Brian Cox: The quantum roots of reality

What do snowflakes, glowing street lamps, and Einstein’s “crazy” idea have in common? Physicist Brian Cox unwinds the surprising origins of quantum mechanics—the theory that shattered classical physics and redefined our understanding of reality.

From Kepler’s insight in a 17th-century snowstorm to Planck’s revolutionary leap in 1900, Cox traces how curiosity and confusion gave rise to the most baffling theory in science.

BRIAN COX: I’m Brian Cox. My full title is Professor of Particle Physics at the University of Manchester, Royal Society Professor for Public Engagement in Science, and Visiting Scholar at the Crick Institute. Or you could just call me Brian.

– [Narrator] Quantifying the universe with Brian Cox. Part one, the power of quantum mechanics. What are considered the earliest glimpses of quantum mechanics?

– I mean, quantum mechanics is, I suppose, grew out of an attempt to describe matter, the structure of matter to understand atoms and molecules. Although it’s worth saying that atoms and molecules in the way we conceive of them today were not known to exist, or the structure of them was not known in 1900. That comes a little bit later with the discovery of the atomic nucleus and so on. But the idea that matter is made of smaller things can be traced back, of course, philosophically to the ancient Greeks. But there’s a beautiful book by Johannes Kepler. So Kepler’s probably most famous, I’m sure you’ve heard of the name in the context of the laws of planetary motion, which laid down the foundations on which Newton built his universal law of gravitation. But there’s a beautiful book that Kepler wrote in 1610 called “On the Six-Cornered Snowflake,” which to me really illustrates the genius of Kepler. And it’s a sort of meditation on patterns in nature. So the story, as Kepler told it, he was walking across the Charles Bridge in Prague in a snowstorm, going to a party at his benefactor’s house in the castle. And he realized that he hadn’t bought him a present, he hadn’t brought him a gift, a New Year’s gift. And so he noticed, he started thinking about the snowflakes landing on his arm. And of course, when you look at a snowflake in some detail, you notice that whilst they’re all different, there is a similarity to them. There’s some things, a sameness, a sixness to them, some kind of symmetry that they all exhibit. And so that got Kepler thinking, why would it be that these things, these snowflakes that fall from the sky all share this similar structure? And I find it wonderful that in that book, he essentially says that it must be something to do with the building blocks. There must be some underlying reason why nature has this symmetry. And then he goes on to think about pomegranate seeds, and beehives, and all sorts of things, and hexagons in nature. But really, what you’re glimpsing there, and Kepler said in the translation of the book, in the English translation, there’s this wonderful line at the end where he says, “I’m knocking on the doors of chemistry.” So I’m not sure where that translation comes from, but it’s correct. What he’s noticed is that that symmetry is, he saw that it was something to do with the building blocks. We now know it’s to do with the water molecule, so the shape of the water molecule, H2O. Two hydrogens bonded to an oxygen in a very famous shape, which kind of goes like that, which you can calculate now from quantum mechanics and the way that electrons are arranged around the oxygen and the hydrogen and so on. Of course, he didn’t know any of that. But I think it’s genius really. You see in that book, I strongly recommend it, the genius of Kepler. Quantum mechanics is, it grew out of an attempt to understand some curious experimental findings, which actually at the time weren’t considered to be so problematic. There were questions about the color of light, or the nature of light emitted by atoms. So very famously, for example, sodium vapor. You remember old sodium vapor streetlights, and they glow kind of yellowy orange. And the question was, why? So there’s a color of light from atoms. The origin of quantum mechanics though probably can be traced to Planck’s explanation of the way that hot objects radiate. So, 1900, the late 1890s, 1900, there was a problem with the calculation of how a hot object radiates in terms of the wavelengths of light that it emits and the calculation. Essentially the calculations of the wavelength of the light from hot things were just wrong. And in 1900, Max Planck made a revolutionary proposal. It was, I’ve read in some biographies of Planck that it was essentially a leap of genius, almost inexplicable. But he famously came up with the idea that a hot object only emits light in little packets, which subsequently we came to know as photons following Einstein, but that was much later. So it’s this idea that a glowing thing doesn’t just emit light at all wavelengths and radiate all sorts of light, but it somehow, for some reason, that was not known to him at the time, emits wavelengths, radiation in little packets. And so that was a huge leap. And actually, he didn’t really at the time think that it was, he thought it was a calculational device. But what’s important is that the fundamental constant of nature that we associate with quantum mechanics, now known as Planck’s constant, appears in the calculation. And so very specifically, Planck found he was able to describe the experimental data if he assumed that light is emitted in little packets, and the relationship of the energy of the little packets, the photon as we would now call it, to the frequency of the light is E = hf, where f is the frequency of the light, E is the energy of the packet, and h is this new constant of nature that we now know as Planck’s constant. So I would say that’s the beginning of modern quantum mechanics.

– [Narrator] How did Einstein’s work on the photoelectric effect impact science?

– So when Planck introduced photons, as we would now call them, well, you get the sense that he certainly didn’t believe that this was real, that light, the electromagnetic field really came in little packets. And he thought it was something to do with perhaps the way matter oscillates, like little oscillators, we call them now, harmonic oscillators in the stuff that emits the light. It was something to do with that, kind of a mathematical trick. He didn’t certainly at the time think that what was being implied was that light really can be pictured as a stream of particles with an energy proportional to their frequency. He didn’t think that at all. Einstein in 1905 wrote a very beautiful paper for which he subsequently got the Nobel Prize. This is the same year that he wrote the Special Theory of Relativity, and the very famous paper on Brownian motion. But it’s a theory for which he was most, I suppose, well known at the time. It’s a theory of something called the photoelectric effect. So the photoelectric effect is, again, it’s an experimental observation that if you shine light on a piece of metal, let’s say, some substance, then the light can hit the substance and cause electrons to be emitted from the substance, from the metal. But what was observed was that if the light is too long a wavelength, or too low a frequency, then no matter how bright the light, then you can make it brighter, and brighter, and brighter, and brighter, no electrons are emitted. This is a mystery. If you think of light as just delivering energy to something and just a knot, like a stream of little particles, then it would seem that if you turn the intensity up, brighter light, then you’d supply enough energy to knock the electrons out of the metal. That’s not what happens. So you find that there’s a minimum frequency. Remember the frequency is the color. So it’s almost like saying, if I shine red light on this thing, then no matter how bright the red light is, nothing happens. But if I make the light a little bluer, you get to a point where electrons start coming off. And then that light can be quite dim, but it will still emit electrons. So this was a mystery, it’s called the photoelectric effect. Einstein explained it following Planck by saying that actually you can think of light as a stream of particles, photons, and then if the photons don’t have enough energy to knock the electrons out of the material, then no electrons will emerge. So you could imagine just having one single photon, but if it has enough energy, then it will come in and knock an electron out, and so that’s essentially the photoelectric effect. It’s important because it’s the first time that we get the sense that this so-called quantization of the electromagnetic field, this chopping up of light into little packets is not to do with the way that matter emits light, it’s to do with light itself. The idea it’s going all the way back hundreds of years to pictures that Newton would’ve had of light being a stream of particles that you can really think of these things called photons almost like little bullets that go and hit things and interact with them. So that’s 1905. And it is worth saying actually historically that that was very controversial at the time. You really get a sense when you read the papers at the time that people thought that this was a calculational device, or something to do with matter, and not to do with the electromagnetic field itself, not to do with light itself. And actually, there’s a very famous letter of reference that Planck wrote for Einstein years later. It was in the 1910s, I think. So for six, seven, eight years later, recommending him for a position for an award. And Planck said that Einstein’s belief in the reality of photons should not be held against him, and this is years after the 1905 paper. So it gives you a sense of the intellectual struggle that quantum mechanics and these early ideas of quantum theory caused, the intellectual problems that it caused for people at the time. And I always remind my students of this, when I teach introductory quantum mechanics, one of the key things, it’s not so mathematically difficult, at least in an introductory presentation, but the ideas themselves are profoundly counterintuitive. And that’s why it took, it wasn’t the mathematics really, that’s why it took decades from these early glimpses of quantum theory at the turn of the 20th century for a coherent theory to emerge, arguably in the 1920s. And then you could argue that even today, the interpretation of what theory is telling us about the nature of reality itself is not universally agreed upon.

– [Narrator] How does quantum physics conflict with classical theory?

– One of the big changes actually that’s happened in teaching quantum mechanics in universities over the last few decades is that it was always when I learned it, so it’s back even in the 1990s, it was common to teach it historically. So you go through the things that we’ve talked about, you go through the photoelectric effect, and the structure of atoms. You get to Niels Bohr and his early explanations of how atoms might work, following on from Ernest Rutherford in Manchester detecting the atomic nucleus. And so this idea that an atom is a nucleus, a dense, positive charge. It wasn’t known exactly what the structure was at that time. With the electrons let’s say orbiting in inverted commas around it, so that there’s a picture of almost like a solar system, but it was known that doesn’t work because you have charged particles moving in the vicinity of other charged particles, and that means that they radiate and they would not be stable. And so there’s all these things going on, confusion, and then Bohr suggests that electrons can only take certain energies, which we now call orbitals, around the atomic nucleus, and all this stuff is going on. And it used to be that we would teach it like that in university. But if you do that, you pick up all the confusion. The confusion, decades and decades of confusion that these great physicists felt in trying to come to terms with this counterintuitive picture of the world. So now, I think it’s more common in universities to start with the theory as we understand it today, and just say, “Well, this is the way the world works.” And perhaps the best introduction would be to think of a property of particles called spin. So you might call these things a qubit. So what is a qubit? So you think of a coin which you would toss in the air, and it can be either heads or tails. So that’s a kind of an intuitive picture of the world. This thing is either heads or it is tails. Now, a quantum coin could indeed have the property that it would be heads or tails. But the difference between quantum mechanics and classical theory is that an object like a coin, a quantum coin can also be in what we call a super position of heads and tails. So that means that it can be in a state where it is, let’s say, if we observe the thing, we’ll talk about that a bit later, but it can be in a state where it could be 30% heads and 70% tails, or 40% heads and 60% tails, or any combination, any mixture of heads and tails. And that is a perfectly legitimate description of the state of the configuration of this thing. Just to give you a sense of a real physical object that would behave that way. Particles like electrons, for example, have a property called spin, which can be up or down, it’s like heads and tails. But that’s the key thing that objects like electrons can not only have definite values of some property, some thing that you can measure, but they can be in a mixture of those things. And it’s not a probability theory in the sense that we would usually think of probability theories. So usually we’d say, well, there’s a 50% chance it’s gonna rain tomorrow. Why do we say that? Why would we say such a thing? It’s because we have incomplete knowledge of the system, in this case, of the weather, and so we have incomplete understanding of where, I suppose at the most basic level, all those water molecules are in the clouds and so on. But we don’t have enough knowledge to make, to precisely calculate what is going to happen, and so we assign probabilities to it, which that reflects our ignorance of the situation. The key difference in quantum theory is that these probabilities are fundamental. They are fundamental to the description of nature. So it is not the case that if we have an electron in some kind of configuration, then our theory predicts probabilities because we don’t quite know exactly how this thing is configured. The probabilities are intrinsic to theory itself. And pretty much all of the intellectual challenges and the confusion around quantum mechanics comes from that very simple property.

– [Narrator] What is the double slit experiment?

– If you look at pretty much any book on quantum mechanics, there is one experiment which you can describe. It’s a very simple experiment which encapsulates all the, I was gonna say weirdness, but let’s say all the properties of the quantum world. It’s called the double slit experiment. And by the way, I’ll strongly recommend, I think it’s almost universally accepted, the best description of the double slit experiment is freely available. It’s in the Feynman Lectures, volume three, first chapter. And I’ve read quantum mechanics textbooks that say, “Go away and read the first two chapters of the Feynman Lectures on physics volume three,” ’cause it’s all in there, can’t be done any better. So I could recommend that if you find this interesting. The double split experiments is essentially, let’s say you have something that will emit let’s say electrons, so particles, electrons. Electron gun that emits particles. And then you have the barrier that has two slits cut in it and a screen. So that’s the setup of the experiment. So we have something that emits electrons, two slits cuts in a screen, and a detector, another screen that the electrons will hit. So you fire the electrons out. So what will that look like? Well, if you think of the electrons as just little particles, little bullets, let’s say, that are emitted from this gun, then you would imagine that the electrons can go through one slit or the other one, depending on how they come out, and you can imagine that they might get deflected around a little bit when they go through the slits. But basically on the screen you would expect most of the electrons to appear opposite one or the other of the slits, with maybe a bit of a spread ’cause they rattle around a bit when they go through. So you get lots here, lots here, and pretty much none in the middle. But that’s not what you see. What you see is a very clear pattern on the screen. You see sort of stripes, a stripe on the screen where you get lots of electrons, and then a stripe where you get very few or none, and then another stripe where you get lots, and then a stripe where you get very few or none, and then another stripe, and then very few or none. So you get this stripy pattern. That pattern is exactly the same pattern that you would get if you sent waves through the slits. Let’s say water waves, any kind of waves. Then it’s easy to understand because what’s happening then, and this follow, physicist knew this back in the 1700s, right, is that you can consider each slit as a source of new waves, and the waves come out, and waves have the property that they can interfere with each other. So you can get the peak of one wave arriving at the screen from one slit, and a trough of a wave arriving at the screen from another slit. And if everything’s lined up correctly, the peak and the trough cancel out and you get nothing. So you get this property where something from each slit, it’s very easy to understand if it’s a big extended wavy thing, lines up in such a way that it cancels out, and then it could line up in such a way that it reinforces and you get a big disturbance there, and then it cancels out again, and then it reinforces again. So you can imagine this stripey pattern on the screen, that’s what you get with waves. The fact that you get it from particles is interesting, but here’s another interesting thing, you still get that pattern if you send one particle at a time through the slits. So it is, and let me use my language carefully, I was gonna say it is as if the electron can somehow explore both paths, just like a wave can, and then interfere with itself to control where it lands on the screen. As if is something that people might object to. Many physicists would say, no, it does. So the statement is that the electron explores both routes at the same time, at once, let’s say, on its root from the electron gun through the slits to the screen. So that’s a very strange picture of reality. We surely think of particles as following definite paths, and it might be that you don’t know quite which path it’s gonna take, but surely you would say, in reality it will go one route or the other route. But that experiment, which I emphasize has been done now many times, tells us that nature is not like that. It tells us that the electron must, in some sense, explore all routes on the way from the gun to the screen. And so the question then becomes, well, what do I mean by in some sense? What you’ll see in the Feynman Lectures is he gives you two pictures of how to think about physics. One is he gives you the way that you would calculate what you’re gonna see on the screen, and that’s really simple as Feynman points out. So what you can do is you can, you can assign, calculate what’s called a complex number for every route that the particle, the electron can take from gun through the slits to the screen. So every route, every path that you can possibly take. A complex number, for those that don’t know about complex numbers, can be pictured as a little clock face. So a complex number has a clock hand, there’s a length of the clock hand, and there’s the time on the clock face. And you can calculate how those clock faces kind of evolve and change and spin around from the moment the electron’s emitted to the moment it hits the screen. And the prescription is very simple. You can calculate what those clock faces look like, what those complex numbers are, and every point on the screen, you have to take them all, every possible path to that point and just add them up. And the length of the clock hand gives you the probability to find the electron there. It’s actually the squared length of the clock hand, but whatever, it’s the length of the hand, that’s it. So you can see that you have this property, you can have interference, you can have one clock arriving at 12 o’clock, and one clock arriving at six o’clock, and they cancel out and so on. You just do that, you calculate it, and you get the right answer. So it’s a very, very simple prescription. But I suppose the problem comes when you say, well, what does it mean? Does it really mean? Is it just calculational? Is this just mathematics? Or does it really mean that the electron explores every possible route? And by that, I mean every possible route. You might consider it going to the Andromeda galaxy and back, right? Every possible route on its journey from when it’s emitted to when it’s detected. And I think many physicists now would say that that is a correct description of reality, the particle does. But I just wanted to emphasize that the mathematics, the way that you make the calculation is pretty simple. It’s a prescription for making a calculation, and you get the right answer to the experiment. The problem with quantum mechanics, I suppose, is when you try to interpret what the calculation means for the nature of reality. I think it’s important to say that there aren’t different rules of the game in the subatomic world and the world that we observe, this world of common sense, let’s say, that we perceive. There aren’t different rules. And it’s pretty well understood, I would say it’s well understood how the world that we see emerges from this rather strange but well-defined behavior that we see in the subatomic world. And it’s not only the subatomic world, by the way, this is now, maybe you could have argued 50 years ago that this is just all philosophy, it doesn’t really matter, whatever. But now we have an increasing number of quantum technologies that are really based on this behavior, quantum computers being a good example. And so you see that this is not just something that you can say, well, we don’t need to think about it really because it’s in the world of atoms and it’s all a bit whatever, and we can just do some calculations. Because we’re using that behavior now in technologies, and so it really does become an important theory to try to understand.

– [Narrator] Why is it important that we seek to solve the mysteries of quantum physics?

– Now, you go back a few decades then I think you could say that the interpretations of quantum mechanics are very interesting and very important, because we’re talking about the nature of reality. But you might say, well, it doesn’t really matter so much practically, right? Now, I have a lot of colleagues in physics who would I think rightly hate that description, because what we’re trying to do is understand reality, what physics is. But now, particularly I think with the possibility of building quantum computers, this attempt to understand how large systems of quantum mechanical objects behave is becoming extremely important, because a quantum computer is a device which is built out of qubits. So remember a qubit, an example would be an electron, which has this property that when you make an observation of the spin, let’s say, of this electron, it behaves like a coin. It can be up or down, heads or tails, however you wanna describe it. But that thing can also exist in a super position, a combination of these things, and it’s a perfectly valid configuration. And you use that, that’s the kind of property that you use in building a quantum computer. You can also then ask the question, well, what happens if I get another one, two electrons together? These can be in what’s called an tangled state. So then you have a much richer structure of this physical system. So an example of an entangled state, a very famous thing called a Bell state would be where you set these things up, so the system of these two qubits. Let’s say they’re up and down these spins, right? So I can have the state up, down, plus, down, up, like that. A complete description of this state, up, down, plus, down, up. What does that mean? So let’s say I take one of these electrons and I separate them. So a very famous paper written by Einstein, Podolsky and Rosen that first considered this in the 1930s, and they get very upset by the behavior. So we’ve got a system, a state, and it’s up, down, plus, down, up, let’s say. And I separate these electrons. I take one to let’s say to Pluto and leave one on planet Earth, right? And then, so what’s the description of this thing in that state? Well, it’s got, and the way I described it, there’s a 50/50 chance that when I make a measurement of this electron the up or downness of it, then there’s a 50/50 chance it’ll be either up or down, and the same for the other one. That’s what that state means. But if it’s up, down, plus, down, up, then it means that if I make a measurement of that one, if I say, well, okay, I know what that is, it’s up, the other one has to be down. Up, down, or down, up. It can’t be up as well. Same for the other one. If I go to Pluto and have a look at this one and it’s down, then this one definitely is up, right? So this is called quantum entanglement. And the reason it bothered Einstein and others is it would appear that something is instantaneously changing, and it’s not just your knowledge of the system that’s instantaneously changing, it would seem that the system itself is instantly configuring itself when you make some measurement. So you might say, well, this is nonsense, there must be something else, and it turns out that as far as we can tell that, and a Nobel Prize was awarded for some of this research a few years ago, then no, there’s nothing hidden there. This is the way that the system is. But you think about that system of two qubits, right? Think about it. So there are, you’ve got these two things, which can be up or down. There are four possible combinations of that system. You can have up, down, down, up, up, up, or down, down. Four for the two qubit system. For a three qubit system, you think about it, ups and downs, you’ll find out there are eight possible combinations, and all mixtures of them. For four qubits, then it’s two to the power four, there’s 16 possible combinations. We are talking about building quantum computers now in which we have 100, 200, 300 qubits all in principle entangled together. The number of possible descriptions of that system then, you have numbers that describe it, there are 100. It’s two to the power 100 different configurations, and any mixture of those things that are states of the system. So pretty soon, two to the power 100 for 100 qubits, what’s the number of atoms in the universe? If you had two to the 500, you’d far exceed 500 qubits. The number of numbers you need to describe that system exceeds the number of atoms in the observable universe. But it’s a thing that we can build. We can build just about, we’re not far off being able to conceive at least of a network of 500 qubits. They’re physical things. They’re kind of like that big, some of them, right? You have 500 of them in this room. So the power that’s hidden in the description of a system like that is immense. And the thing that a quantum computer does is it uses that power, some of that power, some of that vast computational or configurational power of the thing. Very, very difficult to do, and we’ve been able to do it particularly well at the moment. You’ll read many papers online where obviously companies like Google, Microsoft, IBM are investing a lot of money in these devices, because potentially they are, they can carry out computations that no conceivable classical computer could make within the lifetime of the universe, because of this tremendous freedom in the description of the structure of the system. So quantum mechanics and quantum entanglement, these properties of matter, of nature are becoming very real, because we’re beginning to be able to access this tremendously complicated configuration space to do useful things, to make calculations that are useful to us.

– [Narrator] Part two, the fundamental measurements of nature. What are the properties of nature that define how the universe works?

– When we think about the size of things, of course we tend to think of the size of things with reference to ourselves, I mean, even the units of measurement that we’re familiar with. So, you know, the foot, or the meter, or those things, or the inch, or the centimeter, what are those things? Ultimately, historically they’re based on properties of the human body, so they’re based on biology really. So a meter might be, you know, the length of this kind of length, and a foot is kind of that kind of length, and that’s what we did historically, ’cause why would you do anything else? But of course, the history of physics tells us, as we go into the 17th century, 18th century, 19th century, 20th century, we then begin to understand that there are things that are much bigger than us and much smaller than us. And so is the meter, for example, which is based on a property of the length of my arm, or the length of my foot or whatever it is, is that really, is that fundamental? Is that something that tells us something deep about the structure of nature? Well, the answer is no. It tells us about something, it tells us about biology on earth, and how we’ve evolved on this planet, and how big cells are ultimately, I suppose, and how many cells you need to make an intelligent multicellular being like a human, based on the fact that we live on this planet with this particular gravitational force and all those things. So it tells you about all that stuff. But it doesn’t tell you anything profound or deep about the deep structure of the universe. And so Max Planck, so of Planck’s constant fame and quantum mechanics fame, came up with a system of units, right? So a way of saying, well, what are the fundamental quantities as far as we can tell that really tell us something about the structure of nature? We’re looking, I suppose, for units of measurement that we could, you could imagine if we met some aliens from some different civilization that they might be, they might not even have arms, right, or feet, but they might be very different in size and scale from us. So, what would the common language be? Is there some units of measurement that we could all agree on? And so Planck thought about that. So what are the fundamental constants of nature as we understand them? So, things that really tell us about the underlying structure of the universe. So one would be the speed of light. So the speed of light that would be, although we can talk about what it is in meters per second, or miles per hour, or whatever it is, it is a property of the universe. Everything that is massless travels at the speed of light, this speed, whatever it is. And if you have any mass at all, you cannot travel, you cannot accelerate to this speed, a universal speed limit. So it’s something deep about the property of the universe. It’s to do with perhaps the geometry of space time, or we don’t know where it comes from the particular number, but there it is, the speed of light. Another one would be the strength of the gravitational force. So what is the force between two objects of a particular mass? Or in Einstein’s theory, a deeper description, how does a particular amount of matter or energy distort the fabric of the universe? The number that tells you about that is Newton’s gravitational constant, which was first measured back in the 1780s, 1790s. So it’s the strength of gravity, that’s another one. And then there’s Planck’s constant itself. So you can say this is associated with quantum theory, what is it? So you read many different textbooks, you’ll find many different ways in. You could say, for example, that there’s a fundamental limit on how accurately we can know the position of a particle and the momentum of a particle. You can’t know them both with absolute precision. There’s a fundamental limit, and it’s around about Planck’s constant. So the uncertainty on the measurement of the position of something multiplied by the uncertainty on the measurement of the momentum of something is always has to be greater than Planck’s constant. So it’s a fundamental property of the universe. And there are different ways of thinking about it. Planck first introduced it in the context of the frequency or the wavelength of light emitted from hot objects. Photons, what’s the energy of a photon? A packet of light. It’s Planck’s constant multiplied by the frequency. So it’s a deep property of nature. Those three numbers, those three things, speed of light, strength of gravity, and Planck constant allow you to define some distances, a particular distance called the Planck length. I want to do it by reading it off something, because I don’t carry all these numbers around in my head. It would be pointless to do that ’cause you can look them up. So I could take Planck’s constant, multiply it by the strength of gravity, and divide it by the cube of the speed of light, and then take the square root of the whole thing. So it’s hG divided by C cubed, square root. You’ll find that that has, if you put those things in in terms of meters and kilograms and things, you’ll find that has, it’s a length, it has the dimensions of meters, and it’s a tiny length. It’s about 10 to the minus 35 meters, point nought, nought, nought, nought, nought, nought, with 35 noughts one of a meter. But that is a length that we’ve calculated by measuring the strength of gravity, the speed of light and Planck’s constant. So it would seem that that should be, it should have something to do with the deep structure of the universe and indeed it does. How important is it? Well, let me give you some examples of the Planck length. So it turns out that if you ask a question, how much information in bits is stored inside a black hole, right? That would seem to have, what’s that gotta do with all this, right? How much? It turns out in a calculation that was done by Jacob Bekenstein in the 1970s, it turns out that the entropy of a black hole, which is the amount of information hidden within it, is equal to the surface area of the event horizon of a black hole in square Planck lengths. That’s astonishing result. But just think about that for a moment. It’s telling us that the amount of information stored in a region of space, in this case a black hole, is equal to the surface area surrounding that region in square Planck lengths. That’s a bizarre result. So it does seem that the Planck length is fundamentally important. And here’s another property of the Planck length. So let’s say we want to make an observation of some very small thing. So how do you observe something that’s very small? Well, one way to do it is shine a light on it to see where it is, right, to get it. That’s the way that we observe things with our eyes. So you might say, well, it’s tiny, so I have to shine light with a very small wavelength onto this thing to see the tiny thing. The wavelength can’t be bigger than the tiny thing, otherwise you won’t see it. So the smaller this thing is, the smaller the wavelength of the light that I’ve gotta shine on it. But remember, quantum mechanics tells us that the smaller the wavelength of the light, the higher the energy of the photons. So I have to start bombarding this thing with higher energy photons to see it. What happens if you try to approach something that’s a Planck length? You get so much energy in there that what you do is you form a black hole, and then you put more energy in, you try to see what’s going on and the black hole grows. And so you get to a point which is around the Planck length in size where you can’t, in principle, try to resolve the structure of this thing. It starts to go bigger again because you make a bigger and bigger black hole and it grow. So the Planck length does seem to be, I would say is a fundamental property of the universe. And now, the nature of that thing, so if we talk in terms of black holes, then you have these kind of Planck sized pixels, in some sense, tiling the event horizon. Does that mean that these are building blocks of space, that size? It would seem so, but this is where we get to, we’re at the edge of our current understanding. I think it is legitimate to make the argument that given what we know about the universe, given the measurement we make at the strength of gravity, the measurement we make of Planck’s constant, and the measurement we make at the speed of light, then there is something fundamental about this very tiny length, 10 to minus 35 meters. Just one caveat though, one caveat. Is it important that number, 10 to minus 35 meters? There are theories, and we test these theories at places like the Large Hadron Collider, for example. There are theories where, as an example, there are extra dimensions in the universe. So not only the four dimensional space time of Einstein’s theory, but more dimensions. And the dimensions can be curled up at little places in points, or they can be big extended sheets, and there are all different configurations. If there are extra dimensions in the universe, then you find that you can, let’s say that they would, that you could see those extra dimensions, energies just around the energies that we collide particles at the Large Hadron Collider, then the explanation for why gravity is so weak, so our measurement of Newton’s gravitational constant would change at those higher energies. It might mean that this Planck scale would drop, and so the Planck length would expand, and we’d see this kind of physics, much lower energies than we might otherwise have anticipated. So I think it’s worth a caveat that the Planck length itself does seem to be a fundamental property of the universe, but actually, what it is, is a measurement. And at the moment our measurement is given what we measure, then it’s 10 to minus 35 meters. But you could imagine configurations of the universe where it’s rather bigger than that.

– [Narrator] What kind of insights does the Planck scale reveal?

– Now the Planck length, this unimaginably small number in meters, you might say, well, how does that affect our everyday lives, right? Does it come into any calculation of a thing that we can conceive of? And there is a beautiful calculation, it’s one of my favorite calculations in all of physics that was initially done by the great mathematical physicist Chandrasekhar back in the 1930s. And it’s a stunning calculation. It’s about the mass of white dwarf stars. So let’s think about a white dwarf star, what is that? So what is a star, first of all? So a star is some material, it’s mainly hydrogen and helium collapsing under its own gravity. So gravity is trying to squash this thing down. What hold it up? Well, as the star contracts, as it forms, our sun formed around four and a half billion years ago through this process, the gravitational collapse, that means the core heats up, and it heats up, which means that the hydrogen and the helium is wriggling around very fast, and ultimately you switch on nuclear fusion reactions in the core. And the fusion reactions, in the case of our sun, hydrogen is fused into helium, that releases energy, which creates a pressure, which holds the star up. So the star’s a balancing act. Gravity is trying to squash, it heats the core up, fusion reactions, release energy, creates a pressure, holds it up. But of course, that doesn’t exist, it can’t carry on forever, because the star doesn’t have an infinite amount of fuel in its core. And so ultimately, will run out of fuel and it will begin to collapse again, and then stars will start to fuse heavy elements and so on. But ultimately, you could ask the question, well, when there’s no more nuclear fusion can occur in the core, what happens to the star? Does it just collapse without limit? Which would be a black hole, as we now understand it. Or is there something else that can hold it up, some other property of matter? This wonderful calculation is a calculation about what happens to electrons in a collapsing star. So it’s a genuine quantum mechanical calculation. So what happens? One of the properties of the universe, one of the fundamental ideas in quantum mechanics is called the uncertainty principle. Heisenberg’s uncertainty principle. So it says that if you try to confine an electron into a smaller and smaller box, which means you’re trying to measure its position, but you’re trying to confine it and squash it down, then the product of the size of the box, the uncertainty in the position multiplied by the uncertainty and the momentum of this thing has to be greater than Planck’s constant, fundamental property of the universe. So as you try to, this star’s collapsing and all the electrons are getting pushed together and closer and closer together. They try to avoid each other, which is another fundamental property of quantum mechanics called the exclusion principle, which roughly speaking says they don’t like to be in the same place roughly. And so you start to squash ’em, they try to get away from each other. They go into little boxes in the star, and the boxes are shrinking, and so the electrons are getting confined, and so they jiggle faster. The uncertainty on their momentum is faster and faster, and so they start to jiggle around, ’cause they’re getting squashed into each other and trying to stay away from each other. So this is pure quantum mechanics, the uncertainty principle, the Pauli exclusion principle jiggling around. That jiggling is like a temperature in the sense it creates a pressure which can hold the star up. So you could ask, you could do the calculation, but what happens as I squash this down and the electron starts to jiggle more, they make the pressure, they hold the star up. What happens if that jiggling starts to bump into relativity? What happens if it starts to go towards the speed of light? They can’t jiggle any faster. And so ultimately, there must be a limit on the pressure that these electrons in this quantum mechanical process can exert to hold this thing up. So you can do the calculation, and it’s done. I did it in a book called “The Quantum Universe.” There’s a gratuitous bit of advertising. It’s in the appendix, so you can do it. It’s not a hard calculation. Some details are difficult, and Chandrasekhar did this magnificent calculation. If you do that calculation, you find that the maximum mass of a star, which is just a lump of matter held up by this process is 1.4 times the mass of our sun. So it’s astonishing calculation. How does that relate to the fundamental properties of the universe? ‘Cause all we’ve used there, we’ve used quantum mechanics and we’ve used the strength of gravity, those are the things. These are the things, Planck’s constant, the speed of light, Newton’s gravitational constant, those are the things we used when we looked at the Planck units, like the Planck length. So you can use those things, strength of gravity, speed of light, Planck’s constant to construct a mass. It’s called the Planck mass, and it’s rather big actually. So whereas the Planck length is very, very tiny, the Planck mass is about the mass of a grain of dust, a mote of dust. It’s quite a large thing. But you can calculate it, fundamental prophecy of the universe using Newton’s gravitational constant, speed of light, Planck’s constant, comes into that calculation. Turns out when you do the calculation that roughly speaking, that number, the Chandrasekhar limit is the Planck mass cubed divided by the proton mass squared. That’s what it is. You do that calculation, put the numbers in, it’s about 1.4 times the mass of the Sun. But I find it profoundly important. It’s a beautiful, beautiful result, because what we’re saying is that you can calculate the maximum mass of a load of stuff that can hold itself up through this quantum mechanical process. And it just depends on these fundamental properties of the universe, strength of gravity, Planck’s constant, speed of light, that’s it. So it’s a very, very beautiful calculation, but it’s the best example I know of the relationship between these rather abstract quantities perhaps and something that you can look at in a telescope. It’s a beautiful piece of physics.

– [Narrator] How does our comprehension of scale break down?

– So we have this fundamental, it appears, length scale in the universe, 10 to minus 35 meters, a Planck length, unimaginably small. How could you picture that? Well, take a proton. So a proton is pretty unimaginably small, I think, to most people, although it’s pretty big in particle physics terms. We have maps of the interior of the proton, the constituents of the proton that we use in particle physics experiments. It’s kind of a big world, a proton. But if you take a proton and expand it to the size of our solar system, so imagine that, the nucleus of a hydrogen atom, and you imagine expanding that to the size of our solar system, out to the orbit of Neptune, then something that’s the Planck length would extend or expand to let’s say a virus or a living cell. So the ratio in size between the Planck length and a cell, which we can just about under a microscope, is the same ratio as a proton to the solar system. So it’s unimaginably small. So we can just about conceive of the size of a living cell, and then where does our picture of the universe start to break down? Of course the things we can really get a feel for are things that are around, let’s say, a few inches, a few centimeters, to a few meters, or maybe if you’re a runner, you get a sense of what a few miles means. But I think it’s quite difficult to even picture. I suppose 100 miles you can picture, ’cause you can take a train ride, or a few thousand miles you can picture because you can get on an aircraft and fly across the Atlantic. So we have a kind of a picture of that. But when you get much bigger than that, we don’t experience those distances anymore. So I would say that when we start to talk about distances that are much larger than distances that we might travel on the surface of the earth, then I think our feel for those distances begins to break down. Maybe if you spoke to to Buzz Aldrin, then he would have a feel for the distance a quarter of a million miles because he’s flown it, right, to the Moon. So maybe the Earth to the Moon. But then when you start to talk about the distance to the planets or the distance to the Sun, the so-called astronomical unit, 93 million miles, what does 93 million miles mean? I mean, I suppose you could get a feel for that by looking at the Sun in the sky. Not directly, I’ll say. Don’t look at the Sun. But you know what I mean? We know kind of at the sunset, let’s say, when you see that disc of the Sun. And so you can see it’s the same size. It’s very easy to do safely actually, because it’s the same size on the sky as the Moon, so look at the Moon. The Moon is the same radius on the sky as the Sun. You know that because of total solar eclipses. It is a coincidence based on the way that our solar system has evolved, but it’s a nice coincidence. So we can perhaps conceive of what the Sun looks like on the sky 93 million miles away. You can fit a million Earths inside the Sun, so how do we conceive of that? The radius is something like 100 times the radius of the Earth. That means that if you got in a passenger aircraft, and so we have a feel for that, you can fly from London to New York, you know, how long that is, a few thousand miles. What does that diameter of the Sun mean? Well, it’d take something like months, I think something like a year to fly around the sun in a passenger aircraft. It becomes inconceivable. And the Sun’s quite a small star. So then we start to think of bigger distances. So the most distant object that we created, we built, the Voyager 1 spacecraft is now well over 150 astronomical units from the Earth, 150 times the distance from the Earth to the Sun. What does that mean? It takes light over 22 hours to reach it, so a signal at the speed of light. And that’s just about, by some definition, the edge of our solar system. Although actually, if you talk in terms of these icy objects in what’s called the Kuiper belt and the Oort Cloud, it’s really not the edge of our solar system at all. We think that that extends maybe a light year out into the universe, the radius of the Sun’s influence, if you like, a light year. So 22 hours, it’s about a day for light to go to the most distant object we are in communication with, which has been flying since the 1970s, right, on its way out. One day, a light day basically. And then we have 365 times that, a light year, which is to the frozen edge of the Sun’s influence, the edge of the Oort Cloud. Four times further than that, you get to the nearest star, the Proximus Centura, the Alpha Centauri system. That’s about four light years away or so. So that’s inconceivable. Light traveling 186,000 miles a second, 186,000 miles a second, four years to the nearest star. And then you start to talk about the, well, a galaxy then, the Milky Way galaxy. We’re all in orbit around the center of the Milky Way galaxy. How big is this collection of stars? Somewhere between 200 and 400 billion suns in the Milky Way galaxy, about 100 thousand light years across. And that’s a fairly typical size for a large galaxy. One galaxy, one island of stars, 100 thousand years for light to cross it at 186,000 miles per second. And then you say, well, what about the nearest galaxy? So you go outside on a clear night where there’s no moon and it’s dark, away from the city lights, and if you know where to look, you can just about see our nearest neighboring large galaxy. It’s called the Andromeda galaxy. It’s a bit bigger than the Milky Way, but give or take, let’s say 100,000 light years across or so. Maybe double the number of stars we think in the Andromeda galaxy. That galaxy is two and a half million light years away. It means that the light, it’s worth looking at, it’s a beautiful thing to look at, ’cause it means the light entering your eye began its journey before we had evolved on Earth. Took two and a half million years to reach us. But you can see it with the naked eye because it’s so big. It’s very faint. You can certainly see it with binoculars, but it’s about the diameter of a full moon on the sky, and that’s two and a half million light years away, because it’s a big thing. And then you start to say, well, what about the other galaxies? So we’ve measured galaxies now out to close to the edge of the observable universe with instruments like the James Webb Space Telescope, from which the light has journeyed for over 13 billion years to reach us, 13,000 million years to reach us. And the universe has been expanding in that time. So now you say, where are those galaxies? Where’s the most distant thing you can see? So the most distant thing you can see in the universe that we can detect light from is called the cosmic microwave background radiation. So the cosmic microwave background radiation is light that was emitted 380,000 years after the Big Bang. So that’s been traveling for 13.8 billion years or so across the universe to reach us. But then if you ask the question, where is that place now? The place that emitted that photon from the cosmic microwave background radiation, that came across the universe for 13.8 billion years into our detectors, where is it now? ‘Cause the universe has been expanding. You get an answer, which is something like 46 billion light years away now, 46 billion. And even that, so you might say, well, the universe is then, the radius of the universe is, what, 92 billion light years or so. It isn’t because we know, we know that there’s more universe beyond that. That’s just as far as we can see. The universe, for all we know, and given the accuracy of our measurements at the moment might be infinite in extent, so, and that genuinely is inconceivable. But of course, 46 billion light years is inconceivable. 1 billion light years is inconceivable. I would argue that one light year is inconceivable.

– [Narrator] Part three, the frontiers of the future. What opportunities might space colonization offer?

– I think we’re at the frontier of a very exciting time in our history as a civilization, because we are now, I think, on the verge of becoming a space fairing civilization, in the truest sense of the word, let’s say a multi-planetary civilization. So there’s been a revolution in engineering in the last 10 years or so, the last decade, because now we have reusable rockets. So SpaceX, now Blue Origin, have reusable rockets, which means that access to earth orbit is cheap, or at least cheaper than it’s ever been before. So we are industrializing the space above our heads just a few hundred miles above our heads at an ever increasing rate. Of course, it’s been very important to us for many years, decades in fact. So satellite navigation, communications, weather forecasting, earth observation, climate observation, and so on. The observation of Earth from Earth orbit has been part of our lives, whether we think about it or not, for quite some time. But now, because we have the technology to access it cheaply, I think we are seeing a revolution. And so it will not be long before there isn’t just one crude space station in orbit, which is the International Space Station, there will be multiple space stations in orbit. There’ll be scientific research at a much higher level in orbit, commercial scientific research. There’ll of course be space tourism. There’s an increasing demand on communications, for example. So the Starlink satellites, hundreds and hundreds of them up there. There’ll be multiple competing constellations of satellites that allow us to make phone calls and access high speed internet from any points on the earth. And so that process is accelerating and it is going to accelerate further. So, what does that mean? So there’s a tremendous opportunity. It’s incredibly exciting. Before we start thinking, by the way, about going out to the asteroids and mining them, and building cities on Mars, and building cities on the Moon and so on. But let’s just talk about Earth orbit first. It’s tremendously exciting, huge opportunity. But of course, when you start to move outwards to a new frontier, then the frontier can become crowded. You can have competition for the real estate. You can, you need some way of managing conflicts between, by which I mean conflict, physical conflicts between the satellites. What happens if someone’s satellite comes close to another satellite? How do you manage that? Do you allocate particular orbits? Or do you say that we’re gonna have some framework like air traffic control, where you have an avoidance system that everybody agrees on, whereas if two things come close, they avoid each other. That framework is not yet there. I attended several meetings and conferences where there are, of course, many countries and international bodies that are trying to work on the management of space. I find that it’s a challenge, because, of course, it’s always a challenge when different countries and different commercial interests and so on are trying to flesh out agreements about how you manage a frontier. But ultimately, I find it exciting, because what it means is we are now at the stage where, as the great Carl Sagan said, we’re beginning to take our first steps out into the cosmic ocean. And I always remember, and he said, “The water seems inviting.” So it’s a tremendous opportunity. But what kind of opportunities are gonna open up? Well, we know, for example, so already from our experience on the International Space Station that sort of development of new drugs, for example, or development of new ways of building semiconductors, for example, silicon wafers and so on. Lots of experiments have been done that suggests that there might be an advantage to on orbit manufacturing. So it’s in a microgravity environment of certain things, growing crystals and so on, which might be useful. And so as we begin to get more experience operating in microgravity, we begin to see that there are applications for particularly material science and biosciences. But beyond that, so when we start to move outwards beyond near Earth orbit and build the infrastructure that we need close to the planet to begin to move further out into space, then opportunities begin to open up that I find tremendously exciting. So one, a very well-known example would be mining asteroids. So one could argue, there are people that argue that one of the biggest problems we face and have faced historically on Earth is competition for resources. So not only just the pure competition, which leads to conflict and war, if you think those resources are limited, which they are on Earth, but also just the stress of course, that you put on the Earth itself, on the environment as our civilization grows and requires access to more resources. It damages the planet, it creates conflict and so on. But if you have the infrastructure to begin to move outwards, for example, to the near Earth asteroids, then what you find is that resources are no longer limited in any reasonable sense. There are vast amounts of resources out there in space that we will have access to within the next decade or so, or certainly few decades. So that begins to transform the way that we think about our civilization, the way that we think about expanding our civilization, increasing the capability of our civilization and so on, I think. So I think there’s a tremendous opportunity there to grow our civilization crucially, without further damaging the planet that most of us will live on for the foreseeable future. And that’s why, for me, I’m ultimately optimistic about those steps that we are making into space. I mean, I would not have imagined, I think, if you went back 20 years that we would be, we would have so many rockets flying, and coming back to the Earth again, and then flying again. Perhaps within my lifetime, but certainly at this point in the 21st century. So I think it’s exciting, but the challenges, as with all new technologies, and you could extend this debate, by the way, to artificial intelligence, or quantum computing, as well as space flight. The challenges come when we try to build the regulatory framework, and you need a regulatory framework. One of the things I think we are very bad at on planet Earth is recognizing that we all live on planet Earth. So we’re all on the same spacecraft, let’s say, making our way on our journey around the Sun. And ultimately, challenges about the management of space, or the management of artificial intelligence, or the management of the power of potentially quantum computers, I think ultimately are global challenges. And we are very bad historically at facing global challenges together. So that would be my worry. And of course, just to say how you think about space, so it’s literally, it’s only a few hundred miles that way. Up there now, there are satellites whizzing around, other than the geostationary ones, like the International Space Station would be a good idea. It’s in a country’s airspace for a matter of seconds, right? So clearly, you need to develop some way of managing that environment, which is a way which involves international collaboration, because the environment, the objects that are up there doing all the jobs that we want them to do don’t stay in any one country’s airspace for more than a few seconds or minutes. And so it’s kind of obvious to me that we need a framework to manage that.

– [Narrator] How can humanity influence the universe?

– When we contemplate the size and the scale of the universe and our place within it, which you’re forced to do when you think about the distance scales and the sheer size and age of the universe, then I think it’s very natural for us to tend to come to the conclusion that we don’t matter at all. And it is true in some sense, just physically what are we? We’re little specks of just a collection of atoms on one mote of dust, orbiting around one little star in 400 billion stars in one galaxy, amongst 2 trillion galaxies, in a small patch of a potentially infinite universe. So clearly it is true, we are physically insignificant. So I’ve tended in the past to focus arguments or think about arguments of our value in the context of what does it mean to live these finite fragile lives in this infinite universe? And I could make a strong argument, and have many times that notwithstanding our physical insignificance, we may be remarkably valuable because the number of civilizations on the average in a particular galaxy, any given galaxy might be less than one on the average. Many galaxies may not even have civilizations in them. If that is the case, and that, it’s speculative, but if it’s the case, then we would be remarkably valuable, not withstanding our physical insignificance, because we would be perhaps the only place in the Milky Way galaxy where collections of atoms have come together that can think, and do science, and have conversations like this, in a very real sense, bring meaning to an otherwise meaningless galaxy. So that has been my position for some time. I think it’s a good working hypothesis, by the way, as an aside. If you think that, I think Carl Sagan said it many years ago, in some sense, if that’s the case, we have a responsibility to the cosmos itself because, you know, we’re a product of 13.8 billion years of cosmic evolution, but we might be a very rare and special product. But we might only be here, we’ll only be here for a small amount of time. The Sun will only be here for a small amount of time in cosmic timescales and so on. So I’ve tended to make that argument. But one of the great joys about reading other people’s views about essentially being a scientist is that you can come across a point of view and you think, I hadn’t thought of that. I might change my mind given that, that wonderful piece of thought. And I found, it happened to me recently. I was reading a book, it’s a very old book now by David Deutsch, who is one of the greats, one of the founders of quantum computing. So he really is a physicist and a thinker worth paying attention to. And he made a point, which I had heard before actually in a book called “The Anthropic Cosmological Principle” by John Barrow and Frank Tipler, which was a huge influence on me when I was an undergraduate physicist, so I couldn’t believe I’d forgotten this point. But David Deutsch, and Barrow and Tipler pointed out that it’s not necessarily the case that life will always be a spec, right? Something that’s very valuable and local in the universe, but doesn’t make much difference on a cosmic scale. It’s not necessarily the case, because you can imagine, so let’s take the earth as an example. So you might say, well, a planet is a very big thing, and living things are very small, so they don’t make much difference to a planet. That’s wrong, because if you look at the Earth, its atmosphere is the product of life. It’s got oxygen in it in high concentration. It would not have that without photosynthesis. So, and obviously now, our civilization has sculpted the surface of the Earth. You see it, if you look at the Earth from space, you don’t just see oceans, you don’t just see a kind of common or garden planet. On the night side of the planet, you see our civilization. So we have now transformed the Earth as a civilization, but life has been transforming it for billions of years. So you could say, well, okay, so what happens if we stay here? We become a space faring civilization, we don’t destroy ourselves, or we aren’t destroyed by some impact from space, then could you conceive of technology that could start to affect the solar system? And the answer must be yes. We could imagine building cities on Mars. We could imagine in physics, pure physics terms, terraforming Mars, turning it into a habitable world. We could imagine going to the moons of Jupiter or Saturn. We could imagine going to the edge of the solar system. You could even, could you imagine technology in a million years, let’s say, that would allow us to begin to affect the lifetime of the Sun? Could you imagine that? In physics terms, according to laws of physics, I suppose you could. You could imagine a tremendously powerful civilization that could start to, I don’t know, throw material into some, whatever it is. Maybe it was ridiculous thing to do, but you could at least imagine it. And then you go a million years, 2 million years, 3 million years, 10 million years, a billion years into the future, imagine that our civilization expands to the stars, and becomes an interstellar civilization. Imagine our civilization populates the entire galaxy. There’s nothing in the laws of physics that prevent that. And imagine we start to understand the quantum theory of gravity, we start to understand how space time works. Imagine if we start to glimpse some underlying structure in reality that gives us power that we’ve not yet dreamed of. Who knows in a billion years? And so is it really true that in the far future of the universe, then life will play no role? Or could it be that life could play a central role in the far future of the universe? And the reason that it reminded me of Barrow and Tipler’s magnificent book, “The Anthropic Cosmological Principle,” which I strongly recommend, is that in there, they consider a cosmology, which is, it sounds like science fiction, but you can conceive of it given the known laws of nature. It’s a cosmology called the Omega Point cosmology. So they consider a recollapsing universe. Now, at the moment, our universe is accelerating in its expansion, or whether it continues to do that forever, we don’t know. But at the moment, there it is. But in a recollapsing universe, you can at least consider a situation where life in the far future is so powerful that it can begin to control the collapse of the universe, and try to configure it, presumably by moving matter and energy around in some inconceivable way. You can just about construct this thing such that the ability of life to process information increases faster than the rate of collapse of the universe. And so what that means, what does it mean? It means that what’s the appropriate measure of time for a intelligent being? It’s really, I think fundamentally, it should be considered, you should think of it as the time it takes to process one bit of information. And it turns out that you can at least write the equations down for a universe in which the ability to process information diverges to infinity before the universe collapses. So, in that case, you almost say that life manipulates the universe such that it becomes immortal, right, in the far future. Now, I emphasize this is complete, you know, it’s beyond speculative, so I’m not advocating for this position that that’s the way that nature is. But it’s really interesting, it was really interesting to me to just think about it. The point, I think, the key point, which is interesting, is that it’s not necessarily the case that life remains insignificant on a cosmic scale. You shouldn’t assume that, because if life persists sufficiently long, and becomes sufficiently knowledgeable and powerful, then it may be able to influence larger structures, not just planets and not just solar systems, perhaps not just even galaxies, and it’s a very beautiful idea.