Thank you. Thank you very much everybody. It's a wonderful pleasure to be here at the Royal Institution. This is my favorite lecture hall to talk about science in. Of course, other people have talked about science here before me. There's this wonderful legacy that we have, this wonderful history of not just lectures, but demonstrations here at the Royal Institution. From Michael Faraday to Humphrey Davy. And I'm a theoretical physicist. I feel like I'm at a disadvantage. I don't really do demonstrations, but I thought... It's the Royal Institution. I should at least try to do some sort of demonstration. So, we're going to try. There's no guarantee of success. That's the beauty of science, right? You never really know. So, here's what's going to happen. I am going to push a button and my phone is going to send a signal across the internet to a laboratory in Geneva, Switzerland in which a little gizmo will send a photon, a particle of light, toward a partially silvered mirror. And according to the rules of quantum mechanics, the photon will in part pass through the mirror and in part be reflected off. There will be detectors that will find out whether the photon went one way or the other and once that happens, quantum mechanics says, there will literally be two different universes created. One in which the photon went one way and one in which the photon went the other way. A signal will be sent back to my phone in which that will be translated into instructions to either hop left or hop right, which I will then do. Let's see if Michael Faraday could do that. Here we go. And again, this is not a simulation. This is really actually happening. There really is a little beam splitter there in Geneva, and it's telling me that I should hop left. I did it. Thank you. You've been a great audience. Thanks. No, there's more to come, but the point is, according to the theory that I'm going to try to explain to you and maybe even persuade you of its reasonableness, there literally is another version of the universe that has just come into existence where a version of me is standing there and going like this. And I actually believe this is true. And maybe you won't actually believe it's true, but at least you'll understand why someone like me would believe it's true when all is said and done. Okay, now this is the hardest part of the demonstration, which is working the PowerPoint. Is it working? Yes, there we go. Okay. Of course, the topic here is quantum mechanics. If you're not here to hear a lecture on quantum mechanics, something has gone terribly, terribly wrong. The reason why I would like to talk about quantum mechanics, you know, the honest reason, is because I've written a book about quantum mechanics that you could buy right now on your iPhone without leaving your seat. But if you know even a little bit about quantum mechanics, your question should be, why in the world do we need another book about quantum mechanics? And I think that there is a reason, and the reason is... Implied by this famous quote by my Caltech predecessor Richard Feynman, I think I can safely say that nobody understands quantum mechanics. Now I usually don't like to appeal to authority when I'm giving these lectures, but when the thing I'm trying to demonstrate is that physicists don't understand quantum mechanics, I'm allowed to appeal to someone who, if anyone, should have understood quantum mechanics. What in the world does it mean for someone like Feynman to say no one understands quantum mechanics? He used quantum mechanics every day. In fact, we can use quantum mechanics to extraordinary precision. We can make predictions, we can do the experiment, we can see the outcome, the rules of quantum mechanics are obeyed. The problem is we understand quantum mechanics and use it in exactly the same way that I use my iPhone. I can send signals, I can use apps, I can send texts, even phone people on my phone. But if you say, what's going on inside? How do I build one of these? What are the details? I have no idea. That is the relationship that professional physicists have with quantum mechanics. They can use it, but if you ask them what's really going on under the hood, they say, well, we have no idea. And that's perfectly fine when it's me and my phone. It's really embarrassing when it's physicists and quantum mechanics. And the really bad thing is not just that physicists don't understand quantum mechanics. Not understanding is perfectly fine. Right? Not understanding drives science. We don't understand something, so we then try to understand it. The problem is that in the case of quantum mechanics, we don't even try anymore. There was this time in the 1920s and 30s when the greatest physics minds really thought deeply about what it means when quantum mechanical events happened. But then that was... that disappeared, that project of trying to really deeply understand what's going on. It was thought to not be serious work. It was thought to be what one did at the end of one's career, or at the end of the day, there was a little brandy you put on your smoking jacket, and you think about quantum mechanics. It was not really what real physics is made of anymore. So if you ask many physicists today, like, what's really going on with quantum mechanics, they'll say, no, no, no, we don't care about that. We don't want to know. So the metaphor, the parable, that I'd like to borrow from is Aesop's fable of the fox and the grapes. You know this one? The fox sees that it's a nice juicy bunch of grapes up there. It goes, oh yes, I want these grapes. The fox jumps up and down to get the grapes, but the grapes are just out of reach, just a little bit too high. So the fox says, you know what? I never wanted those grapes anyway. They're probably sour. You're not supposed to explain your parables, but just to make things clear, the fox represents physicists. The grapes represent understanding quantum mechanics. Physicists tried, they failed, and now they've convinced themselves they never wanted to try. And I think that that's wrong, and that's embarrassing, and we should do better. So I have an idea, it's not my idea, I have a favorite version of quantum mechanics I would like to pitch to you. But much more important than my favorite version is the idea that we should be able to understand it. It's not mystery, it's not magic, it's just science. So let me remind you where quantum mechanics came from, why we invented this whole scheme. You know, we started out in the 1600s with classical mechanics. Isaac Newton figured out the way the world worked according to a very simple set of rules. And this set of rules was so good, so compelling. That the idea that classical mechanics was not right just never even entered people's minds. It was a framework in which you could do physics and everything else from, you know, electromagnetism to Einstein's theory of general relativity fit into the framework of classical mechanics. Quantum mechanics is something entirely different. It's not an improvement on classical physics. It's a replacement, wholesale. Newton was wrong. Quantum mechanics is saying something very different. And there's no place more vivid. than this picture that you've all seen, the cartoon of an atom, the Rutherford atom. I love giving these talks in England because all these things happened in England, right? And Newton, classical mechanics, Rutherford did his work here at Cambridge. And Rutherford says... We knew about atoms, we came up with atoms in the 19th century, but then there was this plum pudding model where the atom was a big fuzzy thing with charges distributed inside. It was Rutherford who showed that's not right. The atom has most of its mass concentrated in the center, in a nucleus, and then electrons are very light charged particles that orbit around the nucleus. And this is still the picture you are shown today, right? We've all seen this picture. And there's some usefulness to this picture. It gives some intuition about what's going on. It's really the electrons that are doing all the work in something like chemistry or electricity in a material or something like that. The heavy nucleus just sits there. The electrons can jump from atom to atom. But I'm here to tell you this picture is nonsense. It is not the real world. And I can tell you why it's not the real world, because as I alluded to, in the 1800s, people like Michael Faraday invented something called the theory of electromagnetism. James Clerk Maxwell especially put the finishing touches on it. And according to that theory, if I have a charged particle like an electron, there's an electric field coming out of it. So if I move the electron a little bit, the electric field shifts to point toward where the electron is. So if I take the electron and I shake it up and down, there's a wave that propagates out from the electron, and we call that light. We call that electromagnetic radiation. All of the light in this room comes from shaking electrons up and down and watching the vibrations distribute in all directions. Guess what? This picture has an electron zooming around in a circle. It should be emitting electromagnetic waves. It should be emitting light to beat the band. And that means the electron should be losing energy. It should not stay in a stable orbit. It should actually spiral toward the center of the nucleus. And that should happen very quickly. You can run the numbers. You can do the math and show that it takes about a hundred billionth of a second for the electrons to go from their orbits down into the center of the nucleus. So here's an experiment we can all participate in right now. We can ask, you know, here's a table. There's atoms in it. Here's you and me. There are atoms. And I predict that if classical mechanics is true, a hundred billionth of a second from now, they will all collapse into a point. Ready? There. Let's see what happens. So there's something deeply wrong about classical mechanics. And it took a long time, it took a lot of smart people thinking in different ways to come up with an explanation of what might be going on. Here's the explanation they came up with. And it's really dramatic and even though it took a while, to be honest, it's amazing that they came up with it as quickly as they did. The explanation is that electrons are not particles. It's a pretty dramatic explanation, so I wanted to sink in that electrons are deep down, they're really waves. Rather than thinking about the electron as a little point moving in an orbit like a planet in the solar system, you should think of the electron as a cloud, a wave-like cloud concentrated near the atomic nucleus. And for those of you who are tortured by chemistry classes as college students, you recognize these orbitals, which are the different shapes that electron wave can take. Just like if you have a string that is tied down at both ends and you pluck it, there's sort of a fundamental frequency, then there are higher harmonics. Likewise, the electron wave has its lowest energy state and then various higher energy states where it looks more complicated. So the reason why the electron does not spiral in and collapse to the center of the nucleus is because its lowest energy state is not sitting point-like at the center, but being spread out like a wave. Okay? Circa the mid-1920s, people came up with this idea. And you can actually explain data using this. You can explain why the light emitted by atoms has a certain form. Even better... There's an equation. It's important that I show you the equation because at the quiz that will be handed out at the end of the lecture, You'll have to do some problems, sorry. This is the Schrodinger equation invented by Erwin Schrodinger. And actually we're not going to go through the details here. The point is that there is an equation. It's very pretty, it's like a little piece of concrete poetry, if you want to think about it that way. But the point is that not only do we have an idea, electrons are waves, not particles, we have a new equation to replace Isaac Newton's equation. Isaac Newton's equation is F equals mA, force is mass times acceleration. You tell me where a particle is, how fast it's moving, Newton's laws in classical mechanics will tell you what it's going to do next. In quantum mechanics, you tell me the wave function, very boring name, sorry about that, the wave function of an electron, Schrodinger's equation is going to tell you what it does next. On the right-hand side of the equation, it asks how much energy is there in the wave function. On the left, it says here's how fast it's going to evolve over time. So, that makes physicists very happy. Equations are what warm their heart a little bit, because it's full employment, really, for physicists. And it's certainly full employment for physics students. Solving the Schrodinger equation keeps them up at night when you're second year undergraduates doing your quantum mechanics. Here's the problem. Exactly because you have an equation and the equation is unambiguous in what it says happens, you can say, not just for electrons and orbits, but for any phenomenon, period, the Schrodinger equation should apply. If you're saying that quantum mechanics is a fundamental replacement for classical mechanics, you can use this equation to make all sorts of predictions. Here's a kind of quantum mechanical phenomenon. A nucleus of an atom might be unstable, right? It decays. And when it decays, it might emit an electron or another charged particle, and the Schrodinger equation will predict how that electron gets emitted. Remember, the electron is a wave. The way it gets emitted will look more or less like these. It will be like some big spherical cloud that moves away from the radioactive particles. Here is what it actually looks like. This is a real picture of a little bit of uranium in a cloud chamber that is Emitting radioactive particles, and when the charged particle moves through the chamber, it excites the atoms around it and they leave a little track. Okay? So these little trajectories represent particles being emitted from the radioactive substance. What you immediately see is that they're all straight lines. They're trajectories. It's as if a particle has moved through once it was emitted from the radioactive substance. That is not what is predicted by the Schrodinger equation. The Schrodinger equation says there should be a wave, big puffy thing going out in all directions. What you see when you look at it is as if the electron looks like a particle. So it's almost as if the electron is kind of like a wave when you're not looking at it. But it's a particle when you look at it. Okay, so in the late 1920s, the greatest minds in physics thought about this. Einstein, Bohr, Schrodinger, Dirac, Pauli, Heisenberg. They came together, they had meetings, and they fought and everything, and they came up with a theory of what was really going on. Their theory is the following. The electron is like a wave when you're not looking at it, and it's like a particle when you look at it. Sadly, this is the state of the art, even today, and it's called the Copenhagen interpretation of quantum mechanics. So the way that we resolve this apparent paradox is to say that the electron over here on the left has a wave function, it's a spread out kind of thing, some kind of cloud, but then when you look at it, the wave function changes suddenly, dramatically, and unpredictably. You don't know exactly where it will change, but it will collapse onto a point, so it looks like a particle, and the best you can say is to predict the probability that the location of that new particle will be here or there. And the rule is, the bigger the wave function at any one point in space, the higher the probability that the particle will be found there. Okay, these are the rules of quantum mechanics as we currently teach them. Here they are in a little bit more formal form. This is what we teach our students. I'm not making this up. I will not at the end say, ha ha ha, those 1920s physicists just weren't that smart. This is still what we teach our students today. There are two sets of rules for quantum mechanics. The first set of rules apply to quantum systems when you're not looking at them. And they say there's something called the quantum state of the particle, which we call the wave function, and there's an equation that exactly governs what the wave function actually does in time. This is precisely parallel to classical mechanics. There's a state and there's a set of equations that tell you how they evolve. But classical mechanics stops there. Quantum mechanics has a whole new set of rules for what happens when you look. When you look, the wave function changes. Suddenly it collapses to a particular value. Collapse of the wave function. And you don't know where it's going to collapse to. All you can do is say the probability. This is what we teach people in textbooks. So this should bother you a little bit. It's not your fault if it's bothering you a little bit. You should actually be bothered. Many people are bothered when they're students and they first hear this and when they ask questions they are told to shut up. And if they keep asking they're told to leave the field of physics. But just to explain this a little bit more, let's, my favorite thought experiment of course, Schrodinger's cat, right? This is something you've heard of before. Schrodinger's cat is not meant, like a lot of people think the point of the Schrodinger's cat thought experiment is to impress you with how counterintuitive quantum mechanics is. Schrodinger and Einstein were two people who, when this formalism of quantum mechanics was invented, didn't buy into it. Schrödinger, despite having invented the Schrödinger equation, once the full formalism was put together and the interpretation of his equation was as a way to get probability of things, he literally said, I wish I'd never had anything to do with this. He did not return his Nobel Prize, but he momentarily felt bad. The point of this thought experiment, which Schrodinger and Einstein invented over the course of letters sent across the Atlantic Ocean, was not to say, wow, quantum mechanics is impressive, it's to say, surely you don't believe this. So the point is to take a quantum wave function that puts a certain system in a superposition of different possibilities and amplify it from a microscopic system to a macroscopic system. So he takes a radioactive decaying nucleus and puts a detector next to it which will say okay it's decayed or it's not decayed so according to the rules of quantum mechanics the nucleus has a wave function that is a superposition of both I've decayed and I've not decayed so the detector is in a superposition of I have detected you decaying and I have not And according to this gizmo that Schrodinger imagines, if the detector clicks and sees a radioactive decay, it opens up a container that has gas in it. And the gas fills the wider box that's contained in it, which also contains a cat. Now in Schrodinger's original formulation of the thought experiment, the gas was cyanide. His daughter later said, I think my father just didn't like cats. I love cats. So in my version of the thought experiment, it's my lecture, it's sleeping gas in the box, okay? So according to the rules of quantum mechanics, the cat evolves into a superposition of I'm asleep and I'm awake. So it's really important, all these words in that sentence. It's not that we don't know whether the cat is asleep or awake. It's that the state of the cat, according to the rules I just told you, before we observe it, literally is both. A little bit of both, a superposition of both awake and asleep. In other words, classically, we could describe the cat as maybe it's awake, maybe it's asleep, I just don't know. That's an epistemic question, not an ontological one. It's a question about what I know, not what really is, okay? Quantum mechanics is saying something different. So the notation here is classical things are in square brackets, quantum things are in parentheses. Quantum mechanically, the cat can be in a superposition of both awake and asleep at the same time. And then Schrodinger says, if I believe the malarkey you were trying to sell me on the previous slide, only when I open the box and observe it does the cat become one or the other. So let's tell that story according to the textbook interpretation. Part of the ideology of textbook quantum mechanics is that the observer, the physicist doing the measurement, is treated as if they follow the rules of classical mechanics. So, even though you are made of atoms, and we all think the atoms obey the rules of quantum mechanics, according to the Copenhagen interpretation, you do not obey the rules of quantum mechanics. You obey the rules of classical mechanics. So the cat is treated quantum mechanically, parentheses. The observer, in this case played by Niels Bohr, is treated classically. Okay? So there's no wave function for the observer. What happens is the observer opens the box. The cat was in a superposition. Once that observation gets made, either the world is such that the cat was awake and the observer saw it awake, or the world is such that the cat was asleep and the observer saw it asleep. Two different distinct choices, and you can calculate the probability of either one. The problem is, this is clearly crazy pants. This is nutso. No one could possibly take this seriously as a fundamental theory of nature, right? I mean, there's many issues here, and people like Einstein and Schrodinger raised their hands in the back of the room and said, surely you can't believe this, and no one listened to them. So let me just mention two of the problems that are very, very clear here. One is very famous and has been mentioned many times, the measurement problem of quantum mechanics, right? In those rules I taught you, There's a role played by observation or measurement, by looking at things. So the measurement problem is just, what do you mean, look at something? Does it have to be a human being looking at it? Can the cat look at itself? Does that count? What if it were not a cat? What if there was a video camera? What if it were an earthworm or an amoeba? What if I just glance at it? What do you mean a measurement? When does it happen? What qualifies as a measurement? How quickly does it happen? Is it instantaneous? Why is it probabilistic? And again, if you're in the back of the room in your quantum mechanics class and raise your hand and ask these questions, you're told not to ask these questions. You're not given sensible answers. But there's an equally bad problem that I call the reality problem. I said at the beginning of the electron is a wave called the wave function. But is it really? Because the whole point of those rules is that we never see the wave function. Whenever we look at the electron it looks like a particle. Is the wave function really representing reality? Or is it just a tool we use to predict the outcomes of potential measurements we could do? Or do we need more than the wave function? Is wave function part of reality but not all of reality? What is reality? We don't know. And this is why in many discussions of quantum mechanics that physicists try to give to wide audiences, they get confused themselves. You know, is the atom mostly empty space? No, if you think the atom is mostly electron wave function. But yes, if you think the electron is secretly a particle inside the wave function. So we don't know the answer to these very, very basic, easy to ask questions that should be embarrassing. There's a long history, of course, of young people entering the field and saying, I'm going to answer these questions, and then being kicked out of the field. One such person was Hugh Everett, who in the 1950s came up with what is called the Everett Interpretation of Quantum Mechanics. He didn't call it that, but you know. And the wonderful thing is that Everett, in some sense, was being more of a therapist than a physicist. He was giving a way for physicists to accept reality in a way that they apparently were in denial about. To these questions, what is reality, what happens at a measurement, he offers very simple answers. He says the wave function represents reality. That's it. There's no extra stuff, and it's not just a tool to make predictions. It is isomorphic to reality. That's it. And what happens when you make a measurement? There's no collapse of the wave function. There's no sudden, unpredictable, probabilistic, stochastic thing. There's just the Schrodinger equation. The Schrodinger equation applies all the time to everything in the universe. Bold words indeed, but we already gave an argument that that can't be right, right? Because the Schrodinger equation predicts the things coming out of the uranium should go in all directions, but we only see them go in trajectories. But still, before we resolve that, I do want to make it very clear how simple this theory is, right? Compared to the Copenhagen interpretation, the rules of Everettian quantum mechanics are beautifully simple. He just erases all of the rigmarole about observations and measurements and collapses. He says there are wave functions and they evolve according to the equation that you already know. He doesn't add anything at all to the formalism of quantum mechanics. He just takes things away. The problem is how in the world can this map onto the reality that we see, map onto the reality that says when we look at electrons they look like particles. So let's look at There's two things that Everett made use of that are absolutely part of quantum mechanics. He's just saying you should accept them. One is the fact that you are made of atoms and therefore you are part of the quantum world. You are not classical. That might be a nice approximation that works in certain circumstances, but honestly the observer should be treated quantum mechanically just like the thing being observed. The other thing he makes use of is a phenomenon of quantum mechanics called entanglement. This was something that was really first emphasized by Einstein. You know, Einstein, if anything, is underrated. He's rated pretty highly, I know. man of the century, right? Person of the century. But there's this reputation that by the time quantum mechanics was put together in the late 1920s, there's literally a conference, the Solvay meeting in 1927, where Einstein and Bohr and the others hashed out the rules of quantum mechanics. And there's this speech we give ourselves about how by that time, Einstein was a little bit old. He was slowing down. He was too conservative. He couldn't keep up with the new physics. He was 48. I do not want to admit that at that age one is too old to keep up with the latest advances. The truth is that Einstein understood quantum mechanics better than anyone. The problem was he didn't accept it. He didn't think it was done. He didn't think that the Copenhagen interpretation was good enough. And one of the things he invented by thinking hard about it is this phenomenon of quantum entanglement. So I will illustrate it by thinking about the Higgs boson, discovered just in 2012. They didn't know about it in Einstein's time, but it's a nice illustration because other than the Higgs boson, every particle, every fundamental particle that we know about in nature has what we call spin. It rotates. And because of the rules of quantum mechanics, just like when you look at the cat inside the box, you never see it in a combination of awake and asleep. An electron that is spinning, when you observe the spin, you always see it's either spinning clockwise, which we call spin up, or it's spinning counterclockwise, which we call spin down. It's never actually any superposition of those two possibilities. The rules of quantum mechanics say that when you're not looking at it, it is a superposition of those two possibilities. The Higgs boson does not have any spin, but it can decay into two particles that are themselves spinning. And the nice thing about that is the total amount of spin in the universe stays the same when that happens. So if a non-spinning particle converts into two spinning particles, you know that the two spinning particles have to be spinning in opposite directions so that their spin cancels out. So here is the quantum mechanical prediction. The Higgs boson with zero spin decays into two particles, a particle and an antiparticle. We don't know, if we were to observe the spin of either particle, what answer we would get. But we do know, if we observe the spin of one of the particles, the other one is opposite. So the thing that the Higgs boson decays into by the rules of quantum mechanics is a combination, a superposition, of particle one is spin up, particle two is spin down. plus particle 1 is spin down, particle 2 is spin up. There's no possibility of their both spin up. That would violate the conservation of spin, the conservation of angular momentum, okay? So this just comes out of the need to preserve conservation of angular momentum, but it's a very profound thing. This is saying the following very, very big difference between classical mechanics and quantum mechanics. In classical mechanics, you have a bunch of particles, and I could give you their states one by one. This particle is doing that, this other particle is doing the other thing. You might think that for quantum particles, they each have a wave function. Particle one is some combination of spin up and spin down, so is particle two. But no, that is not how it works. There are not separate wave functions for every bit of the universe. There is only one wave function, whatever it called the universal wave function, what Stephen Hawking calls the wave function of the universe. And according to the wave function of the universe, these two particles are related. They are entangled. We don't know what answer we will get if we measure the spin of particle one, but we know that it will be the opposite of the spin of particle two. This is something that they didn't really know about in the 1920s, but Einstein and his friends pointed out in the 1930s. And it wasn't until 20 years later that Hugh Everett put it to work to understand the measurement problem. So here is the Schrodinger's cat experiment according to Everett. There is only one wave function, the wave function of the universe, and you are part of it. So now the observer is in parentheses, the observer is a quantum system, the role of the observer is now being played by Hugh Everett. And we're not going to have any magical wave function collapses, etc. All we're going to do is run the equation, the Schrodinger equation. You and I obey the Schrodinger equation just like electrons and cats. So when you open the box, there's nothing mystical, nothing magical, nothing sudden. There is an interaction, a physical relationship that comes into being between the observer and the thing being observed. And that entangles those two things. So it is absolutely unambiguous that the Schrodinger equation says that what you get when you open the box is a superposition that is entangled such that the cat's awake and the observer saw it awake or the cat's asleep and the observer saw it asleep. Everyone agrees. That's what the equation predicts. The problem is no one has ever entered, opened a box, looked inside and felt like they're in a superposition of having seen the cat awake and having seen the cat asleep. No one has ever felt like they're in a superposition of having seen the electrons spin up and spin down. So it's not that this makes no sense mathematically, the claim is this is not the world. This is not the world that we experience, okay? How, Mr. Everett, are you going to map this very beautiful theory onto reality? The answer is I left something out. Maybe you were clever enough to catch that I cheated a little bit. I just told you there's not a separate wave function for every bit of the universe. There's only one wave function for everything at once. And yet I wrote this wave function as if the only thing that exists is a cat and Hugh Everett. I really should technically include the entire rest of the universe in my wave function. Do not be alarmed. This is easy to do. We invent a word for the rest of the universe. We call it the environment. Here's a picture of the environment, okay? It doesn't matter. So the environment with a specific state doesn't really matter. What matters is the environment is going to interact, according to the Schrodinger equation, with the cat and with the observer. So the environment, for example, in this room, it's everything I don't keep track of. It includes all the atoms in the air, it includes all the photons of light coming from the light. Oh look, there's a whole balcony up there. Hi everybody. You're a great audience, yes. You're not part of the environment. I do care about you. But in the box, there's the environment, as well as outside the box. So what happens is, long before you open the box, the environment, the photons and the atoms inside the box, interact with the cat. You know, you imagine if the cat is walking around and awake, a certain photon might be absorbed by the cat. Whereas if the cat were lying down and asleep, the same photon might go right on by. So this is a phenomenon called decoherence. That cat does not... maintain its separate identity just by being in two different places, depending on if it's awake or asleep, it instantly becomes entangled with the environment. So we have a situation where before I've opened the box, there's a cat that's awake and the environment has measured the cat to be awake, or the cat is asleep and the environment has measured the cat to be asleep. And then I open the box, and that's what I call measurement, but the action has really already happened. I then become entangled with the cat and the environment, And now this is just slightly different than what I showed you before. It's still a situation where there's part of the wave function where the cat's awake, and part of it where the cat's asleep, but again, I don't keep track of the environment. I don't really know what's going on in it, but what I know from this kind of analysis is it's completely different in the world where the cat's awake and the world where the cat's asleep. So different. that what's going on in the part of the wave function where the cat's awake is now completely independent of what's going on in the part of the wave function where the cat's asleep. If I change, if I perturb or tweak one part of the wave function, it doesn't affect the other part anymore. So what's happening, in other words, is that decoherence, the entanglement of the cat with the environment, has branched the wave function to two different pieces which evolve independently from then on for the rest of the history of the universe. They do not affect each other, they do not care that each other exists, it is as if they have become two separate worlds. That's why the Everett interpretation of quantum mechanics was later dubbed the many worlds interpretation of quantum mechanics. It predicts, just like the phone, that every time I measure a quantum system by entangling it with the wider world, two copies of the world, or many more copies of the world, are created, each of which a different measurement outcome was obtained. What I want to emphasize is Everett didn't take an infinite number of worlds and add them to quantum mechanics, right? Everett just accepted that the worlds were always there. If an electron can be in a superposition of spin up and spin down, and you trust quantum mechanics, then you can be in a superposition of having seen the electron spin up and having seen the electron spin down. And if you trust that, then the universe can be in a superposition of one or the other, and the math says those different parts of the superposition go their own way. They're independent. They don't interact anymore. So, it's not that Everett put a whole bunch of worlds in to solve the measurement problem. He said that they were already there, and he says, you know what? It's okay. Just let the worlds be there. Trust your equations. Ask what you would observe if the world were like that. It's what you actually do observe. So this is the many worlds interpretation of quantum mechanics. Now, shockingly, not everyone agrees that this is the right interpretation of quantum mechanics. I could go through a long list of, you know, I had in different slides, I deleted the slides, but there's a whole bunch of things I had which were the dumb objections to the many worlds interpretation of quantum mechanics, but then, you know, you worry that someone in the audience believes those objections, and I'm calling you dumb. I don't want to do that. But let me just... ...preempt one objection that is very, very common, and sadly, it's the objection I do the least good job of explaining why it's not an objection, but it's the one point in the talk where I feel like what I really want to say is, just believe me on this, okay? Just, if you knew the math, it would all be crystal clear. And the question is, where does the energy come from? to make all of these universes. Like we look around in the universe, there's again tables and things, and floors and planets and galaxies. There seems to be a lot of energy, a lot of stuff. And you're telling me when I put the button on my phone, there's now twice as much stuff. That seems like hard to reconcile with our ideas that energy is conserved. So again, the math here is crystal clear, and it's very difficult because our intuition doesn't stretch there to translate this into ordinary language. But the point is that worlds are not created equal. There's a thickness or a weight that you can imagine attaching to the different worlds in the many worlds interpretation of quantum mechanics. And what happens is, as more worlds are created, they get thinner. The total thickness of all the worlds remains the same. They're exactly proportional to the wave function squared, which gives you the probability of finding yourself in one world or another. So if you weight the amount of energy in each branch of the wave function by the thickness of the branch, that's a number that remains precisely identically conserved over time. So, according to the equations, there is something that is conserved that you can call energy, and it's a certain weighted combination of the energy of all the different worlds. It does not take more energy to make the worlds. Again, despite the fact that this is compelling and obviously true, there are people who don't buy it, so I do want to give some airtime to the possible alternatives because... The phrase that is often used for this kind of questioning are the interpretations of quantum mechanics. And it makes it kind of sound like literary criticism, you know, that we're looking at the world and sort of thinking about it in different subjective ways. But that might have been true in the battle days of the 30s and 40s. These days, the alternatives to many worlds, like many worlds itself, are legitimate, rigorous, well-defined physical theories that are distinct from each other. They're not interpretations of quantum mechanics, they're just different physical theories. So one possibility are hidden variable theories. David Bohm is the name that is most famously attached to these. He, you know, his PhD advisor was Robert Oppenheimer, J. Robert Oppenheimer, famous physicist, who supported him a lot until he invented an alternative theory of quantum mechanics. And then the quote that Oppenheimer gave at a seminar was, you know, if we can't stop Bohm, we must at least agree to ignore him. And the hidden variables theory, which Einstein was also sympathetic to, is a very straightforward way of dealing with this problem that electrons seem to be wave-like when you're not looking at them and seem to be particle-like when you are looking at them. It's to say there are both. That the wave function is not all of reality, the wave function is part of reality, but in addition to the wave function there are also particles. So these particles are the so-called hidden variables that pick out the place in the wave function that you actually end up observing. Another possibility is that wave functions really do collapse. And Roger Penrose is someone who's advocating an idea like this. There's another idea called GRW theory, where this measurement process is not induced by someone looking at it, but just something that will randomly happen if you wait long enough. For one particle, a particle whose wave function is all spread out, will spontaneously localize once every 300 million years. That takes a long time, but in a table there's a gigantic number of particles. So the table stays in one coherent spatial location because one or more of its particles is always localizing and they're entangled with everything else. So these are two different real physical theories with different variables, different equations, potentially different experimental consequences, and that is the state of the art. So if you agree with me... that we should try to understand quantum mechanics, but disagree with me that many worlds is the best theory, there are alternatives that you can try to explore. What I want to do in the last third of the talk, you all know there's a rule when you give talks, right? Science talks, where the first third of the talk is understandable to everybody. The second third is understandable to people who bought your book. And the last third is not supposed to be understandable to anyone at all. We are about to enter the last third of the talk. But at least if the details are not perfectly crystal clear, the moral should be clear. The moral that I want to try to get across is it matters what goes on in quantum mechanics. It's not just that, you know, we can't maybe say exactly what happened when a measurement occurs, but still it's good enough to make progress in physics. I think it's actually not true. I think that by not facing up... To the fact that we don't understand quantum mechanics, we have been held back in our attempts to do other questions in physics. We have this idea that the world is quantum mechanical, but we don't act that way. Even when I say we, I mean professional physicists, highly paid smart people, okay? We all have an intuition that is basically based on classical mechanics. We think that there's something called a table and it has a location in space. Very old fashioned to think that. And nevertheless, that's how we talk. And it extends to how we develop new theories of stuff in the universe, whether it's the electromagnetic field or quarks or oscillators or whatever. We start with a classical theory and then we quantize it. We try to promote that classical theory to a quantum mechanical theory. The problem is... Nature doesn't do that. Nature doesn't start with a classical theory and then quantize it. Presumably nature just is quantum from the start and classical mechanics is some approximation, some limit, some version of a very narrow part of reality that works pretty well in certain very specific circumstances. So therefore, there's no reason why this procedure of starting with a classical theory and quantizing it must work. all the time. Maybe when the things that we're trying to understand are very subtle and nuanced, you have to start with the quantum description from the beginning and find the classical description as an approximation to it somehow. That's a job that is perfectly suited for the many worlds interpretation of quantum mechanics. The Many Worlds Interpretation talks about wave functions and the Schrodinger equation. It talks about entanglement and evolution through time, purely quantum mechanical notions. You can put in classical notions like positions and momenta if you want, but they're not intrinsic to the theory. Unlike every other version of quantum mechanics, it doesn't rely on any pre-existing classical baggage. So let's see if we can't make a little bit of progress on a hard problem. For example, quantum gravity. is a hard problem. What does that mean, quantum gravity? Here's Einstein again. Everyone shows you pictures of Einstein in his later years, where the hair was big and gray, and he was wearing the rumpled sweater. But back in the day, when he was inventing relativity, he was a well-dressed young man, and someone was combing his hair. And he had these wonderful ideas, special relativity and general relativity. Special relativity, 1905, he kind of weds space and time together. The speed of light is an absolute maximum. I think there's an upcoming Royal Institutional lecture about the speed of light, right? Gets rid of the ether and so forth. Ten years later, in General Relativity, he says, you know, this space-time thing, this four-dimensional place where we live, has a life of its own. It's dynamical. It can be curved and bent. And you and I perceive and interpret that curvature of space-time as gravity. The reason, according to Einstein, why apples fall from trees is because the Earth exerts a force on space-time itself to curve space-time so that apples want to naturally fall with the trees not holding them up. So this is a wonderfully successful theory of gravity that fits perfectly into the classical Newtonian paradigm. It's different than Newton's laws of physics. But it fits into that world where in principle you have a something, the curvature of space-time. There's an equation cleverly called Einstein's equation that tells you how space-time curvature evolves over time. There's nothing quantum mechanical about it. But of course we also have quantum mechanics and we want to reconcile general relativity with quantum mechanics. That's the goal of quantum gravity. Now, for every other force of nature that we know about, electromagnetism or the little nuclear forces, the Higgs boson, the electrons and the quarks, this idea of starting with the classical theory and quantizing it works pretty well. It hasn't always been easy, right? Richard Feynman won his Nobel Prize for quantizing electromagnetism. It took a lot of real brain power to do that. But still, eventually you get the right answer. For gravity, we fail. If you try to quantize general relativity, you get nonsense. Quantities that should be finite numbers are infinite. You don't even know what the terms mean. It's just kind of a mess. So I would like to suggest that's because we've been doing the wrong thing. I need to mention one more thing. There's the motto at the bottom there. Geometry is related to energy. This is the very, very simple essence of general relativity. The geometry of space-time is influenced by, and in turn influences back, the energy of the stuff. within it. So to turn that into a quantum theory, what I want to suggest is that maybe you shouldn't be quantizing gravity. Maybe what you should be trying to do is to find gravity within quantum mechanics, within the wave function of the universe. I mean, after all, we say, oh, we have not been able to understand quantum gravity, but then we admit we don't even understand quantum mechanics. What right do we have to think that we should be able to understand quantum gravity? So let's try something new. Now, when we do this, we're allowed to sort of cheat just a little bit by using features of the world that we do understand and that we do know. Well, one thing we know is that when we forget about gravity and just think about the other forces and particles of nature, the best way we have of describing them is this framework called quantum field theory. All the talk that I've been giving you about electrons and protons and particles is kind of just an approximation to the real underlying thing, which are quantum fields. And we're in the right place to talk about that. The person more responsible than anyone else for saying the world is... Starting the idea that fields are fundamental was Michael Faraday with the electric and magnetic fields. So here's a magnet. Right? You put the magnet, and if you don't put any iron filings around it, it's just empty space outside. But you and I know there is secretly a magnetic field everywhere around the magnet. In modern quantum field theory, what we say is that literally everything, not just forces like electricity and magnetism, but even matter particles like electrons and neutrinos and quarks, are really part of vibrating fields that fill all of space. So, that's a big change in perspective from a particle-based view, at least when it comes to the nature of empty space. In a particle view, you have particles that have locations, and then in between the particles, there's nothing but empty space. There's nothing going on. Empty space is boring. Whereas, in the field-based view, a particle is just a way of talking about a field vibrating more than it does in empty space. But even empty space, the fields are there, they're just in their lowest energy state. They're doing the minimal thing it's possible to do. So we talk about modes, the different vibrational frequencies of the quantum fields. Even in the emptiest region of empty space, there's an electron field, a magnetic field, an electric field, a gravitational field. All of them have a certain quantum state. Those modes of the fields are doing something. What they're doing is looking like empty space. But they're there, and that's very important. Because what that lets us do... is talk about the entanglement of those different fields. Remember, if we're being quantum first, we don't have a lot of words to work with, but one of the words we have is entanglement. So you will not be surprised to hear that if you have different regions of empty space with different vibrating quantum fields in them, those fields will be entangled with each other. And guess what? The closer they are to each other, the more entangled they are. So, if you start with empty space and you have a geometry, whether it's Euclidean or Riemannian or whatever you want, whatever level of sophistication you've reached, it will be the case that the empty space parts of the quantum fields have a very simple relationship. You know how close things are just by measuring their entanglement and vice versa. So the idea, the proposal, the suggestion, the guess, the hypothesis is that we can reverse that. Rather than saying the closer the quantum, the areas are, the more entangled they are, we can say the more entangled these bits of the quantum field are, the closer they are. We will define what it means to be nearby to mean highly entangled. And we will define what it means to be far away to be not very entangled, okay? So what we're doing here is asking whether space itself and the geometry of space, right, distances and angles and all that stuff, can emerge in some natural way from a quantum wave function that does not have space built into it from the start. And the answer is yes. If the wave function has certain properties, if the entanglement structure works out in a certain way, you can map that quantum wave function and say, oh, this is three-dimensional space. A different quantum wave function would represent five-dimensional space or a two-dimensional plane with different amounts of curvature and so forth. So as it shows on the top, there's a relationship between geometry of space and the entanglement of quantum fields in that space. Meanwhile, there's also a relationship between the entanglement of the fields and the energy that they have. In this picture I showed you right here, there are no particles. This is literally supposed to represent empty space, okay? Let's put some particles in it. What does that mean in this language? That means we take the quantum fields and we vibrate them a little bit. And what that does is it breaks the entanglement between that little vibrational mode in that region of space and everything around it. So by Decreasing the entanglement, we did something that we know in our intuition is equivalent to putting energy in the system by putting a particle there. If you add a bunch of particles until you made a table, you would have to break a lot of the entanglement of the vacuum modes of this region of space with the region around it. And in fact, you can make this into equations. Again, full employment for graduate students at Caltech, figuring out how to relate the amount of entanglement in a region of empty space to the amount of energy that you would perceive being there. And there's an opposite relationship. The more energy, the less entanglement, and vice versa. So what does that mean? That means we can start with entanglement, which is a purely quantum mechanical notion, nothing classical about it. We can say that under the right circumstances, a certain geometry of space emerges from the entanglement structure of the quantum wave function, and at the same time, we can associate a certain amount of energy with the amount of entanglement we have in the wave function. Therefore, by arrows, there's a relationship between geometry of space in this emergent description and the amount of energy. that is lurking there in the space. And that is exactly what Einstein taught us a little bit over 100 years ago in general relativity. Einstein did not speak the language of entanglement when he was doing this. He just said there's a direct relationship between energy and the geometry of space. I have an equation for it. I call it Einstein's equation. We're deriving Einstein's equation with a whole bunch of assumptions, but we can say we can see where this comes from at a more fundamental level. This is an ongoing program. I don't want to like, you know, give you too much of a sales pitch. It's completely possible that everything I gave you in the last three or four slides is utter nonsense. Okay? This is a speculative program in which we don't try to quantize gravity, but we try to ask how the features we know about gravity can emerge from a purely quantum mechanical description. So far, it seems to be pretty promising. It looks like it might be able to work. Now, stay tuned. Right? Wait a few years, let's see if this works. There's a lot of smart people pursuing other versions of quantum gravity who will say this is all unlikely to succeed, but we just don't know yet. That's what it's like at the edge of theoretical physics. What I like about it is that it really uses at least the philosophy of Everettian quantum mechanics. That you don't start with positions and locations and particles, you start with a quantum wave function, everything else comes from that. So I will close with a quote from another British physicist, David Deutsch. a proponent of Everettian quantum mechanics, who says, despite the unrivaled empirical success of quantum theory, the very suggestion that it may be literally true as a description of nature is still greeted with cynicism, incomprehension, and even anger. So I hope that what I've told you tonight at least lowers your incomprehension a little bit. Thank you very much.