With a topic as seemingly complicated as quantum physics, where can you start if you want to build your understanding?

In just 22 minutes, physicist and professor Brian Cox unpacks the subatomic world, beginning with the theories as we understand them today.

BRIAN COX: 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, 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, we have an increasing number of quantum technologies that are really based on this behavior. The 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." Because we are using that behavior now in technologies. And so it really does become a, an important theory to try to understand.

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

- You could argue that even today, the interpretation of what the theory that is telling us about the nature of reality itself is not universally agreed upon. 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 about 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 stretch 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 that, 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 "superposition" 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 we would say such a thing? It's because we have incomplete knowledge of the system in this case, 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 were, that reflects our ignorance of the situation. The key difference in quantum theory is that these probabilities are fundamental. They're 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 what, how this thing is configured. The probabilities are intrinsic to the theory itself. And pretty much all of the intellectual challenges and the confusion around quantum mechanics comes from that very simple property. 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 it's, 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 because it's all in there, can't be done any better. So I could recommend that if you find this interesting, the double-slit 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 a 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, and you, 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 because 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 slips, let's say what water waves, any kind of waves, then it's easy to understand because what's happening then, and this follow, physicists 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 stripy 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 slips. 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 it, 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 roots 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 it can possibly take. A complex number, for those that don't know about complex numbers, can be pitch 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 electrons 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 this 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 it 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 in bank, all right, every possible route on its journey from the, from when it's emitted to when it's detected. And I think many physicists now would say that is a correct description of reality. The particle does. But I just want 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 what 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 our philosophy, it doesn't really matter, whatever, but now we have an increasing number of quantum technologies that are really based on this behavior, the 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, but, and we can just do some calculations. Because we are using that behavior now in technologies and so it really does become a, an important theory to try to understand. 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? If that 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 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 electronic 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, a two electrons together? These can be in what's called an "entangled 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, by 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. It's 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, 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, in the way I described it, there's a 50, 50 chance that when I make a measurement of this electron that the up or downness of it, then there's a 50, 50 chance of 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 seems 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 noble prize was awarded for some of this researcher 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, I think about it. So there are, you 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're talking about building quantum computers now in which we have a 100, 200, 300 qubits, all in principle and tangled together. The number of possible descriptions of that system then, you have numbers that describe it. If there are a 100, it's two to the power of 100, different configurations and any mixture of those things that are states of the system. So pretty soon, two to the power 100, for a 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 are not far off being able to conceive at least of a network of 500 qubits. They're physical things, the 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 not been able to do it particularly well at the moment. You'll read many papers online where obviously Compass like Google, Microsoft, IBM are investing a lot of money in these devices because potentially they are, that 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, nature, are becoming very real. Because we're getting, 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.

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