Sean Carroll: Quantum Mechanics and the Many-Worlds Interpretation | Lex Fridman Podcast #47

1. 0:00 – 15:00

   The following is a…

   1. LFLex Fridman0:00

      The following is a conversation with Sean Carroll, part two, the second time we've spoken on the podcast. You can get the link to the first time in the description. This time, we focus on quantum mechanics and the many worlds interpretation that he details elegantly in his new book titled Something Deeply Hidden. I own and enjoy both the e-book and audiobook versions of it. Listening to Sean read about entanglement, complementarity, and the emergence of space time, it reminds me of Bob Ross teaching the world how to paint on his old television show. If you don't know who Bob Ross is, you're truly missing out. Look him up. He'll make you fall in love with painting. Sean Carroll is the Bob Ross of theoretical physics. He's the author of several popular books, a host of a great podcast called Mindscape, and is a theoretical physicist at Caltech and the Santa Fe Institute, specializing in quantum mechanics, arrow of time, cosmology, and gravitation. This is the Artificial Intelligence Podcast. If you enjoy it, subscribe on YouTube, give it five stars on iTunes, support it on Patreon, or simply connect with me on Twitter, @LexFridman, spelled F-R-I-D-M-A-N. And now, here's my conversation with Sean Carroll. Isaac Newton developed what we now call classical mechanics, that you describe very nicely in your new book, as you do with a lot of basic concepts in physics. So, with classical mechanics, I can throw a rock and can predict the trajectory of that rock's flight. But if we could put ourselves back into Newton's time, his theories work to predict things, but as I understand, he himself thought that they were, the interpretations of those predictions were absurd. Uh, perhaps he just said it for religious reasons and so on.

   2. SCSean Carroll1:58

      (laughs)

   3. LFLex Fridman1:58

      But in particular, sort of a world of interaction without contact. So action at a distance. It didn't make sense to him on a sort of a human interpretation level. Does it make sense to you that things can affect other things at a distance?

   4. SCSean Carroll2:16

      It does, but, you know, that, so that was one of Newton's worries. You're actually right in a slightly different way about the religious worries. He, um, he was smart enough... This is off the topic, but still fascinating. Newton almost invented chaos theory as soon as he invented, uh, classical mechanics. He realized that in the solar system... So he was able to explain how planets move around the sun, but typically, you would describe the orbit of the Earth ignoring the effects of Jupiter and Saturn and so forth, just doing the Earth and the Sun. He, he kind of knew, even though he couldn't do the math, that if you included the effects of Jupiter and Saturn, the other planets, the solar system would be unstable. Like, the orbits of the planets would get out of whack. So he thought that God would intervene occasionally to sort of move the planets back into orbit, which is how you could, only way you could explain how they were there presumably forever. Um, but the worries about classical mechanics were a little bit different. The worry about gravity in particular. It wasn't a worry about classical mechanics, it was a worry about gravity. How in the world does the Earth know that there's something called the Sun 93 million miles away that is exerting a gravitational force on it? And he said, he literally said, "You know, I leave that for future generations to think about, because I don't know what the answer is." And in fact, people underemphasize this, but future generations figured it out. Pierre-Simon Laplace in, uh, circa 1800 showed that you could rewrite Newtonian gravity as a field theory. So instead of just talking about the force due to gravity, you can talk about the gravitational field or the gravitational potential field, and then there's no action at a distance. It's exactly the same theory empirically. It makes exactly the same predictions. But what's happening is instead of the Sun just reaching out across the void, there is a gravitational field in between the Sun and the Earth that obeys an equation, Laplace's equation, cleverly enough, and, uh, that tells us exactly what the field does. So, even in Newtonian gravity, you don't need action at a distance. Now, what many people say is that Einstein solved this problem because he invented general relativity, and in general relativity, there's certainly a field in between the Earth and the Sun, but also there's the speed of light as a limit. In Laplace's theory, which was exactly Newton's theory, just in a different mathematical language, there could still be instantaneous action across the universe. Whereas in general relativity, if you shake something here, its gravitational impulse radiates out at the speed of light, and we call that a gravitational wave, and we can detect those. So, but I, I really... It rubs me the wrong way to think that we should presume the answer should look one way or the other. Like, if it turned out that there was action at a distance in physics and that was the best way to describe things, then I would do it that way. It's, uh, actually a very deep question because when we don't know what the right laws of physics are, when we're guessing at them, when we're hypothesizing at what they might be, we are often guided by our intuitions about what they should be. I mean, Einstein famously was very guided by his intuitions, and he did not like the idea of action at a distance. We don't know whether he was right or not. It depends on your interpretation of quantum mechanics and it depends on, uh, even how you talk about quantum mechanics within any one interpretation.

   5. LFLex Fridman5:24

      So if you see every force as a field, or any other interpretation of action at a distance, I... Just stepping back to sort of caveman thinking, like, do you really, can you really sort of understand what it means for a force to be a field that's everywhere? So if you look at gravity... Like, what, what do you think about-

   6. SCSean Carroll5:48

      I think so. (laughs)

   7. LFLex Fridman5:49

      Is this something that you've been conditioned by society to think that... To map the fact that science is extremely well predictive of something-

   8. SCSean Carroll6:01

      Mm-hmm.

   9. LFLex Fridman6:01

      ... to believing that you actually...... understand it, like you can intuitively under the, the, how, as, to the degree that human beings can understand anything, that you actually understand it. Are you just trusting the beauty and the power of the, the predictive power of science?

   10. SCSean Carroll6:19

       That depends on what you mean by this idea of truly understanding something.

   11. LFLex Fridman6:24

       Right.

   12. SCSean Carroll6:25

       Right? You know, I mean-

   13. LFLex Fridman6:25

       (laughs)

   14. SCSean Carroll6:25

       ... can I truly understand Fermat's Last Theorem? You know, it's easy to state it, but do I really appreciate what it means for incredibly large numbers, right? Um, yeah, I think yes. I think I do understand it, but like if you want to just push people on, "Well, but your intuition doesn't go to the places where Andrew Wiles needed to go to prove Fermat's Last Theorem," then I can say, "Fine, but I still think I understand the theorem." And, uh, likewise, I think that I do have a pretty good intuitive understanding of fields pervading space time, whether it's the gravitational field or the electromagnetic field or whatever, the Higgs field. Um, of course, one's intuition gets worse and worse as you get trickier into quantum field theory and all sorts of, uh, new phenomena that come up in quantum field theory, so our intuitions aren't perfect, but I think it's also okay to say that our intuitions get trained, right? Like, you know, I have different intuitions now than I had when I was a baby. That's okay. That's not, an intuition is not necessarily intrinsic to who we are. We can, we can train it a little bit.

   15. LFLex Fridman7:27

       So that's where I'm gonna bring in Noam Chomsky for a second, who thinks, uh, that our cognitive abilities are sort of evolved through time, and so they're, they're biologically constrained, and so there's a l- a s- clear limit, as, as he puts it, to our cognitive abilities, and it's a very harsh limit. But you actually kind of said something interesting, the nature versus nurture, uh, thing here, is we can train our intuitions to sort of build up the cognitive muscles to be able to understand some of these tricky concepts. So do, do you think there's limits to our understanding that's deeply rooted, hardcoded into our biology that we can't overcome?

   16. SCSean Carroll8:09

       There could be limits to things like our ability to visualize, okay? But when someone like Ed Witten proves a theorem about, you know, hundred-dimensional mathematical spaces-

   17. LFLex Fridman8:21

       Yeah.

   18. SCSean Carroll8:21

       ... he's not visualizing it. He's doing the math. Uh, that doesn't stop him from understanding the result. I, I think, and I, I would love to understand this better, but my rough feeling, uh, which is not very educated, is that, you know, there's some threshold that one crosses in abstraction when one becomes kind of like a Turing machine, right? One has the ability to contain in one's brain, uh, logical, formal, symbolic structures and manipulate them, and that's a leap that we can make as human beings that, that, uh, dogs and cats haven't made, and once you get there, I'm not sure that there are any limits to our ability to understand the scientific world at all. Maybe there are. There's certainly abil- limits in our ability to calculate things, right? You know, people are not very good at taking cube roots of million-digit numbers in their head, uh, but that's not a- an element of understanding. It's certainly not a limited principle.

   19. LFLex Fridman9:15

       So, of course, as a human, you would say there doesn't feel to be limits to our understanding, but sort of, um, ha- have you thought that the universe is actually a lot simpler than it appears to us, and we just will never be able to, like, it's outside of our... Okay, so us, our cognitive abilities combined with our mathematical prowess and, uh, whatever kind of experimental simulation devices we can put together, is there limits to that? Do, do y- is y- is it possible there's limits to that?

   20. SCSean Carroll9:53

       Well, of course, it's possible-

   21. LFLex Fridman9:55

       (laughs)

   22. SCSean Carroll9:55

       ... that there are limits to that. Uh, is there any good reason to think that we're anywhere close to the limits is a-

   23. LFLex Fridman10:01

       Ah, I see.

   24. SCSean Carroll10:01

       ... harder question. Look, imagine asking this question 500 years ago to the world's greatest thinkers.

   25. LFLex Fridman10:06

       Right.

   26. SCSean Carroll10:07

       Right? Like, are, are we approaching the limits of our ability to understand the natural world? And by definition, there are questions about the natural world that are most interesting to us that are the ones we don't quite yet understand.

   27. LFLex Fridman10:19

       Okay.

   28. SCSean Carroll10:19

       Right? So there's always, we're always faced with these puzzles we don't yet know. And I don't know what they would have said 500 years ago, but they didn't even know about classical mechanics, much less quantum mechanics. So we know that they were nowhere close to how well they could do, right? They could do enormously better than they were doing at the time. I see no reason why the same thing isn't true for us today. So of all the worries that keep me awake at night, the human mind's inability to rationally comprehend the world is low on the list. (laughs)

   29. LFLex Fridman10:48

       (laughs) Well put. So one interesting philosophical point that quantum mechanics bring up is the, that you talk about, the distinction between the world as it is and the world at, as we observe it.

   30. SCSean Carroll11:00

       Mm-hmm.
2. 15:00 – 30:00

   Yeah. …

   1. LFLex Fridman15:00

      conveniently most of the interesting ideas are acting in the moment. You don't need to know the history-

   2. SCSean Carroll15:07

      Yeah.

   3. LFLex Fridman15:07

      ... of time or the future that-

   4. SCSean Carroll15:09

      And of course, this took a long time to get there, right?

   5. LFLex Fridman15:12

      Right.

   6. SCSean Carroll15:12

      I mean, the conservation momentum itself took hundreds of years. Uh, it's weird 'cause like someone would say something interesting and then the next interesting thing would be said like 150 or 200 years later, right? They weren't even talking to each other. They were just reading each other's books. And probably the first person to directly say that in outer space, in the vacuum, a projectile would move at a constant velocity was, uh, Avicenna, Ibn Sina in the Persian Golden Age, circa 1000. And he didn't like the idea. He used that just like Schrodinger used Schrodinger's cat to say, "Surely you don't believe that," right?

   7. LFLex Fridman15:44

      Mm-hmm.

   8. SCSean Carroll15:45

      Um, Ibn Sina was saying, "Surely you don't believe there really is a vacuum. Because if there was a really vacuum, things could keep moving forever" (laughs) , right? But still, he got right the idea that there was this conservation of something, impetus or mile he would call it. And, uh, that's 500 years, 600- 600 years before classical mechanics and Isaac Newton. So, you know, Galileo played a big role in this, but he didn't exactly get it right. And, uh, so it just takes a long time for this to sink in 'cause it is so against our everyday experience.

   9. LFLex Fridman16:12

      Do you think it was a big leap, a brave or a difficult leap of sort of, uh, math and science to be able to say that momentum is conserved?

   10. SCSean Carroll16:26

       I do. You know, I think it's a example of human reason in action. You know, even Aristotle knew that his theory had issues because you could fire an arrow and it would go a long way before it stopped. So if his theory was things just automatically stop, what's going on? And he had this elaborate story, I don't know if you've heard this story, but the arrow would push the air in front of it away, and the molecules of air would run around to the back of the arrow and push it again.

   11. LFLex Fridman16:53

       (laughs)

   12. SCSean Carroll16:53

       And, like, anyone reading this is going like, "Really? That's- that's what you thought?" But it was that kind of thought experiment that ultimately got people to say like, "Actually no, if it weren't for the air molecules at all, the arrow would just go on by itself." And it's always this give and take between thought and experience, back and forth, right? Theory and experiment we would say today.

   13. LFLex Fridman17:13

       Another big question that I think comes up certainly with, uh, quantum mechanics is, what's the difference between math and physics to you?

   14. SCSean Carroll17:25

       To me, you know, very, very roughly, math is about the logical structure of all possible worlds and physics is about our actual world.

   15. LFLex Fridman17:34

       And it just feels like our actual world is a gray area when you start talking about interpretations of quantum mechanics. Or no?

   16. SCSean Carroll17:43

       I'm certainly using the word world in the broadest sense, all of reality. So, um, I think that reality is specific. I don't think that there's every possible thing going on in reality. I think that there are rules, whether it's the Schrodinger equation or whatever. So I think o- I think that there's a sensible notion of the set of all possible worlds, and we live in one of them. The world that we're talking about might be a multiverse, might be many worlds of quantum mechanics, might be much bigger than the world of our everyday experience, but it's still one physically contiguous world in some sense.

   17. LFLex Fridman18:15

       But, so if you look at the overlap of math and physics, it feels like when physics tries to reach for understanding of our world, it uses the tools of math to sort of reach beyond the limit of our current understanding. Th- what do you make of that process, of sort of using math to, uh, to start maybe with intuition, or you might start with the math and then build up an intuition? Or but this kinda reaching into the darkness, into the mystery of the world with math.

   18. SCSean Carroll18:50

       Well, I think I would put it a little bit differently. I think we, we, we have theories, theories of the physical world, which we then extrapolate and ask, you know, "What do we conclude if we take these seriously well beyond where we've actually tested them?" It is separately true that math is really, really useful when we construct physical theories, and, you know, famously Eugene Wigner asked about the unreasonable success of mathematics and physics. I think that's a, a little bit wrong, because anything that could happen, any other theory of physics that wasn't the real world but some other world, you could always describe it mathematically. It's just that it might be a mess. (laughs) The surprising thing is not that math works, but that the math is so simple and easy that you can write it down on a T-shirt, right? I mean, that's what is amazing. That's an enormous compression of information that seems to be valid in, in the real world. So that's an interesting fact about our world, which maybe we could hope to explain or just take as a, a brute fact. I don't know. But, uh, once you have that, you know, it, there's this, th- indelible relationship between math and physics. But, but philosophically I do want to separate them. What we, what we extrapolate, we don't extrapolate math, because there's a whole bunch of wrong math, you know, that doesn't apply to our world, right? We extrapolate the physical theory that we best think explains our world.

   19. LFLex Fridman20:10

       Again, an unanswerable question. Why do you think our world is so easily compressible, uh, into beautiful equations?

   20. SCSean Carroll20:20

       Yeah, I mean, like I just hinted at, I don't know if there's an answer to that question.

   21. LFLex Fridman20:23

       Okay.

   22. SCSean Carroll20:23

       There could be.

   23. LFLex Fridman20:25

       What would an answer look like?

   24. SCSean Carroll20:26

       Well, an answer could look like if you showed that there was something about our world that maximized something, you know, the, the, the mean of the simplicity and the powerfulness of the laws of physics. Or, you know, whether... maybe we're just generic. Maybe in a set-

   25. LFLex Fridman20:42

       (laughs)

   26. SCSean Carroll20:42

       ...of all possible worlds, this is what the world would look like, right? Like, I r- I don't really know. I, I tend to think not. I tend to think that there is something specific and rock-bottom about the facts of our world that don't have further explanation, like the fact that the world exists at all, and furthermore, the specific laws of physics that we have. I think that in some sense, we're just gonna... at, at some level we're gonna say, "And that's how it is." And, you know-

   27. LFLex Fridman21:05

       Mm-hmm.

   28. SCSean Carroll21:05

       ...we can't explain anything more. We, I don't know how, if we're anywhere close to that right now, but that seems plausible to me.

   29. LFLex Fridman21:12

       And speaking of rock bottom, one of the things sort of your book kind of reminded me or revealed to me is that what's fundamental and what's emergent, (laughs) it just feels like I don't even know anymore what's fundamental in, in, uh, in physics, if there's anything. It feels like everything, especially with quantum mechanics, is revealing to us, is that most interesting things that I would as a h- as a limited human would think are, uh-

   30. SCSean Carroll21:40

       (laughs)
3. 30:00 – 45:00

   And where quantum mechanics…

   1. SCSean Carroll30:00

      times as heavy as electrons are. Uh, electrons are much lighter, but they're... Because they're lighter, they give all the life to the atoms. So, when atoms get together, combine chemically, when electricity flows through a system, it's all the electrons that are doing all the work.

   2. LFLex Fridman30:16

      And where quantum mechanics steps in, as you mentioned, with position or velocity with classical mechanics, and quantum mechanics is modeling the behavior of the electron. I mean, you can model the behavior of anything-

   3. SCSean Carroll30:29

      Oh, definitely.

   4. LFLex Fridman30:29

      ... but the electron because that's where the fun is.

   5. SCSean Carroll30:31

      The electron was, was the biggest challenge, right from the start. Yeah.

   6. LFLex Fridman30:34

      So, what- what's a wave function? You said it's an interesting detail. (laughs)

   7. SCSean Carroll30:38

      Yeah.

   8. LFLex Fridman30:39

      But, uh, in any interpretation, what is the wave function in quantum mechanics?

   9. SCSean Carroll30:45

      Well, you know, we had this idea from Rutherford that w-... atoms look like little solar systems. But people very quickly realized that can't possibly be right, because if an electron is orbiting in a circle, it will give off light. All the light that we have in this room comes from electrons zooming up and down and wiggling, and that's what electromagnetic waves are. And you can calculate how long would it take for the electron just to spiral into the nucleus, and the answer is 10-11 seconds, okay? A hundred billionth of a second. So that's not right. Meanwhile, people had realized that light, which we understood from the 1800s was a wave, had properties that were similar to that of particles, right? This is Einstein and Planck and stuff like that. So if something that we agree was a wave had particle-like properties, then maybe something we think is a particle, the electron, has wave-like properties, right? And so a bunch of people eventually came to the conclusion, don't think about the electron as a little point particle orbiting in, like a solar system. Think of it as a wave that is spread out. And they cleverly gave this the name the wave function, which is the dopiest name in the world for one of the most profound things in the, in the, in the universe. The, there's literally, you know, a number at every point in space, which is the value of the electron's wave function at that point.

   10. LFLex Fridman32:04

       And there's only, there's only one wave function.

   11. SCSean Carroll32:07

       That, yeah. They eventually figured that out. That took longer.

   12. LFLex Fridman32:10

       Mm-hmm.

   13. SCSean Carroll32:10

       But when you have two electrons, you do not have a wave function for electron one and a wave function for electron two. You have one combined wave function for both of them, and indeed, as you say, there's only one wave function for the entire universe at once.

   14. LFLex Fridman32:26

       Yeah, and that's where this, uh, beautiful dance...

   15. SCSean Carroll32:30

       Yep.

   16. LFLex Fridman32:30

       Can you say what is entanglement? Ooh, it seems one of the most fundamental ideas of quantum mechanics.

   17. SCSean Carroll32:35

       Well, let's temporarily buy into the textbook interpretation of quantum mechanics. And what that says is that this wave function, so it's very small outside the atom, very big in the atom. Basically, the wave function, you take it and you square it, if you square the number, that gives you the probability of observing the system at that location. So if you say that for two electrons, there's only one wave function, and that wave function gives you the probability of observing both electrons at once doing something, okay? So maybe the electron can be here or here or here or here, and the other electron can also be there. But we have a wave function set up where we don't know where either electron is going to be seen, but we know they'll both be seen in the same place, okay? So we don't know exactly what we're gonna see for either electron, but there's entanglement between the two of them. There's a sort of conditional statement. If we see one in one location, then we know the other one's gonna be doing a certain thing. So that's a feature of quantum mechanics that is nowhere to be found in classical mechanics. In classical mechanics, there's no way I can say, "Well, I don't know where either one of these particles is, but if I know, if I find out where this one is, then I know where the other one is." That just never happens. They're truly separate.

   18. LFLex Fridman33:43

       And in general, it feels like if you think of a wave function like as a dance floor, it seems like entanglement is strongest between things that are dancing together closest. So there's a, there's a closeness that's important, uh...

   19. SCSean Carroll33:57

       Well, that's another, that's another step. We have to, we have to be careful here-

   20. LFLex Fridman33:59

       Sure.

   21. SCSean Carroll33:59

       ... because in principle, if you're, if you're talking about the entanglement of two electrons, for example, they can be totally entangled or totally unentangled no matter where they are in the universe. There's no relationship between the amount of entanglement and the distance between two electrons. But we now know that, you know, the reality of our best way of understanding the world is through quantum fields, not through particles. So even the electron, not just gravity and electromagnetism, but even the electron and the quarks and so forth are really vibrations in quantum fields. So even empty space is full of vibrating quantum fields, and those quantum fields in empty space are entangled with each other in exactly the way you just said. If they're nearby, if you have like two vibrating quantum fields that are nearby, then they'll be highly entangled. If they're far away, they will not be entangled.

   22. LFLex Fridman34:50

       S- so what do quantum fields in a vacuum look like, empty space? Just so-

   23. SCSean Carroll34:54

       Looks like empty space. It's as empty as it can be.

   24. LFLex Fridman34:56

       But there's still a field.

   25. SCSean Carroll34:57

       Uh-huh.

   26. LFLex Fridman34:57

       It's just-

   27. SCSean Carroll34:58

       Yeah.

   28. LFLex Fridman34:59

       ... it, it, uh... What does nothing look like? (laughs)

   29. SCSean Carroll35:02

       Just like right here, this location in space, there's a gravitational field, which I can detect-

   30. LFLex Fridman35:06

       Yes.
4. 45:00 – 1:00:00

   So are the worlds…

   1. SCSean Carroll45:00

      The electron was there and you think you saw it there. The electron was over there and you think you saw it there," et cetera. So, and all of those different parts of the wave function, once they come into being, no longer talk to each other. They no longer interact or influence each other. It's as if they are separate worlds. So, this was the invention of Hugh Everett III, who was a, uh, graduate student at Princeton in the 1950s, and he said basically, "Look, you don't need all these extra rules about looking at things. Just listen to what the Schrodinger equation is telling you. It's telling you that you have a wave function, that you become entangled, and that the different versions of you no longer talk to each other. So just accept it." It's just, he did therapy more than anything else, you know? He said like, "It's okay, you know. You don't need all these extra rules. All you need to do is believe the Schrodinger equation. The cost is, there's a whole bunch of extra worlds out there."

   2. LFLex Fridman45:50

      So are the worlds being created whether there's an observer or not?

   3. SCSean Carroll45:57

      The worlds are created any time a quantum system that's in a superposition becomes entangled with the outside world.

   4. LFLex Fridman46:03

      What's the outside world?

   5. SCSean Carroll46:06

      It depends. Let's back up.

   6. LFLex Fridman46:07

      Yep.

   7. SCSean Carroll46:08

      What Everett really says, what his theory is, is there's a wave function of the universe and it obeys the Schrodinger equation all the time. That's it. That's the full theory right there, okay? The question, all of the work is, how in the world do you map that theory onto reality, onto what we observe, right? So part of it is carving up the wave function into these separate worlds, saying, "Look, look, it describes a whole bunch of things that don't interact with each other. Let's call them separate worlds." Another part is distinguishing between systems and their environments, and the environment is basically all the degrees of freedom, all the things going on in the world that you don't keep track of. So again, in the bottle of water, I might keep track of the total amount of water and the volume. I don't keep track of the individual positions and velocities. I don't keep track of all the photons or the air molecules in this room. So that's the outside world. The outside world is all the parts of the universe that you're not keeping track of when you're asking about the behavior of some subsystem of it.

   8. LFLex Fridman47:10

      So h- how many worlds are there? So-

   9. SCSean Carroll47:14

      Yeah, I don't know that one either. (laughs)

   10. LFLex Fridman47:17

       (laughs)

   11. SCSean Carroll47:17

       There could be an infinite number. There could be only a finite number, but it's a big number one way or the other.

   12. LFLex Fridman47:22

       So it's a very, very big number. I, in one of the other talks, somebody asked, "Well, if it's, uh, if it's finite..." So actually I'm not sure exactly the logic you use to derive this, but, um, is there, you know, going to be, uh, uh, you know, overlap, uh, a duplicate world that you return to? So you, you've mentioned, and I'd love if you can elaborate on sort of idea that it's possible that there's, like, some kind of equilibrium that these splitting worlds arrive at.

   13. SCSean Carroll47:56

       Mm-hmm.

   14. LFLex Fridman47:56

       And then maybe over time, maybe somehow connected to entropy, you get a large number of worlds that are very similar to each other.

   15. SCSean Carroll48:05

       Yeah, so this question of whether or not Hilbert space is finite or infinite dimensional is actually secretly connected to gravity and cosmology. Uh, this is the, the part that we're still struggling to understand right now. But we discovered back in 1998 that our universe is accelerating, and what that means, if it continues, which we think it probably will, but we're not sure. But if it does, that means there's a horizon around us. There, there's... Because the universe is not only expanding, but expanding faster and faster, things can get so far away from us that from our perspective it looks like they're moving away faster than the speed of light. You'll never see them again. So there's literally a horizon around us, and that horizon approaches some fixed distance away from us. And you can then argue that within that horizon, there's only a finite number of things that can possibly happen, a finite dimensional Hilbert space. In fact, we even have a guess for what the dimensionality is. It's 10 to the power of 10 to the power of 122. That's a very large number.

   16. LFLex Fridman49:05

       Yes.

   17. SCSean Carroll49:06

       Just to compare it, the age of the universe is something like 10 to the 14th, uh, seconds, 10 to the 17 or 18 seconds maybe. The number of particles in the universe is 10 to the 88th. But the number of dimensions of Hilbert space is 10 to the 10 to the 122. So that's just crazy big.If that story is right, that in our observable horizon, there's only a finite dimensional Hilbert space, then this idea of branching of, of the wave function of the universe into multiple distinct separate branches has to reach a limit at some time. Once you have branched that many times, you've run out of room in Hilbert space. And roughly speaking, that corresponds to the universe just expanding and emptying out and cooling off and, and entering a phase where it's just empty space literally forever.

   18. LFLex Fridman49:53

       What's the difference between splitting and copying, do you think? Like, in terms of... A- a lot of this is, um, an interpretation that's, that helps us sort of, uh, model the world, so perhaps shouldn't be thought of as, like, you know, philosophically or metaphysically, but in, even at the physics level, do you see a difference between sort of generating new copies of the world or splitting?

   19. SCSean Carroll50:27

       I think it's better to think of, in quantum mechanics and many worlds, the universe splits rather than new copies, because people otherwise worry about things like energy conservation.

   20. LFLex Fridman50:36

       Right.

   21. SCSean Carroll50:36

       And no one who understands quantum mechanics worries about energy conservation 'cause the equation is perfectly clear, but if all you know is that someone told you the universe duplicates, then you have a reasonable worry about where all the energy for that came from. So, a preexisting universe splitting into two skinnier universes is a better way of thinking about it, and mathematically, it's just like, you know, if you draw an X and Y axis and you draw a vector of length one at 45 degree angle, you, you know that you can write that vector of length one as the sum of two vectors pointing along X and Y of length one over the square root of two. Okay? So I write one arrow as the sum of two arrows. But there's a conversation of arrow-ness, right?

   22. LFLex Fridman51:16

       (laughs)

   23. SCSean Carroll51:16

       Like, there's now two arrows, but the length is the same.

   24. LFLex Fridman51:19

       Yeah.

   25. SCSean Carroll51:19

       I just, I'm describing it in a different way, and that's exactly what happens when the universe branches. The, the wave function of the universe is a big old vector.

   26. LFLex Fridman51:27

       So, to somebody who brings up a question of saying, "Doesn't this violate the conservation of energy?" Can you give a further elaboration?

   27. SCSean Carroll51:38

       Right. So let's just be super-duper perfectly clear.

   28. LFLex Fridman51:41

       Yeah.

   29. SCSean Carroll51:42

       There is zero question about whether or not many worlds violates conservation of energy.

   30. LFLex Fridman51:46

       Yes.
5. 1:00:00 – 1:15:00

   So start with, uh,…

   1. SCSean Carroll1:00:00

      is that there's something called modern physics, (laughs) with quantum fields and quantum gravity and holography and space-time, doing things like that. And when you take any of the other versions of quantum theory, they bring along classical baggage. All of the other versions of quantum mechanics prejudice or privilege some version of classical reality, like locations in space, okay? And I think that that's a barrier to doing better and understanding the theory of everything and understanding quantum gravity and the emergence of space-time. Whenever, if you change your theory from, you know, here's a harmonic oscillator, oh, there's a spin, here's an electromagnetic field, in hidden variable theories or dynamical collapse theories, you have to start from scratch. You have to say like, "Well, what are the hidden variables for this theory?" Or, "How does it collapse?" Or whatever. Whereas many-worlds is plug and play. You tell me the theory and I can give you its many-worlds version. So when we have a situation like we have with gravity and space-time, where the classical description seems to break down in a dramatic way, then I think you should start from the most quantum theory that you have, which is really many-worlds.

   2. LFLex Fridman1:01:07

      So start with, uh, the quantum theory and try to build up a model of space-time. The emergence of space-time.

   3. SCSean Carroll1:01:16

      Definitely.

   4. LFLex Fridman1:01:17

      Okay. So, I thought space-time was fundamental. (laughs)

   5. SCSean Carroll1:01:21

      Yeah. I know.

   6. LFLex Fridman1:01:22

      So this sort of dream that Einstein had, that everybody had and everybody has, of, you know, the theory of everything. So how do we build up from many-worlds, from quantum mechanics, uh, a model of space-time, a model of gravity?

   7. SCSean Carroll1:01:39

      Well, yeah, I mean, let me first mention very quickly why we think it's necessary. You know...We've had gravity in the form that Einstein bequeathed it to us for over 100 years now. Like, 1915 or 1916, he put general relativity in the final form. So gravity is the curvature of spacetime, and there's a field that pervades all the universe that tells us how curved spacetime is.

   8. LFLex Fridman1:02:00

      And that's a fundamentally classical...

   9. SCSean Carroll1:02:01

      That's totally classical, right, exactly. But we also have a formalism, an algorithm for taking a classical theory and quantizing it. This is how we get quantum electrodynamics, for example. And it could be tricky. I mean, you could, you think you're quantizing something, so that means taking a classical theory and promoting it to a quantum mechanical theory, um, but you can run into problems. So they ran into problems when they did that with electromagnetism, namely that certain quantities were infinity, and you don't like infinity, right?

   10. LFLex Fridman1:02:30

       No.

   11. SCSean Carroll1:02:30

       So, uh, Feynman and Tomonaga and Schwinger won the Nobel Prize for teaching us how to deal with the infinities, and then Ken Wilson won ano- another Nobel Prize for saying you shouldn't have been worried about those infinities after all. But still, that was the, the, it's always the thought that that's how you will make a good quantum theory. You'll start with a classical theory and quantize it. So if we have a classical theory of general relativity, we can quantize it or we can try to, but we run into even bigger problems with gravity than we ran into with electromagnetism. And so far, those problems are insurmountable. We have not been able to get a successful theory of gravity, quantum gravity, by starting with classical general relativity and quantizing it. Um, and there's evidence that there's a good reason why this is true, that the, whatever the quantum theory of gravity is, it's not a field theory. It's something that has weird, non-local features built into it somehow that we don't understand. And we get this idea from black holes and Hawking radiation and information conservation and a whole bunch of other ideas I talk about in the book. So if that's true, if the fundamental theory isn't even local in the sense that an ordinary quantum field theory would be, then we just don't know where to start in terms of getting a classical precursor and quantizing it.

   12. LFLex Fridman1:03:41

       Right.

   13. SCSean Carroll1:03:42

       So the only sensible thing, it's, or the, at least the next obvious sensible thing to me would be to say, "Okay, let's just start intrinsically quantum and work backwards, see if we can find a classical limit."

   14. LFLex Fridman1:03:51

       So the idea of locality, the, the fact that locality is not fundamental, uh, to the nature of our existence, uh, sort of, you know, I guess in that sense, modeling everything as a field makes sense to me. Stuff that's close by interacts, stuff that's far away doesn't. So what's, what's locality and why is it not fundamental?

   15. SCSean Carroll1:04:15

       Well-

   16. LFLex Fridman1:04:15

       And how's that even possible?

   17. SCSean Carroll1:04:16

       Yeah, I mean, locality is the answer to the question that Isaac Newton was worried about back at the beginning of our conversation, right? I mean, how can the Earth know what the gravitational field of the Sun is? And the answer, as spelled out by Laplace and Einstein and others, is that there's a field in between. And the way a field works is that what's happening to the field at this point in space only depends directly on what's happening at points right next to it. But what's happening at those points depends on what's happening right next to those, right? And so you can build up an influence across space through only local interactions. That's what locality means. What happens here is only affected by what's happening right next to it. That's locality. The idea of locality is built into every field theory, including general relativity as a classical theory. It seems to break down when we talk about black holes. And, you know, Hawking taught us in the 1970s that black holes radiate. They give off, they, they will eventually evaporate away. They're not completely black once we take quantum mechanics into account. And we think, we don't know for sure, but most of us think that if you make a black hole out of certain stuff, then like Laplace's demon taugh- taught us, you should be able to predict what that black hole will turn into if it's just obeying the Schrodinger equation. And if that's true, uh, there are good arguments that that can't happen while preserving locality at the same time. It's just that they're, the information seems to be spread out non-locally in interesting ways.

   18. LFLex Fridman1:05:44

       And people should, uh... You talk about holography with Leonard Susskind on your-

   19. SCSean Carroll1:05:48

       That's right.

   20. LFLex Fridman1:05:48

       ... Mindscape podcast. People should listen to-

   21. SCSean Carroll1:05:50

       Oh, yes, I have a podcast. I didn't even mention that. This is... I'm terrible at marketing it.

   22. LFLex Fridman1:05:53

       No, I'm gonna, I'm gonna ask you questions about that, too.

   23. SCSean Carroll1:05:55

       Okay.

   24. LFLex Fridman1:05:56

       And, and I've been not shutting up about... It's my favorite science podcast, so... Or not... It's, uh, it's not even a science podcast. It's like a... It's a scientist doing a podcast. (laughs)

   25. SCSean Carroll1:06:06

       That's right. That's what it is, absolutely. Yes.

   26. LFLex Fridman1:06:08

       Yeah. Okay, anyway, uh-

   27. SCSean Carroll1:06:09

       Yeah, so holography is this idea when you have a black hole, and, and black hole is a region of space inside of which gravity is so strong that you can't escape. And there's this weird feature of black holes that, again, is totally a thought experiment feature, because we haven't gone and probed any yet. But there seems to be one way of thinking about what happens inside a black hole as seen by an observer who's falling in, which is actually pretty normal. Like, everything looks pretty normal until you hit the singularity and you die. But from the point of the, uh, view of the outside observer, it seems like all the information that, that fell in is actually smeared over the horizon in a non-local way. And that's puzzling, and that's holo- so holography, because that's a two-dimensional surface that is encapsulating the whole three-dimensional thing inside, right? Still trying to deal with that. Still trying to figure out how to get there. But, um, it's an indication that we need to think a little bit more subtly when we quantize gravity.

   28. LFLex Fridman1:07:02

       So b- because you can describe everything that's going on in the th- in three-dimensional space by looking at the two-dimensional projection of it-

   29. SCSean Carroll1:07:11

       Yeah.

   30. LFLex Fridman1:07:11

       ... means that locality doesn't... is not necessary.
6. 1:15:00 – 1:20:53

   Right. …

   1. SCSean Carroll1:15:00

      between the past and future. So-

   2. LFLex Fridman1:15:01

      Right.

   3. SCSean Carroll1:15:02

      ... there's space, but there's no arrow of space. You don't feel that space has to have an arrow, right? You could live in thermodynamic equilibrium. There'd be no arrow of time, but there'd still be time. There'd still be a difference between now and, and the future or whatever.

   4. LFLex Fridman1:15:14

      Ah. So okay. (laughs) So if nothing changes, there's still time.

   5. SCSean Carroll1:15:18

      Well, things could even change. Like, if the whole universe consisted of the Earth going around the Sun-

   6. LFLex Fridman1:15:25

      Yeah.

   7. SCSean Carroll1:15:25

      ... okay, it would just go in circles or ellipses, right?

   8. LFLex Fridman1:15:28

      That's an equilibrium.

   9. SCSean Carroll1:15:29

      Uh, things would change, but it's not increasing entropy. There's no arrow. If you took a movie of that and I played you the movie backward, you would never know.

   10. LFLex Fridman1:15:38

       So the arrow of time can theoretically point in the other direction for brief, briefly? So in-

   11. SCSean Carroll1:15:46

       To the extent that it points in different directions, it's not a very good arrow. I mean, the arrow of, of time in the macroscopic world is so powerful that there's just no chance of going back. When you get down to tiny systems with only three or four moving parts, then entropy can fluctuate up and down.

   12. LFLex Fridman1:16:00

       What does it mean for space to be an emergent phenomena?

   13. SCSean Carroll1:16:03

       It means that the fundamental description of the world does not include the word space. It'll be something like-

   14. LFLex Fridman1:16:08

       (laughs)

   15. SCSean Carroll1:16:08

       ... a vector in Hilbert space, right? And you have to say, "Well, why is there a good approximate-"

   16. LFLex Fridman1:16:12

       Crazy.

   17. SCSean Carroll1:16:12

       "... description which involves three-dimensional space and stuff inside it?"

   18. LFLex Fridman1:16:17

       Okay. So time and space are emergent. We kind of mentioned in the beginning, but can you elaborate? What do you feel hope is fundamental in our universe?

   19. SCSean Carroll1:16:30

       A wave function living in Hilbert space.

   20. LFLex Fridman1:16:32

       A wave function in Hilbert space that we can't intellectualize or visualize, really.

   21. SCSean Carroll1:16:37

       We can't visualize it. We can intellectualize it very easily.

   22. LFLex Fridman1:16:40

       Like, well, how do you think about...

   23. SCSean Carroll1:16:42

       It's a vector in a 10 to the 10 to the 122 dimensional vector space.

   24. LFLex Fridman1:16:45

       (laughs)

   25. SCSean Carroll1:16:46

       It's a complex vector, unit norm. It evolves according to the Schrodinger equation.

   26. LFLex Fridman1:16:50

       Got it. I think it, um, when you put it that way...

   27. SCSean Carroll1:16:53

       What's so hard, really? (laughs)

   28. LFLex Fridman1:16:55

       (laughs) It's, it's like, uh, um, yep. Quantum computers. There's some excitement, actually a lot of excitement with people, that it will allow us to simulate quantum mechanical systems. What kind of questions do, about quantum mechanics, about the things we've been talking about, do you think, do you hope we can answer through quantum simulation?

   29. SCSean Carroll1:17:21

       Well, I think that there are... There's a whole fascinating frontier of things you can do with quantum computers, both sort of practical things with cryptography or money, privacy, eavesdropping, um, sorting things, simulating quantum systems, right?

   30. LFLex Fridman1:17:40

       So it's a, it's a broader question, maybe even outside of quantum computers. Some of the theories that we've been talking about, what's your hope? What's most promising to test these theories? What are, what are kind of experiments we can conduct, whether in simulation or in the physical world, that, uh, would validate or disprove or expand these theories?

Episode duration: 1:29:57