Time seems linear to us: We remember the past, experience the present and predict the future, moving consecutively from one moment to the next. But why is it that way, and could time ultimately be a kind of illusion? In this episode, the Nobel Prize-winning physicist Frank Wilczek speaks with host Steven Strogatz about the many “arrows” of time and why most of them seem irreversible, the essence of what a clock is, how Einstein changed our definition of time, and the unexpected connection between time and our notions of what dark matter might be.

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Transcript

STEVEN STROGATZ: All of us are aware of the passing of time. We’ve felt it in the changing of the seasons, the rhythms of song and dance, our kids growing up and getting older. Like it or not, time is a fundamental part of life. And over the millennia, scientists have generally regarded time as a one-dimensional thing, an arrow that keeps moving forward, never backward. But the closer we look at time, the more complicated and mysterious it gets. Scientists today are divided over whether time, or our experience of it at least, is real or illusory. Perhaps we’re not really moving through time. Perhaps the present, past and future are all equally real.

[Theme plays]

I’m Steve Strogatz, and this is “The Joy of Why,” a podcast from Quanta Magazine, where my co-host, Janna Levin, and I take turns exploring some of the biggest unanswered questions in math and science today.

In this episode, we’ll ask theoretical physicist Frank Wilczek, “What is time?” How have we defined it in the past? And how might quantum physics redefine it in the future?

Frank is the Herman Feshbach Professor of Physics at M.I.T., a distinguished professor at Arizona State University, and a professor at Stockholm University. He’s the winner of the 2004 Nobel Prize in Physics and the 2022 Templeton Prize. And he’s the author of a number of books, including, most recently, Fundamentals: Ten Keys to Reality. Frank, welcome to “The Joy of Why.”

FRANK WILCZEK: Thank you. Happy to be here.

STROGATZ: Well, I’m very happy to be chatting with you again. I loved your whole book Fundamentals, and the explanation you gave of time and how to think about time for me was one of the most poignant and beautiful. But I’d like to begin with a sort of personal question about your experience of time, just as a son and a person, a husband, I don’t know. How do you experience time as a person, and is it different from how you experience it as a scientist?

WILCZEK: Well, this year I’ve been confronted with time in a very nice way. This, this is the 50th anniversary of both of my first scientific paper and also, not coincidentally, of my marriage. That’s been 50 years…

STROGATZ: (laughs) Wow.

WILCZEK: And I’ve reflected on the passage of time and in a way traveling back in time to revisit those seminal moments.

It’s a very interesting question you ask, that time as it appears in our equations is… Well, it’s the master variable, under which the world unfolds. So it’s a symbol, t, that appears in our equations. And by following the equations, we get hints about what t is. And that tells you what its properties are, as reflected in the things we see around us and their behavior.

But time takes on a life of its own, so to speak, because you can discuss its properties independent of the things it acts on, notably its symmetry.

But going back to the experience of time versus a physical definition of time — the thing that introduces a wrinkle, literally, in it is that by storing information about the past and by thinking about the future, we can travel through time in ways that physical objects obeying the equations of physics really don’t.

Only neighbors in time really talk to each other in the equations. But in our minds, we can store memories. Or we can think about the future. We can really travel in time.

STROGATZ: That’s great. That there’s something in the equations that we only look infinitesimally forward. As you say, it’s neighbors in time that matter, right? The current conditions predict what will happen in the neighboring moment in the future.

WILCZEK: Yes, certainly in the presently understood framework of fundamental law, that’s the way it works. It’s fun to speculate that ultimately maybe there’s a more global structure, that there are conditions that we haven’t yet captured that make the unfolding of the universe inevitable and unique.

But as it is now, the laws tell you about how the state of the world at one moment unfolds into what it is at the next moment.

STROGATZ: What would you say are the big mysteries about time?

WILCZEK: I think one mystery that’s very fruitful, and I think maybe we’ve made a lot of progress on clearing up, is that the fundamental laws of physics look to be almost reversible in time, although everyday experience of the world is not.

So that poses two questions, which are: How can you get from fundamental laws that have that reversibility property to experience, which drastically doesn’t?

And then, secondly, why in the world did the laws have that property when it’s not only not necessary to describe experience, but it’s kind of an embarrassment? It poses a problem, a challenge. How do we reconcile that property of the laws with experience, which seems to, if not contradict, at least be in tension with it.

Those are two great problems, which I think are largely solved, actually, but still very fruitful, especially the first one: Why are the laws that way?

And then, an even bigger problem, which — or an even more mysterious and profound problem is, is the way we formulate our description of the world now — in terms of laws that tell you how the world unfolds from moment to moment — is that complete?

It seems in a way philosophically unsatisfactory because it divides the description of the world into two pieces. One is the equations and the other is the state of the world at one time that you have to somehow inject in to get things started.

STROGATZ: So let’s see if I get this. The questions are something about why do the laws have this near-reversibility property.

WILCZEK: Yeah.

STROGATZ: The question of “equations versus initial conditions,” we could put it.

WILCZEK: Yes, yes.

STROGATZ: Some people out there will know that you’re saying initial conditions without saying it.

WILCZEK: Right.

STROGATZ: And there’s this jargon also, the “arrow of time,” about — that it feels in our experience like time flows forward only. And you say that one feels like it has a good resolution. We think we understand the arrow of time.

WILCZEK: I think so. It’s a long story that has gotten more and more convincing over time. But I think there are apparently many different arrows of time, many different ways in which the future is different from the past. There certainly is a psychological phenomenon. Also, the second law of thermodynamics. It tells you that things become more random, very roughly speaking, but also has a precise formulation. There’s the radiation arrow of time, that radiation tends to go out from things and not come in. There’s this arrow of time associated with evolution of life. And many others you could invent on the fly. Everywhere you look, there are arrows of time. There are asymmetries between the future and the past.

But I think all of them now — we can wrap them all up into one arrow. Just like the “One Ring that rules them all,” there’s one arrow that rules them all, and that’s the cosmological arrow of time.

And so, you might say we’ve solved the mystery, but I think it would be more accurate to say that we’ve wrapped all the mysteries into one, which is: Why was there a Big Bang in the first place?

Gravity likes things to clump, but the early universe at the time of the Big Bang in space was very, very uniform. So gravity was way out of equilibrium. And what’s been happening ever since is gravity struggling to reestablish equilibrium.

So the matter expands and cools, and then it clumps and makes (eventually) stars that start to liberate nuclear energy and planets on which creatures can evolve. There’s a very plausible story that’s richly detailed that aligns all the arrows with that one arrow of cosmic evolution.

STROGATZ: I find it very — not even sure what adjective I would put on this, but the idea that our experience of time as flowing only from the present to the future and that eggs don’t unscramble themselves and that kind of thing, that this is somehow tied into the evolution of the whole universe from its hot uniform state to its current clumpy, you know, galaxy-laden, star… It’s just wild to think that that stuff that seems so remote is affecting my backaches now that I’m an old man, you know? Like, really, right? Ultimately, that is what you’re saying.

WILCZEK: It’s certainly not an obvious story, and without mountains of evidence that’s been developed over the whole course of modern science, it would be incredible. So it’s absolutely astonishing.

STROGATZ: If things didn’t change — like if we could imagine some thought experiment where nothing was changing, would time still exist? Does time exist separate from events? Or is time some kind of measure of the fact that things are changing?

WILCZEK: Well, you can certainly imagine — and in fact, you can construct solutions of the basic laws of physics — so consistent with all the basic principles we know where nothing happens, and t is still an ingredient of those equations —

STROGATZ: So an empty universe would still have time?

WILCZEK: Yeah, time would still be in the equations. And you could ask, even in that situation, the question of what would happen if you made a little disturbance in this universal equilibrium? And then time would be unveiled. So time would be kind of latent, but it would still seem to be necessary in formulating what the situation is. We’re talking about something that’s independent of time, but that you can’t formulate that without saying that there’s something that it could have depended on that it doesn’t.

STROGATZ: It’s already an interesting answer. I’m a little surprised that you say it. I mean, you like philosophy, as I recall. I think you’ve studied a bit of philosophy, right?

WILCZEK: Very amateur, in a very amateurish way. But I actually have been thinking about this recently, at a technical level. But think about a river, the flow of a river. There are two different descriptions you could imagine of a river that is flowing in a very regular way.

So, in one description, which technically is called the Euler description, you would specify what the velocity of flow is at every position, and that would give you a complete description of the flow of the river. And if the flow is regular, that could be nothing happening. The velocities wouldn’t change in time.

STROGATZ: Right.

WILCZEK: However, there’s another description, associated with the name of Lagrange. It’s sort of an interior description where you follow the flow of individual molecules of water. And then those samples move along at the local velocity. And as time goes on, they’re in a different place, so they see a different velocity. Even though the velocity originally was a function of a position, but not of time. But looked at from the inside, when you follow the flow itself, then things are happening.

So, so both descriptions are valid. If we call this river a universe, the universe in one sense is not changing. But as experienced from the inside, it is changing. There’s plenty of room for dynamical development when you are within the river and going with the flow.

And I think that may be at a deep level what’s happening in the universe. If you want to have an interior description — a Lagrangian description, as opposed to the Euler description — it’s not a contradiction. It’s just a different way of looking at the same object, the same reality from the interior or from the exterior. A human’s eye view versus a god’s eye view.

STROGATZ: I do want to explore with you, you know, different conceptions of time in the history of science as we move, say, from Newton to Einstein. But at this moment, I would just like to ask you — and it’s funny, of course, we keep talking about time as we discuss time. Like I say, “at this moment, I’m going to ask you a question about time.”

WILCZEK: It’s hard to escape, isn’t it?

STROGATZ: It’s hard to escape!

WILCZEK: That’s what they say. If it’s an illusion, it’s a pretty convincing illusion.

STROGATZ: It’s a very convincing illusion. So here’s what I was going for: that Einstein, we know, was influenced a lot by a scientist/philosopher named Mach, Ernst Mach. We talk about the Mach number in sound, but it’s that same Mach. Okay, but so: Mach. Was this guy very interested in operational definitions of things. So Einstein, sitting there in the patent office, thinking about time, starts to say, “Time is what clocks measure.“

And you write a lot about that in Fundamentals, and I thought that was a very interesting take on things. You want — can you riff on this idea? Like, should we think of time as what clocks measure, as opposed to some more nebulous definition of time?

WILCZEK: Well, I think so, if we want to think scientifically and fruitfully about time at a fundamental level. But let me qualify it a little.

STROGATZ: It needs some unpacking.

WILCZEK: The English word “time” covers a lot of ground and can be used in different senses, just like “energy,” OK? Energy means something very specific in the context of scientific discussion. But in common language it has a much broader meaning that also has fuzzy edges.

So, similarly with time, when I say, “time is what clocks measure,” I’m referring to the scientific concept of time that’s extremely fruitful and can be carried very far with great precision. And to properly understand that statement, you also have to broaden the concept of what a clock is.

A clock is anything in the world that, that changes in any way, because the laws are formulated in terms of how things change as a function of this variable t. And everything changes, and things change in different ways. They move. They undergo chemical reactions. They age in the biological sense. And the remarkable statement is that this one variable in the equations underlies it all.

So you can have clocks which work on very, very different principles. You can have things that monitor the motion of the earth around the sun. You can have things that monitor the flow of water, water clocks. You could have a clock based on watching how someone ages, a human being ages. That wouldn’t be a very precise clock, but, in principle, and if you dug down into the biochemistry, it could be made precise. Many, many different kinds of clocks, but they’re all consistent with one another.

So, when I say time is what clocks measure, that’s more than an operational statement. It has very nontrivial content. It says all clocks that are properly calibrated and understood, no matter what principle they’re based on, will be able to come to a consistent agreement about what time is.

STROGATZ: We’ll be right back.

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STROGATZ: Welcome back to “The Joy of Why.”

Switching gears a little bit from philosophy here into history of science, it seems to me that a big part of the story of the success of science, especially in what we often call the scientific revolution of the 1600s and later, had to do with the ability to start measuring time pretty well. That it’s no accident that Galileo and Huygens and Newton and, you know, their successors were around at the same time that good pendulum clocks started to be made. And that you could get the laws of motion in a way that you would have had trouble getting them before you had good timekeeping devices.

Do you think that’s right? That the — that our scientific progress really depended on an ability to measure time well?

WILCZEK: It certainly helped. And especially if you broaden the definition of time to include the regular motion of planets, like Kepler’s law that the planets sweep out equal areas in equal times. And of course that observation was central to the formulation of Kepler’s laws, which together with Galileo’s study of pendula and falling bodies, all this led to the pinnacle of the scientific revolution: Newton’s formulation of classical mechanics and the laws of gravitation. So yeah, that all very much based on considerations that, broadly speaking, brought in time.

STROGATZ: So then, if we fast forward — of course, still sticking with these time puns here — zooming ahead now to Einstein. In Einstein, we start to really get some very strange — for many people, counterintuitive things happening.

WILCZEK: Well, in formulating a richer description of the gravitational interaction that goes beyond the Newtonian understanding, and even before that, in trying to do justice to the symmetry of the equations of electrodynamics, Einstein was led to a more flexible concept of time.

So let me start with the special theory of relativity, which historically came first. If you’re in a closed laboratory and, and just did experiments within laboratories that move with respect to one another at a constant velocity, you would arrive at the same laws, no matter what that velocity is. That’s the essence of special relativity. But to do that, it turns out that what one guy would call time, the other guy calls a mixture of space and time. It’s a mathematically simple mixture. It’s what we call a linear combination, but it definitely is a mixture of space and time. So, this introduces the idea that there’s some flexibility in defining what time is.

You can get valid laws of physics with the same content using either some time t or a different time, t $latex ^{prime}$ [t-prime], that’s a mixture of t and x, where x is the position. So that was special relativity.

And then that was kind of a big surprise. because Newton, for instance, thought of time as one thing. Newton was very much a theologian, and very much thought that what he was doing in his work was understanding how God worked. And he thought of God as, you know, imposing His psychological time on the world, I think. There was — the idea that there could be different valid definitions of time would have been very alien to Newton.

But that’s what Einstein postulated, and that allows you to get very nice formulations of the laws of physics and find regularities in them that would be very difficult to find otherwise.

And then, in general relativity, it gets even stranger because you allow different people at different places get to pick their own t version, which of these times to choose. That’s called local Lorentz invariance. Each person can choose their own mixture of space and time to use. And you have to formulate the equations in such a way that they allow these choices. They have what’s called symmetry. Although the formulation of the equations will look very different if people make different choices, their content will be the same. And only very special equations have that property.

And Einstein, in an incredible feat of genius, was able to —from that principle — derive an improved theory of gravity. Time becomes merged with space, and the whole space-time can curve. Those effects are very, very small on laboratory scales. But when you talk about macroscopic scales — the scale of the Earth and the Earth’s gravitational field, or the universe, or in very extreme conditions, like where there’s a very vast concentrations of mass that curve space in black holes. Then more flexible, bendable or even liquefied forms of time come into their own.

STROGATZ: Hmm. I mean, there are many tests of relativity, experiments of carrying atomic clocks around on airplanes. If people haven’t heard these things that you were just mentioning, it’d probably sound pretty fantastical. But we have very good, strong evidence that they’re all true, including even the GPS gadgets that we use in our cars. You know, I mean, if general and special relativity, if we didn’t account for those…

WILCZEK: Well, the GPS wouldn’t work, because it’s very important to get time exactly right in GPS. In the workings of the GPS system, you use very precise timing to infer distances, relying on the fact that the speed of light is, is a universal constant. I’m oversimplifying a little bit, but this is basically the truth, yeah.

And because the speed of light is very, very large compared to everyday speeds, very small mistakes in the measurement of time get reflected into significant changes in distance. So if you make small errors in how you treat time, they become magnified into much bigger errors, important errors in space. So you have to be really, really accurate about your treatment of time in order to make GPS a useful system.

STROGATZ: Right, so the fact that the satellites are up high, where the gravitational field is weaker. You know, there’s all these satellites that are part of the GPS system, and they’re moving pretty fast up there. All those things have to be taken into account and corrected for, and I just think it’s a great example of how, you know, you might think our Einstein is only about black holes or the whole universe, but —

WILCZEK: Well, it’s really remarkable that if you go back to Einstein’s original special relativity paper, he talks about synchronizing and correlating different stations, if you like, so that they can agree on the definition of space and time. And with a little bit of a sense of humor, you can see that what he’s describing there is the GPS system.

STROGATZ: Wow.

WILCZEK: You know, people moving around with rods and clocks and using the speed of light as the way of synchronizing and, and, and then measuring distance. It’s exactly — it is the GPS system, right.

STROGATZ: Oh, I never thought about this. There’s so many things I want to ask you about. How about dark matter? I know that’s one of your favorites. Let’s hear about that. What does dark matter have to do with time?

WILCZEK: Logically, it has at best a tenuous connection to time, but it’s a very interesting story that’s very exciting and I’m heavily involved in at the moment. So dark matter is the observation that there are a whole network of phenomena where it appears that there’s more gravity, more gravitational force than we can track down to the presence of matter.

It looks very much like it could be a new kind of particle that just happens to interact very, very feebly with the kinds of matter that that we’ve been dealing with for decades but yet still exerts gravity. And I think I know what it is, and there’s kind of an emerging consensus that this is a good idea — something called axions. And now, finally, comes the connection to time.

Axions were introduced into physics not as a way of generating dark matter, but as a way of addressing the weird property of the laws: that they’re very nearly the same or very nearly have the same content if you change the direction of time. So, although macroscopic experience doesn’t behave that way, the microscopic laws do behave that way.

Why? We have a very nice story of that.

The principles of relativity and quantum mechanics and the deep symmetries of the Standard Model — the so-called gauge symmetries that govern the essence of the other forces — powerfully restrict the interactions that matter can have. So if you assume that those principles are correct, you get powerful restrictions on the laws of physics.

And it turns out that as almost an accidental consequence of those restrictions, the laws run almost the same forwards and backward in time. So that’s a tremendous triumph of theoretical understanding.

But it’s not quite finished. And there’s one interaction that is consistent with the fundamental laws, the fundamental principles, I should say, that would obey all those principles, but not be reversible in time. And it’s found that that interaction also is very, very small.

So to understand that in a profound way, the leading idea is to introduce another big principle. This is something called Peccei-Quinn symmetry after the physicists who introduced it.

Then some of us realized that as a consequence of this new principle, there’s a prediction that there has to exist a new kind of particle that I call the axion, that has absolutely remarkable properties. It’s predicted to interact very, very weakly with ordinary matter. And then we realize that if you run the equations through the Big Bang, it’s produced in just the right way to make the dark matter that astronomers had observed.

It’s very encouraging, to say the least, that it automatically addresses this other cosmological problem. And the wonderful thing that’s happened over the last few decades — but especially now at an accelerating rate — is that it’s possible to design experiments which will detect them if they’re out there.

The experiments are very difficult. It’s like the problem of detecting neutrinos, but harder — maybe once we learn the right tricks, it won’t appear so hard anymore. But those experiments are being mounted. We’ll know much more in five to 10 years.

STROGATZ: I like that you’re gonna end our show here with that mention of five to 10 years because I want to conclude on some kind of hopefully poignant or emotional note that a lot of the work that you’re especially known for, that you got a Nobel Prize for, was at the beginning of your career. Wouldn’t it be a delightful thing if in five to 10 years these axions are measured and found to be just right.

WILCZEK: It would make my day. I hope it wouldn’t be the end of my career, but it would definitely make my day.

STROGATZ: Well, I’m very thrilled to have been able to talk to you again, Frank. So we’ve been speaking with theoretical physicist Frank Wilczek about the mystery and the beauty of time. Frank, thanks so much for being with us today.

WILCZEK: Thank you. It’s an honor and a privilege, as they say.

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“The Joy of Why” is a podcast from Quanta Magazine, an editorially independent publication supported by the Simons Foundation. Funding decisions by the Simons Foundation have no influence on the selection of topics, guests or other editorial decisions in this podcast or in Quanta Magazine.

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I’m your host, Steve Strogatz. If you have any questions or comments for us, please email us at [email protected]. Thanks for listening.