268 | Matt Strassler on Relativity, Fields, and the Language of Reality

0:00:00.3 Sean Carroll: Hello, everyone. Welcome to the Mindscape Podcast. I'm your host, Sean Carroll. One thing we do a lot here on Mindscape or for that matter, I do in my life, otherwise even off the podcast, is to try to explain difficult concepts in physics to a broad audience, right? Whether it's quantum mechanics, quantum field theory, relativity, cosmology, what have you, taking these ideas that have been developed by lots of smart people over many years and bringing them to a broader audience, which I think is very important and is absolutely doable if you put the effort into it. But many people try to do this, we're not the only ones who try to do this, and there are a couple of patterns which are kind of bad that many physicists, or scientists more broadly fall into when they're trying to explain their concepts to a broader audience. One is just from the fact that scientists, physicists, but also other kinds of scientists or other kinds of academics for that matter, are typically professors, they are college professors, and they've developed a pretty good set of techniques for teaching students who are going to major in that area. So physics professors as part of their job will teach young undergraduates and then up to graduate students how to be a physicist, so they know what steps they have to go through, they've taken the courses themselves, they've taught the course or they've read the textbook or whatever, there's a set of ideas you have to march through.

0:01:27.6 SC: And one failure mode, I would say, for reaching out to the public is people try to take that way of teaching physics, the way that we teach our undergraduates and just water it down, right? Teach exactly the same stuff, exactly the same concepts in the same order, but try to remove some of the equations or something like that, and that's not always the right way to reach a different kind of audience. I've come across this, of course, in my recent attempts to write "The Biggest Ideas in the Universe," where I'm trying to reach a broad audience with equations, but without any prior exposure to those equations or those ideas. It's even harder if you're trying to explain without any equations at all. It's really weird when you just take the usual steps that you would go through in an undergraduate physics education and de-mathify them and expect people to understand. Another failure mode is that sometimes we do search for analogies, stories, metaphors, allegories, pictures, ways of getting across the basic idea without going into the equations, and it's a little bit easy to forget that people take these analogies seriously, maybe more seriously than they should, right? When a physicist presents an analogy for a deep physical concept, they know which aspects of the analogy actually apply and which do not apply to this situation, and the poor person listening doesn't know that, so they just take the analogy at face value.

0:02:58.1 SC: So because of these failure modes, there's an enormous value to be placed on actually stepping back, thinking deeply about the ideas we want to convey, forgetting about how we teach our undergraduates, to really think about how we should just talk to people who are not going to become physicists down the line, but want to understand the ideas. And today's guest, Matt Strassler is really, really good at exactly that. Matt is an accomplished physicist, someone I've known for a long time, but he's put enormous amount of work... I can vouch for this. I've been talking to Matt for years about this book that is about to come out, called "Waves In An Impossible Sea: How Everyday Life Emerges From The Cosmic Ocean." And the cheap way of saying what the book is about is it's about quantum field theory in modern physics, but the real charm of the book is that he really take seriously the challenge of talking about these ideas in a way that is as honest and true to the material as possible, without just watering down the usual years long physics curriculum or relying on analogies that give you some good ideas and some bad ideas at the same time. So it's a novel take on trying to understand these ideas, and we're gonna go from basic ideas like relativity and quantum field theory to maybe some fun research-level things because Matt's a very good explainer of these things.

0:04:31.3 SC: So it's physics, it's the kind of stuff we talk about all the time, but maybe with a slightly fresh take on it. So, let's go.

[music]

0:04:56.9 SC: Matt Strassler, welcome to the Mindscape Podcast.

0:05:00.2 Matt Strassler: Thank you, Sean. It's a pleasure to be here.

0:05:01.2 SC: So, you know, like I do that, a bit over a decade ago, we discovered the Higgs boson, and I wrote a whole book about the Higgs boson. I remember this famous story, and apparently there was a competition, it was inspired by some British government official who didn't understand the Higgs boson, and so the physicist said, who can come up with the best metaphor for what it is, and they came up with this metaphor of people of different levels of fame walking through a party. I would start by asking you, what was that metaphor? Is it any good or does it do more harm than good?

0:05:39.9 MS: Well, the image that was brought to mind by the winner of this competition has some... It has some general merit to it, in that it gives a sense of perhaps what things might be like, in that a person who is totally unknown can just make their way through the party, nobody pays any attention, they just have to sort of shove their way through the people who are in their way, and that's all there is to it. So that would be your experience and mine. But if Margaret Thatcher walks into the room, suddenly everybody wants to talk to her, and so she makes it in a meter or so, and then she finds herself stopped, and then she tries to go another few meters and she's stopped again. And so it just takes a very long time, she's slowed down by all the people in the room. And so the image that this particular metaphor is trying to convey is that the Higgs field is like the substance that fills the room and those things that interact with that substance are slowed down, and that has to do with why they have mass.

0:06:45.6 SC: And is that good?

[laughter]

0:06:49.9 MS: Well, no.

[laughter]

0:06:50.5 SC: Yeah.

0:06:52.5 MS: It's pretty bad, actually. And again, this is not to criticize the inventors of this metaphor, because they were supposed to come up with something that fits in a paragraph, and the fact of the matter is that some aspects of the universe don't fit in a paragraph, and this is one of them. But what's unfortunate about this particular metaphor is not merely that it doesn't really capture the essence of what's going on, but it actually flies in the face of an even more important principle of nature, and that is the relationship between mass and motion. And if, as this metaphor suggests, you get the idea that, oh, mass has to do with slowing things down, with obstruction, with obstructing motion, then your conception of the world ends up back in the Middle Ages, and you really don't wanna end up there. I mean, they really... They were smart people, but they were confused, and we would prefer to avoid that confusion. Now, what am I talking about here? What is going wrong with this metaphor is that it contradicts the principle of relativity, which if you even don't know much physics, you've never taken a class on it, you've never heard much about it, violating the principle of relativity sounds like a pretty bad idea, and it is. And the reason it's such an important principle is that it explains many of the fundamentally counterintuitive aspects of the basics of being in this world, for example, why it is that we're all...

0:08:37.3 MS: I'm sitting down, you're sitting down, both of us feel like we're not going anywhere, but of course we are. The earth is spinning. The earth is going around the sun, the sun is going around the Galaxy, and the speeds involved are enormous. The earth is going... The earth and sun are going around the Galaxy at 150 miles per second. Now, why don't we feel that and why, if the earth has so much mass, and this metaphor were right, why isn't it slowing down? This picture of Margaret Thatcher having a lot of mass because she's being slowed down by the crowd, well, the earth has a lot more mass than she does, why isn't the Higgs field slowing the earth down? And well, the answer is that the metaphor doesn't work. And you therefore have to try to find a way back to the principle of relativity to start the process of explaining what the Higgs field really does. And so that's why the book I've recently written starts at that place.

0:09:39.0 SC: I do like the fact that you can date the origin of the metaphor so precisely, just by the fact that it was Margaret Thatcher who they picked as the famous person who would have trouble walking through the party.

0:09:50.9 MS: Yes. And you can imagine that today it would be Elon Musk, but he would certainly have trouble, but he's very wealthy, but his mass is not that big.

[laughter]

0:10:02.0 SC: Well, this is what I like about your book, because of course, quantum field theory is a mutual interest of ours, and I think that we both agree that it will be nice if everyone in the world understood quantum field theory a little bit better than they do. If I were to explain it, I would probably start with quantum mechanics and then say, okay, what if you do fields to it and you take a very different approach, really starting with relativity and spacetime and mass and how those things work. So tell us what relativity is. It's not, it didn't come from Einstein originally.

0:10:37.1 MS: It did not. And indeed, Einstein in a way, saved it more than created it as we understand it today. And the person who was perhaps most responsible, although clearly there were other people who were thinking about it, historically, was Galileo. In the 1630s, Galileo wrote a famous passage into one of his texts, in which he explained that if you were on a boat and you're inside the boat, so the wind isn't blowing in your hair, you're just inside in one of the rooms and the boat is moving really steadily, it's not a wavy day, it's just, the boat is just smoothly moving through the water, you will have no idea that the boat is in motion, you will not be able to tell how fast it's going or which direction it's going. And he gives lots of examples of things that you could do to try to check it, you might think that, well, if I drop something and the boat is moving, then as I drop it, it will move towards the back of the boat, but that's not true. Maybe you might think the flies in the room will be all pushed to the back of the room, but that's not true. And when you think it through, he argued, you realize that there's nothing, absolutely nothing you can do which would show that you are in motion as long as that motion is steady. And he infers from this, that the laws of nature do not depend in any way on whether you are moving, if that motion is steady.

0:12:13.9 MS: And when you think about it, that's the thin end of the wedge on the question of why you and I don't feel our motion. And so we go from a situation where even in 1600, 50 years after Copernicus, really great thinkers like Tycho Brahe, Kepler's boss, could write things down saying that it's just not possible that the earth is spinning and moving around the sun, that makes no sense, we would feel it. A heavy body like the earth shouldn't be moving. To the modern day where we realized that the earth in fact is flying through the heavens at extraordinary speed and doing all sorts of gyrations, and yet we are completely unaware of it here on Earth, and the explanation for that is Galileo's realization about how motion is a relative thing. There is no such thing as absolute motion. You can't say, in this universe, whether you are moving or not, you can only say how fast you're moving relative to another object.

0:13:19.8 SC: You and I had a longer than it should have been conversation once about whether the earth goes around the sun.

0:13:26.5 MS: Or the sun around the earth.

0:13:27.9 SC: Well, or is it up to you because you can choose coordinate systems. Did you ever personally come down to the right answer in your mind there?

0:13:36.0 MS: I did, and this is a wonderful question. Although it's a question fundamentally about Einstein's general...

0:13:44.9 SC: I know, we're skipping ahead but that's okay. It's just a podcast. It's all right.

0:13:47.5 MS: But I'll give you the short answer. And of course, I wrote about this extensively on my blog because I thought, this is such an interesting question, and here, there are professors at significant universities who actually argue that no, you really can't say whether the earth goes around the sun or vice versa. And the reason that's a mistake, I believe, is that it's not just about two objects, one orbiting the other, you really are asking the question, is the earth orbiting the sun subject to gravity? In other words, it's not just a matter about what its path is, but why its path is the way it is. And you can easily tell that the earth is going around the sun in sun's gravity and not the other way around as simply as... By simply looking at Kepler's third law of mechanics, which tells you that the planets have a rule by which their orbital times are related to their orbital distances from the sun, and the earth satisfies Kepler's law for the sun. Whereas the earth also has a Kepler's like law. The moon satisfies it. The space station satisfies it, but the sun does not. And so in a way, it's as simple as that. Now you can go into more detail and talk about the fact that orbits are an entire class of motions and not just the earth's motion alone, and come up with all sorts of ways of saying this in more technical detail.

0:15:18.4 MS: But in the end fundamentally, it's not true that the sun goes around the earth gravitationally, and that's really what's at stake here. The earth goes around the sun gravitationally and not the other way around.

0:15:28.5 SC: Yeah, and so I am one of the people who would disagree with you about this, but of course, it's interesting precisely because you and I 100% agree on the physics. It's just a matter of how to match up the words in the English language to the physics that we understand, and that's gonna be a theme throughout your book and your attempts to discuss relativity and quantum mechanics and so forth.

0:15:52.2 MS: Yeah, I think just in the sense there's an even larger issue, which is the fact that scientists could agree on the physics and disagree on the way to talk about the physics, even colleagues like you and I, is a clear problem for a person who is not an expert trying to understand what scientists do know and what scientists are still disagreeing about. And so I think for both you and I and for other people who spend a lot of time trying to convey how science works, the important thing to do is be very clear about what it is we know and about why it is we are explaining in the way that we are, so that a non-expert could read what I write about it and could read what you write about it and come away with the correct impression, namely, we're not disagreeing about the math, we're disagreeing about the way to look at the math. But that's not in the end what physics is. Physics is about prediction based on mathematics, and the fact that you wanna talk about it in a different way does not make it a contradiction, it simply makes it a different perspective on the same thing.

0:17:08.6 SC: Good, we'll see how that shows up as we go, but I don't wanna leave Galileo behind entirely because I've made the case most clearly in my book, "The Big Picture," to me, the specific idea that motion just continues on by itself, that the natural state of things is for things to keep moving at a constant velocity. If you wanna promote that to conservation of momentum or something like that, you can. But to me, that is maybe the single biggest realization in the history of science, because it removes the need for explaining why things are moving. In the Middle Ages point of view, it was weird when things are moving and you needed a force or mover to do it and post-Galileo and his other predecessors like Ibn Sina, who set this up, now we can just think of the universe as kind of a mechanism following patterns.

0:18:05.7 MS: That's right, and there's a very close tie between the law of inertia or what comes up in physics classes as Newton's first law of motion, although he wasn't the first person to write it down by any means, and Galileo's principal that these two are in some sense two sides of the same coin, because what Galileo says is you can't tell the difference between steady motion and no motion. And so if you believe that if you are stationary, you will remain stationary unless something does something to you, then it must also be true that if you're in steady motion, you will remain in steady motion until somebody does something to you. So they are very closely tied together, these notions.

0:18:51.0 SC: Did either Galileo or Newton say those words that you just said, make that argument?

0:18:57.7 MS: That's a great question. I don't know the history enough to know of a precise point at which either one might have said that. It's something I should maybe look into. It's an interesting question, but I don't... Of course, the way we learn history is we learn the history of the great thinkers, but there are always smaller personalities who have certain insights and write certain things down. And so to trace that back and find out which one or which set of people first had these insights would be a real challenge even for a historian of science, since we're talking several hundred years ago. But it's probably known to the experts in that field.

0:19:35.9 SC: So we're already coming up across something, even at this pretty easy to understand level of what Galileo was talking about, but something that's nevertheless pretty non-intuitive, right? The idea that there is no universal standard of rest, there is no way to just say, here is the speed of something, full stop. This is going to be something we got to continue to fight against all the way up through modern physics, right?

0:20:00.6 MS: Absolutely. It goes... It's a fascinating thing that we teach physics to college students, and this is almost the first thing we teach them. And in the classes that... In the class where I was taught and in the classes where I've been expected to teach, the idea is you teach Newton's first law maybe in the first week or maybe in the second week, and then you move on without grappling with the fact that this is a remarkably counterintuitive notion. We never see this experience this in ordinary life. Anything that we want to move, we typically have to keep it moving.

0:20:38.8 SC: Yeah.

0:20:40.2 MS: Cars need engines. Planes need engines. We have to keep pushing. Walking tires us out. We can't just sort of glide down a highway without doing anything. And that's because friction and other forms of drag are ubiquitous in a world, on the earth. And so we grow up in an environment, and we have an intuition that motion requires activity. But it's only by understanding that motion does not require activity that we can understand astronomy, that we can understand why the earth does what it does and the moon does what it does. And so, again, this is why astronomy was so counterintuitive and took so many hundreds, thousands of years to understand. So, yes, this is a profoundly counterintuitive notion, and we don't fundamentally know why it should be true, why it has to be true. We just have experimental evidence that makes it seem that it appears that it's true throughout the universe. And yet, and this is in some sense where we get into the really interesting aspects of modern physics, it almost broke down. It was on the verge of breaking down when people tried to understand what light is. So that maybe is...

0:22:01.7 SC: And we're going to get to that. [laughter] Okay, good. Yeah. No, it's always a back and forth. Like one generation's precious principle that we can't violate is another one's antiquated relic that we have to overcome.

0:22:17.5 MS: Absolutely.

0:22:18.9 SC: And speaking of which, a topic that you go into great detail in the book, you've mentioned Newton's first law, then there's, which says that we're going to go in straight lines if you don't act on us with a force. But the second law, that's where Newton really made his money, right? That's F equals MA. That's what made modern physics possible. And there's all three of those symbols. F and M and A are kind of interesting. But let's talk about M. What is that parameter that appears in Newton's law? Was he the first to talk about that? Where did it come from?

0:22:52.5 MS: Well, in a way, it has a long, complex history, like most concepts. But the original confusion about what we now call mass is its conflation with the concept of weight.

0:23:12.3 SC: Yeah.

0:23:12.4 MS: And before Newton, people assumed these two concepts were essentially the same, as far as I understand. And Newton was the first to realize, no, you have to separate them. And to talk about it in modern language rather than try to confuse ourselves with the way people used to think about it, mass is a property that tells you how hard it is to change an object's motion. Now, again, this is in contrast to that Higgs metaphor and Margaret Thatcher that we started with.

0:23:39.7 SC: Yeah, exactly.

0:23:41.0 MS: Which suggests that mass is about how quickly things slow down. It's quite the reverse. Things will continue in a straight line unless you do something to them. And mass is how hard it is to change something's direction or slow something down or speed it up. And so, that is an aspect of an object which reflects, not its motion, but in some sense, its stubbornness that prevents change in motion. Now, what is weight? Weight is how heavy an object is, literally, how hard it is to hold an object up against the pull of gravity. And on Earth, these two things are completely connected to each other. The more mass an object has, the more weight it has. And so it was natural for people living on Earth and never having gone anywhere else and never really having thought that hard about anyplace else to imagine these were the same thing. But Newton's key recognition was this couldn't be true. If there was some way to understand the moon's motion in terms of gravity or the planets in terms of gravity, it had to be that weight, for something that's far enough away would be smaller, even though its mass remained the same.

0:25:00.3 MS: So the moon has an enormous mass, but its weight, that is to say the degree to which it is pulled by the earth's gravity, is much smaller than you would imagine if you thought mass and weight were the same thing. And we carry this conflation of mass and weight with us wherever we go. That's why we're always interested in watching our weight and keeping our weight under control. Whereas, in fact, if you just wanted to lose weight, you could go to the moon. But I don't think your body shape would change at all. So one should keep in mind that what one really wants to lose is mass. And I'm kind of surprised that physics teachers don't sort of teach this right at the beginning of the section on gravity. But it seems an obvious point to make that we conflate these two ideas. But to understand modern physics, even to understand Newtonian physics, you have to first pull these ideas apart.

0:25:52.1 SC: And what's interesting about that is that you need to bring in gravity into the discussion. And I think that from the Ask Me anything questions I get for the podcast, et cetera, I think that this is a very natural confusion that people have. Like is mass somehow intrinsically linked to the idea of gravity, or is it something separate? And the answer is implicit in what you said, but let's make it explicit.

0:26:14.7 MS: Well, it's even... It is, but it's a little subtle, too, which is that when we get to Einstein, we're even going to have to keep track of the fact that what you mean by mass is ambiguous if you're not careful.

0:26:30.2 SC: Yeah.

0:26:30.3 MS: But at the time of Newton, the idea was that mass has to do with motion, as we just described, has to do with preventing changes or getting in the way of changes of motion. But it also, for some reason that Newton did not understand, has to do with gravity, in that the force between two objects involves multiplying their two masses together. And the more mass things have, the more gravity they inflict on other things. What we know today is that the chain of logic linking those different types of, those different aspects of mass is more complicated.

0:27:08.1 SC: Yeah.

0:27:09.2 MS: And that, in fact, gravity comes from energy and momentum, and not directly from what we would call rest mass, which is the type of mass that affects motion in the simplest sense, and also, most importantly, the type of mass called rest mass is what appears in Einstein's most famous formula, e=mc2. Interpreted as saying that the mass of an object that's at rest, that's stationary, has to do with the amount of energy that's inside it. So what Einstein does, he says, well, look, mass, at least rest mass, the mass of a stationary object, comes from its energy. And separately, gravity is an effect that comes from energy. So when you put those two things together in simple situations, you get Newton's notion that gravity comes from mass, because gravity comes from energy, and mass is a form of energy. But when you pull them apart, you get the much more varied and much richer notion of what gravity can do that you know better than I in the context of general relativity and Einstein's theory of gravity.

0:28:17.2 SC: And speaking of Einstein's theory of gravity, he was led to his insights in part because of the principle of equivalence, which people give credit to Einstein for. But Newton noticed a version of the principle of equivalence, right?

0:28:35.6 MS: Sure, in the sense that all objects already, just from the start, all objects fall to the earth at the same rate. In a way, even Galileo knew this. And Newton, in a way, gave it an explanation because he noted that the acceleration of an object is related to the force on it divided by its mass and in gravity, the force on it is proportional to its mass. And so in the acceleration, the mass cancels out. There's a mass in the numerator, there's a mass in the denominator. And so acceleration is the same for all objects falling on the earth. And so that means that if I take a little paperclip and I take a heavy book and I drop them at the same time, they land at the same time. And if you haven't ever seen this yourself, try it. It's amazing how many people sort of know this, but have never actually tried to drop something really light and something really heavy, making sure that that very light thing isn't affected by air resistance. And in that case, you'll really see it's as though it looks like magic. And it is, in a way, a sort of magic, because it's what leads to Einstein's conception that gravity could be an aspect of the geometry of space and time, rather than some just generalized force. It has some very special properties.

0:29:49.8 SC: Well, I think that's why Newton maybe didn't explain it as completely as Einstein did, right? I mean, yes, Newton noticed that the parameter mass that appears in his second law and the parameter mass that appears in the law of gravity are the same parameter. But why are they the same parameter was a little bit unclear, and that was kind of mysterious. I'm not sure that Einstein does completely explain it. He accounts for it. It is a true fact in general relativity. But if someone just sat back and said, did it have to be that way? I'm not even sure what the right answer is.

0:30:28.1 MS: Well, that's a really good question, because in a way, there is an explanation that comes out of quantum field theory. If you accept that gravity comes from a gravitational field that is associated with what a particle physicist would call a particle of spin 2. And what's interesting about that is, in Einstein's theory, yes, there is an association of gravity with a field with certain properties, such that its particles have spin 2. And then it does follow from mathematical consistency that you must be able to interpret space and time in terms of, interpret gravity in terms of the geometry of space and time. But one thing that's often forgotten, although, again, people like you know this very well, is that there was a competing theory of gravity at that time by a fellow named Nordstrom. And in Nordstrom's theory, instead of spin 2, there was a spin zero object. And it was a perfectly good theory, but it would not have had... In retrospect, the mathematics would not have required it to have the properties that Einstein wanted it to have. Whereas with a spin 2 field, you are sort of forced into it by the math.

0:31:51.7 MS: That's not something Einstein knew at the time. That was something that was learned later. So, in a way, Einstein got lucky. He had some principles. They led to a particular theory. It turns out that there weren't many options beyond the one he came up with that would be mathematically consistent. And so, but at the time, like any good theorist, he had some principles he was working with, and it led him to an answer, but it wasn't obvious that it was the correct answer.

0:32:21.9 SC: Yeah.

0:32:23.2 MS: That depended on experiment.

0:32:26.2 SC: I think that the idea of thinking of gravity as arising from a spin 2 particle is a really fun and important one. And we should talk about it again, but we have to eat our vegetables a little bit first and work our way up.

0:32:37.1 MS: Sure.

0:32:38.7 SC: Let's just remind ourselves what happened to the poor principle of relativity? I mean, Galileo put it out there. Newton had a theory that embodied it. But then something happened with electricity and magnetism, and the world was never the same.

0:32:55.4 MS: Yes, in a way... We could certainly talk about electricity and magnetism in their details, but in a way, the problem is even deeper, which is that, which is the simple observation that light somehow makes it across the universe. Light can travel a very long distance, and it doesn't lose its oomph. It clearly maintains its color, its frequency as it goes. Somehow it has this property that somehow it can travel through the universe itself. And if you think light is just a bunch of particles, as Newton did, that might not be so surprising. If the universe is mostly empty and you're sending bullets through it. Well, the bullets will just keep going according to Newton's first law.

0:33:42.2 SC: Yeah.

0:33:42.7 MS: Nothing there to stop them or slow them down. But there was a debate for two centuries as to whether light was a wave or made of particles. And then around 1800, there was definitive evidence from interference effects that no, light is really a wave. And now we hit a puzzle, a very serious puzzle. Because sound waves are waves in air. They don't go through the universe. Why not? Because there's no air there. A sound wave is a vibration of the air. If there's no air, there's no sound waves. Same idea if you go to the beach, right, the ocean waves come to the beach and they stop. They don't keep going because there's no water. So if light waves can go through the universe, there must be something out there. There must be a thing that you would naturally think that is vibrating, in which the waves are a vibration. So what is this thing? And why doesn't it slow the earth down? So we hit a puzzle, not a contradiction.

0:34:47.9 SC: Don't keep us hanging here, Matt, tell us what the answer is.

[laughter]

0:34:53.4 MS: Well, I mean, at a certain level, we don't entirely know the answer. What Einstein did was point out that... Well, let me back up one step.

0:35:03.7 SC: Sure.

0:35:05.4 MS: The point that seems obvious is even if you're confused about what this stuff is, you should be able to measure whether you're moving through it or not. For example, if you're in a boat, you can easily tell if you're moving through the water or not. If you turn off your engine, if you're moving through the water, you will very quickly slow down. And although Galileo says you can't measure whether you're moving in a steady motion, if you're slowing down, you certainly feel that. So, same thing for a plane that's flying through the air. If it were stationary, it would be doing one thing, and if it's flying through the air without an engine, it's going to slow down and so forth. So you can tell whether you are in motion and how you are in motion with respect to ordinary substances. So the basic idea was we ought to be able to tell if we're moving through this magical substance, which was called the luminiferous aether, a name, which has got lovely resonances to it.

0:36:05.0 SC: It's a great name compared to a lot of other dumb names.

0:36:06.0 MS: It's a wonderful name, I mean just...

0:36:08.5 SC: Physicists came up with.

0:36:10.5 MS: Such a shame it doesn't seem to be there.

0:36:10.9 SC: Too bad it doesn't exist. I know.

0:36:11.7 MS: Or maybe it is. We'll come back to that. But in any case, the idea was, all right, there should be some measurement we can make that can tell us something about this substance in which light is a wave. And in the 1880s, the right technology came along, and that was invented by Albert Michelson, who, along with Edward Morley, built a machine, a device that could very accurately measure the speed of light in different directions. And if you think about it, if you're moving through the water and you're looking at ocean waves, ocean waves that are going in the same direction that you're going will seem relative to your boat, to move more slowly than ocean waves going the other direction. And so this is a similar idea that Michelson had in mind, that you should be able to tell that light moves at different speeds relative to this medium, depending on how fast the earth is going through the medium. And, of course, the earth goes in different directions every... As it goes around the sun. So if you measure this a few times a year, you measure this in different directions, you should be able to tell the difference. And famously, Michelson and Morley saw no difference at all. The speed of light seemed to be the same from all directions at all times.

0:37:26.0 MS: And that seems to be in contradiction with the idea that there's a substance in which light is a wave. Now, this is where we come back to Galileo, because if it had been true that Michelson's experiment had worked, if it were possible to tell how fast the earth were moving through this luminiferous aether, then it would not be true that all types of steady motion are the same. There would be experiments that you could do even in a closed room, even under the deck of a ship, as Galileo suggested, there would be experiments you could do, you could do Michelson's experiment and tell how fast you are moving through the aether. But since the aether apparently is everywhere in space, after all light goes through universe from all directions and for many places, then you would conclude that Galileo's idea, although it might apply to some things, is not fundamentally correct. And so, Michelson's experiment, had it shown a difference in the speed of light from different directions would have been the death now for Galileo's relativity.

0:38:35.6 MS: Now came a brief period of 25 years where people try to explain what does Michelson's experiment mean? Why can't we detect this thing? And there were various ideas which we don't have to go into, but all of them would still have violated Galileo's relativity. And then Einstein pointed out, as a 26-year-old student, that actually, if you insist that Galileo's relativity is correct, and you relinquish your notions of space and time as you always thought they worked, you can write down math that can both explain why light travels as a wave, particular a wave of the electromagnetic fields, and yet can travel from your perspective at the same speed from all directions, independently how far you are moving or the object that's emitting the light is moving. And that was an extraordinary thing to point out, obviously one of the great ideas in scientific history because it show that the only way to reconcile light's amazing ability to travel the universe is to give up your notions how space and time work.

0:39:53.5 SC: [chuckle] It seems like a big ask, but it paid off.

0:39:56.8 MS: It's a huge ask. And needless to say, people were curious, interested, but very skeptical. But in the end, it doesn't matter what people think, it matters what experiment says. Experiment said, these ideas are correct.

0:40:12.7 SC: You make the case very nicely that Einstein's insight here really wasn't the word relativity in any sense at all. Relativity was already there, and then there was this experimental idea that the speed of light was constant to everyone. He figured out how to reconcile those two amazing facts that sound innocuous together, but kind of have tension between them.

0:40:36.6 MS: Yeah, that's right. Einstein's theory of relativity is not the invention of the idea of relativity, it is a revision of the idea of relativity as Galileo had it. Because Galileo didn't worry about time, Galileo just worried about how things move, but assumed time is just time.

0:40:52.4 SC: Sure.

0:40:53.9 MS: And Einstein is now already, even before general relativity, starting to make us wonder how we should think about time and what it means if everybody who's moving around has a different clock than the notion of simultaneity and the notion of synchronized clocks. It's all starting to come at risk. And general activity tears that all apart.

0:41:15.6 SC: Well, I got a question recently, why don't people consider special relativity as one of the great triumphs of unification of physics, 'cause it unified space and time together. And my answer was, what do you mean? I always talk about it that way. That's exactly what it was. And many other unifications came with it. This is where we can now finally talk about e=mc2 and how mass and energy are related to each other.

0:41:44.4 MS: Even in some sense, the unification of electricity and magnetism, which I think fairly can be attributed to Maxwell, there is a way in which that unification becomes not only true, but necessary, once you have Einstein's understanding of how it works. You simply can't talk about one without the other, because what is electric from one person's point of view can be part electric, part magnetic from another person's point of view, and that's deeply integrated into the math on the theory.

0:42:14.9 SC: And we're left with a picture where eventually, Einstein's general relativity, we don't need to go into great details about that, but it leaves us hanging a little bit with this issue of whether space or spacetime, if you want, is a medium by itself. It's not, the aether we can't measure our velocity with respect to it, but it's something, it has a geometry, et cetera, how are we supposed to think about space and spacetime?

0:42:43.6 MS: Well, I think that remains one of the great questions of modern physics today, in the sense that as you... Just to say what you said, but in a slightly different way, there is a fundamental tension that still remains conceptually. It's not a tension in the mathematics, but it's tension and how we think about it in that we know today, thanks to Einstein, that space and time is somehow thought of together, they're kind of like a fabric in that they can stretch in the expanding universe, that's what's happening, they can warp, that's what gives us gravity, they can ripple, that's what gives gravitational waves, which were the subject of a Noble Prize just in the last few years.

0:43:32.1 MS: And yet, this fact that we can't measure this substance, whatever it is, we can't measure whether we're moving forward or not, because that would violate Galileo's principle. So to say it again, space as sort of a thing, does stuff, but we are not able to measure whether we are moving through it, and more generally, we're not able to measure its presence or its... We can see some of the things it does, and yet we can't see kind of what it is, we can't grab hold of it or bottle it. It's not like a substance, the way water is a substance or like any other substance we're used to. And so this conflict between a substance-like thing which acts like it's there, and this thing which sometimes act like it's nothingness, that fundamental conflict is a deep conceptual conflict for our brains. The math is okay with it, but it's such a deep problem that it might even make you wonder whether space is real.

0:44:31.9 SC: Good. Go ahead.

0:44:35.7 MS: And physicists do really wonder about this. This is an active area of research, there are various reasons for that, which are kind of another discussion. But certainly, we live in a universe whose basic fundamental properties are very strange, strange enough that we should certainly worry that maybe there's another level of understanding behind them that we have yet to encounter.

0:45:00.4 SC: I'm really glad that you put it that way, 'cause it's very honest, you weren't trying to claim more certainty than we have, which some people will sometimes try to do. And also, I personally at the research level, am increasingly sympathetic to notions where this lack of a rest frame, what we call Lorentz invariance in the technical lingo, is only an approximation, that in fact, it comes out in the wash at long wavelengths, slow energies, things like that, like many other things do. But maybe it's actually not a fundamental feature of the universe. I'm not wedded to that idea, but I think it's absolutely on the table as a possibility and a very exciting one, both theoretically and experimentally.

0:45:42.9 MS: Yeah, I think... I've written this book as though we're sure about Galileo's principal of relativity. But of course there are no principles about which we are sure, they're always subject to experimental verification at more and more precise levels as our technology improves, and it's always possible that something we have held as almost certainly true for hundreds of years, may fall apart at some point, just as Newton's law of gravity did after more than 200 years. So we have to be humble about what we do and don't understand. But there is also the possibility that even the notion of space is an approximation to something far stranger, and those people who think about quantum gravity along certain modern lines face that because we have found equations, not necessarily the equation to describe our universe, but we have found equations in which space is an epiphenomenon, an emergent concept, and the basic thing you start with is just a very large collection of objects that don't have any notion of space at all.

0:46:55.2 MS: So we know there's a lot we know, there's a lot we don't know, and any particular way of looking at the world that we have now has to be viewed as a progress report, a very successful progress report at the moment, but one which has plenty of holes in it that could turn out to be quite large in the end.

0:47:13.5 SC: Good. But this question of the realness of space, the thinginess of space, I don't know if you know, do you know about the Clarke-Leibniz correspondence? Have you heard this principle before?

0:47:26.2 MS: Yes. You and I have spoken about this and I recall it. Clarke and Newton...

0:47:28.3 SC: Sort of read about them in my book, 'cause you are a reader.

0:47:29.5 MS: And Leibniz and Newton arguing through Clarke, yes.

0:47:32.2 SC: Is space relational or substantival, is it a thing or is it just a collection of relations? And we still don't know. Like in Einstein's world it was a substance, but maybe we're post-Einstein now. But another fact to keep in the back of our minds when we're contemplating that question is that space isn't really empty or it's not a featureless anyway, 'cause it's filled with all of these fields like the electromagnetic field. You do a great job in your book talking about what a field is, the idea of the fundamentality of fields, which is very bizarre to people. They always wanna know what the fields are made of that I got to say like, no, no, no. The things are made of fields, not the other way around.

0:48:15.8 MS: Right. And part of the problem with talking about fields and what they are, is that fundamentally we don't know. It's always harder to explain something you don't really understand. We understand what fields do with remarkable precision, in many cases. We have math that describes what they will do in all sorts of circumstances, we can predict all sorts of wonderful details. But just because you can predict what something does doesn't mean you really understand fundamentally what it is. And an analogy I like to use that I think is reflective of the right way to think about fields is that if you think about the atmosphere, just think about the air of the earth, it has all sorts of features that you can measure. It has pressure, it has temperature, it has wind, wind meaning how fast it's flowing in a particular location. And these things; pressure, temperature, wind, humidity, these are properties of the air that you can measure anywhere, there's some machine you can use for measuring the wind speed and direction, et cetera, et cetera.

0:49:19.0 MS: But imagine that you didn't know what air was, and all you had was these measuring devices. You could measure this thing, which you call pressure, but you don't have the conception that it is literally the pressure of a gas, you just call it P. And you measure this thing called T. It's temperature, but you don't know that. And something called W, which is wind, but you don't know that. So you have these things you can measure and you can figure out equations which describe how they work, and you can even predict the weather if you're clever enough to figure out the right equations. Because the equation stand on their own, they tell you how these things you can measure change over time and how they relate to each other.

0:49:58.4 MS: But if you don't know what air is, or even necessarily that it exists, then you don't know what pressure... How to think about pressure. You don't know what property of air it's referring to, and since you don't even know what air is, you can't even sort of talk about what property it might be. And this may be our situation with the fields of the universe where the vast majority of the fields with one interesting exception that I'll come back to, they seem to be properties of the universe, the way pressure is a property of air, that might be the right way to think about them, but we have no idea which properties and we have no idea what the substance of the universe is. And the one interesting exception is gravity, which is ironic because in many ways, gravity is the one we understand the least from the point of view of quantum physics. But in the case of gravity, the gravitational field is telling you about the property of space, which we call curvature, the degree to which it's warped.

0:51:00.9 MS: So it is possible that the electromagnetic field is telling us some property of space and time that is not obvious, some sort of hidden property that we have yet to learn. In string theory, for example, that's a common situation, not to say anything pro or con against string theory, but it is an example of a context in which the luminiferous aether does exist. It's a part of spacetime. And so it may be that this notion that space and time are a substance that has many properties and those properties are the fields of nature, that may be a perspective which is at least useful and maybe even somewhat fundamental. But we still have to deal with the fact that space is very strange because you can't measure your motion with respect to it. So if it's like a material, it's not like anything we've ever seen.

0:52:00.9 SC: I just wanna be sure, because the audience has different levels of understanding here, if we put aside for the moment, our desires to be super duper careful and clear and correct, what is a field?

0:52:14.4 MS: A field is something that is found... Well, let me back up one step. A cosmic field, the field of the cosmos is something that can be measured anywhere in the universe. It's some sort of property which has the feature that if you change it in one place, it has effects in other places in the future. In some sense, that's the most important aspect of what a field is, it's something which is everywhere, and it's not just randomly everywhere, it has this feature that it's somehow what you do at point A effects later what happens at point B and vice versa. In the context of air as an analogy, the fields of air are found everywhere in the air, and if you change the wind in one place, it's going to cause the wind to change somewhere else, and in fact, that's what weather prediction is all about. It's about saying, okay, I know what the fields of air are today. I know what the pressure and the temperature and the wind are right now. Can I predict in the future what they will be? And the fact that the future depends in such detail on the past, and not just on the past at my current location, but on the past that all locations nearby, and the further back in time I go for my predictions, the more of these fields I need to know in further, further distances.

0:53:43.3 MS: This is what's characteristic of a field. So if you think about weather prediction and about the properties of the air and how they affect each other, and now you extend that to properties of the universe, now you're thinking about fields, I think, in a sensible way.

0:53:57.4 SC: Okay. And that's very good. And if we were to add quantum mechanics to the mix...

0:54:02.4 MS: Oh, my.

0:54:02.5 SC: There's this wonderful fact that... And we don't need to talk about many worlds or the measurement problem, that's okay, that's a different podcast, but we should talk about the fact that when you quantize a field, when you take fields and put them into your quantum mechanical brain, out pop particles. I don't know if you wanna just take that for granted right now, or do you have a favorite way of thinking about that remarkable fact?

0:54:24.5 MS: Well, I think it's useful maybe to step back a moment, obviously the purpose of... I should say something about the reason why the book that I've just written is called "Waves in an Impossible Sea," we've just been talking about the sea, that's the universe, and we've been talking about why it's impossible because it has these very strange features that it both seems to be there and seems not to be there, depending on what question you ask. But then there are the waves. And the reason to talk about waves is that fundamentally, the things we call elementary particles; electrons, quarks, photons, they are in the language of quantum field theory, more wavelike than particle-like. And to understand what that means requires dealing with the fact that there's a history to the notion that electrons are both particles and waves, that's a trope that comes out of the 1920s and '30s, but it's one that got modified over the decades, and in ways that aren't always made explicit.

0:55:34.6 SC: It's a mess.

0:55:37.1 MS: And the word particle and the word field are, again, misleading in how we use them compared to how they're used in daily English. And so one has to really take a moment to just parse all that. So, with that preamble, let me start. So, when we talk about particle in ordinary English, we always mean something like a grain of sand or a dust particle. Something looks like a little ball, maybe irregular shaped, but you can... It's this little thing that moves around on some path. And when people first discovered electrons, that's what they thought they were. So they called them particles. And when it turned out that's not what they were, they still called them particles. So, we often face this problem in science and science communication that things are named before they are understood. And very rarely are they renamed once it becomes clear what's actually going on.

0:56:44.0 SC: Very true.

0:56:46.9 MS: That's a problem. So there's that problem. We have to first take the word particle and understand that we're not going to use it the way our English conception of particle is used in ordinary language. And then wave is a problem, too. When we say light is a wave, we do not mean that light is like a wave breaking at the beach. At the beach, we mean, here comes a big wave. What we mean is here is a high point in the water separated from the next high point by a low point behind it and a low point in front of it. Whereas when we talk about sound waves coming from a musical instrument or from somebody's voice or we talk about light waves coming from a light bulb, we are talking about a long sequence of high and low points. A long sequence of wave crests and wave troughs, which we often call in ordinary English, if we were at the beach, we would call it a wave set or a series of waves. So what we mean by wave singular in physics may have many crests and troughs, which is not the way we would talk about things at the beach.

0:57:51.5 SC: Good.

0:57:53.2 MS: So that's important because when we say light is made from particles, I don't want you to think about the individual particles as being individual crests in a wave train. That's the wrong picture.

0:58:05.5 SC: Okay. I won't.

[chuckle]

0:58:10.0 MS: So now, how do we understand that we are made from waves? This is a very strange thing, again, to... It's such a strange thing that took people a long time to make sense of it, because we from ordinary life have a lot of intuition about waves, and we have all seen houses made of bricks and made from stones and made from concrete. But you have never seen a house made from sound waves. You've never seen a house made from earthquake waves. Waves are not things that we think of as objects from which you can make structured objects that will stay together and stay organized for centuries.

0:58:51.7 MS: And so the idea that we and the walls and the table and so forth are made from waves requires already some sort of conceptual leap. And the conceptual leap is that, and again, it's due to Einstein, although not in a single step, is that even the waves of light, which are definitely waves in the sense that there are crests and troughs. These things have a frequency and a wavelength just like sound waves do. Nevertheless, they are made from, well, we call them particles. Let's not call them particles. Let's just say they're made from things, we'll call them photons. And now let's figure out what they are. And so the way I like to talk about this that I think is useful is that we have many examples of objects that we know are kind of granular or particulate, but not in the sense that they're made from particles per se.

0:59:53.2 MS: So yes, if you go to a beach, it looks continuous, but if you look closely, there's all sorts of sand grains that make it up. In that case, the objects are really particles of sand. But if you take a giant pile of spaghetti, dried spaghetti before you cook it, well, if you look at it from far enough away, it just look like a giant pile. But if you go in there and dig around, you realize there's lots of individual strands of spaghetti there. Or if you take a giant stack of paper, you've never seen one before, it may not be obvious to you whether it's continuous or discrete, whether we know what it's made of. But if you start taking it apart, you will very quickly realize it's made from sheets of paper. And so when we look at a laser beam, it is not obvious to us that it isn't a continuous thing.

1:00:37.5 MS: And then in fact, it's made from individual strands in a sense the way a rope is made from individual strands of twine. It's not that it's made literally from particle-like objects, but it can be disassembled into individual pieces. And those pieces of a light wave, again, they're not individual crests and troughs. Each one of them is a series of crests and troughs, and we call those things photons. So photons are waves, but they are particulate, they cannot be divided into smaller pieces. And they are the things out of which more dramatic waves like those in a laser beam are constructed. And this is far from obvious, just as it would not be obvious to a person seeing a rope for the first time that you could disassemble the rope into individual strands. And that's why people before the 20th century didn't have... It wasn't obvious to people before the 20th century that this was true. You needed the technology and you also needed the right set of experiments to give you a clue that this is something that might be the case.

1:01:51.8 SC: And this is a specifically quantum mechanical aspect of light. Maxwell's equations did a perfectly good job of talking about light waves in a classical way. And this photon language only becomes relevant once quantum mechanics comes on the scene.

1:02:07.4 MS: In a way, you can say it's the definition of the first aspect of quantum physics. The statement that light is made from photons is a more general statement that there are large classes of waves in our universe, and in particular, all of the waves of the elementary fields of the universe are made from these individual pieces, which are called generally, quanta. That's where the word quantum initially comes from historically, is Einstein trying to suggest that light is made from these individual strands or packets or whatever you want to call them. And it was only 15-20 years later that people gave these bits of light the name photon. And even five years after that that they realized that there was an analogy between photons and electrons. That electrons were not actually these dotlike particles, the ones we draw in the cartoon of atoms, but they're more like photons.

1:03:04.7 MS: They have wavelike properties. They are particulate waves rather than being particles in the English sense. And so, this is really the language of quantum field theory that comes out of the 1950s. And it's different from the language of the quantum mechanics physicists of the 1920s and '30s whose famous statements such as an electron is both a wave and a particle, or sometimes it's a wave and sometimes it's a particle. That's a language which Niels Bohr popularized, but it was left in the historical dust as far as the math. And yet, it maintained a life of its own in the culture. So most people who teach quantum physics still use this language when they teach quantum mechanics to juniors in college. And it certainly has survived in most of the popular science books. So that causes a lot of confusion.

1:04:04.4 MS: And that's one of the reasons why in my book I spent a whole chapter trying to make this really clear that we don't think about an electron as a dot. And in fact, you can't understand its most critical properties such as the fact that it has mass if you think of it as a dot. Because if it's really a dot, and it's really true that e=mc2, and therefore the mass of the electron has something to do with the energy that it carries with it when it's stationary, well, why would a stationary dot have energy? Especially if it's really a pointlike object in some sense, where would that energy be? But when you understand an electron, even an electron that is stationary is a wavelike object and like the wave on a guitar string, it is vibrating, and is sitting in place, it's not going anywhere, but nevertheless there is vibration associated with it. Then you understand, ah, there's energy associated with the vibration and that's where the mass comes from. And if you thought of an electron as a dot just sitting there, instead of thinking of it as a wave that's vibrating, you have no way into this idea. And that's why it's so important that in quantum field theory, we do not think about electrons as dots. And we do have an understanding of what their mass is associated with.

1:05:29.0 SC: Not to mention the fact that at least at face value a dotlike electron would collapse to be a black hole.

1:05:35.9 MS: Well, there is that problem too, but I think it's useful to understand that this particular problem is independent of gravity.

1:05:50.1 SC: Sure.

1:05:50.6 MS: And would be there even in the absence of gravity. So, while it's certainly true that pointlike objects without some sort of wavelike structure have all sorts of conceptual issues associated with them, there's an independent conceptual problem, which is that if you carry this notion of a dotlike electron with you too far, even if you take Bohr seriously, that some of the time it's like a particle and some of the time it's like a wave, you've lost the fact that its wavelike property, the fact that it's a vibrating object, is essential in its existence. And its basic properties such as its mass simply are not explicable. If you somehow try to make that pointlike object work in your head, it doesn't work. And we see this in these fundamental properties of electrons and all the other elementary particles, too.

1:06:40.0 SC: For the listeners who have followed us this far into the podcast, we're allowed to get a little more technical and wild here. So I'm going to fearlessly ask you about the difference between electron fields and photon fields. We have our fermions and our bosons, and they're fundamentally different kinds of fields. And that contributes to why conceptually we tend to think of matter and light as two different kinds of things.

1:07:13.2 MS: Right. And of course, you and I have... Well, the word matter is another one of those words that is really problematic. So let's be a little clear.

1:07:21.2 SC: I'm just throwing it out just 'cause I know it'll get a rise out of you.

1:07:24.3 MS: Yeah. You went there, the target was right on. But let's just talk about atoms and light. And there is this, as you said, this remarkable feature of our world that is not to be taken for granted. You have to work out in the mathematics of quantum fields to show that there's only two types of fields. Or rather you can divide all of the fields that could possibly be part of our cosmos into two classes. One of those classes is called bosonic fields, the other class is called fermionic fields. The particles, that is to say that these waves that are the minimal waves that you can have in the electromagnetic field that we call photons, they are bosons. Then there is an electron field, not to be confused with the electric field.

1:08:19.8 MS: There is an electron field that is fermionic, and its minimal waves are what we call electrons. And all of the different elementary particles of nature can be understood. Each one is a wave of a particular field, and each field has to be either bosonic or fermionic, and each particle has to either be a boson or a fermion. Now what's the key difference? The key difference, we already learned some of it in undergraduate chemistry. Electrons cannot do the same thing at the same time. No two electrons can do identical things. This is known as the Pauli exclusion principle. And it was discovered as people tried to understand the properties of atoms back in the 1920s. And the whole structure of atoms would be completely different if electrons were bosons, because bosons don't have an exclusion principle.

1:09:12.4 MS: In fact, they are perfectly happy to do exactly the same thing. And that's why lasers can be made out of photons. So you couldn't make atoms like ours if electrons were bosons instead of fermions, and you couldn't make lasers out of light if light was made from fermions. So these are very obvious differences, but the degree to which they affect our macroscopic experience is a little less obvious. And so one of the remarkable things is that if electrons were bosons, not only would atomic structure be very different, but if you tried now to pile a large number of atoms together, instead of forming crystals or blocky structures that you could make tables and microphones and people out of, they would just collapse in on themselves. And so, the very basics of the macroscopic world depend on the fact that electrons are fermions, but they also depend on something else because the Pauli exclusion principle would not apply if electrons weren't literally identical.

1:10:29.4 MS: And why are electrons literally identical? Well, that is one of the key predictions of quantum field theory. If electrons were just dots, we would have no idea why they are identical. But they are waves in a field, and it's the same field. There's just one electron field, and the minimal wave in an electron field is an electron. And it doesn't matter where you make it, it doesn't matter when you make it, it doesn't matter how long it's been around for, it remains a minimal wave of the electron field. And so any two electrons, they're the same type of thing. They are literally identical. And because of that, the Pauli exclusion principle can apply to them. And because of that, our world can have macroscopic objects in it that don't collapse.

1:11:16.6 SC: And it's really important and fascinating to me in the context of quantum field theory, that you have your electrons, you have your electromagnetic field, but there's not an infinite variety of possible kinds of fields. There's a tiny handful and essentially almost all the ones that we think are possible are there between gravity and Higgs and electromagnetism and other force fields and electrons and so forth. It's a really limited set to draw from.

1:11:49.8 MS: Well, this is an interesting feature of the discoveries that physicists on the theoretical side and mathematical physicists have made about how quantum field theory can work. When you go into a subject which has some mathematical content like physics, you could wonder whether the world that you see is just one example of possible worlds. Maybe there's an enormous number and you're living in just one for some reason. Or you can imagine maybe there's only one possible world that's consistent with quantum field theory or with quantum field theory and gravity together, and we live in it because there's simply no other type of world that you could have. And the reality turns out to be somewhere in between. It's remarkable how many mathematical constraints there are. When you try to combine quantum physics and special relativity that is say, pre-gravity, and then when you try to combine it with gravity as well, you find that the mathematics is somewhat rigid. You can't do anything you want. You can only do a relatively limited set of things.

1:13:05.7 MS: It's still a very big set but it's a lot smaller than you might have thought. And on your point that there's a limited set of types of fields, that's true with a caveat, which is that this assumes that the fields have particles either whose mass is zero or that their masses come from a limited set of possibilities. Once you allow there to be... Once you allow for particles that can get their mass any old way, you have a wider set of possibilities. But experimentally, we find that all of the particles that we know of so far, with one exception, either don't have any, their particles either don't have any mass like the photon, or if they do have mass like the electron, they get it in a very special way. And that's from this strange substance called the Higgs field that we started our discussion with. So it is true that once you know experimentally that there are some limits to the types of fields we find in nature, then you find that the possibilities are very limited indeed. And so it's some mix of theory and experiment that tell us that we're in this strangely or maybe not strangely limited situation.

1:14:20.5 SC: Well, let's close the circle here by getting the Higgs boson right. Because I think that as we discussed with people with the best of intentions, physicists try to explain things and they smooth over some rough edges, and they say the Higgs field is responsible for mass. And I get very well-intentioned members of the general public saying, well, mass creates gravity. So without gravity, would there be no Higgs field, or is the Higgs responsible for gravity or something like that? Hopefully, everyone who's been following along with what you've said so far, knows why that's not right. But let's help 'em out a little bit.

1:14:57.2 MS: Well, indeed, it's a natural confusion to have if you think that the Higgs field is responsible for mass. But that is not correct. In fact, the Higgs field is not responsible for most of your mass [laughter] and mine because protons and neutrons, which are the majority of the mass in an atom, do not get their mass from the Higgs field. So we can dispense with that idea. The Higgs field is responsible for the mass of certain elementary particles, but it's not responsible for the mass of protons and neutrons and the story of where they get their mass from... Okay, I'm afraid that we'll have to leave that for the book.

1:15:30.0 SC: Yeah.

1:15:31.6 MS: But we don't have time for that right now. But now there's the question, okay, so electrons do get their mass from the Higgs field, so do up quarks and down quarks... And so most of the elementary particles that we're made from do get their masses from the Higgs field, even if the more complicated objects, the protons and neutrons, and therefore the atoms, do not. So simply because of that, it's clear that the Higgs field and gravity can't be directly linked because protons and neutrons have lots of gravity.

1:15:58.4 SC: Yeah.

1:15:58.8 MS: But they're not really getting much mass from the Higgs field. And there are other reasons which we could discuss, but let's leave that aside for now. So they're independent ideas and now the question comes well, all right, so we started with this and Margaret Thatcher in a room analogy, where the Higgs field is like a crowd that slows people down as they try to move through it and the more well known they are, the harder they have... Okay. Well, what's wrong with that is partly that it is in conflict with the principle of relativity, and that's pretty bad. But in a way, the broader way in which it's wrong is that it suggests that the Higgs field has to do with motion and that it affects the properties of the motion of objects directly.

1:16:47.4 MS: But that's not how it works. And we have to go back a moment and remember that what are or, you know, what electrons are. Electrons are waves in the electron field. And the Higgs field does not, in some direct sense, give mass to electrons. It does not provide the energy that an electron carries, that gives it mass. What it actually does is it changes the properties of the electron field. The Higgs field affects other fields. That's the real, direct connection. And the way in which it affects the electron field changes the way that the electron field vibrates. And since electrons are vibrations in the electron field, that changes the properties of electrons.

1:17:43.1 SC: Yeah.

1:17:45.5 MS: So it's that more indirect route that is the way that the Higgs field does its thing. And so really the fundamental story is not how does the electron, how does the, sorry, how does the Higgs field affect elementary particles, it's really, how does the Higgs field affect the fields whose waves are elementary particles? And so it's the interactions between fields, the Higgs field and other fields, that is at the fundamental heart of how the Higgs field is able to affect the world in such a dramatic way. And just to add one side comment to that again, to just make sure it's all clear, the big news in 2012 was the discovery of the Higgs boson, a type of particle. The type of particle is itself a ripple, a minimal wave in something. What is it a ripple in? It's a ripple in the Higgs field. So the discovery of the Higgs particle was really not the big story, it was the means to an end.

1:18:45.9 MS: The discovery of the Higgs particle proved that there must be a Higgs field. 'Cause, you know, particles are just manifestations of ripples of fields. And so the discovery of the Higgs field, that was the big deal. The Higgs particle doesn't give mass to anything.

1:19:00.6 SC: Yeah. [laughter]

1:19:00.7 MS: And it doesn't affect anything. Despite the name God particle that's been given to it, it has essentially no role in the universe at all. And if you make a Higgs particle, it's gone in a tiny fraction of a second. But the Higgs field, that's another matter, it's present everywhere in the universe, just like the electromagnetic field. But it has an additional feature that has allowed it to change the properties of other fields, and thereby the properties of elementary particles, on which our lives fundamentally depend.

1:19:29.0 SC: I'm fond of pointing out that we shouldn't call it the God particle anymore, because now we have evidence that it exists. [laughter] Goes over...

1:19:36.7 MS: Oh, I love that.

1:19:37.4 SC: Goes over separately with different audiences, depending on who you're talking to. But [laughter] that was very helpful. Good. And I think that we can actually wind things up with this leads us directly to, okay, mass, gravity, et cetera. You brought up the fact that one way of thinking about gravity is through the gravitational field, which at the quantum field theory level, looks like a spin 2 particle, the graviton. And I know that this is a lot of, this is definitely an area where people struggle trying to understand what we physicists are saying because on the one hand we're saying gravity's not a force, right? Einstein seemed to imply that gravity is a feature of spacetime, not a force. On the other hand, it's a particle, just like the photon is a particle, which makes it seem kind of force-like. And on the... Well, I mean, there's many hands we can go down here but we don't understand gravity at the quantum level. Is that an obstacle to talking about things like gravitons? Gravitons have never been detected, should we really be sure that they're there? I'm just gonna dump all these questions in your lap and [laughter] give you 30 seconds to close it out. You get more than 30 seconds, don't worry. But, however long it takes.

1:20:51.0 MS: Well, I think the way to understand what we know and don't know about gravity and what we suspect about how it works, is really to make sure that your understanding of electromagnetism and the photon is complete because the analogies are almost exact.

1:21:10.5 SC: Yeah.

1:21:12.6 MS: The notion that the electric force has to do with the exchange of photons, this is another phrase that's common in the world of science communication. I hate it [laughter] because I think it really fundamentally miscommunicates what particles are. And what we learn in first year physics class is that electric forces are associated with the electric field is still just as true as it was before people invented quantum mechanics.

1:21:44.3 SC: Yeah.

1:21:44.9 MS: The electric field does generate the effect that we call electric force. And to try to talk about it in terms of photons moving back and forth is kind of a math trick and not fundamental from my perspective to the actual physics. Photons, as as we said, are the basic elements out of which a light wave is constructed. Now, we can import these ideas to gravity, that gravity is caused by the gravitational field, which itself, in this case, we have some idea of what it might be. It reflects the curvature. It's the property of spacetime, which we call curvature. And waves in the gravitational field we call gravitational waves, just as a laser beam is a very bright wave of light, the gravitational waves that were recently measured, they're very bright, even though they're extraordinarily difficult to measure and they're very dim by human standards, they're extraordinarily bright by quantum standards.

1:22:44.3 MS: And if you could make a sufficiently dim gravitational wave, you would discover that it's made from individual gravitons. Just as if you take a sufficiently, if you take a laser and make it sufficiently dim, you'll discover that it's made from photons. Now, that is still conjecture, but that is the analogy that we make, and we believe it's likely true. Unfortunately, to test it experimentally, is far beyond current technology. But as far as the math goes, that math analogy works just fine. The problems of quantum gravity do not arise with that analogy, they arise when you try to make sense of the more quantum properties of spacetime itself. And so that's sort of a more sophisticated application of quantum physics. There's no problem with imagining gravitons, they can be put into the equations. They can be calculated. One can even calculate things that they do like scatter off of objects.

1:23:41.4 MS: And we have reason to think that gravitons may exist, but it's always possible that our understanding of gravity is wrong and that some aspect of it will break down even before we get to the quantum level. And if that's the case, then the story will be more complicated. That's for experiment to decide.

1:24:00.7 SC: I would still argue, maybe disagree, but I would still argue that there's essentially zero credence we should put on gravitons not existing. Maybe they're not fundamental, but even in the wind, there's sound waves and we can quantize them to get phonons, right? I mean, there's going to be something that is the quantum of the gravitational field, whether it's fundamental or not.

1:24:25.7 MS: Well, this is an interesting physics point that I am not 100% sure my own understanding is as good as it should be, it's kind of one of those things which I looked into at some point. It's certainly true that sound waves in a piece of metal are made out of phonons in the same way that light waves are made from photons. But it is, I think, not the case that there are phonons in air.

1:24:57.2 SC: Oh.

1:24:58.9 MS: I think this is true. This is something where I might be embarrassing myself here. The point is that when the amplitude gets sufficiently low and you're starting to tell whether they're, you're trying to tell whether the sound wave is really something you could pull apart, the whole structure of the material starts to become important.

1:25:17.9 SC: Sure.

1:25:20.3 MS: And so your ability to describe it as a collective sort of wave breaks down before you get to the quantum effects. So I think it is possible that something similar is true for gravity, and that we will have to change the way we talk about it before we really get to individual quanta. And that if you try to get to individual quanta, you would discover that there's something wrong about the way you're thinking of space and time. Now, again, I don't say this with 100% confidence 'cause I haven't actually worked through the math and tried to understand this in detail. I do remember reading something of this sort. And so I think both you and I have some reading to do to settle this issue.

1:25:57.8 SC: That's always true. And that's very helpful because that's something, a point I hadn't thought about. So that's useful. But maybe tell me if I am oversimplifying, but for the people out there who are still trying to get straight on whether gravity is a force or not, I would say there's a language that says gravity's not a force, it's the curvature of spacetime. There's another language that says gravity is a force, it follows the inverse square law like Isaac Newton said. There's a third language that says gravity can be thought of as a manifestation of a bunch of spin 2 particles grouped up into some condensate. And all of these languages are correct. They're mutually incompatible. You had to choose one at one time. But they all describe the same underlying phenomenon in slightly different linguistic choices.

1:26:46.7 MS: Well, this is, I think, this reflects a very important aspect of physics and mathematics that I view as one of the really important conceptual points that is poorly understood outside of the experts. But even the experts forget about it. They know it. And the first time we physicists learn that there's not going to be one unique language for talking about anything, is when we're learning Newtonian physics.

1:27:23.9 SC: Yeah.

1:27:24.8 MS: Because we first learn everything that everybody learns in first year of physics, which is that there are forces and there's accelerations and that's the way you should describe things. And then we learn three entirely different ways of saying the same thing. Lagrangians, Hamiltonians, Hamilton-Jacobi theory, each one of these is a different way of talking about Newton's laws. And you can prove mathematically that all the predictions that you will get from these different ways of saying the same thing are identical, which means that there are multiple conceptual languages based on multiple ways of writing down the same math, which have exactly the same experimental consequences and cannot be distinguished by an experiment.

1:28:10.8 MS: So how should we think about this? I mean, math can be written in different ways. Adding a positive number to a negative number can be thought of as subtraction.

1:28:24.5 SC: Yep.

1:28:26.0 MS: Subtracting a positive number from a positive number. So is it addition or is it subtraction? [laughter] Well that's kind of a... Clearly you could do it either way. And if you wanted to base your world on addition and negative numbers, you could view the world that way. And if you wanted to think about, no, all numbers are positive, but I can do addition or subtraction, that would be a different way to do it. And there's nothing wrong with either one, but it might change the way you talk. So the different languages which you described for talking about general relativity, there are different ways of writing the math or viewing the math that have exactly the same consequences. And so a professional will use any and all of them. Whenever a particular one is convenient, we'll use that one. If it makes the calculation simpler, we'll use it.

1:29:14.3 MS: And what we learn is that we should not be too wedded to a particular conceptual viewpoint. We simply can't be. We can't decide on the basis of experiment which one of these viewpoints is correct, nor should we try. The math is what we use to make predictions. The language in which we talk about the math or the version of the math that we use, as long as they're literally identical in all predictions, they are simply equivalent and common ways, just like you can describe a table using English or French or German, it doesn't make it any less a table.

1:29:48.0 SC: I think that's a wonderful lesson to wrap up with. So Matt Strassler, thanks so much for being on the Mindscape Podcast.

1:29:54.1 MS: Thank you very much, Sean.

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