# The Universe Is Not in a Box[1]

THE UNIVERSE IS NOT IN A BOX

I'm asking questions that I've been asking myself now for a very long time. Basically, what is time? What is motion? Even more so, why do we have such a strong sense of moving forward in time, and that things in many ways are getting more and more interesting in the universe?

This has been a puzzle for a long time in science. All the laws of physics suggest there's no distinguished direction of time. The laws of physics work in exactly the same way. For example, if you film two billiard balls colliding and run it backwards, it looks exactly the same. However, you take a film of someone diving into a swimming pool and run that back, it looks completely different. It's been an issue now for about 170 years—why that can be if the laws suggest it should be exactly the same.

About seven years ago, I got an idea that might solve that problem, which came out of more fundamental questions I'd been asking. Just how do you define distance? How do you define motion? We always see things relative to other objects in the universe. Newton had introduced this concept called absolute space. It's a little bit like a room with the walls taken away. In this room where I'm sitting with you now, my position relative to the chair and the walls is perfectly clear. You can see that. Newton somehow imagined that we move in a space, which is as if the room was there but the walls have somehow disappeared. This has been a mystery in physics for a very long time, and it was the stimulus that led Einstein to create his general theory of relativity, which, in the end, finished up in rather a muddled state because Einstein didn't try and do it directly; he worked indirectly.

I'd never forgotten this issue of why things seem to unfold in one direction when the laws that Newton first found, and then Einstein found, and more recent laws of particle physics all suggest that you can run things in either direction of time and it should look the same. As I said, when you run a film backwards of two billiard balls colliding, it looks exactly the same, but when you run a film of somebody diving into a swimming pool backwards, it looks totally different. This fundamental fact was noticed in a paper in 1852 by William Thomson, who later became Lord Kelvin. He published a short paper, the title of which was "On a Universal Tendency in Nature to the Dissipation of Mechanical Energy."

Everything seems to be running down, and we see this everywhere we look. We all get older in the same direction. We never meet anyone getting younger. Moreover, all the billions upon billions of stars that the astronomers see in the sky are all getting older in the same direction. Their ageing process is very well understood. Where does this fantastic sense of direction come from if you can't see it in the underlying laws?

Quite by chance, an idea came to me about seven years ago. There was a famous bit of work done in 1772 by the great Italian-French mathematician Joseph Lagrange, who was studying the Earth-Moon-Sun system. That was a problem that gave Newton headaches. Lagrange made the interesting discovery that if the system has either zero energy or positive energy—so, it's not a bound system like the solar system where the planets can never escape from the sun—as time goes on, the size of the system in both directions of time, both to the past and the future, will grow without limit. It will go up to infinity in both directions, and there's just one unique point where the size is at its minimum. I suddenly thought, well, maybe that's something to do with the problem of where the arrow of time comes from. Why? Because if you start from the central point, the system gets bigger and, under gravity, more structured. It's very uniform at the point of minimal size, and as you go away from it in one direction, it gets more structured. And as you go in the other direction, it also gets more structured. This applies not only to the three particles that Lagrange was studying, but any number of particles you have.

It occurred to me that if you're thinking about a system of objects in the real universe, the whole of the background universe defines the direction of time for you. And you just say, well, this system went through minimal size and then it grew again. That was the past, and that's the future. But if you're saying this is a toy model of the whole universe, that background arrow, with which we're all so familiar, just isn't there. This situation in which I have a uniform distribution of particles and in both directions away from it a more clustered, more structured distribution, if I was to show that to my grandson who's nearly five and say, "If you were to point to interesting things that are happening, which direction would they go?" He would say, "One arrow goes from here in that direction, and one goes in the other direction."

This then gave me the idea of a Janus point, from the Roman god Janus who looks in two opposite directions at once. If this was just my model universe and I was asked to say in which direction time flows, I would have to say there are two directions from that central Janus point. There's one arrow of time going this way and one arrow going that way. If we had observers inside this universe, they would think, well, maybe this is the beginning of time back here, this Janus point, and we're going forward to the future away from it. If they could look backwards, they would see confusion here where everything is rather uniform—a bit like a swarm of bees that are uniformly distributed and moving in all sorts of different directions at once. You can do the calculations on the computer and show this happening. Then there would be another universe on the other side where time is going in the other direction, but the people on this side couldn't see what's happening on that side and vice versa.

This has the potential to completely resolve the mystery of how the laws can be symmetric, but you can be in a situation where you only see asymmetric things happening, where there's a very pronounced sense of direction. The overall solution in this case is completely symmetric. The two halves are qualitatively similar; they differ in details, but they're basically the same. So, the solution is symmetric, but because observers can only be on one side or the other, they see things very asymmetrically. There's a profound sense of the direction of time on either side of the Janus point, although the symmetry of the law and the symmetry of the solution are respected. That was the idea that occurred to me back in 2012, and I've been developing that with collaborators since then.

Back in 1999, The End of Time came out, which was very much concerned with the same issue of where our sense of coming from a past and going to a future comes from. At that stage, I was still thinking that size had some real objective meaning. It's quite clear as I sit in this room that I'm smaller than the room, and you can see that because you can see the background of the walls of the room. Size is always relative to something else. My hands are basically the same size, but my fingers are shorter than my complete hand. Science should always be about ratios, particularly if you're thinking about the whole universe.

Twenty years ago, I was just beginning to develop these ideas that it's only ratios that count, and that overall size of the complete universe may be a dangerous concept. I was just beginning to develop these ideas in The End of Time. There are just three pages where I talk about shape space, and I can illustrate that idea quite easily. Think of a triangle, the simplest nontrivial geometrical object. It's amazing how much you can get out of a triangle. A triangle has a shape and a size, and in many ways the shape is clearly much more fundamental. Suppose I hold an equilateral triangle up in front of my face and move it backwards and forwards, the shape doesn't change, but the size does as the image is projected onto the retina of my eyes. I started then to think that it would be better just to think about the shape of the universe and how that changes, and not worry so much about the size.

In the course of developing these ideas, I had this new insight about how the universe might have a minimum size and grow either side of it and become more structured. One could characterize this change of structure in a way that tells you how the shape is changing, not how the size is changing. This has led to quite an interesting way of thinking about Einstein's great theory of general relativity, which is talking not about space-time and how the curvature of space and time changes, but how the shape of the universe at any instant changes. My collaborators and I call this shape dynamics. In many ways, it's a more fundamental way of looking at general relativity. It's removing all the parts of this wonderful theory that are not absolutely essential and leaving all the bits that you must have, otherwise it would fall apart. You've always got to have three sides of a triangle; if you take one of them away, you've lost your triangle. It's gone. The shape is absolutely minimum. You've got to have the three sides or two internal angles, and this is boiling things down to the absolute bare minimum.

Surprisingly, this hasn't been done in science before, in thinking about the universe. It's not been a way that people have thought about it. Though there are some important parts of general relativity that do rely upon that. I was lucky to work for several years with someone who had done important work on that. In fact, all the work that's now done with predicting what gravitational waves would look like when two black holes circle around each other and then collide and give off gravitational waves—all those predictions couldn't be done without this work, which is really talking about how the shape of the universe changes in accordance with Einstein's theory. Hidden inside that wonderful theory of Einstein's, there is a theory of shape dynamics, which I hope we have brought out.

An increasing number of people are taking that seriously, so this has been an important input in my story. Quite a lot of the ideas that I had in my book from twenty years ago have survived, with the redundant elements taken out. The most important ideas have survived. And this first step to thinking about the shape of the universes was already in the book then.

The End of Time made certain predictions that required very difficult mathematics to be done. In a way, that book of mine was based much more on intuition than the present ideas I've got, which do have solid mathematical results behind them in a way that the other book didn't. I'm very pleased about that. The starting point of the new ideas is a very important result in Newton's theory, which is now 250 years old, and it's a very solid result. It's not so much something being disproved by an observation as mathematical results being brought forward, which are much more secure and on a sure basis.

If we are on a promising new direction, we may be able to make predictions about the universe, which nobody has thought that the universe would look like. Maybe if things work out well in twenty years from now, a space probe might be sent up to make observations and confirm these things. Meanwhile, it looks as if the Janus-point idea has the potential to solve a very longstanding problem.

I've discussed this with some leading physicists. None of them have found anything wrong with it. The first paper was published in Physical Review Letters back in 2014, which is the top physics journal in the world. The editors must've been quite worried about our paper because we were making fairly big claims. They sent it to five referees, three of which said it was very interesting and definitely worth publishing. One referee just said it was wrong and can't be published, but didn't give any reason. And the fourth one was skeptical, but we won that referee round. Then the editors chose the paper as "Editors' Choice." They had a comment piece written about it by a well-known expert in quantum gravity. It attracted a lot of attention online, and there were a number of features about it, so it went down well. We've given talks at many seminars, and nobody yet has come up with a flaw.

I've got three main collaborators now. One is an Englishman, one is a German, and one is an Italian. The Englishman is David Sloan, who's a cosmologist and has also worked in quantum gravity with Abhay Ashtekar, who's fairly well-known in the quantum gravity field. Then there's Tim Koslowski, who also has a background in quantum gravity and was at the Perimeter Institute for several years. He's now in Germany. Then there's Flavio Mercati, the Italian.

One of the great books in science was published in 1824 by a young Frenchman called Sadi Carnot. It is one of the most wonderful books, the title of which is Reflections on the Motive Power of Fire. In about six pages, Carnot explains how you would make a steam engine that would work with the absolute maximum efficiency possible. It was almost entirely ignored, and he died before anything much could come out of it. It was rediscovered in 1849 when William Thomson, who later became Lord Kelvin, wrote a paper that publicized this work. Within a couple of years, thermodynamics had been created as a science.

It caused a tremendous lot of excitement from the 1850s onwards. The key thing about this work of Carnot's is that if you have a steam engine, the steam has to remain in a cylinder in a box. You want the steam engine to work continuously, so you keep on having to bring the steam and the cylinder back to the condition it was before. It's remarkable that the development of what's called statistical mechanics—to understand how steam behaves—led to the discovery of entropy, one of the great discoveries in the history of science, and with it the mystery of the arrow of time. And it all followed out of this work of Carnot on how steam engines work. And moreover, it was very anthropocentric thinking about how human beings could exploit coal to drive steam engines and do work for them. At that stage, nobody was thinking about the universe as a whole; they were just thinking about how they could make steam engines work better.

This way of thinking, I believe, has survived more or less unchanged to this day. You still find that people who work on this problem of the arrow of time are still assuming conditions that are appropriate for a steam engine. But in the 1920s and early 1930s, Hubble showed that the universe was expanding, that we live in an expanding universe. Is that going to be well modeled by steam in a box? My belief is that people haven't realized that we have to think out of the box. We have to think in different ways. My collaborators and I keep on finding ways in which the mathematics that was developed before to understand systems confined in a box have to be modified with quite surprising consequences and, above all, possibly to explain why we have an incredibly powerful sense of the passage of time, why the past is so different from the future.

In the modern age, certainly in physics and cosmology, there's tremendous competition for ideas. It's quite difficult for people to notice new ideas often because each scientist is working on his/her own idea, so they generally don't look at other things. There are certainly a lot of problems with confirming the speculative ideas that theoreticians in string theory and loop quantum gravity have been trying to develop.

Where things may become very interesting but will take time is from astronomical observations. It is amazing the new instruments that are being developed. Only a few days ago we had the results of the Event Horizon Telescope, which has shown us what a black hole looks like. That was a major project to get going. These things that rely on observations of the whole universe can take up to a couple of decades or longer from the first plan through to either building a huge telescope in Northern Chile in the Atacama Desert or putting a telescope in space. It takes a tremendous amount of time.

It's getting incredibly expensive and difficult now to go beyond this great discovery of the Higgs boson at the Large Hadron collider in Geneva. These take a lot of time. People are a bit discouraged by that. I'm hoping we might be able to find something that could be tested. Maybe the material is already there, it just needs to be looked at in a different way. Or maybe the Janus-point idea can suggest a new experiment that could be made.

The idea we have that the history of the universe consists of two parts where what we normally think of as the Big Bang, the start of time, is just a middle point in the timeline of the universe with two arrows of time pointing away from it in opposite directions, suggests that we should be able to say something rather precise about what the conditions are like at that critical central point. This would, say, give an idea of how the universe started in a way that's more precise than now, which then might lead to predictions as to what the universe should look like now. That's a hope that we're working on. We did have some ideas about that which are not totally discouraging, but it's a long way to develop them.

There is a theory called inflation, which explains the structure of the universe now. It's very widely accepted by cosmologists, but it's not without its difficulties. It's a little bit ad hoc. It makes one wonderful prediction, but a lot of other ones you have to know what the answer is and then adjust the theory to make sure it gives that. It's possible that the ideas we're developing could solve some of those problems for inflation, or show that inflation is not necessary at all. That would be definitely an interesting development. It probably wouldn't be welcomed by the people who work on inflation, but there are quite a lot of people who distrust inflation. One of the problems that people who do like inflation admit is that it doesn't have a rival theory at the moment. If we were able to develop some serious alternative to it, people would welcome that because it's never a healthy situation where you have just one theory and that theory isn't 100% predictive. It makes one prediction, which is confirmed very well indeed, but there are a lot of other things it can't predict and you have to put in by hand. People are not totally happy with inflation.

One of the things that is most interesting about this is how it completely changes the way people think about the universe ever since the law of entropy increase was discovered in the 19th century as a result of the work that Sadi Carnot had originally done on the steam engine. Then there was a great German scientist called Rudolf Clausius. He was the person who developed the notion of entropy and then said that the entropy of the universe tends to a maximum, and this also matched the idea of the heat death of the universe, that the universe is going to be a completely bleak future with nothing interesting there. We could completely change that by saying that there's a lot of evidence the universe has been getting a much more interesting shape.

This is maybe because of the anthropocentric way people thought about the steam engine. The steam engine was doing work for human beings. What may not have been noticed is that the steam engine was making the universe into a more interesting shape, a more interesting story. There's a very famous image of the evolution of the universe, which NASA has put out, showing how it starts from a mysterious quantum Big Bang, then there's an inflationary period, then stars and galaxies form, and finally you get life forming on the Earth and ever more detailed things happening. This goes completely counter to the idea that the entropy, which means the disorder of the universe, is increasing from the Big Bang to now.

People have the idea that the universe started in a special, ordered state, and it's been getting disordered ever since then. We're suggesting it's completely the other way around. The universe, in our view, starts in the most disordered way possible and, at least up to now, it's been getting ever more interesting. This, on the face of it, looks like a more positive view of the world. It's not quite like that awful image of the heat death. Now it may be, nevertheless, that the universe in some senses will die, but in a very beautiful form. This is fairly speculative, but certainly we are suggesting that the universe, up to now at least, is not getting more disordered; it's getting more interesting and more structured, and this corresponds to what we see.

Certainly, near the Big Bang you and I couldn't be talking to each other the way we are now. Here we are with modern technology talking to each other in London. It's a pretty amazing universe we live in, and my colloaborators and I think that we possibly have the underlying explanation of why that can be. It lies in certain mathematical theorems, which in the past, when you had to have steam in a box, led to the steam, if it was originally in a small corner of the box, spreading out and becoming very uniformly distributed in the box. You would have what is called equilibration taking place. However, if there's no box, the system can spread out, and as it does that, it can take a much more interesting shape.

It's that removal of the box that seems to suggest why the universe is so extraordinarily interesting. This is potentially a totally different way of thinking about things. It's all to do with saying that there isn't a box there at all.

There's a nice analogy with this back when Kepler was trying to work out what the planets did. He thought about certain observations that Tycho Brahe had made of a comet in 1577. Brahe had shown that the comet was very far away. It couldn't be up in the sky the way people had thought comets were meteorological things in the atmosphere of the Earth because Brahe had showed it was fairly far away. Kepler went further in saying it was very far away, and it must have gone clean through the crystal spheres, which people thought carried the planets around in the sky. Kepler said, "Henceforth the planets must find their way through the void, like the birds through the air. We must philosophize about these things differently." And what I'm suggesting is that, quite amazingly, all that we have thought about entropy and how disorder grows has all been because people have been thinking in terms of everything being in a box. If the universe is not in a box, just like Kepler said, we must philosophize about things differently. That changes things totally.