QM_1.txt PDF

This is audible. These lectures are titled The Many Hidden Worlds of Quantum Mechanics. Your expert is Sean Carroll, the Homewood Professor of Natural philosophy at Johns Hopkins University and a member of the Fractal Faculty at the Santa Fe Institute. He is the author of Something Deeply H...

This is audible. These lectures are titled The Many Hidden Worlds of Quantum Mechanics. Your expert is Sean Carroll, the Homewood Professor of Natural philosophy at Johns Hopkins University and a member of the Fractal Faculty at the Santa Fe Institute. He is the author of Something Deeply Hidden Quantum Worlds and the Emergence of Space Time, and the host of the Mindscape podcast. Lecture one. Why? Suppose there's more than one world? This course is going to explore a truly mind bending idea that quantum mechanics, which is our most successful framework for doing fundamental physics, has a remarkable implication. It predicts the existence of a large number of separate universes parallel to our own, almost identical to the one that we live in, but with small variations between them. This idea is known as the many worlds interpretation of quantum mechanics. The first thing to say is that it's not really an interpretation of anything. It's a full blown scientific theory. We talk about interpretations when we have some kind of specific thing in front of us, like a text, a novel, a work of art. And we're asking, what does it mean? That's an interpretation. Back in the old days, the old days of quantum mechanics. So the first decades of the 20th century, this used to be something that was thought to be needed. When it comes to quantum mechanics. We had some rules. We had some principles. We weren't really sure what it all meant, how to think about it, how to interpret it. But these days we know better. We're in a different situation. We have several competing, honest scientific theories. They all make similar predictions to the old rules of quantum mechanics, and we're trying to decide which of them, if any, is the correct one. What we're doing here is science, not literary criticism. The idea that there are many universes parallel to our own. That's a dramatic claim. You have a right to be skeptical at first. I'd be disappointed if you were not initially skeptical. But I'll try to explain why physicists have been led to such a wild conclusion. And importantly, it is a conclusion. It is not an assumption. We'll see how the very simple and innocuous postulates of quantum theory lead us directly to the existence of these other worlds. The postulates could, of course, be wrong. But then you got to say, how are you going to change them if you think they're wrong? And it turns out that changing them is tricky. Many of us believe that the best theoretical approach is simply to accept the prediction that the basic postulates make. Not everyone does. There's no consensus, at least not yet. But Many Worlds is one of the leading contenders for a rigorous underlying formulation of quantum mechanics. So in this lecture, the very first one, we're going to briefly summarize this dramatic punchline. And then we're going to back up just a little bit. Try to justify how and why we got there. So let's start by getting the basic idea on the table. What is quantum mechanics. It's a framework. It's a framework for doing physics. It's a replacement for classical mechanics, which was the incredibly successful framework established in the 17th century by Isaac Newton and others. The big difference between classical mechanics and quantum mechanics is how we think about the process and the notion of measuring something. In classical mechanics, measurement is easy. You just go and measure things. Measurement is basically a trivial process. We don't even talk about it. We don't write about what it means to do a measurement in classical mechanics. In particular, you don't need to specify extra rules about how to do it. For example, in classical mechanics, a standard situation is you have an object. It has some properties. It has a position, it has a velocity, and then you measure them. That's just all you do if you do it clumsily. If you're bad at measuring things, you might end up disturbing the system or changing its properties. But there's no obstacle in principle to measuring things carefully, to measuring the system without changing it in any important way. Quantum mechanics, which came along in the early 20th century, tells a radically different story. Unlike classical mechanics, in quantum theory, at least according to the textbook version that we teach our students, even today, we do need special rules to handle what happens when we measure a quantum system. You can do measurements, but unlike in classical mechanics in general, we cannot precisely predict what the measurement outcome is going to be. All we could do in quantum mechanics is predict the probability of getting different measurement outcomes. The probability that a spinning particle will be spinning clockwise or spinning counterclockwise, or that some other particle will be observed, have a certain position or momentum. And it gets worse or better, depending on your perspective. A fundamental idea in physics is what we call the state of a system. By that we mean the state of a system. Is everything relevant there is to know about it? Basically, everything you need to know to predict what is going to happen next. In classical mechanics, for example, we have states of systems. The state of a system is specified by the position and the velocity of each part of which the system is made. And in principle, there's no obstacle to measuring the position and velocity of everything. Precisely. Once you tell me the position and velocity of a rocket ship or a baseball, I can use the laws of physics to say what it will do next. Similar setup in quantum mechanics, but the details matter. A quantum system is also specified by its state, and we call the state something called a wave function. As we'll see, wave functions can get broken. Complicated. But in the simple example of a single particle, the wave function looks like a wave. Rather than describing a particle as a point with some specific location. The wave function in quantum mechanics takes on a numerical value at every possible point in space. The wave function is generally going to be large in some places, fading to zero elsewhere. If you took chemistry in high school or college and you were shown pictures of orbitals of electrons in atoms, you were looking at basically pictures of wave functions. The trick is, unlike the classical story in quantum mechanics, we can never measure the wave function itself. All we can measure are certain what we call observables, such as position or momentum or spin. And then when we do that, when we make our measurement, the wave function generally changes dramatically, no matter how careful we were before the observation. The wave function is generally spread out. It includes many possible measurement outcomes. But what we see when we perform a measurement is some actual specific position, not a spread over many of them. And then maybe most dramatically of all. Once you make that measurement, the wave function changes very suddenly. It collapses to be concentrated purely on the outcome we actually obtain. So before we did the measurement, the wave function had in it a set of various different possible measurement outcomes. When we did the measurement, we saw one of them and all the other possibilities disappeared. It's important to emphasize. Nobody ever wanted this kind of thing. This was not something that people were aiming for. Physicists were very happy with the classical Newtonian paradigm. And in that paradigm, measurements are simple and precisely predictable, at least in principle. Of course, you have complicated systems where it's hard to make exact predictions, but in principle, once again, if we were smart enough and good enough, we could absolutely do it. This quantum shift in perspective was forced on us by trying to explain the data in the period between about 1919 27. Physicists trying to explain phenomena such as radiation from hot objects or the structure of atoms, they were forced to postulate an increasingly confusing set of new rules and principles, including carving out a special role for measurements and what you see when you look at a system. This was back then, and it still remains today, an extremely puzzling feature. Why should a fundamental theory of physics care about measurements at all? It sounds very anthropocentric. It sounds very human centered. And after all, what really counts as a measurement? When does a measurement precisely happen? This set of questions, which again, we don't agree on the answers to them right now. This has become known as the measurement problem of quantum mechanics. Approaches to the measurement problem have generally been referred to as interpretations of quantum mechanics. That's where the word comes from. As if we were discussing a novel or a painting rather than a theory of physics. We talk of interpretations and we all agree on the underlying thing being discussed, but we're not sure how it relates to other things. In some very real sense, that was what physicists were doing back in the 1920s. But the state of the art today has become a bit more advanced as a consequence of this advance. Practitioners in the field think of themselves as working on the foundations of quantum mechanics, discussing honest scientific theories, not just the interpretations of quantum mechanics. We're being scientists. We're trying to figure out what is actually going on in nature, the physical mechanisms that lead to the predictions of quantum mechanics. Quantum mechanics as a framework was put together gradually. In my view, a milestone was what we called the Fifth Solvay Conference in 1927. Albert Einstein and Niels Bohr and many other leading physicists of the day came together and had long arguments over whether quantum mechanics, as it existed then, was a complete and correct theory, or whether it needed to be revised and extended. Somehow. Out of this conference and other discussions among physicists emerge something called the Copenhagen interpretation. That's the story we've just been telling. But even back in the 20s, Einstein and other leading people thought that it might not be the final answer. They remained skeptical. They appreciated the empirical successes of the quantum theory that existed at the time in fitting the data. They just didn't think that our work was yet done. In the 1950s, a graduate student in physics named Hugh Everett started reconsidering the foundations of quantum mechanics. He developed what he called the theory of the universal wavefunction. In that picture, every possible measurement outcome actually happens. The secret is each one happens in a different world. This approach was later not by Everett, but by others. Dubbed the Many Worlds interpretation. As we'll see, the worlds of the many worlds interpretation come out of the equations. They are not put in by hand. They are a prediction. They're not part of the postulates of the theory. Many worlds is a very specific and quantitative theory. It's not a vague idea that just says it's quantum mechanics. Anything goes. It makes predictions. There are equations, everything you want from an honest scientific theory. So let's think just a little bit. We'll fill in the picture later. Let's think a bit about where these worlds come from. You may have heard that in quantum mechanics, something like an electron, an elementary particle sometimes acts like a particle and sometimes acts like a wave. To me, that statement has always been annoyingly vague. When does it act like a particle? When does it act like a wave? Because there is an answer to this question. To be more precise, an electron acts like a wave when it's not being measured. It acts like a particle when it is measured. That's not very helpful. It's still mysterious, but at least it tells you what we mean when we say something. Times a particle, sometimes a wave. By wave, we mean that the state of the electron is described by this thing we called the wave function. It's a dumb, boring name for the crucially important idea, but we're kind of stuck with it. A wave function in the case of a single particle, like an electron, is basically a smooth function of space. At every point in space, the wave function takes on a specific numerical value. And the reason why that's true is because points in space are possible measurement outcomes. If we're measuring the question where is the electron? Every possible outcome is some location in space. So we can think of this wave function as what we call in quantum mechanics a superposition. That's a weighted combination of every possible measurement outcome. This wave stretching through space is really assigning a different weight to every location we could see the particle, and the same kind of thing holds true for the spin of the electron, or for other observable quantities. The wavefunction is a superposition, a weighted sum of every possible measurement outcome. The trick that some people didn't want to admit is that we have a wave function. Two A person is a physical system. Physical systems are described by quantum mechanics at the end of the day, and therefore we have a wave function describing what's going on. It's just that our wave functions or anything we describing a large macroscopic system, is typically going to be very localized around some particular location in space. So that to a very good approximation, we can talk about people using the language of classical mechanics. We appear essentially classical, but the claim is that deep down, even we are quantum mechanical and wave functions obey an equation. The equation that we care about is called the Schrodinger equation after physicist Erwin Schrödinger. This equation tells us, for any initial choice of wave function, how that wave function is going to evolve over time. Now the equation, the Schrodinger equation is not imprecise. It's not vague or fuzzy. It's not even deterministic. The Schrodinger equation tells us exactly what the wave function is going to do. So the Schrodinger equation tells us how the combined system of us plus the electron is going to evolve with time. We can ask questions about it. It provides definite answers. What happens when we human beings measure the position of an electron? Is that the overall wave function of both of us evolves into a very specific kind of superposition. The electron was at position x, and I observed it to be at x plus the electron was at y, and I observed it to be at y plus every other possible outcome. And then amazingly, according to Everett, each one of those parts of the superposition evolves independently as its own world. Of course, this raises questions. We're not just supposed to accept this quietly. Precisely. How do these worlds come into existence? Why are they truly independent? It's no surprise that these seem like difficult questions. The ordinary physics with which you and I are familiar doesn't have any such issues. We have no practice thinking about them. We have no experience to guide us. But as we'll see in later lectures, often there are pretty straightforward ways to answer these questions. So let's just mention some of the highlights to get you in the mood. It's tempting to think that branching worlds somehow correspond to different decisions that we could have made. A human being deciding to have pizza or Chinese food creates two different universes, but that's not really right. You do not create new worlds just by thinking about them and making decisions. Worlds come into existence in a very specific, physical, tangible way. When quantum systems are measured. So the important question is what do we mean by measured? In the Copenhagen version of quantum mechanics, that was always left a little vague. But this question has a precise answer in the many worlds interpretation. Unfortunately, we're going to have to lay a little bit of groundwork to make the answer very clear, but we'll sketch it right now. Instead of having measurement as a primitive notion. As part of the postulates of the theory, in many worlds, we can simply describe the conditions under which the universe branches into multiple copies. And the answer is that happens whenever a quantum system that is in a superposition becomes entangled with the outside world. So we'll have to explain what entanglement means, where it comes from, and things like that. But what matters for right now is it has nothing at all to do with consciousness or with being a living observer or anything like that. If an atomic nucleus decays, for example, and then it interacts with its environment and becomes entangled with the world around it, that counts as a quantum measurement. It counts even if no living being is ever aware that the thing happened. Okay. The usual way of thinking about measurements that some human agent learned about some physical quantity. That's one kind of example when the universe would branch. But it is not the only one or the most common one. So another question that arises with many worlds, and it's a very natural question, is exactly how many worlds are there supposed to be? I hate to let you down, but the right answer is we don't know. It could be infinitely many. That's not really a worry. It's just a way of saying the set of worlds is smooth. It's continuous rather than discrete. In that case, the question of how many worlds isn't really well-defined any more. Then how many numbers are there between 0 and 1? There's infinity, but that's not very helpful. But it's also possible that once we understand the laws of physics perfectly, we will realize there are only finitely many worlds, in which case the question does have a good specific answer. The state of the art right now just isn't good enough to say either whether the answer is finite or infinite, or what the finite number might be. We'll get into this question more later. So Many Worlds is therefore an example of a theory that predicts a multiverse, many different universes that simultaneously exist. There's other such theories, but they're all kind of different in where they start from and what they imply. There is the cosmological multiverse that got a lot of press in recent decades, based on string theory and inflationary cosmology. And that theory, what we call different universes, are actually just all part of the same spacetime. It's just that there are regions of spacetime that are enormously far away from us so far that we cannot be in contact with them or notice that they're there. And in those other regions, conditions are very different up to and including what people living there would call the local laws of physics. So for many reasons, both because they're very far away and because conditions are different, we can think of them as practically separate universes. That's an entirely different story than the many worlds of quantum mechanics. The many worlds of the many worlds interpretation are not far away. They don't have a location in space at all. The way to think about it is space exists inside each world. The worlds don't exist in some space, and the quantum worlds that we're talking about come into existence all the time right in front of our noses. Whenever we do a measurement that's going to lead to a branching of the wavefunction of the universe and the creation of a new world. We do measurements all the time. Time. This is not due to any speculative cosmological mechanism about the early universe. Many worlds, even though its philosophical implications are kind of radical. It's actually a much more down to earth idea than the cosmological multiverse. There is also, in the world of multiverses, a more purely philosophical notion that is the set of all possible worlds. David Lewis, who's an American philosopher, is closely associated with this idea. He used the idea of the set of all possible worlds to think through philosophical problems about causation and counterfactuals and things like that. So the set of all possible worlds is a completely conceptual idea. It's the idea that we can simply conceive of all sorts of different universes, whether they actually exist or not. Most philosophers don't think that every other possible world really exists, but the idea is a useful conceptual tool. Many worlds of the quantum mechanical version is once again completely different. The quantum worlds we get out of many worlds interpretation do not represent everything possible in the many worlds interpretation, only some things happen. The ones that are predicted by the equations and allowed by the laws of physics. In no world is a proton turn into an electron, for example, because that violates a cherished principle the conservation of electric charge. Now, admittedly, there will be some crazy worlds out there. There's going to be some worlds in the set of the many worlds of quantum mechanics that look very unusual and weird to us, but they're all obeying the underlying laws of physics. So in both of these cases, again, the idea of a multiverse, whether it's the many worlds multiverse or the set of all possible worlds isn't being explored just because it sounds kind of kooky and fun. It's because it follows naturally from other reasons. The cosmological multiverse is an inevitable outcome of certain theories of what happened near the Big Bang in our early universe, and those theories were invented to explain the initial conditions of the universe that we actually do see. They weren't just invented, they were prodded by observations. Whereas the set of all possible worlds is an important theoretical construct. When we try to account for counterfactual statements, you say things like, I was late because of traffic. What does that mean? Why is it the traffic that gets the blame here? Because you're trying to say in a possible world that is almost exactly the same as ours, except there wasn't as much traffic. I promise you, I would have been on time. That's why you need to invoke other possible worlds to make sense of statements like you and I make all the time. Anyway, the Many Worlds theory of quantum mechanics provides us a compelling, simple picture of what's really going on when we measure the properties of quantum systems. But despite its completeness and its simplicity, not everyone agrees that it's on the right track. There are other possible alternatives in the foundations of quantum mechanics. There's still a lot of working physicists who hold on to the old fashioned Copenhagen approach, or some modern, slightly souped up version thereof. The crucial thing about those pictures is that we don't treat observers as quantum, even though you might be made of quantum particles, you yourself are classical and according to this way of thinking. And we don't also treat wave functions as representing reality. We think of a wave function is just a tool for predicting what observers who are classical will measure. And there are other approaches. There's approaches where everything is quantum indeed, and the wave function really is something about reality. But how the wave function evolves can be different. Maybe the wave function doesn't always obey the Schrodinger equation. Maybe it really, honestly does collapse, not just from our point of view. Or maybe the wave function is real, but there's other things that are also real. Maybe it's those other things, sometimes called hidden variables, that are the things we actually observe when we make a measurement. All of these approaches are currently alive and viable. We'll talk about them and try to delineate their pros and cons. But one thing is for sure that many worlds is the simplest of any of them. Sometimes you will hear the accusation that the many worlds interpretation is overly extravagant. It has all of these worlds in it, right? But Hugh Everett and or anyone else didn't put the worlds in. The worlds were already there, implicit in the basic formalism of quantum mechanics. If you believe that when we talk about an electron as being in a superposition of different states, and you believe that's really a description of what's going on, you should be able to believe that the universe can be in a superposition of different states. It's the alternatives to many worlds that somehow have to do work to get rid of those other worlds. So although Many worlds tells a simple and compelling story, at the end of the day, it might not be the right answer. So I will try to be as fair as possible in explaining the worries that people have about this theory. I'm going to opine very strongly that some of those worries are just misplaced. They're not really very worrisome at all. Once you actually understand what's going on. But also there are honest worries. There are real worries, there are puzzles to which we don't yet know the answers. I personally think that the many worlds interpretation is probably correct, but I'm not completely sure. And absolutely I think there's still remaining work to be done. So one worry just to whet your whistle for it is the idea of probability. In ordinary quantum mechanics, we say things like there's a 30% chance to observe the electron to be spinning clockwise. Many worlds says every possible outcome comes true in one world or another. There's going to be a world where the electron is spinning clockwise, in another world where it's spinning counterclockwise with 100% probability. So the basic idea that we will try to get across is that probability should be thought of as subjective. It's a matter of a person's knowledge, not a matter of an objective feature of the world. In the ordinary course of quantum evolution, you will find yourself either on a branch where the electron is spinning clockwise, or the one where it's spinning counterclockwise, and there will be a little moment when you don't know which one you are on. In that moment, you have no choice but to assign a probability. I think there's a chance I'm on the spin up branch, a chance I'm on the spin down branch. The worlds you find yourself in that you could possibly find yourself in are not created equal. As we'll see quantitatively, there can be more of some worlds and less of others. Essentially, the worlds have different weights or thicknesses, and this turns out to be super duper important for explaining the outcomes of experiments. Thicker worlds correspond to a higher probability of observing that measurement outcome a deeper problem. But one of my favorites to think about is the question of the emergence of the classical world. Our everyday lives, like we said, are accounted for pretty well by good old fashioned Newtonian classical physics. Why? Why is that such a good approximation to this very different quantum setup? In alternatives to many worlds. The classical picture is typically just. Put in by hand. They include classical ideas like the position of a particle as part of the postulates of the theory. But in many worlds, there's no room for that. You've already said there are wave functions and they evolve in this way. That's the end of the theory. So somehow we have to derive how things like the classical notion of the position of a particle come into being in many worlds. The good news is we can take this particular lemon that the classical world must be derived rather than postulated, and we can make lemonade. There are many unanswered questions in physics, and a famous one is how to reconcile quantum mechanics with gravity. Right? The famous problem of quantum gravity. In particular, we have general relativity, Einstein's theory of curved space time, which is a very good classical theory of gravity. It doesn't play well with quantum mechanics. Maybe the many worlds interpretation or the many worlds viewpoint can help us with that. The other forces other than gravity, we have successfully quantized them. We start with a classical theory. We turn it into a quantum one that hasn't worked with general relativity, but also in the back of our minds we remember that nature doesn't quantize classical theories. It is quantum from the start. Maybe we should instead start with a purely quantum theory and find the classical world within it. Many worlds provides the perfect setup for doing this. The foundations of quantum mechanics are a touchy subject. Many physicists have outright ignored the topic for decades now, and some of the ones who did think about it had to do so in secret. That attitude is still around, but it's beginning to change. It's become a bit more respectable to think out loud and in public about what's really going on during a quantum measurement. In my view, Many Worlds gives us the best theory we have. But you have to admit, it's a challenging way of thinking about our usual picture of the world. Even though it's a very simple theory, to state many worlds is extremely far away from how we usually think about things. So in that kind of situation, it makes perfect sense to be methodologically cautious, to admit that we don't have an entirely firm grasp about what's going on, and to think very, very carefully about the implications of our ideas. On the other hand, it's also kind of fun to be bold and see what happens. So let's start exploring.