Transcription
It would be great to talk about what is the many-worlds interpretation, and what is the fundamental problem or problems with it. Okay, so, open questions, other interpretations. I haven't said very much about Everettian quantum theory. What about Everettian quantum theory? What about the many-worlds interpretation?
Here is the story of the Everettian approach. There's a cartoon picture. In the cartoon picture of Everettian quantum theory, every time you do a quantum measurement, the universe splits into branches. You have a cat, the cat's, you know, superposition of alive and dead, this is the cartoon version. You measure the cat, and now, you split. There's a universe in which there's a you and an alive cat, and there's a universe in which there's a different you and a dead cat. Okay, this is how the cartoon picture is supposed to work. And it seems kind of intuitive, and if you want to take wave functions to be fundamental, it seems like, well, this is the natural thing to do with them, if you sort of want to take them seriously.
But you run into problems almost immediately with this cartoon picture. One problem is that it's not always 50-50. If the wave function is root two-thirds alive cat and root one-third dead cat, you still get two branches. So in what sense is one of them now two-thirds likely and one of them is one-third likely? If they're two branches, how do we, what does it mean to say that one of the two branches has a two-thirds probability and the other one has a one-third probability? How do we connect the branches with the notion of probability I was talking about before, randomness? If you've got a 50-50 random sequence, we expect to see zeros and ones according to some distribution that looks random. How do we get that picture of probability out of the branch picture of probability? This is not obvious.
Now one thing you might try to do is argue that somehow when you have a root one-third branch and a root two-third branches, we should think of the root two-thirds branches as really two branches, and there's three branches now. But it turns out that branch counting arguments don't work very well. There's a well-known paper from 1989 in Annals of Physics by Farhi, Goldstone, and Gutman called How Probability Arises in Quantum Mechanics, and you can link it, people can look at it. They try to get this sort of counting picture, you know, you just consider infinitely or large numbers of experiments, large numbers of repeated trials of experiments, and somehow argue that certain branches in the long run survive and others don't, and you can sort of count them in some sense, and this is where probability comes from. These sorts of arguments just, they fall out of favor because they don't work very well.
So what do you do? Well, you could just add an axiom. You could just say axiomatically when there are branches, the Born rule tells you what probabilities they have. The problem is how do we relate these probabilities back to the randomness probabilities we're talking about? What does it mean to say just by fiat there's a probability here? But there's actually a deeper problem. You see, remember we talked about different bases you could use? In the Everetting approach, there's just a giant universal wave function, and there are infinitely many bases you could pick, and if you change what basis you pick, then the branches change, right? All the components of the universal state vector are the branches, and if you change your basis, you change the branches. Which basis are the probabilities referring to? If there is, in fact, parallel universes with probabilities assigned to them, in which basis do we do this? This is known as the preferred basis problem, and I would add one more thing. Probability, when you say something has a certain probability, what you're saying is that there are n possible ways it could happen, only one of which is realized, and in many worlds approach, they all happen. So is this even a probability at all? Is it even coherent to talk about this using probabilistic language? And many worlds interpretation forces us to be skeptical about some things that we just see around us. I mean, we do experiments, we get a single outcome, the outcomes appear to be happening probabilistically, and the many worlds interpretation denies that that's true, right? If you're going to do that, you better have good evidence for it, okay.
So what do you do with all these problems? One argument is to say, okay, the preferred basis problem is kind of a problem, but maybe nature dynamically picks out a basis. Maybe as you let the universe evolve, decoherence works out well in only one basis. There's a particular basis in which, a particular way to decompose the universal wave function, so that when you decompose it in that way, decoherence gives you branches that no longer interfere with each other noticeably. I think that's Sean Carroll's argument in the Mad Dog Everett lecture, and I think you were there. Yep, yep. It's also the view that is at the center of David Wallace's 2012 book, The Emergent Multiverse. This idea is that we don't presuppose a particular basis in which the branches happen. The universe just evolves, and decoherence just doesn't work in most bases. But in a certain basis, we get nice, emergent, decoherent, no longer interfering branches, and that's what dynamically is the correct branching. And the branches are not fundamental. The world's not fundamental. They're not fundamentally there. They're just useful, convenient ways to describe the wave function.
But now we have a problem. If the branches are not fundamental, if they're emergent, we can't have a probability axiom that assigns them probabilities. You see, the axioms, the fundamental axioms of your theory are supposed to refer to fundamental things. If the branches are emergent, approximate things, not fundamental things, the axioms cannot say, oh, if at some point in the future we develop these emergent approximate branches, then by axiom they'll be assigned probabilities. If the branches are now not fundamental, but merely emergent, merely just convenient ways to describe what's going on, then it's very difficult to think about how you would make an axiom that they should be assigned probabilities. If we're not gonna get the probabilities from the axioms, we now have a fundamental problem. And this is where so much of the work in Everettian quantum theory has happened, this problem of probabilities. If the branches are emergent things, not fundamental, and we can't assign them probabilities by fiat through the axioms, how do probabilities happen?
Now I think the argument I would make here is that they don't. If you were compelled to believe in an outlandish metaphysical picture like the many worlds interpretation because you had to, because it was empirically unavoidable, like we look out into outer space and we see galaxies many, many, many billions of light years away. We see countless galaxies billions of light years away. That leads us to believe that there is a big universe out there. We see clocks on airplanes move at slightly different rates, atomic clocks move at slightly different rates. That's hard to believe, but we can do the experiments and we see this repeated rigorously many times. It's not that we should never believe outlandish things, but as Carl Sagan said, extraordinary claims require extraordinary evidence. The many worlds interpretation says that there is an uncountable, an uncountable profusion of universes that are coming at every single moment, not even just measurements, but all the time. That's an outlandish statement and sure, we could believe it if we were compelled to by either rigorous logical reasoning or by just unavoidable empirical results, but we're just not.
And when you're formulating many worlds interpretation and you run into this problem of, well, I have the preferred basis problem, I guess I can deal with that by letting the branches be emergent to decoherence, but then I can't axiomatically assign probabilities anymore. At that point, you should just give up because you're no longer compelled through rigorous logic or empirical data that you have to believe in many worlds. So why are you still trying to chase it down, right? That is, this extravagant, outlandish metaphysical picture is no longer forced upon us logically or by experiment, so why are we chasing it down, right? Why are we starting with the assumption that they should be there and we need to somehow gerrymander our axioms and principles and assumptions to get the many worlds picture to come out? And that's the impression that I get when I see some of the work going on right now, right? We're not compelled to take many worlds on as a serious idea. We can only get it off the ground by adding lots more stuff. Why are we doing this?
So let me just describe a couple of the routes people have taken and then we can quit because that's basically the end of it. One route is the route that David Wallace takes in his book, The Emergent Multiverse. It is an excellent book. You should list it on the YouTube channel and I recommend everybody interested should read it. David Wallace is a fantastic, brilliant philosopher and also trained in physics and the book is a beautiful book. I recommend it to everybody who's interested in quantum foundations. In that book, he tries to solve this problem of probability. How do we get probabilities assigned to these things? By introducing a large number of additional assumptions and when I have people read this book, I tell them read it and then just make a list of every extra assumption he has to make. He assumes that we should have the same metaphysical relationship to many copies of ourselves as we would if there were only a unique individual we were to become. That means you have to take kind of a stand on old questions like the metaphysical teleporter problem in metaphysics. The theorem he uses requires invoking a notion of free will that requires taking a compatibilist stance because in many worlds interpretation, there's just a deterministically evolving universal wave function. And yet, he has in his proof of the Born Rule, agents, which is already a dangerous idea, agents, we're bringing back agents, making choices about which unitary operations they're going to perform. This is a crucial part of the proof. And he has a little footnote where he admits, yes, this does entail certain assumptions about free will, but free will is a big problem, no one solved it. But that doesn't make the case. If you're resting on an unsolved problem, it doesn't make the case that what you're doing is going to work. He introduces a number of what he calls richness axioms and rationality axioms. The rationality axioms are supposed to be general good practices of what it means to be a rational observer. These were developed in a one-world kind of picture, and the assumption is that they also work in a many-worlds picture. Basically, the way that one tries to proceed here is one says, what does it mean to be rational? It means that you want to use the tools of decision theory, the formal, precise, probabilistic tools for making good decisions called decision theory. And people who use the tools of decision theory, who are rational, will end up assigning probabilities to branches according to the Born rule. That's roughly, in very gross outline, how this argument is supposed to work.
Now, John Norton, again, philosopher at University of Pittsburgh, raised an objection to really any such approach to try to get probability out. In a deductive argument, the conclusion cannot be any stronger than the premises. If you're trying to get probability to emerge as a conclusion, there must have been probability already in your premises. In this proof of the Born rule, one is trying to get probability out, so there must be probability somewhere in the premises. If you don't assume probability somewhere in the premises, somewhere you must be doing something that is not legitimate. And you can see how this unfolds for this decision theoretic argument, which goes back to David Deutsch also. There's an earlier version of it in a 1999 paper by David Deutsch. It's called Quantum Theory and Decisions. You can also link to that. The argument is that if you obey the rules of being a rational observer and use decision theory, you're going to end up assigning probabilities according to the Born rule. But you can ask, why is that the definition of rationality? I mean, in a many-worlds type universe, there are going to be observers who behave rationally according to the dictates of decision theory. Some of those observers are going to be very successful over 10 years. And others are going to be very unsuccessful because in the many-worlds interpretation, everything will happen on some branch. But there are also observers who do not obey the rules of decision theory. There are some very irrational observers who just choose not to follow any of the rules of decision theory. And there are going to be branches in which they're going to be unsuccessful over 10 years. And there are going to be branches in which they're successful over 10 years. All those observers are just there. And to say that, well, you should just be rational and obey decision theory by axiom does not solve the probability problem.
In a one-world picture where only one future actually happens, it seems to be the case that people who are rational and think very carefully about their decisions and use something like a decision theoretic approach, in the long run over 10 years, tend to make more money or healthier or live better lives, whatever it is that you want. And that gives us reason to think, oh, these are good rational principles. If people who follow these principles tend to do better, I see people who exercise and people who make good financial decisions and hedge their investments, they do better. I go, oh, well, there are good reasons, therefore, to do what they do and take on their principles. But you can't turn it around and say that we're going to start with axiomatically this is the way to be rational and then go backward and show that that then entails this is how probability should work. And that's kind of the sort of reverse argument that's taking place. I should say that not all Everetians take this decision theoretic view. Simon Saunders, for example, tries to do probability in a more Boltzmannian, statistical mechanical way by coarse graining and actually counting in some sense. But it's still in its embryonic form. Yeah. So there are a lot of approaches to many worlds interpretation. And at present, none of them seem to find a way to get probability off the ground. And I don't think that you can. And to the extent that you can by just taking on more and more assumptions, you're doing the thing where you're adding on extra empirical assumptions that can't be verified in an experiment. I mean, I don't know how experimentally to test that I should have the right relationship to many copies of myself. I mean, that's an extra empirical statement. If you have to take many of those on in order to get the picture off the ground, I don't know how credible it is. How much credence should I give to a theoretical picture that relies on a tower of SMHs, speculative metaphysical hypotheses? I feel like if you have to do all that work to get the theory off the ground, then it lowers your credence that we should take on such an outlandish idea that there are all these many worlds. So that's basically where I end up with the many worlds approach. And this is one of the reasons why I think there's room for another interpretation that's much more conservative that says, well, we do experiments, we see one outcome. Maybe that's because there is just one outcome. And the experiments look probabilistic. Maybe that's because they are in fact probabilistic. Nature is telling us it's probabilistic. We should listen to nature rather than saying, nope, nope, nope. Got to be deterministic. There's a universal wave function evolving deterministically. It's got to be Markovian. You know, maybe we should just listen to nature and build a theory around what nature is telling us. That's, I think, the conservative non-outlandish approach that one should take.
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