[Viliam1234]

If you insist that MWI must mean "a discrete number of clearly separated worlds", then yes, such interpretation would have a problem with the Born rule.

(That is apparently the definition the author of the linked article uses, guessing by his reaction: "Wait, what??? There is no 'well defined notion of how many branches there are?'")

I can only say that I have never met a proponent of MWI who meant this.

[lisper]

I am the author.

> I can only say that I have never met a proponent of MWI who meant this.

What can I say? There are a lot of MWI proponents who profess to believe this. Here, for example, is Sean Carroll answering the question, "How many parallel universes are there?"

https://www.youtube.com/watch?v=7tQiy5iCX4o

Of course, he doesn't actually give a concrete answer, but he very strongly implies that the question has an answer, i.e. that the question is a meaningful one to ask, and that implies that the MWI does in fact mean that there is a discrete number of clearly separated worlds.

In fact, I challenge you find a single example of a prominent MWI proponent saying something in public (which is to say, in a public forum or a publication whose target audience is the general public) that even implies that the many-worlds of the MWI are not distinct, countable entities. I only know of one example, and it is very well hidden.

There is a more fundamental problem: if the MWI does not mean "a discrete number of clearly separated worlds" then it fails as an interpretation of QM, i.e. as a solution to the measurement problem. The whole point is that measurements appear to produce discrete outcomes despite the fact that the math says that everything is one big quantum superposition. If all you have to say about this is, "Yeah, it's all one big quantum superposition" then you have failed to solve the problem. You have simply swept the hard part under the rug.

[Viliam1234]

> Of course, he doesn't actually give a concrete answer, but he very strongly implies that the question has an answer, i.e. that the question is a meaningful one to ask, and that implies that the MWI does in fact mean that there is a discrete number of clearly separated worlds.

In the video, Sean Carroll talks to a non-expert audience, so he must simplify some things, and then it is your or my guess about what the unsimplified version was supposed to be. He says something like: "we don't know, even whether it is finite or infinite, but if it is finite it is a very large number such as 10^10^123". But notice that he also uses as an analogy an interval from 0 to 1, which can be split to half as many times as you need.

You see this as him believing in discrete separated universes, of which there is a definite number (potentially infinite). Yes, that makes sense.

I see another possible understanding, that he is talking about "meaningfully different" universes, because that is what we care about on the macro level. To explain what I mean, imagine that we observe two particles. Any of them can be in a huge number of possible positions, moving in a huge number of possible directions, at a huge number of possible speed. But if we ask whether those two particles hit each other and transformed into another particle, that kinda collapses this huge possibility space into a "yes / no" question. Out of practically infinity, two meaningfully different options.

On a macro level, either the cat is alive or it is dead. Those are two meaningfully different states. If we focus on one particle in the cat's body, there is a continuum of where precisely that particle could be, and what momentum it has. So from the particle's perspective, there is a continuum of options. But from the cat's perspective, and the cat's owner's perspective, this continuum does not matter; unless it changes the macro state, i.e. the particle kills the cat, or at least maybe hits its neuron and makes it do something differently. So it seems possible to me that Sean Carroll talks about the number of worlds that are different from human perspective.

Then there is another problem in physics that we don't know how/whether the very space and time are quantized. We use the mathematical abstraction of a "real number" that has an infinite number of digits after the decimal dot, but of course that infinite number of digits can never be observed experimentally. We don't know. Maybe it is something like what Wolfram says, that on a deep level, spacetime is a discrete graph evolving according to some rules. If something like that would be the case, that would reduce the possible number of states in the universe, even on the micro level, to a huge but finite number. And the mixed state of the multiverse would consist of this finite number of branches, each of them assigned a tiny complex amplitude. So that's another way how things could get finite.

And I am saying this just as a random guy who never studied these things, I just sometimes read something on the topic, and some ideas feel to me like obvious consequences of the stuff that is "in the water supply". So I believe that if I see a solution to a problem, then if it makes sense, someone like Sean Carroll is 10000x more likely to notice the problem and the solution, and develop it much further than I ever could. Or when you make a survey, and a half or a third of people who study quantum physics for living say that some version of MWI seems like the correct interpretation to them, I don't believe there is a simple devastating argument against it that all of these people have simply missed.

[lisper]

> I am saying this just as a random guy who never studied these things

OK, well, let me tell you as a non-random guy who has studied these things extensively that the MWI is very commonly misrepresented. It is not a case of simplification for a lay audience, it is flat-out lying, at least most of the time. The math does not say that there are parallel universes. All the math tells you is that in order to recover the results of experiments you have to throw away some of the information contained in the wave function. MWI proponents interpret this by saying that the discarded information has to correspond to something real, and they call that thing "parallel universes". But there are three problems with this. First, the MWI does not explain the Born rule. Second, the math doesn't tell you whether or not the discarded parts of the wave function describe something real or not. It is possible that mathematical operation of discarding parts of the wave function actually corresponds to real physical phenomenon, i.e. that whatever is described by the discarded parts of the wave function actually ceases to exist. This is a tenable scientific hypothesis. It's not easy to actually make it work, but it can be done and has been done. It's called GRW collapse [1]. So anyone who tells you that the MWI is the only possible scientifically tenable interpretation of QM is lying. And anyone who leaves open even the possibility that the "parallel universes" contained in the wave function are discrete is also lying. The only MWI proponent I've ever seen being intellectually honest about this.David Deutsch in his book "The Beginning of Infinity" chapter 11.

The third problem with the MWI is something called the "preferred basis problem". This one is harder to describe succinctly, and some people claim it has been solved, but I don't agree with them. In a nutshell, all two-state QM experiments rely on some macroscopic apparatus to split a particle into a superposition of two states. But if you model the entire universe as a quantum system, this apparatus is itself a quantum system that can be in a superposition of states, so you can't say, "The polarizing beam splitter is aligned vertically or it is aligned horizontally" any more than you can say "the cat is alive or it is dead" without begging the question.

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[1] https://en.wikipedia.org/wiki/Ghirardi%E2%80%93Rimini%E2%80%...

[GoblinSlayer]

You got the preferred basis problem backward. It's one branch interpretations that have this problem, since the extant branch is absolute reality and its basis is absolute reality basis, hence the problem of privileged basis. In MWI all branches are relative and none is absolute reality, so their basis can't be thought of as absolute reality basis, branches and basis exist, but they are equal to others. This produces other criticism: universal wave function thus becomes spaghetti in which classical behavior is difficult to see when you look at it from outside, because the basis of classical behavior isn't privileged.

[lisper]

No, MWI has this problem too because it still has to account for the branch I am in.

The only interpretation that does not have this problem is the NCI because in that interpretation I am part of the fundamental ontology, at least some of the time.

[GoblinSlayer]

>Second, the math doesn't tell you whether or not the discarded parts of the wave function describe something real or not.

The math tells that there are no privileged parts of wave function.

>So anyone who tells you that the MWI is the only possible scientifically tenable interpretation of QM is lying.

Didn't you admit yourself that if MWI works it's a big deal and will kick the chair from under other interpretations?

[lisper]

> The math tells that there are no privileged parts of wave function.

That's true. But my senses tell me that there is a privileged part of the wave function, namely, the branch that I'm in.

The way I think about it nowadays is that QM is like a Necker cube. You can look at it in two different ways. You can take the God's-eye view and look at the entire wave function, or you can take the mortal's eye view and look at only a proper subset of the wave function (which is necessary in order to recover classical reality). But you can't do both at the same time. For my day-to-day life, I have no choice but to take the mortal's-eye view because I am a mortal. All of the things that matter to me depend on classical reality, and so depend on my suspension of disbelief and acting as if my branch of the multiverse is privileged, even if I can intellectually jump out of the system momentarily and recognize that the mortal's eye view is necessarily incomplete.

> Didn't you admit yourself that if MWI works it's a big deal and will kick the chair from under other interpretations?

That depends on what you mean by "works". If someone can derive the Born rule from the Schrodinger equation that will be a big deal, a slam-dunk Nobel prize. But no one has done it, and I'm pretty sure it can't be done. I'm pretty sure that the Born rule is an emergent property of our branch of the multiverse. I believe the same is true of the Second Law and even three-dimensional space. You can slice-and-dice the wave function to give you physical spaces with any number of dimensions, but three is the magic number that gives you atoms and stars and planets with stable orbits [1] and so on. So I'm pretty sure the Born rule can only be explained by the anthropic principle. There's probably a Nobel prize waiting for the person who turns that intuition into a theorem.

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[1] https://physics.stackexchange.com/questions/50142/gravity-in...

[GoblinSlayer]

>But my senses tell me that there is a privileged part of the wave function, namely, the branch that I'm in.

You could also sense that your location is privileged, because the observable universe is neatly centered at it, but science will prioritize Copernican principle over your senses.

>But you can't do both at the same time.

This doesn't match what you do. Tracing extracts mortal's-eye view from God's-eye view, so in God's-eye view you have both.

>depend on my suspension of disbelief and acting as if my branch of the multiverse is privileged

If your branch exists, it's sufficient for your day to day life, there's not much else to disbelieve. There's no need for it to be privileged. Do you worry that Earth isn't more privileged than Mars?

>But no one has done it, and I'm pretty sure it can't be done.

But quantum physics doesn't allow it. It's quantitative science where all observed phenomena are computable. If they aren't computable, then quantum physics doesn't predict them and thus diverges from observation. And Schrödinger equation is how predictions are made, collapse and measurement only act on what already exists before them and don't create anything new. So if Born rule is an observed phenomenon, it must be computable from Schrödinger equation. Also if Born rule holds with certainty, then it's a pure state, and observation won't do anything to it, so Born rule can't be created by observation.

>There's probably a Nobel prize waiting for the person who turns that intuition into a theorem.

This was argued by Max Tegmark https://arxiv.org/abs/gr-qc/9702052 I thought it's a famous diagram https://en.wikipedia.org/wiki/File:Spacetime_dimensionality....