than others. Or we can use our metric of beauty. Uh, some dimensions are more beautiful than others. Once you have an actual understanding of what actually happens in those dimensions in our physical world, as opposed to sort of all the possible things that could happen.

   26. PWPeter Woit48:19

       In some sense, I mean, just the basic fact is you need to get rid of them. We don't see them, so you- you need to somehow explain them. What you have to... The main thing you're trying to do is to explain why we're not seeing them. And so you- you can... You have to come up with some theory of these extra dimensions and- and how they're going to behave, and string theory gives you some ideas about how to do that, but- but the bottom line is where you're trying to go with this whole theory you're creating is to just make all of its effects essentially unobservable. So it's a- it's not a really... (laughs) It- it's an inherently kind of dubious and worrisome thing that you're trying to do there. Why are you just adding in all this stuff and then trying to explain why we don't see it? I mean, it just...

   27. LFLex Fridman49:03

       This may be a dumb question, but it's, is this an obvious thing to state, that those six dimensions are unobservable, or anything beyond four dimensions is unobservable? Or do you leave a little door open to saying the current tools of physics, and obviously our brains aren't unable to observe them-

   28. PWPeter Woit49:26

       Yeah.

   29. LFLex Fridman49:27

       ... but we may need to come up with methodologies for observing them? So as opposed to collapsing your mathematical theory into four dimensions, leaving the door open a little bit to maybe we need to come up with tools that actually allow us to directly measure those dimensions.

   30. PWPeter Woit49:42

       Yeah, so I mean, but you, I mean, you can certainly ask, you know, assume that we've got model... Look, look at models with more dimensions and ask, you know, what would the observable effects, how would we-
5. 1:05:16 – 1:25:24

   Theory of everything

   1. LFLex Fridman1:05:16

      Um, what about experimental validation? Is that, uh, is that a fair standard to hold before a theory of everything that's trying to unify quantum mechanics and gravity?

   2. PWPeter Woit1:05:29

      Yeah, I mean, u- ultimately to be really convinced that, you know, that, that un-... some new y- idea about unification really works, you need some kind of a... You need to look at the real world and see that this is telling you something, something true about it. I mean, you know, either, either telling you that if you do some experiment and go out and do it, you'll get some unexpected result and that's the kind of gold standard or it may be just that, like, all those numbers that are we don't know how to explain, it, it will show you how to calculate them. I mean, it can, it can be various kinds of experimental validation, but that, that's certainly ideally what you're looking for.

   3. LFLex Fridman1:06:08

      How tough is this, do you think, for a theory of everything, not just string theory? So for something that unifies gravity and quantum mechanics, so the, the very big and the very small, is this, um... Let me ask it one way, is, uh, is it a physics problem, a math problem or an engineering problem?

   4. PWPeter Woit1:06:28

      My, my guess is it, it's a combination of a physics and a, and a math problem that you really need... It's, it's not really engineering. It, it's not like there's some kind of well-defined thing you can write down and, and we just don't have enough computer power to do the calculation. It... That's not the kind of problem it is at all. Um, but the question is, you know, what mathematical tools you need to properly formulate the problem i- i- is unclear, so one reasonable conjecture is the way... the reason that we haven't had any success yet is just that, um, we're missing... either we're missing certain-... physical ideas, or we're missing certain mathematical tools which, or some combination of them, which would, uh, whi- which we need to kind of properly formulate the problem and see w- and, and, and see that it, it has a solution that looks like the real world.

   5. LFLex Fridman1:07:17

      But does she need, uh, I g- I guess you don't but, there's a sense that, uh, you need both gravity, like, all the laws of physics to be operating on the same level, so this isn't, it feels like you need an object like a black hole or something like that, um, in order to make predictions about. Otherwise, you're always making predictions about this joint phenomena. Uh, or, or can you do that as long as the theory is consistent and doesn't have special cases for each of the phenomena?

   6. PWPeter Woit1:07:48

      Well, your, your theory should mean, s- if your theory is gonna include gravity, our current understanding of gravity is that you should have, um ... there should be black hole states and then you should be able to describe black holes in this theory, and, um, and just one aspect that people have concentrated a lot on is just this kind of questions about if your theory includes black holes like it's supposed to, and it includes quantum mechanics, then there are certain kind of paradoxes which come up. And so that's, that's been a huge focus of kind of quantum gravity work, work has been not just those paradoxes, but ...

   7. LFLex Fridman1:08:20

      So stepping outside of string theory, uh, can you just say first at a high level, what is a theory of everything? What is a theory of everything seek to accomplish?

   8. PWPeter Woit1:08:32

      Well, I mean, this is very much a kind of reductionist point of view in, in the sense that so it's not a theory. This is not gonna explain to you, you know, anything. It doesn't really, this kind of theory, theory, this kind of theory of everything we're talking about doesn't ex- say anything interesting, particularly about like macroscopic objects, about what the weather is gonna be tomorrow, or, you know, things that are happening at this scale. But just what we've discovered is that as you look at, um, the universe that kind of, you know, if you kinda start break, you can start breaking it apart into ... and yet you end up with some fairly simple pieces, quanta, if you like, and w- and which are doing, which are interacting in some fair- in some fairly simple way. And it's, um, it's got th- so what we mean by a theory of everything is a theory that describes all, a- all the object, all the correct objects you need to describe what's happening in the world and describes how they're interacting with each other at a most fundamental level. How you get from that theory to describing some macroscopic incredibly complicated thing is, there that becomes m- again more of an engineering problem than ... you may need machine learning or you may, you know, a lot of very different things to do it, but ...

   9. LFLex Fridman1:09:45

      Well, I don't even n- think it's, uh, just engineering. It's also science. It-

   10. PWPeter Woit1:09:50

       Yeah.

   11. LFLex Fridman1:09:50

       One thing that I find, um, kind of interesting talking to physicists is, is a little bit ... there's, um, a little bit of hubris. Some of the most brilliant people I know are physicists, both philosophy and just in, in terms of mathematics, in terms of understanding the world. But there is a kind of a, either a hubris or w- what would I call it? Uh, like a confidence that if we have a theory of everything, we will understand everything. Like, this is the deepest thing to understand. And I would say, and like the rest is details, right? That's the, the old Rutherford thing. Uh, but to me, there's like, this is like a cake or something. There's layers to this thing and each one has a theory of everything.

   12. PWPeter Woit1:10:41

       Yeah.

   13. LFLex Fridman1:10:42

       Like at, at every le- level from biology, like how life originates, that itself, like complex systems.

   14. PWPeter Woit1:10:52

       Yeah.

   15. LFLex Fridman1:10:52

       Like, that in itself is like this gigantic thing that requires a theory of everything. And then there is the, wha- in the space of humans psychology, like intelligence, collective intelligence, the way it emerges among species. That feels like a complex system that requires its own theory of everything. On top of that is things like in the computing space, artificial intelligence systems.

   16. PWPeter Woit1:11:16

       Yeah.

   17. LFLex Fridman1:11:16

       Like that feels like it needs a theory of everything. And it's almost like, um, once we solve, uh, o- once we come up with a theory of everything that explains the basic laws of physics that gave us the universe, even stuff that's super complex like, uh, how, like how the, uh, universe might be able to originate, even explaining something that you're not a big fan of like multiverses or stuff that we don't have any evidence of yet-

   18. PWPeter Woit1:11:42

       Yeah.

   19. LFLex Fridman1:11:43

       ... still we won't be able to have a strong explanation of, uh, why food tastes delicious. (laughs)

   20. PWPeter Woit1:11:52

       Oh, yeah, yeah. No, no anyway, I, I, yeah, I agree completely. I mean this, there is something kind of completely wrong with this terminology of theory of everything. It, it, it's not, um, it's really in some sense very bad ter- very hubristic and bad ter- terminology because it's not, um ... this is explaining, this is a purely kind of reductionist point of view that you're, you're trying to understand cer- certain, uh, certain very specific kind of things which, you know, in principle other things, you know, emerge from. But to actually understand how anything emerges from this is i- it's ho- it can't be understood in terms of this, this underlying fundamental theory is gonna be ho- hopeless in terms of kind of telling you what a- about this, um, this various emergent behavior. And as you go to different levels of explanation you're gonna need to develop new, you know, different, completely different ideas, completely different ways of thinking and I guess there's a famous kind of, um, Phil Anderson's slogan is that, you know, more is different.

   21. LFLex Fridman1:12:54

       (laughs)

   22. PWPeter Woit1:12:54

       And then, yeah, so, and, i- i- it's just, it's, it's ju- yeah, e- even once you understand how what a couple thing ... well, if you have a collection of stuff and you understand perfectly well how each thing is interacting with it-... with, with the others. What the whole thing is gonna do is just a completely different problem, and it's just not ... And you need completely different ways of thinking about it.

   23. LFLex Fridman1:13:13

       What do you think about this ... Uh, I gotta ask you. At a few different attempts at a theory of everything, especially recently, uh, so I've been, for many years, a big fan of cellular automata, complex systems, and obviously if, uh, because of that, a fan of Steven Wolfram's work on, in that space. But he's recently been talking about a theory of everything through his physics project-

   24. PWPeter Woit1:13:36

       Yeah.

   25. LFLex Fridman1:13:36

       ... essentially. Uh, what do you think about this kind of discrete theory of everything for like from simple rules and simple objects and hypergraphs emerges all of our reality, where time and space are emergent. Basically everything we see around us is emergent.

   26. PWPeter Woit1:13:53

       Yeah, I, yeah, I- I have to say, unfortunately, I've kind of pretty much zero sympathy for that. I mean, I don't, um, I s- I spent a little time looking at it, and I just don't see ... It doesn't seem to me to get anywhere. And, and it, it really is, just really, really doesn't agree at all with, with what, what, with what I'm seeing. This, the kind of unification of math and physics that I'm kind of talking about around certain kinds of very deep ideas about geometry and stuff. This, if you wanna believe that, that your things are really coming out of cellular automata at the most, um, fundamental level, you have to believe that everything that I've seen my whole career and, and as, as beautiful, powerful ideas, that that's all just kind of a mirage which is kind of randomly is emerging from these more basic, very, very simple-minded things. And I'm ... You have to give me some serious evidence for that, and I'm seeing nothing.

   27. LFLex Fridman1:14:46

       So, mirage. You, you don't think there could be a consistency where, um, things like quantum mechanics could, could emerge from much, much, much smaller, discrete like computational-type systems?

   28. PWPeter Woit1:15:00

       Well, I think from the point of view of, certain mathematical point of view, quantum mechanics is already mathematically as simple as it gets. It really is a story a- a- about really f- ... The fundamental objects that you work with and when you write down a quantum theory are in some s- in some f- one point of view precisely the fundamental objects at these deepest levels of mathematics that you're working with. They're exactly the same. So, and cellular automata are something completely different which don't fit into these structures, and so I just don't see why. Any- anyway, I don't see it as, as a promising, uh, you know, promising thing to do, and then just looking at it and seeing does this go anywhere? Does this solve any problem that I've ever, that I didn't ... Does this solve any problem of any kind? It ju- I just don't see it.

   29. LFLex Fridman1:15:46

       Yeah. To me, cellular automata and these hypergraphs, I'm not sure if solving a problem is even the standard to apply here at this moment. To me, the fascinating thing is that the question it asks have no good answers.

   30. PWPeter Woit1:16:02

       Yeah.

Episode duration: 2:15:56