Sean Carroll: uncertainty

Transcript context

…Well, can you first explain it and then maybe speak to the flak you may have gotten? Sure. The classic experiment to explain quantum mechanics to people is called the Stern-Gerlach experiment. You’re measuring the spin of a particle. And in quantum mechanics, the spin is just a spin. It’s the rate at which something is rotating around in a very down to earth sense, the difference being is that it’s quantized. For something like a single electron or a single neutron, it’s either spinning clockwise or counterclockwise. Let’s put it this way. Those are the only two measurement outcomes you will ever get. There’s no it’s spinning faster or slower, it’s either spinning one direction or the other. That’s it. Two choices. According to the rules of quantum mechanics, I can set up an electron, let’s say, in a state where it is neither purely clockwise or counterclockwise but a superposition of both. And that’s not just because we don’t know the answer, it’s because it truly is both until we measure it. And then when we measure it, we see one or the other. This is the fundamental mystery of quantum mechanics is that how we describe the system when we’re not looking at it is different from what we see when we look at it. We teach our students in the Copenhagen way of thinking is that the act of measuring the spin of the electron causes a radical change in the physical state. It spontaneously collapses from being a superposition of clockwise and counterclockwise to being one or the other. And you can tell me the probability that that happens, but that’s all you can tell me. And I can’t be very specific about when it happens, what caused it to happen, why it’s happening, none of that. That’s all called the measurement problem of quantum mechanics. Many-worlds just says, “Look, I just told you a minute ago that there’s only one way function for the whole universe, and that means that you can’t take too seriously just describing the electron, you have to include everything else in the universe.” In particular, you clearly have to interact with the electron in order to measure it. Whatever is interacting with the electron should be included in the wave function that you’re describing. And look, maybe it’s just you, maybe your eyeballs are able to perceive it, but okay, I’m going to include you in the wave function. Since you have a very sophisticated listenership, I’ll be a little bit more careful than average. What does it mean to measure the spin of the electron? We don’t need to go into details, but we want the following thing to be true: If the electron were in a state that was 100% spinning clockwise, then we want the measurement to tell us it was spinning clockwise. We want your brain to go, “Yes, the electron was spinning clockwise.” Likewise, if it was 100% counterclockwise, we want to see that, to measure that. measurement to tell us it was spinning clockwise. We want your brain to go, “Yes, the electron was spinning clockwise.” Likewise, if it was 100% counterclockwise, we want to see that, to measure that. The rules of quantum mechanics, the Schrodinger equation of quantum mechanics, is 100% clear that if you want to measure it clockwise when it’s clockwise and measure it counterclockwise when it’s counterclockwise, then when it starts out in a superposition, what will happen is that you and the electron will entangle with each other. And by that I mean that the state of the universe evolves into part saying, “The electron was spinning clockwise, and I saw it clockwise,” and part of the state is it’s in a superposition with the part that says, “The electron was spinning counterclockwise, and I saw it counterclockwise.” Everyone agrees with this; entirely uncontroversial. Straightforward consequence of the Schrodinger equation. And then Niels Bohr would say, “And then part of that wave function disappears,” and we’re in the other part. And you can’t predict which part it’ll be, only the probability. Hugh Everett, who was a graduate student in the 1950s, was thinking about this, says, “I have a better idea. Part of the wave function does not magically disappear, it stays there.” The reason why that idea, Everett’s idea that the whole wave function always sticks around and just obeys the Schrodinger equation was not thought of years before is because naively, you look at it and you go, “Okay, this is predicting that I will be in a superposition, that I will be in a superposition of having seen the electron be clockwise and having seen it be counterclockwise.” No experimenter has ever felt like they were in a superposition. You always see an outcome. Everett’s move, which was genius, was to say, “The problem is not the Schrodinger equation. The problem is you have misidentified yourself in the Schrodinger equation.” You have said, “Oh, look, there’s a person who saw counterclockwise, there’s a person who saw clockwise; I should be that superposition of both.” And Everett says, “No, no, no, you’re not,” because the part of the wave function in which the spin was clockwise, once that exists, it is completely unaffected by the part of the wave function that says the spin was counterclockwise. They are apart from each other. They are un-interacting. They have no influence. What happens in one part has no influence in the other part. Everett says, “The simple resolution is to identify yourself as either the one who saw spin clockwise or the one who saw spin counterclockwise.” There are now two people once you’ve done that experiment. The Schrodinger equation doesn’t have to be messed with, all you have to do is locate yourself correctly in the wave function. That’s many-worlds.…

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