Sean Carroll: Capacity of the Human Mind to Understand Physics

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. Perhaps he just said it for religious reasons and so on, 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. Other things at a distance?

It does, but, you know, so that was one of Newton's worries. You're actually right in a slightly different way about the religious worries. He was smart enough. This is off the topic, but still fascinating. Newton almost invented chaos theory. As soon as he invented 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 described the orbit of the Earth, ignoring the effects of Jupiter and Saturn and so forth, just doing the Earth and the Sun. He kind of knew, even though he couldn't do the math, that if you included the effects of Jupiter and Saturn in 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 the only way you could explain how they were there, presumably forever. But the worries about classical mechanics were a little bit different. Different. The worry about gravity in particular. It wasn't a worry about classical mechanics. It was 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 gravitational force on it? And he literally said, 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 Simone Laplace in 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 like Laplace's equation, cleverly enough. And 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, it's gravitational, Gravitational impulse radiates out at the speed of light, and we call that a gravitational wave, and we can detect those. But 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 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 even how you talk about quantum mechanics within any one interpretation.

So if you see every force as a field or any other interpretation of action at a distance, he's 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 do you think about? I think so is this something that you've been conditioned to. By society to think that, to map the fact that science is extremely well predictive of something to believing that you actually understand it like you can intuitively? How, as 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?

That depends on what you mean by this idea of truly understanding something. Right. I mean, can I truly understand Fermat's last theorem? It's easy to state it, but do I really appreciate what it means for incredibly large numbers? Right. I think Yes, I think I do understand it, but 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. And I can say, fine, but I still think I understand the theorem. And 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. Of course, one's intuition gets worse and worse as you get trickier in the quantum field theory and all sorts of 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.

So that's where I'm going to bring in Noam Chomsky for a second, who thinks that our cognitive abilities are sort of evolved through time, and so they're, they're biologically constrained. And so there's a. There's a clear limit, 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 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 you think there's limits to our understanding that's deeply rooted, hard coded into our biology that we can't overcome?

There could be limits to things like our ability to visualize. Okay, but when someone like Ed Witten proves a theorem about 100 dimensional mathematical spaces, he's not visualizing it, he's doing the math. That doesn't stop him from understanding the result. I think, and I would love to understand this better, but my rough feeling, which is not very educated, is that 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 logical, formal, symbolic structures and manipulate them. And that's a leap that we can make as human beings that 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 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. But that's not an element of understanding. It's certainly not a limit of principle.

So of course, as a human, you would say there doesn't feel to be limits to our understanding, but sort of. 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 whatever kind of experimental simulation devices we can put together, is there limits to that? Is it possible there's limits to that?

Well, of course it's possible that there are limits to that. Is there any good reason to think that we're anywhere close to the limits? Is a harder question. Look, imagine asking this question 500 years ago to the world's greatest thinkers, 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, 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.

Well put.

Sam.