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

1. 0:00 – 2:16

   Newton, gravity, and the fear of action-at-a-distance

   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?

2. 2:16 – 5:24

   From forces to fields: Laplace’s rewrite and Einstein’s speed limit

   1. 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.

3. 5:24 – 10:48

   What it means to “understand”: training intuition vs biological limits

   1. 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-

   2. SCSean Carroll5:48

      I think so. (laughs)

   3. 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-

   4. SCSean Carroll6:01

      Mm-hmm.

   5. 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?

   6. SCSean Carroll6:19

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

   7. LFLex Fridman6:24

      Right.

   8. SCSean Carroll6:25

      Right? You know, I mean-

   9. LFLex Fridman6:25

      (laughs)

   10. 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.

   11. 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?

   12. 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-

   13. LFLex Fridman8:21

       Yeah.

   14. 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.

   15. 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?

   16. SCSean Carroll9:53

       Well, of course, it's possible-

   17. LFLex Fridman9:55

       (laughs)

   18. 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-

   19. LFLex Fridman10:01

       Ah, I see.

   20. SCSean Carroll10:01

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

   21. LFLex Fridman10:06

       Right.

   22. 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.

   23. LFLex Fridman10:19

       Okay.

   24. 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)

4. 10:48 – 12:29

   Perception vs reality and the expanding reach of cognition

   1. 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.

   2. SCSean Carroll11:00

      Mm-hmm.

   3. LFLex Fridman11:02

      So staying at the human level for a second, how big is the gap between what our perception system allows us to see and the world as it is outside our mind's eye, sort of? Sort of not at the quantum mechanical level, but-

   4. SCSean Carroll11:17

      Yeah.

   5. LFLex Fridman11:18

      ... as just our, th- these particular tools we have, which is a few senses and, uh, cognitive abilities to process those senses?

   6. SCSean Carroll11:26

      Well, that last phrase, having the cognitive abilities to process them, carries a lot, right? I mean,-

   7. LFLex Fridman11:31

      Mm-hmm.

   8. SCSean Carroll11:32

      ... there is our sort of intuitive understanding of the world. Uh, you don't need to teach people about gravity for them to know that apples fall from trees, right? That's something that we figure out pretty quickly. Object permanence, things like that. The three-dimensionality of space, even if we don't have the mathematical language to say that, we kind of know that it's true. Um, on the other hand, no one opens their eyes and sees atoms.

   9. LFLex Fridman11:55

      Right.

   10. SCSean Carroll11:56

       Right? Or molecules, for g- or cells, for that matter. Forget about quantum mechanics. So-But we got there. We got to understanding that there are atoms and cells using the combination of our senses and our cognitive capacities. So, th- adding the ability of our cognitive capacities to our senses is adding an enormous amount, and I- I don't think there's a hard and fast boundary. You know, if- if you believe in cells, if you believe that we understand those, then there's no reason you believe we- we can't, uh, believe in quantum mechanics just as well.

5. 12:29 – 17:13

   A favorite idea: conservation of momentum and the end of teleology

   1. LFLex Fridman12:29

      What to you is the most beautiful idea in physics?

   2. SCSean Carroll12:36

      Conservation of momentum.

   3. LFLex Fridman12:38

      Can you elaborate?

   4. SCSean Carroll12:39

      Yeah. If you were Aristotle, when Aristotle wrote his book on physics, he made the ver- following very obvious point. We're on video here, right? So people can see this.

   5. LFLex Fridman12:46

      Yeah.

   6. SCSean Carroll12:47

      So if I push the bottle... Let me cover this bottle so we do not have a mess. But okay.

   7. LFLex Fridman12:51

      (laughs)

   8. SCSean Carroll12:51

      So I push the bottle, it moves, and if I stop pushing, it stops moving.

   9. LFLex Fridman12:55

      Yes.

   10. SCSean Carroll12:55

       And this is, this kind of thing is repeated a large number of times all over the place. If you don't keep pushing things, they stop moving. This is a indisputably true fact about our everyday environment. Okay? And for Aristotle, this blew up into a whole picture of the world in which things had natures and teleologies, and they had places they wanted to be. And when you were pushing them, you were moving them away from where they wanted to be and they would return and- and stuff like that. And it took 1,000 years or 1,500 years for people to, um, say, "Actually, uh, if it weren't for things like dissipation and air resistance and friction and so forth, the natural thing is for things to move forever in a straight line, uh, at a constant velocity, right? Conservation of momentum." And that is... The reason why I think that's the most beautiful idea in physics is because it shifts us from a view of natures and teleology to a view of patterns in the world. So when you were Aristotle, you needed to talk a- a vocabulary of why is this happening? What's the purpose of it? What's the cause, et cetera. Because, you know, it's nature does or does not want to do that. Whereas once you believe in conservation momentum, things just happen. (laughs) They- they just follow the pattern. You give me... You have Laplace's demon ultimately, right? You give me the state of the world today, I can predict what it's going to do in the future. I can predict where it was in the past. It's impersonal and it's also instantaneous. It's not directed toward any future goals, it's just doing what it does given the current state of the universe. The- I think even more than either classical mechanics or quantum mechanics, that is the profound deep insight that gets modern science off the ground. You don't need natures and purposes and goals, you just need some patterns.

   11. LFLex Fridman14:45

       So it's the first moment in our understanding of the way the universe works, where you branch from the intuitive physical space to kind of the space of ideas. And also the other point you said, which is conveniently most of the interesting ideas are acting in the moment. You don't need to know the history-

   12. SCSean Carroll15:07

       Yeah.

   13. LFLex Fridman15:07

       ... of time or the future that-

   14. SCSean Carroll15:09

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

   15. LFLex Fridman15:12

       Right.

   16. 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?

   17. LFLex Fridman15:44

       Mm-hmm.

   18. 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.

   19. 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?

   20. 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.

   21. LFLex Fridman16:53

       (laughs)

   22. 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.

6. 17:13 – 21:12

   Math vs physics and why laws compress reality so well

   1. 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?

   2. 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.

   3. 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?

   4. 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.

   5. 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.

   6. 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.

   7. LFLex Fridman20:10

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

   8. SCSean Carroll20:20

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

   9. LFLex Fridman20:23

      Okay.

   10. SCSean Carroll20:23

       There could be.

   11. LFLex Fridman20:25

       What would an answer look like?

   12. 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-

   13. LFLex Fridman20:42

       (laughs)

   14. 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-

   15. LFLex Fridman21:05

       Mm-hmm.

   16. 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.

7. 21:12 – 25:31

   Fundamental vs emergent: tables, atoms, and broader domains of validity

   1. 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-

   2. SCSean Carroll21:40

      (laughs)

   3. LFLex Fridman21:40

      ...fundamental are, can actually be explained as emergent from the, the, the more deeper l- laws.

   4. SCSean Carroll21:49

      I mean, we don't know, of course, is, you know, we had to get that on the table. Like-

   5. LFLex Fridman21:52

      Yeah.

   6. SCSean Carroll21:52

      ...we don't know what is fundamental. We do know, we do have reason to say that certain things are more fundamental than others, right?

   7. LFLex Fridman21:59

      Mm-hmm.

   8. SCSean Carroll21:59

      Um, atoms and molecules are more fundamental than cells and organs. Quantum fields are more fundamental than atoms and molecules. Um, we don't know if that ever bottoms out. I, I do think that there's sensible ways to think about this. The, if you, if you describe something like this table as a table, it has a height and a width and it's made of a certain material and it has a certain solidity and weight and so forth. Um, that's a very useful description as far as it goes. There's a whole nother description of this table in terms of a whole collection of atoms strung together in certain ways. The language of the atoms is more comprehensive than the language of the table. You could break apart the table, smash it to pieces, still talk about it as atoms, but you could no longer talk about it as a table, right? So I think of this comprehensiveness, the domain of validity of a theory gets broader and broader as the theory gets more and more fundamental.

   9. LFLex Fridman22:52

      So, what do you think Newton would say, maybe write in a book review if he read your latest book on quantum mechanics, something deeply hidden?

   10. SCSean Carroll23:03

       It would take a long time for him to, uh, think that any of this was making any sense.

   11. LFLex Fridman23:08

       You catch him up pretty quick in the beginning.

   12. SCSean Carroll23:10

       Yeah. (laughs)

   13. LFLex Fridman23:11

       You, you give him a shout-out in the beginning. (laughs)

   14. SCSean Carroll23:13

       Exactly. That's right. I mean, he is the man. I, I, I'm happy to say that Newton was the greatest scientist who ever lived. Um, I mean, he invented calculus in his spare time, which would have made him the greatest mathematician, just all by himself, right, all by that one thing. But of course, you know, it's funny because Newton was, in some sense, still a pre-modern thinker. Rocky Kolb, who is a cosmologist at, at the University of Chicago, said that, you know, Galileo, even though he came before Newton, was a more modern thinker than, than Newton was. Like, if you got Galileo and brought him to the present day, it would take him six months to catch up and then he'd be in your office telling you why your most recent paper was wrong. Whereas Newton just thought-

   15. LFLex Fridman23:52

       (laughs)

   16. SCSean Carroll23:52

       ...in this kind of more mystical way, you know?

   17. LFLex Fridman23:54

       Yeah.

   18. SCSean Carroll23:55

       He, he wrote a lot more about the Bible and alchemy than he ever did about physics. And, uh, but he was also more brilliant than anybody else, and, and way more mathematically astute than Galileo. So, I really don't know. You know, he, he might have, he might just, yeah, say like, "Give me the textbooks, leave me alone for a few months and then be caught up." Uh, but he, but he, or he might have had, uh, mental blocks against, against seeing the world in this way. I really don't know.

   19. LFLex Fridman24:20

       Or perhaps find an interesting mystical interpretation of quantum mechanics.

   20. SCSean Carroll24:24

       Very possible, yeah.

   21. LFLex Fridman24:25

       Is there any other scientists or philosophers through history that you would like to know their opinion of your book?

   22. SCSean Carroll24:34

       That's a good, that's a good question. Um, I mean, Einstein is the obvious one, right? We all... And he was not that long ago, but, uh-

   23. LFLex Fridman24:40

       (laughs)

   24. SCSean Carroll24:40

       ... I even speculate at the end of my book about what his opinion would be.

   25. LFLex Fridman24:43

       Yeah.

   26. SCSean Carroll24:44

       I am curious as to, you know, w- what about older philosophers, like Hume or Kant, right? Like, what would they have thought? Or Aristotle, you know? Um, what would they have thought about modern physics? Because they do... In philosophy, your predilections, uh, end up pa- playing a much bigger role in your ultimate conclusions, 'cause you're not as tied down by what the data is. In physics, you know... Physics is lucky, because we can't stray too far off the reservation, as long as we're trying to explain the world that we actually see in our telescopes and microscopes. But, it- it's- it's just not fair to play that game, because the people we're thinking about didn't know a whole bunch of things that we know, right? Like, we l- we lived through a lot that they didn't live through. So, by the time we got them caught up, they'd be different people. (laughs)

8. 25:31 – 27:51

   Quantum mechanics in a nutshell: wave function + measurement problem

   1. LFLex Fridman25:31

      (laughs) So, let me ask a bunch of basic questions. I think it'll be interesting, useful for people who are not familiar, but even for people who are extremely well familiar. Let's start with, what is quantum mechanics?

   2. SCSean Carroll25:47

      Quantum mechanics is the paradigm of, of physics that came into being in the early part of the 20th century that replaced classical mechanics, and it replaced classical mechanics in a weird way that we're still coming to terms with. So in classical mechanics, you have an object, it has a location, it has a velocity. And if you know the location and velocity of everything in the world, you can say w- what everything's gonna do. Quantum mechanics has an aspect of it that is kind of on the same lines. There's something called the quantum state or the wave function, and there's an equation governing what the quantum state does. So, it's very much like classical mechanics. The wave function is different. It's sort of a wave. It's a vector in a huge dimensional vector space, rather than a position and a velocity. But okay, that's a detail, and the equation is the Schrodinger equation, not Newton's Laws, but okay, again, a detail. Where quantum mechanics really becomes weird and different is that there's a whole nother set of rules in our textbook formulation of quantum mechanics, in addition to saying that there's a quantum state and it evolves in time. And all these new rules have to do with what happens when you look at the system, when you observe it, when you measure it. In classical mechanics, there were no rules a- about observing. You just look at it, and you see what's going on. That, that was it, right? In quantum mechanics, the way we teach it, there's something profoundly fundamental about the act of measurement or observation, and the system dramatically changes its state. Even though it has a wave function, like the electron in an atom is not orbiting in a circle, it's sort of spread out in a cloud, when you look at it, you don't see that cloud. When you look at it, it looks like a particle with a location. So, it dramatically changes its state right away, and the effects of that change can be instantly seen in what the electron does next. So, that's the... Again, we need to be careful because we don't agree on what quantum mechanics says.

   3. LFLex Fridman27:38

      Of course.

   4. SCSean Carroll27:38

      So I need... That's why I need to say, like, in the textbook view, et cetera, right? But in the textbook view, quantum mechanics, unlike any other theory of physics, places a... gives a fundamental role to the act of measurement.

9. 27:51 – 32:30

   Atoms, electrons, and why the electron must be a wave

   1. LFLex Fridman27:51

      So, maybe even more basic. What is an atom and what is an electron?

   2. SCSean Carroll27:57

      Sure. This all came together, you know, in a few years around the turn of the last century, right? Around the year 1900. Atoms predated then. Of course, the word atom goes back to the ancient Greeks-

   3. LFLex Fridman28:08

      Hm.

   4. SCSean Carroll28:08

      ... but it was the chemists in the 1800s that really first got experimental evidence for atoms. They realized, you know, that there were two different types of tin oxide-

   5. LFLex Fridman28:20

      (laughs)

   6. SCSean Carroll28:21

      ... and in these two different types of tin oxide, there was exactly twice as much oxygen in one type as the other. And like, why is that? Why is it on- why is it never 1.5 times as much, right? And so, uh, Dalton said, "Well, it's because there are tin atoms and oxygen atoms-"

   7. LFLex Fridman28:37

      (laughs)

   8. SCSean Carroll28:37

      "... and one form of tin oxide is one atom of tin and one atom of oxygen, and the other is one atom of tin and two atoms of oxygen."

   9. LFLex Fridman28:44

      Mm-hmm.

   10. SCSean Carroll28:44

       And on the basis of this... So this is th- uh, you know, a speculation, a theory, right? A hypothesis. But then on the basis of that, you make other predictions, and it, the chemists became quickly convinced that atoms were real.

   11. LFLex Fridman28:54

       Yeah.

   12. SCSean Carroll28:54

       The physicists took a lot longer to catch on, but eventually they did. And I mean, Boltzmann, who believed in atoms, uh, was... got a... He had a really tough time his whole life, 'cause he worked in Germany where atoms were not popular. They were popular in England, but not in Germany.

   13. LFLex Fridman29:09

       And there, in general, the idea of atoms is, it's the most, the smallest building block of the universe for, for them. That's the kind of... how they thought about-

   14. SCSean Carroll29:18

       That was the Greek idea, but the chemists in the 1800s, uh, jumped the gun a little bit. So, these days, w- an atom is the smallest building block of a chemical element, right? Hydrogen, tin, oxygen, carbon, whatever. But we know that atoms can be broken up further than that, and that's what physicists discovered in the early 1900s, Rutherford especially and, and his colleagues. So, the atom that we think about now, the cartoon is that picture you, you've always seen of a little nucleus and then electrons orbiting it like a little solar system. And we now know the nucleus is made of protons and neutrons. So, the weight of the atom, the mass is almost all in its nucleus. Protons and neutrons are something like 1800 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.

   15. 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-

   16. SCSean Carroll30:29

       Oh, definitely.

   17. LFLex Fridman30:29

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

   18. SCSean Carroll30:31

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

   19. LFLex Fridman30:34

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

   20. SCSean Carroll30:38

       Yeah.

   21. LFLex Fridman30:39

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

   22. 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.

   23. LFLex Fridman32:04

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

   24. SCSean Carroll32:07

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

   25. LFLex Fridman32:10

       Mm-hmm.

   26. 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.

   27. LFLex Fridman32:26

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

   28. SCSean Carroll32:30

       Yep.

10. 32:30 – 35:10

    Entanglement, quantum fields, and the meaning of “empty” space

    1. LFLex Fridman32:30

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

    2. 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.

    3. 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...

    4. SCSean Carroll33:57

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

    5. LFLex Fridman33:59

       Sure.

    6. 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.

    7. LFLex Fridman34:50

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

    8. SCSean Carroll34:54

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

    9. LFLex Fridman34:56

       But there's still a field.

    10. SCSean Carroll34:57

        Uh-huh.

    11. LFLex Fridman34:57

        It's just-

    12. SCSean Carroll34:58

        Yeah.

    13. LFLex Fridman34:59

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

    14. SCSean Carroll35:02

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

    15. LFLex Fridman35:06

        Yes.

    16. SCSean Carroll35:06

        ... by dropping something, right?

    17. LFLex Fridman35:08

        Yes.

    18. SCSean Carroll35:08

        I g- I don't see it, but there it is.

11. 35:10 – 42:43

    Hilbert space, entropy, and getting comfortable with infinity

    1. LFLex Fridman35:10

       (inhales deeply) So we got a little bit of a idea of entanglement. Now, what is Hilbert space and Euclidean space?

    2. SCSean Carroll35:24

       Yeah, you know, I think that, uh, people are very welcome to go through their lives not knowing what Hilbert space is. But if you-

    3. LFLex Fridman35:29

       (laughs)

    4. SCSean Carroll35:29

       ... if you, when I dig in a little bit more into quantum mechanics, it becomes necessary. You know, the English language was invented long before quantum mechanics or various forms of higher mathematics were invented. So we use the word space to mean different things. Of course, most of us think of space as this three-dimensional world in which we live, right? I mean, some of us just think of it as outer space. (laughs)

    5. LFLex Fridman35:51

       (laughs) All right.

    6. SCSean Carroll35:51

       But, okay, but space around us gives us the three-dimensional location of, of things and objects. But mathematicians use any gen- (clicks tongue) generic abstract collection of elements as a space.

    7. LFLex Fridman36:04

       Mm-hmm.

    8. SCSean Carroll36:05

       Okay? A space of possibilities, you know, momentum space, et cetera. So Hilbert space is the space of all possible quantum wave functions, either for the universe or for some specific system. And it could be an infinite dimensional space, or it could be just really, really large dimensional, but finite. We don't know, because we don't know the final theory of everything. But this abstract Hilbert space is really, really, really big and has no immediate connection to the three-dimensional space in which we live.

    9. LFLex Fridman36:31

       What, what do dimensions in Hilbert space mean?

    10. SCSean Carroll36:35

        You know, it's just a way of mathematically representing how much information is contained in the state of the system. How many numbers do you have to give me to specify what the thing is doing? So in classical mechanics, I give you the location of something by giving you three numbers, right? Up, down, le- X, X, Y, Z coordinates.

    11. LFLex Fridman36:53

        Mm-hmm.

    12. SCSean Carroll36:54

        But then I might want to give you its entire state, physical state, which means both its position and also its velocity. And the velocity also has three components. So its state lives in something called phase space, which is six dimensional, three dimensions of position, three dimensions of velocity.... and then if it also has an orientation in space, that's another three dimensions, and so forth. So, as you describe more and more information about the system, you have an abstract mathematical space that has more and more numbers that you need to give, and each one of those numbers corresponds to a dimension in that space.

    13. LFLex Fridman37:29

        So, in terms of the amount of information, what is entropy? This, uh, mystical word that's overused in math and physics but, uh, has a very specific meaning in, in this context.

    14. SCSean Carroll37:42

        Sadly, it has more than one very specific meaning. This is, this is the reason why it is hard. Entropy means different things even to different physicists. But one way of thinking about it is a measure of how much we don't know about the state of a system, right? So if I have a bottle of water molecules, and I know that, okay, there's a certain number of water molecules. I could weigh it, right? And figure out. I know the volume of it, and I know the temperature and pressure and things like that. I certainly don't know the exact position and velocity of every water molecule, right? So there's a certain amount of information I know, a certain amount that I don't know, that is, that is part of the complete state of the system, and that's what the entropy characterizes. How much unknown information there is. The difference between what I do know about the system and its full exact microscopic state.

    15. LFLex Fridman38:28

        So, when we try to describe a quantum mechanical system, is it infinite or finite but very large?

    16. SCSean Carroll38:37

        Yeah, we don't know. That's (laughs) -

    17. LFLex Fridman38:38

        It's-

    18. SCSean Carroll38:38

        ... depends on the system, you know, it's easy to mathematically write down a system that would have a potentially infinite entropy, an infinite dimensional Hilbert space. So, let- let's, let's go back a little bit. We said that the Hilbert space was the space in which quantum wave functions lived. For different systems, that will be different sizes. They could be infinite or finite. So that's the number of numbers, the number of pieces of information you could potentially give me about the system. So, the bigger Hilbert space is, the bigger the entropy of that system could be, depending on what I know about it. If I don't know anything about it, then, you know, it has a huge entropy, right? But only up to the size of its Hilbert space. So, we don't know, in, in the real physical world whether or not, you know, this region of space that contains that water bottle has potentially an infinite entropy or just a finite entropy. We have, we have different arguments on different sides.

    19. LFLex Fridman39:31

        So if it's infinite, how do you think about infinity? Is it something you can, uh, your cognitive abilities are able to process? Or is it just a mathematical tool?

    20. SCSean Carroll39:44

        It's somewhere in between, right? I mean, we can say things about it. We can use mathematical tools to manipulate infinity very, very accurately. We can define what we mean, you know? For any number N, there's a number bigger than it, so there's no biggest number, right? So there's something called the total number of all numbers, and it's infinite. But it is hard to wrap your brain around that, and I think that gives people pause because we talk about infinity as if it's a number, but it has plenty of properties that real numbers don't have. You know, if you multiply infinity by two, you get infinity again, right? (laughs) That's a little bit different than what we're used to.

    21. LFLex Fridman40:19

        Okay, but are you comfortable with the idea that in thinking of what the real world actually is, that infinity could be part of that world?

    22. SCSean Carroll40:28

        Sure.

    23. LFLex Fridman40:28

        Are you, are you comfortable that a world, in some dimension, in some -

    24. SCSean Carroll40:31

        I'm comfortable with lots of things. I mean, you know, I, I don't want my level of comfort to affect what I think about the world, you know? I'm pretty open-minded about what the world could be at a fundamental level.

    25. LFLex Fridman40:44

        Yeah, but infinity is a, is a tricky one. It's not almost a question of comfort. It's a question of, um, is it an overreach of our intuition? Sort of a, it could be a convenient, almost like when you add a constant to an equation just because it'll help. (laughs) It just feels like it's useful to at least be able to imagine a concept, not directly, but in some kind of way that this feels like it's a description of the real world.

    26. SCSean Carroll41:14

        Think of it this way.

    27. LFLex Fridman41:15

        Okay.

    28. SCSean Carroll41:15

        There's only three numbers that are simple.

    29. LFLex Fridman41:19

        Hmm.

    30. SCSean Carroll41:19

        There's zero, there's one, and there's infinity (laughs) . A number like 318-
12. 42:43 – 47:10

    Many-Worlds as a response to measurement: observers are quantum systems

    1. LFLex Fridman42:43

       So coming back to the textbook definition of quantum mechanics, this idea that we, I don't think we talked about, can you... This, uh, one of the most interesting philosophical points we talked at the human level, but at the, at the physics level, that at the, at least the textbook definition of quantum mechanics separates what is observed and what is real. H- one, how does that make you feel? And, and, uh, and two, what does it then mean to observe something, and why is it different than what is real?

    2. SCSean Carroll43:20

       Yeah. You know, I, my personal feeling, such as it is, is that things like measurement and observers and stuff like that are not going to play a fundamental role in the ultimate laws of physics. But my feeling that way is because so far, that's where all the evidence has been pointing. I could be wrong, and there's certainly a sense in which it would be infinitely cool if somehow observation or mental cogitation did play a fundamental role in the, in the nature of reality. But I don't think so, and again, I don't see any evidence for it, so I'm not spending a lot of time worrying about that possibility. So what do you do about the fact that in the textbook interpretation of quantum mechanics, this idea of measurement or, or looking at things seems to play an important role? Well, you, you come up with better interpretations of quantum mechanics, and there are several alternatives. My favorite is the many worlds interpretation, which says two things. Uh, number one, you, the observer, are just a quantum system like anything else. There's nothing special about you. Don't get so proud of yourself.

    3. LFLex Fridman44:25

       (laughs)

    4. SCSean Carroll44:25

       You know, you're just a bunch of atoms.

    5. LFLex Fridman44:27

       Yeah.

    6. SCSean Carroll44:27

       You have a wave function. You obey the Schrodinger equation like everything else. And number two, when you think you're measuring something or observing something, what's really happening is, you're becoming entangled with that thing. So when you think of it as a wave function for the electron, it's all spread out, but you look at it and you only see it in one location. What's really happening is that there's still the wave function for the electron in all those locations, but now it's entangled with the wave function of you in the following way. There's part of the wave function that says, "The electron was here and you think you saw it there. 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."

    7. LFLex Fridman45:50

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

    8. SCSean Carroll45:57

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

    9. LFLex Fridman46:03

       What's the outside world?

    10. SCSean Carroll46:06

        It depends. Let's back up.

    11. LFLex Fridman46:07

        Yep.

    12. 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.

13. 47:10 – 49:53

    How many worlds, cosmic horizons, and why branching may have a limit

    1. LFLex Fridman47:10

       So h- how many worlds are there? So-

    2. SCSean Carroll47:14

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

    3. LFLex Fridman47:17

       (laughs)

    4. 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.

    5. 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.

    6. SCSean Carroll47:56

       Mm-hmm.

    7. 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.

    8. 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.

    9. LFLex Fridman49:05

       Yes.

    10. 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.

14. 49:53 – 54:31

    Splitting vs copying and the non-issue of energy conservation

    1. 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?

    2. 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.

    3. LFLex Fridman50:36

       Right.

    4. 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?

    5. LFLex Fridman51:16

       (laughs)

    6. SCSean Carroll51:16

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

    7. LFLex Fridman51:19

       Yeah.

    8. 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.

    9. 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?

    10. SCSean Carroll51:38

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

    11. LFLex Fridman51:41

        Yeah.

    12. SCSean Carroll51:42

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

    13. LFLex Fridman51:46

        Yes.

    14. SCSean Carroll51:46

        It does not.

    15. LFLex Fridman51:47

        Great.

    16. SCSean Carroll51:48

        And I say this definitively because there are other questions that I think there's answers to, but they're-

    17. LFLex Fridman51:52

        Yeah.

    18. SCSean Carroll51:52

        ... legitimate questions, right? About, you know, where does probability come from and things like that. This conservation of energy question, we know the answer to it-

    19. LFLex Fridman52:00

        Yeah.

    20. SCSean Carroll52:00

        ... and the answer to it is that energy is conserved.

    21. LFLex Fridman52:02

        Yes.

    22. SCSean Carroll52:02

        All of the effort goes into how best to translate what the equation unambiguously says into pl- in plain English, right?

    23. LFLex Fridman52:10

        Right.

    24. SCSean Carroll52:11

        So this idea that there's a universe that has, that, that, that the universe comes equipped with a thickness and it sort of divides up into thinner pieces, but the total amount of universe is, is conserved over time, is a reasonably good way of putting English words to the underlying mathematics.

    25. LFLex Fridman52:27

        So, one of my favorite things about many-worlds is, uh, I mean, I love that there's something controversial in science. (laughs)

    26. SCSean Carroll52:35

        (laughs)

    27. LFLex Fridman52:35

        And for some reason, it makes people actually not, like, upset, but just get excited. Why do you think it is a controversial idea? So there's, there's a lot of... It's actually one of the cleanest ways to think-

    28. SCSean Carroll52:51

        Yeah.

    29. LFLex Fridman52:51

        ... about quantum mechanics.

    30. SCSean Carroll52:52

        Yeah.
15. 54:31 – 1:01:22

    Interpretation “candidates”: hidden variables, collapse, and epistemic views

    1. LFLex Fridman54:31

       Can you describe the alternatives? I don't think we touched on it, sort of the Copenhagen interpretation and, uh, the many-worlds. Maybe there's a difference between the Everett, Everettian many-worlds and many-worlds as it is now. Like, has, uh, the idea sort of developed and so on? And just in general, what, what is the space of promising contenders? We have democratic debates now.

    2. SCSean Carroll54:56

       Yeah. (laughs)

    3. LFLex Fridman54:56

       There's a bunch of candidates.

    4. SCSean Carroll54:57

       (laughs) 12 candidates on stage, right.

    5. LFLex Fridman54:58

       12 candidates on stage. What are the quantum mechanical candidates on stage for the debate?

    6. SCSean Carroll55:02

       So if you had a debate between quantum mechanical contenders, it'd be no problem getting 12 people up there on stage.

    7. LFLex Fridman55:10

       Right.

    8. SCSean Carroll55:10

       But there would still be only three frontrunners, I guess. (laughs)

    9. LFLex Fridman55:13

       (laughs)

    10. SCSean Carroll55:14

        And right now, the frontrunners would be Everett, uh, hidden variable theories are another one. So the hidden variable theories say that the wave function is real, but there's something in addition to the wave function. The wave function is not everything. It's part of reality, but it's not everything. What else is there? We're not sure, but, uh, in the simplest version of the theory, there are literally particles. So, many-worlds says that...... quantum systems are sometimes, are wave-like in some ways and particle-like in another because they really, really are waves. But under certain observational circumstances, they look like particles. Whereas hidden variable says, they're- they look like waves and particles 'cause there are both waves and particles involved in the dynamics. And that's easy to do if your particles are just non-relativistic, Newt- Newtonian particles moving around. They get pushed around by the wave function roughly. Uh, it becomes much harder when you take quantum field theory or quantum gravity into account. The other big contender are spontaneous collapse theories. So in the conventional textbook interpretation, we say when you look at a quantum system, its wave function collapses and you see it in one location. A spontaneous collapse theory says that every particle has a chance per second of having its wave function spontaneously collapse. The chance is very small. For a typical particle, it will take hundreds of millions of years before it happens even once, but in a table or some macroscopic object, there are way more than 100 million particles, and they're all entangled with each other. So when one of them collax- collapses, it brings everything else along with it. There's a slight variation of this. That's a spontaneous collapse theory. There are also induced collapse theories, like Roger Penrose thinks that when the gravitational difference between two parts of the wave function becomes too large, the wave function spun- uh, collapses automatically. So those are basically, in my mind, the three big alternatives. Many-worlds, which is just, there's a wave function and always obeys the Schrodinger equation. Hidden variables, there's a wave function that always obeys the Schrodinger equation, but there are also new variables. Or collapse theories, which the wave function sometimes obeys the Schrodinger equation and sometimes it collapses. So you can see that the alternatives are more complicated in their formalism than many-worlds is, but they are closer to our experience.

    11. LFLex Fridman57:34

        So just this moment of collapse, do you think of it as, uh ... So is a wave function fundamentally sort of a probabilistic description of the world? And is collapse sort of, uh, reducing that part of the world into something deterministic? Where again, you can, uh, now describe the position and the velocity in this simple classical model?

    12. SCSean Carroll57:56

        Well, there is, um-

    13. LFLex Fridman57:57

        Is that, is that how you think about collapse?

    14. SCSean Carroll57:58

        There is a fourth category, there's a fourth contender. There's a meropet of, uh, quantum mechanical-

    15. LFLex Fridman58:03

        (laughs)

    16. SCSean Carroll58:03

        ... interpretations. Which are called epistemic interpretations. And what they say is, all the wave function is, is a way of making predictions for experimental outcomes. It's not mapping onto an element of reality in any real sense. And in fact, two different people might have two different wave functions for the same physical system, because they know different things about it, right? The wave function is really just a prediction mechanism. And then the problem with those epistemic interpretations is, if you say, "Okay, but it's predicting about what?" (laughs) Like, "What is the thing that is being predicted?" And they say, "No, no, no." (laughs) "That's not what we're here for. We're just here to tell you what the observational outcomes are gonna be."

    17. LFLex Fridman58:44

        But the other, the other interpretations kind of think that the wave function is real.

    18. SCSean Carroll58:48

        Yes. That's right. So that's an ontic interpretation of the wave function. Ontology being the study of what is real, what exists. As opposed to an epistemic interpretation of the wave function. Epistemology being the study of what we know.

    19. LFLex Fridman59:02

        I would actually just love to see that debate on stage.

    20. SCSean Carroll59:06

        There was a version of it on stage, at the World Science Festival a few years ago. That you can look up online.

    21. LFLex Fridman59:11

        On, on YouTube?

    22. SCSean Carroll59:12

        Yep. It's on YouTube.

    23. LFLex Fridman59:13

        Okay. Awesome.

    24. SCSean Carroll59:14

        Um-

    25. LFLex Fridman59:14

        I'll link it and watch it.

    26. SCSean Carroll59:16

        Many-worlds-

    27. LFLex Fridman59:16

        Who won?

    28. SCSean Carroll59:16

        I won. (laughs)

    29. LFLex Fridman59:19

        (laughs)

    30. SCSean Carroll59:19

        No. Of course, I don't know. There was no vote.
16. 1:01:22 – 1:08:31

    Quantum gravity, holography, and why spacetime/locality may be emergent

    1. 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?

    2. 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.

    3. LFLex Fridman1:02:00

       And that's a fundamentally classical...

    4. 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?

    5. LFLex Fridman1:02:30

       No.

    6. 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.

    7. LFLex Fridman1:03:41

       Right.

    8. 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."

    9. 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?

    10. SCSean Carroll1:04:15

        Well-

    11. LFLex Fridman1:04:15

        And how's that even possible?

    12. 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.

    13. LFLex Fridman1:05:44

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

    14. SCSean Carroll1:05:48

        That's right.

    15. LFLex Fridman1:05:48

        ... Mindscape podcast. People should listen to-

    16. SCSean Carroll1:05:50

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

    17. LFLex Fridman1:05:53

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

    18. SCSean Carroll1:05:55

        Okay.

    19. 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)

    20. SCSean Carroll1:06:06

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

    21. LFLex Fridman1:06:08

        Yeah. Okay, anyway, uh-

    22. 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.

    23. 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-

    24. SCSean Carroll1:07:11

        Yeah.

    25. LFLex Fridman1:07:11

        ... means that locality doesn't... is not necessary.

    26. SCSean Carroll1:07:15

        Well, it means it somehow... It's only a good approximation. It's not really what's going on.

    27. LFLex Fridman1:07:20

        How are we supposed to feel about that? (laughs)

    28. SCSean Carroll1:07:22

        You're supposed to feel liberated. (laughs) You know, space is just a good approximation, and this was always gonna be true once you started quantizing gravity. So we're just beginning now to face up to the dramatic implications of quantizing gravity.

    29. LFLex Fridman1:07:38

        Is there other weird s- stuff that happens with quantum mechanics and black hole?

    30. SCSean Carroll1:07:43

        I don't think that anything weird has happened with quantum mechanics. I think weird things happen with spacetime. I mean, that's what it is.
17. 1:08:31 – 1:16:00

    Living in one branch: no hopping, no rewinding, and the arrow of time

    1. LFLex Fridman1:08:31

       So a couple questions on Many-Worlds. How does Many-Worlds help us understand our particular branch of reality? So, okay, that's fine and good that as everything is splitting-

    2. SCSean Carroll1:08:43

       Yeah.

    3. LFLex Fridman1:08:43

       ... but we're just traveling down a single branch of it, so how does it help us understand our little unique branch?

    4. SCSean Carroll1:08:51

       Yeah, I mean, that's a, that's a great question, but that's the point is that we didn't invent Many-Worlds because we thought it was cool to have a whole bunch of worlds, right? We invented it because we were trying to account for what we observe here in our world.

    5. LFLex Fridman1:09:02

       Yeah.

    6. SCSean Carroll1:09:03

       And what we observe here in our world are wave functions collapsing, okay? We do have a positi- a situation where the electron seems to be spread out, but then when we look at it, we don't see it spread out. We see it located somewhere. So what's going on? That's the measurement problem of quantum mechanics, that's what we have to face up to. So Many-Worlds is just a proposed solution to that problem, and the answer is nothing special is happening, it's still just the Schrodinger equation, but you have a wave function too. And that's a different answer than would be given in hidden variables or dynamical collapse theories or whatever. So the entire point of Many-Worlds is to explain what we observe, but it- it- it tries to explain what we already have observed, right? It's not trying to, uh, be different from what we've observed, because that would be something other than quantum mechanics.

    7. LFLex Fridman1:09:50

       But, you know, the idea that there's worlds that we didn't observe that keep branching off is kind of, I- is, is, uh, you know, it's stimulating to the imagination. So, uh, ch- is it possible to hop from, you mentioned the branches are independent.

    8. SCSean Carroll1:10:07

       Yeah.

    9. LFLex Fridman1:10:07

       S- Uh, is it possible to hop from one to the other?

    10. SCSean Carroll1:10:10

        No.

    11. LFLex Fridman1:10:10

        It, it's, so it's a physical limit.

    12. SCSean Carroll1:10:12

        Yes.

    13. LFLex Fridman1:10:13

        There's im- it, the theory says it's impossible.

    14. SCSean Carroll1:10:16

        There's already a copy of you in the other world, don't worry.

    15. LFLex Fridman1:10:18

        Yes.

    16. SCSean Carroll1:10:18

        But then leave them alone. (laughs)

    17. LFLex Fridman1:10:20

        No, but, there's a, there's a fear of missing out, uh, FOMO.

    18. SCSean Carroll1:10:25

        Yes.

    19. LFLex Fridman1:10:25

        That, uh, I feel like e- immediately start to wonder if that other copy is having more or less fun (12:48) sorta helping them out.

    20. SCSean Carroll1:10:33

        Yeah, well, the downside of Many-Worlds is that you're missing out on an enormous amount.

    21. LFLex Fridman1:10:37

        (laughs)

    22. SCSean Carroll1:10:37

        (laughs) And that- and that's always what it's gonna be like.

    23. LFLex Fridman1:10:40

        And, uh, I mean, there's a certain stage of acceptance in that.

    24. SCSean Carroll1:10:43

        Yes.

    25. LFLex Fridman1:10:44

        In terms of rewinding, do you think we can rewind the system back? Sort of the, uh, the nice thing about Many-Worlds, uh, I guess, is it really emphasizes the, maybe you can correct me, but the determi- the deterministic nature of a branch, and it feels like it could be r- rewound back. Uh, is it, is, do you see it as something that could be perfectly wound back, r- rewinded back? Yeah.

    26. SCSean Carroll1:11:12

        You know, if you're at a fancy French restaurant-

    27. LFLex Fridman1:11:14

        Yes.

    28. SCSean Carroll1:11:14

        ... and there's a nice linen white tablecloth, and you have your glass of Bordeaux, and you knock it over and the wine spills across the tablecloth-

    29. LFLex Fridman1:11:21

        Yeah.

    30. SCSean Carroll1:11:22

        ... if the world were classical, okay, uh, it would be possible that if you just lifted the wine glass up, you'd be lucky enough that every molecule of wine would hop back into the glass.
18. 1:16:00 – 1:21:51

    What’s fundamental, what QM can test, and why consciousness isn’t quantum

    1. LFLex Fridman1:16:00

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

    2. SCSean Carroll1:16:03

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

    3. LFLex Fridman1:16:08

       (laughs)

    4. SCSean Carroll1:16:08

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

    5. LFLex Fridman1:16:12

       Crazy.

    6. SCSean Carroll1:16:12

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

    7. 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?

    8. SCSean Carroll1:16:30

       A wave function living in Hilbert space.

    9. LFLex Fridman1:16:32

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

    10. SCSean Carroll1:16:37

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

    11. LFLex Fridman1:16:40

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

    12. SCSean Carroll1:16:42

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

    13. LFLex Fridman1:16:45

        (laughs)

    14. SCSean Carroll1:16:46

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

    15. LFLex Fridman1:16:50

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

    16. SCSean Carroll1:16:53

        What's so hard, really? (laughs)

    17. 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?

    18. 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?

    19. 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?

    20. SCSean Carroll1:18:03

        Well, I think for... The- there's two parts of that question. One is many-worlds and the other one is sort of, uh, emergent space time. For many-worlds, you know, there are experiments ongoing to test whether or not wave functions spontaneously collapse. And if they do, then that rules out many-worlds and that would be falsified. What if there are hidden variables? There's a theorem that seems to indicate that the predictions will always be the same as many-worlds. I'm a little skeptical of this theorem. I'm not completely... I haven't internalized it. I haven't made it in part of my intuitive, uh, view of the world yet. So there might be loopholes to that theorem. I'm not sure about that. I... Part of me thinks that there should be different experimental predictions if there are hidden variables, but I'm not sure. But otherwise, it's just quantum mechanics all the way down. And so there's-

    21. LFLex Fridman1:18:47

        (laughs)

    22. SCSean Carroll1:18:47

        ... there's this cottage industry in science journalism of writing breathless articles that say, you know, "Quantum mechanics shown to be more astonishing than ever before thought," and really, it's the same quantum mechanics-

    23. LFLex Fridman1:18:59

        Yeah. (laughs)

    24. SCSean Carroll1:18:59

        ... we've been doing since 1926. Whereas with the emergent space time stuff, we know a lot less about what the theory is. It's in a very primitive state. Uh, we don't even really have a, a safely written down, respectable, honest theory yet, so there could very well be experimental predictions we just don't know about yet. That is one of the things that we're trying to figure out.

    25. LFLex Fridman1:19:19

        Yeah, but for emergent space time, you need really big stuff, right?

    26. SCSean Carroll1:19:24

        Well, or really fast stuff, or really energetic stuff. We don't know. That, that's the thing, you know? So there could be violations of the speed of light if you have emergent space time. Um, not going faster than the speed of light, but the speed of light could be different for light of different wavelengths, right?

    27. LFLex Fridman1:19:41

        Hmm.

    28. SCSean Carroll1:19:42

        That'll be a dramatic violation of physics as we know it, but it could be possible, um, or not. I mean, it's not an absolutely prediction. That's, that's, that's the problem. The theories are just not well developed enough yet to say.

    29. LFLex Fridman1:19:54

        Is there anything that, uh, quantum mechanics can teach us about human nature or the human mind? If you think about sort of consciousness and these kinds of topics, is there...It's certainly excessively used, as you point out.

    30. SCSean Carroll1:20:10

        (laughs)

Episode duration: 1:29:57