Please join me in welcoming Professor Jim Al Khalili. Thank you. Thank you very much, Richard. Good evening, ladies and gentlemen. I'm glad you've all made it here. My worry is that if I blow your minds with some uh this philosophical topic on the nature of time, I might might make you overheat even more. So I'll just try and try and try and keep it nice and nice and easy. Uh it's a real pleasure to be giving this Thomas Gresham lecture this year. On the nature of time. Now, when I've given science public lectures in the past over many, many years, I tend to talk about, I mean if I'm talking about quantum physics or cosmology or even things like the history of science or the scientific method, usually it's what in science communication we we've used to call the deficit model. You know, I am I'm the the expert and you're there, the empty vessels to be filled with my wisdom. Um when it comes to the nature of time, that's a that's a topic that I think we all feel we uh have views on, right? Where we have a theory about whether time flows, whether time is real, and so on. So it it's a it's a challenging subject, but it's also challenging scientifically and philosophically to study, because unlike other areas of science where you can uh come up with a theory or hypothesis, then make an observation uh or or gather data or carry out an experiment, we're embedded within time. We can't extract ourselves from it to study it objectively. And yet, over the millennia, scientists, thinkers, philosophers have tried to understand what time is. Is time even real? Is it just an illusion? Uh why is there past, present, and future? Does time flow and so on? So I want to address some of these issues, uh, particularly from uh a modern physics uh perspective. And I've divided my talk into five chapters. So chapter one, the problems of time. Now, there are different problems depending on who you talk to, depending on what field people work in, there are different problems of time. I've divided them up into two categories. Um, these categories mostly are philosophical issues, questions that go back all the way to the ancient Greeks. Um two Greek philosophers in particular were obsessed with the meaning and nature of time, and they both had sort of completely diametrically opposite views. So Parmenides uh uh and and indeed his his uh student assistant uh Zeno, Parmenides believed that everything that exists is permanent and unchanging. There's no such thing as the flow of time, everything just is is, and so time itself is an illusion. And then you had Heraclitus who believed that time flows, time is based on change, everything changes, and therefore time is real. And everything is in flux, always becoming but never being. So on the one hand, you've got thinkers saying time is an illusion, doesn't exist, the other, and on the other hand, you've got someone saying that everything changes, the flow of time is very real. Um, of course, modern scientists, or going all the way back to people like Newton, who also thought about the nature of time. Philosophers have really obsessed about it. In particular, for example, one might argue there must be some truth somewhere between these two extreme views. Um, one philosopher, John McTaggart, over a hundred years ago, argued about uh for the unreality of time. I don't want to go into details about what John McTaggart said, but let me just give you an outline of how ridiculous these ideas are. He said time is basically a sequence of events, right? Series of events, things that happen. Uh you've got your A series and your B series. He said the A series is that you know an event can be in different locations or temporal locations. It's it uh at some point it's in your future, and then when it arrives, it's at the present moment, then after that it's in the past. And he said, so there's change, but a single event can't be in these three different categories at the same time: future, present, and past. That's inconsistent. And he he goes into some long arguments about why that is inconsistent. He says, therefore, there must be a B series. Now, the B series says that all events are not fixed in particular uh um uh temporal locations, past, present, and future, they're just fixed where they are, and all you can talk about is you know the one event happened a week after the other, or two events happened simultaneously. He said, but in the B series, there's no change. Events are just fixed. He said, but we need change. So the B series needs the A series and the A series is inconsistent, therefore time doesn't exist. And and that's that. I mean, philosophers, um, not all philosophers, but philosophers very often will work their way into sort of these logical rabbit holes, which uh which frustrates physicists. But then physicists do dumb things that frustrate philosophers, so I I'm just I just want to make clear that I'm not taking sides. Um okay, two types of problems with time. We've got the philosophical problems of time. There are two of them. Why do we we perceive the philosophical problems of time to do with our psychological um um how we perceive time internally? Why do we perceive time to flow, right? The moment is coming, future's arriving, uh, we're moving through time. There's some flow to it. And yet nowhere in physics is there any evidence of something flowing. Time just is. Moments in time, things happen, and you can uh uh predict from your equations if if this the state of some system is like this at this moment in time, what it would be like at another moment in time, but it's all just moments in time. Uh and then the second uh problem is why is the past different from the future? To us, it's like that's a that's a really stupid question. Of course, the past is what we remember, that's happened, the future is what we anticipate or predict, but it hasn't happened yet. How could there be anything clearer about you know the difference between these two? Um they're divided by the present moment, but but there again, nowhere in physics is there a now, a present moment. That's just the what we perceive to be that that point in time that we are conscious of that is ever changing, gobbling up the future, spitting out the past. So these are philosophical problems. Why is the past different from the future? What is the meaning of now? And does time flow? Then you have physical problems of time, which is what the physicists worry about. Um, for example, and I will talk a little bit about this in a few minutes, how do you reconcile the notion that in some equations of physics time is just uh a number, a parameter? It's called coordinate time. You you plug in a value for in it, if you've seen an equation in physics that where something is changing over time, there's a symbol little t for time. So you plug in a value for t, crank the handle of the equation, evolve it, you can evolve it forwards in time to see what that system will be doing at a later value of t. So it's just a number. But in relativity, time isn't a number, it's a dimension. It's the fourth dimension. In relativity, all times coexist, not just a single moment. Um, usually physicists don't talk about this as a problem of how to reconcile different aspects of time. They talk about it in terms of reconciling uh our fundamental theories of physics, namely quantum mechanics and Einstein's general theory of relativity, looking for a theory of quantum gravity, a theory of everything. But really, what they're also trying to do is understand how these different ways of looking at reality uh uh think about time in different ways. The second problem of physical time is how do we reconcile the fact that all our laws of physics, all our equations of physics that involve something changing over time, are symmetric in time. By which I mean you can evolve a system into the future and into the past, and the equations work. Everything is symmetric. And yet, we don't perceive time to be moving backwards, only forwards. And we are saved by one area of physics that tells us you're right, and that is thermodynamics. Thermodynamics is an area of physics developed in the 19th century, talking about the nature of uh energy and and and work and uh um it it evolved into what's called statistical mechanics and and information theory. But in thermodynamics, there is a direction to time, and it's only pointing from past to future. But in all other areas of physics, there is no arrow of time, time is symmetric. What's going on? And I'll talk about this uh in a moment. Okay, chapter two. So I think about time in two ways. There's there's there's physical time and there's also manifest time. Manifest time, another word for it, would be psychological time, the time that we perceive. So that's where we would have to tackle the philosophical problems of time. Um, Heraclitus, one of the Greek philosophers, he was the one who argued that everything changes. He actually was the person who came up, we believe, with the phrase the river of time. Flowing time. So, what does that river of time look like? Well, if you're standing on the banks of the river of time, time is flowing past in some some sense. Um, and it's not pointing from past to future, it's pointing from future to past because it's flowing upstream from the future, going past you and becoming the past. But maybe you're not standing watching time flow past, maybe time is carrying us along, and now it does carrying us a lot, carry us along from the past to the future. But even that isn't quite right because we don't face the future, we face the past. We see the past receding away from us with our backs to the future. It's a weird way of thinking about it. The way I like to think about it is imagine you're driving along a road, and the road is the road of time. Um, your windscreen is blacked out, so you can't see where you're going, but your rear view mirror is working. So you can see the past receding behind you as you move forward into an unknown future. So these are this is how we think of the you know the flow of time, and yet, as I said earlier, there is no evidence that time flows at all. What about the idea that we are crawling along the time axis uh uh and and where we are is what I'm our consciousness is what I define as the present moment, because that's the only time we can ever be conscious of, right? You can we're not conscious of the future or the past. So you might think the past exists like the present because we can remember the past. But the past doesn't exist anymore. Anything to do with the past is stored in records, in our memories, in books, in photos, in films. Um and how do and we can only ever access those records in the present moment, so the past is gone. So the present is the only moment in time that we are conscious of. But what does it mean, our now? Is the f are we static? This is again another idea to do with like the river flowing past us or us going down the river. Does the future just sort of come at us and and as soon as it arrives at the present, instantly it becomes the past, or are we moving along the line from the past to the future? These are philosophical questions, they don't really have much to do, or physicists can't really say much about them because there is no flow of time in physics, there is no uh uh present moment that's special. There is one aspect of the past, present, and the future that does uh have a bearing on physics, and that is whether we can predict the future. I'll give you the a spoiler. First, no. We can't, and it's impossible, and people who say they can are can't. Um mathematician who who uh uh talked about this at great length was Pierre Laplace, French mathematician in the 19th century. And he argued this is sort of this is before modern physics, so before quantum mechanics and Einstein's relativity and so on. So it was Newtonian, the Newtonian picture of the world, a clockwork universe, a deterministic universe, cause and effect. And he he argued that what if there was some super intellect, some which became known as Laplace's demon, I was gonna say Maxwell's demon, that's another uh interesting uh made-up character. Uh Laplace's demon, this hypothetical being that would know the positions and state of motion of every particle in the universe at a given moment. In principle, in a deterministic universe, one in which everything is determined and the things don't happen just randomly, then that demon would be able to predict the future with precision. We now know that Laplace's demon cannot exist, it's impossible. Replace the demon with, let's say, a supercomputer, an all-powerful computer that can store information about everything in the universe. Well, firstly, the computer itself is part of the universe. So to store information about everything, it has to store information about itself. Now, where does it store that information? Is it in in position of electrons in a in you know in in a uh in information theory, in terms of logical bits of zeros and ones? Um to store information uh uh it has to have has to know itself, so it has to store information about the information that's stored about the outside world and so on. So it cannot know itself. Also, it would have to be of equivalent complexity to the universe in order to store all the information about the universe. But it cannot extract itself from the universe. Nothing, and this is a this is a theme I'll come back to again, nothing is truly isolated within the universe. Everything is interacting with everything else, even at a tiny level. So it can't extract itself outside, even if it was powerful enough and and and uh had enough memory to store information about all every particle in the universe, it can't extract itself from within the universe. And then finally, it would need to know when I say uh I'm capable of positioning on. No, I haven't even used the word precise. So it would need to know precisely everything uh where everything is in the universe. By precisely this, by which I mean to infinite accuracy. It would have to know the state of every particle to infinite accuracy, because so this is the butterfly effect writ large. That in order to evolve or predict how some system will evolve into the future, you'd have to know its present state to infinite accuracy, otherwise tiny, tiny uncertainties, errors, perturbations will accumulate. Um, the weather is is a very good example. Um yes, forecasters told us this heat wave was coming because they were only a few days away from it and they could see the the the pattern of the weather, how it's evolving. But they're not going to tell you whether that we will have a heat wave uh uh in in June in 2030. They can't tell us that. Why? Because they don't know the the conditions so precisely to evolve that far into the future. And for those who may be obviously no one in this audience, but for those who are climate, um anthropogenic climate change deniers, it's oh yeah, you uh if you can't predict uh if it's gonna rain you know three weeks from now, how can you predict that the you know how the temperature is gonna be uh uh in 2050? Uh and you have to explain very carefully to them there's a difference between weather and climate. Uh and it's a bit like saying I can't predict to the toss of one coin whether it's gonna be heads or tails, but I can tell you if I toss it a thousand times, half of them will be heads and half will be tails. So that's sorry, that's just my pitch to climate change deniers. Okay, physical time, but now we can start to get into sort of the nitty-gritty rather than to being rather too fluffy and hand-wavy. Physicists even today will argue, or some will argue, that time is just an illusion. Uh, there are different views on the fundamental reality of time itself. There and I'll I'll list three different uh uh views here. The first one is that time is just our subjective way of uh ordering events, things happening cause and effect, one happening before the other, organizing a changing world, time, but never in the end, time is just that thing that clocks measure. It's not a real thing, it's just a tool that we use. Uh or time is is real and part of the fabric of space-time, as Einstein would argue. Or, and and and this is a um a growing view among uh philosophers of physics and cosmologists, for example, uh, is that time is real but it's not fundamental. There's something deeper from which time emerges. So, time is an emergent property of reality. Um what does emergence mean? Well, the the simplest example is temperature, right? Temperature isn't a real thing. It it's uh if you dig down in a gas that has a certain temperature, uh, and it's really down to just the kinetic motion, the vibrations, movements of the molecules. So in in at down at the level of individual molecules, you've just got kinetic energy, things moving around. There's no temperature that you can assign to it. But you zoom out into out uh to look at trillions of molecules, and now you can talk about their bulk property and talk about temperature. So temperature is an emergent property, and they uh in a more fundamental uh level, it's been argued that time itself is also some emergent property from something deeper. Uh quantum entanglement is one one one option that's uh quite fun to think about. Okay, so even within physics, there are hugely varying views on not only the nature of time, but the reality of time itself. Um so this is a nice this is a nice slide. I've I've I've talked about this uh uh uh a little bit. Um different areas of physics have different ways of defining what time is. So you've got the dynamical equations. So these are the equations of physics that describe how things change. Now it could be Newton's laws of motion, throwing a ball and uh or under the force of gravity or rolling things down inclines or springs, whatever, pendulum swinging, or the equations of quantum mechanics, which talk about how the quantum state of an atom or an electron changes over time. These are dynamical equations in which time appears as a parameter, just a number. Okay, it's called coordinate time. But then you've got relativity theory, Einstein's general theory of relativity, developed just over a hundred years ago, in which time is part of the fabric of four-dimensional space-time. Time is is a real almost, I'm trying to think of the right word for it, substance, right? Because gravity causes space-time to curve. So it's something that can be affected by gravity. It's part of the geometry of the universe. So it's the fourth dimension along with the three dimensions of space. And then you've got thermodynamics, which says, no, time isn't a number or dimension, time is an arrow pointing from past to future in the direction of what's called entropy, the increase of entropy. Entropy is disorder, and I'm gonna say something about that in a moment. So you've got time as a number, time as a dimension, time as an arrow. Very different definitions. It's almost as though you're talking about very different things, but they're all referring to time itself. How do you bring these together? How do you come up with a single definition of what time is by unifying these different uh theories of physics? Well, the one that's probably most uh the closest to what most physicists think is is is the truth uh is relativity theory. So uh general relativity is regarded as our current best theory about the nature of time. And it talks about four-dimensional space-time. Uh, very often we talk about what's called the block universe. Now, so we have three dimensions of space, we know we live in three dimensional space, and um then time is the fourth dimension. But you can't imagine what four dimensions are, so what we tend to do is throw around one of the dimensions of space, uh, which means we can we can just divide uh think. About space as a flat sheet, two-dimensional, and then the third axis we can uh reserve for time. So the block universe is an idea that's very useful in relativity theory, in which all times coexist in the same way that all points in space exist. So just as I can go from here to there and come back again and move around different points in space, there are all coexisting points along the time axis. The difference is, of course, I'm not free to move up and down the time axis at will. We're sort of carried along within this flow. But what's good about this is we can talk about events happening, we can talk about us one slice through it, which is now. So it's all it's it's um at some point in time along the time axis, but every point on this sheet is a different point in space, but all at a single moment in time, so we call that now. On one side is the past, on the other side is the future, some point there is the here and now. So you might think, well, there was that philosophical problem of time about what does it mean to have a a now that divides the past from the future? Ah, okay, relativity theory rescues us. It gives us in this picture block universe in which time is and is a dimension and all times coexist. A slice is now, and then we can argue about how that now is sort of moving along from left to right as we pass through from the go from the past to the future. The problem in relativity is there is no such thing as a universal now. That picture is of the block universe only applies to one point of view, what we call one reference frame. If if if that's your now slice, and you can say, right, uh, you know, a point, a point over here and a point over there, they both, you know, or an event, say a flash of light here and a flash of light there, they are similar simultaneous flashes of light because they both happen on the same now sheet. But for someone moving past you close to the speed of light, let's say, they have a different now sheet that's at an angle to you. So if you are on so observer one, this is their now sheet, A happens, n is happening now, C will be happening in the future, B has already happened, it's in the past. But for observer two, A, B, and C all sit on their same now sheet and they're simultaneous events. So we're arguing now about what is now. We can't even agree on when now is, because it depends on your state of motion, and neither observer one or two is wrong. Time is relative, and even when now is is relative. Um, of course, the block universe isn't quite exact. We understand when we apply it to the whole universe, um, space is expanding. So this is a much better picture of the block universe. Time moves by, but space is getting bigger. Those twirls are galaxies, I'm sure you knew that. Okay. Right. Um in relativity, then time isn't absolute, time is relative. And there's some lovely uh implications of this in relativity. For example, it can be stretched and time, that is, can be stretched and squeezed. Clocks tick at different rates depending on what you know, if you a clock is moving past you close to the speed of light, you'll see it ticking by more slowly than than your clock. Someone with that clock will see your clock ticking more slowly. Um time slows down close to the speed of light. Time runs slower in stronger gravity. Um, it's very true that uh my feet are aging more slowly than my head. Because my head is further away from the center of the earth. So it feels slightly weaker gravity than my feet. So time is running more slowly and my feet than my head, right? So they are so time is running, so they're aging slower, sorry, yeah, and my head is aging faster. But tiny amounts, not much, not much, not not enough to worry about. Um but it's true, and in fact, GPS satellites uh and and using Google maps wouldn't work if we didn't take this into account because clocks on board satellites, the atomic clocks on board satellites, are ticking by slightly faster than clocks uh uh at sea level, and so that has to be adjusted for, otherwise, Google Maps wouldn't work. And even time in travel into the past is theoretically possible according to general relativity, although there are all sorts of paradoxes which suggest that surely that can't be true. Um my favorite time, uh well, in fact, my favorite science fiction movie is is Interstellar, and if you've seen it, uh there's the moment when Matthew McConaughey and and the the crew of his spaceship, the Endeavour, they they um they land on this planet that's orbiting a supermassive black hole. And he knows that every hour they spend near this black hole, seven years go by on Earth. Now you might think, yeah, but that's Hollywood science fiction nonsense. No, that that if you did do that, if you did find a supermassive black hole, and they exist out there, they're a long way away, but they exist out there, if you did go and travel to a near black hole, that's what you what would happen. Uh in fact, one of the producers of Interstellar is a Nobel Prize-winning physicist, Kip Thorne, and he knows what he's talking about. Um, gravity slows time down. A black hole has very strong gravity, and it really slows time down. And so in the movie, Matthew McConaughey knows that uh he doesn't want to spend any any more time than he has to on board this planet, and sure enough, they do get delayed there, so when he gets back to Earth, his young daughter's now an old lady, and you you think it's all delicious nonsense, but actually, gravity that is really what gravity would do. Um back to physics, and I mentioned earlier that the concern that you know how do you reconcile the first problem of physics, the uh physical problem of time, uh, is how do you reconcile time as a as a as a number in say quantum mechanics with time as a dimension in relativity theory? Well, physicists have tried to do that, and and there are lots of uh uh uh potential uh theories and ideas that are being developed today towards finding that reconciliation, that theory of quantum gravity. So by gravity I mean general relativity. So the that physicists use that interchangeably. When I'm talking about general relativity, I mean Einstein's theory of gravity. How does that reconcile with the the theory of the very small, the theory of the quantum world? And physicists, so so there are things like string theory, loop quantum gravity, there are various candidate mathematical constructs which are candidates for potential theory of quantum gravity. We haven't got there yet. Um, one interesting early attempt is called the Wheeler-Duitt equation back in the 1960s. What's fascinating about this is by unifying in their sort of rough way quantum mechanics and relativity, time disappears completely. There is no time in there in their equation. I thought I'd give this is the one equation to show you because it's quite a simple equation. Um anyone with a physics background will will see that the left-hand side looks something like what's called the Schrdinger equation in quantum mechanics. You've got what's called the Hamiltonian, and grandly that Greek letter psi is the wave function of the universe. Um it's a simple equation, but of course, it's buried within it is rather complicated maths. Um but the point of this equation is that there is no time in there. And the argument is well, maybe the universe overall is timeless, but for us embedded within it, we do see time changing. And there are arguments to explain that. But but it's just it's fascinating that you know trying to find a theory incorporating all physical phenomena, all the physical forces and and and uh and equations into one neat equation, and it does away with time completely, suggesting that time, well, maybe maybe it doesn't exist after all. Okay. Um the arrow of time in thermodynamics is fascinating. Uh we know that things happen in one direction in time. That jug dropping and falling and crashing, you you see it happening, you know that's time moving forward. But we could equally have run this film backwards and have these pieces come together, reconstitute themselves, and form the jug again, and you know that's a film being run backwards. You know that that this isn't what happens in our world ever. Right? So thermodynamics tells us things move from an ordered state to a disordered state, not the other way around. Not entirely impossible, it's not zero probability, but rather unlikely that that will happen. The simplest way I like to explain it is in terms of shuffling a deck of cards. Okay, so you start off with a deck of cards that is uh all ordered in suits and and numbers, uh, and you shuffle it and you get a mixed-up deck. We took refer to the ordered deck of cards as some uh as one of uh low entropy and you increase entropy to a shuffle deck. And the second law of thermodynamics, famous law in physics, says that things move from uh order to disorder, from low entropy to high entropy. And so that gives us an error of time. That's why thermodynamics says there is an error of time, where other areas of physics say there isn't. Um but the dynamical equations of physics, for example, motions of planets around a star, you could run that movie backwards and it would be fine. Uh likewise if you've just got particles or molecules of gas bouncing around in a box, you run that backwards and it's symmetric in time. Uh so we do see examples of systems where you can't tell whether time is moving forwards or backwards. Fine. That doesn't mean there isn't a direction of time, it just means that the system you're looking at isn't giving you a direction time. But if you look at that box of gas, for example, uh uh and just look at isolate two particles um and and to film those two particles colliding. So uh so this is the old movie reel type picture. You've got a white ball coming towards a black ball, hits it, and they both scatter. I think of a game of a pool, for example, and they both go in different directions. If you watch this film in reverse, what you would see is a white ball and black ball coming in from the right, hitting each other with the white ball slightly ahead, uh, rendering the black ball stationary, it's a stun shot, and the white ball carries on. Um it might be less likely to happen in a real game of pool, but that's perfectly allowed. When you just have two particles, the equations of motion are time symmetric, they work both ways. But you stick lots of particles in a box, say have them all ordered up in the corner, and allow time to go by, they will spread out. If you saw that movie in reverse, you know there's some trickery going on because that doesn't happen. Okay, so how how why is it? Why is it some sometimes you see there's symmetric uh uh things happening symmetrically in time, sometimes you see they they don't. Imagine you have a box of gas at three o'clock in the afternoon where all the molecules of gas are all in one order, in one corner. At a later time at 4 p.m., they've spread out evenly into what's called uh thermal equilibrium. The laws of physics that are time symmetric, that don't have an hour of time, will say you should equally well be able to run time backwards and arrive at 2 p.m. when they're all spread out. But that's there's a flaw here. How did they get to be the way they were at 3 pm? Well, clearly there was some influence from outside that gathered them up and and pushed them all into one corner, uh, in which case they're not gonna go backwards, they actually can carry on forward. They started at 2 pm all uh spread out, and at 3 pm we brought them together, and at 4 pm they spread out again. There is an arrow of time. Um now this is this is a problem that goes back to the 19th century called Los Schmidt's paradox. Uh you see, the real issue here is that these symmetric equations that say time can run forwards and backwards only apply to isolated systems, systems that aren't being interfered with from the outside. Entropy always increases in isolated systems. So the real problem is how does entropy always increase, and yet the dynamical equations uh say they can it entropy can decrease as well. Loschmitt's paradox says it shouldn't be possible to deduce irreversible process from time-symmetric dynamics. And physicists have argued about this for 150 years, going all the way back to Boltzmann and Maxwell and others. The problem is it only applies to isolated systems, and the only truly isolated system is the whole universe, as we as we as I discussed earlier with Laplace. There is no system truly isolated from everything else. Everything ultimately will interact with its surroundings, however hard we try to isolate it. How do you um apply it to the whole universe? Well, here's a clever idea that cosmologists have come up with. They've said, look, if entropy today is what it is, you know, the as a measure of the disorder of the universe, tomorrow the universe's entropy will be greater. Now the symmetric equations of physics, because the universe is isolated in the sense that it has no outside, they say that in the past, yesterday, the entropy of the universe should also have gone greater. So it gets greater into the future from now and greater into the past from now. But what's so special about now? There's nothing special about now. Um we could any moment in time we could apply this same argument. So they say, right, okay, so here's a clever idea. What if we push that special moment in which time is symmetric all the way back to the Big Bang? Then from the Big Bang into the future, yes, entropy is increasing, and that's what we see. Hurrah! What about back? Well, there's no before the Big Bang, so it doesn't even apply, so we don't have to worry about it. So, and and that's called the past hypothesis, and it's it's it's tied in with why our universe started off in a very special state, and it's one of the big outstanding problems in physics. How come our universe started off in this low entropy state? Uh the same as how come it started off in a state that would eventually lead to me giving this lecture to you, because it could have evolved in very different ways. Um but within the universe, nothing is isolated, okay? And within the universe, these time-symmetric equations that we deal with are idealizations, they don't exist because nothing is truly isolated, they are um special cases. What is deeply true is that in our universe there is an arrow of time. It's baked into the universe from the start. So my argument is that time is real and that there is an arrow of time that starts from the Big Bang and points towards the future. And anyone who says time, yes, but time is symmetric, I say no, you are only applied, you can only apply that to isolated systems. And the only isolated system I believe you when you talk about is the entire universe. And if you want a timeless universe, the De Wheelage equation, knock yourself out. Fine, great. I'm talking about things that I can observe, which inevitably have to be within the universe. Okay, so final chapter, very final, just a few minutes. I want to say something. If time is an arrow and it points from the past to the future, then does it have a beginning and does it have an end? You won't be surprised to hear that we're still arguing about this. It could have started at the Big Bang, it might have been around forever, it might end at the end of the universe, it might go on forever. So I just wanted to give you a sample of the options on the table. Did time start at the Big Bang? Well, relativity theory tells us yes. But it turns out general relativity isn't probably the final word on the subject. We there are still more that we can say. Um there's something called eternal inflation. Our universe, our universe may have started at the Big Bang. But that doesn't mean time itself started at the Big Bang. There may have been something bigger, greater, the multiverse. And our universe is just a bubble in one of uh one of an infinite number of parallel universes within the multiverse that is eternally inflating, getting bigger and bigger. And every bubble that appears it forms its own universe within it, and it can never contact any of the other bubble universes. It almost gets to be like metaphysics or religion at this point, because how how do you include this within real science? How do you carry out uh um observations to confirm or refute such an idea? There's the idea of the cyclic universe. Um Nobel Prize winner, Roger Penrose, one of the long-term collaborators of uh Stephen Hawking. Very good friend of mine. I I know him, I know he's 95, I know because he's the same age as my dad. Um and he for many years has been arguing for uh a theory called the cyclic universe, which our unit the universe expands after the Big Bang, reaches some maximum expansion, uh, and then that reaches some point when that becomes mathematically, it's a very clever trick of maths, that becomes then a big bang for another universe. It's not the universe is collapsing and uh expanding and collapsing, that's slightly slightly different. But that our universe is just one epoch in a in an eternal, uh eternalist liking universe. Then there's the equipyrotic universe, the idea that our universe is really uh uh something called a brain, not brain as in brain your head, but as in brain short for membrane, and membranes in higher dimensions collide with each other and they form big bangs. Again, interesting maths, very far from uh uh uh reality, I guess. Mirror universe, the idea that um that's a neat way of explaining what happens to the time pointing backwards from the Big Bang. Maybe there's another universe that's moving into the past, what we would regard as the past, expanding from a Big Bang in the other direction in time. So that means the Big Bang now really is symmetric in time. For us moving forward, they're in the past. For them moving into the past, we're in their past. And it could be a whole nother universe on the mirror on the other side of the Big Bang. Nice, nice ideas, okay? Just suggesting that we but we don't know uh which of them uh is is right. And then finally, is does time come to an end? Does the arrow of time have an ending? Well, here you'd think we might have a better idea because we know what's happened in the past, we know what the universe is like in the present. You surely we should be able to extrapolate into the future and see how the universe is going to end up. If it weren't for a tricky uh uh um notion called dark energy. Dark energy is this mysterious stuff that is causing our universe to expand ever more quickly. And we don't know enough about dark energy to be able to tell us how the universe will evolve in the very, very, very, very distant future. It may end up in what's called the heat death, the big freeze. So basically, the universe will carry on expanding forever and ever, uh, everything getting further and further away from everything else. Stars will die, some will turn into black holes, those black holes will eventually actually evaporate away. You end up with an empty universe of just cold particles and and radiation that's getting ever colder and nothing ever happens. In thermal equilibrium. But that doesn't mean that time stops. Time carries on, it's just that no one's around to see it and uh or even measure any change because nothing is changing anymore. But just because nothing is changing doesn't mean there isn't time continuing. Then there's the big crunch. This is the idea that the universe will reach some maximum expansion. If dark energy for some reason fades away and gravity still manages to win the battle and stop the universe from expanding, gravity is the attractive pull of everything in the universe on everything else, and it will implode in on itself. We could end up with the equivalent of a big bang, but in reverse. Big bang, expand, maximum, come back to a big crunch. But maybe the big crunch is just a big bang for another universe. You end up with a big bounce and and expands, collapses, expands, collapses. Then the worst of all is what's called the big grip. If dark energy turns out, and we don't know for sure, if dark energy turns out to be changing over time uh and actually getting stronger, it's possible, we don't know enough about it, then it's not just going to cause the space between the galaxies to expand, to stretch. Even the space within the galaxies will start to stretch, then the space between the stars and then the space within stars and planets. Things will start being being ripped apart, even matter itself would get ripped apart, and ultimately, even atoms themselves. It's a horrible scenario. Um so I give these ideas because people think, oh, you know, the big freeze, the thermal, the heat death of the universe, that's really depressing. Yeah, well, hey, have you heard the alternatives? I'd I'd much rather have a heat. And the heat death of the universe is gonna like happen in like 10 to a thousand years from now. We have more immediate problems to be worried about as a species than how the universe will end. Uh, and so just wanted to end with uh conclusions. For me, and not all physicists and cosmologists and philosophers will agree with me, but would agree with me, but I say time is real, the arrow of time is fundamental, it's baked into the universe. Um, we may be able to resolve the problems of physical time, reconciling uh quantum mechanics with relativity theory, but we are not there yet. Uh will it help us understand the problems of manifest time, of psychological time? Will it help us understand where the time flows? Uh what why the past is different from the future? Time will tell. Thank you very much.