Deutsch is wrong.
http://blog.rongarret.info/2019/07/the-trouble-with-many-wor...
http://blog.rongarret.info/2019/07/the-trouble-with-many-wor...
The multiverse interpretation accounts for cases where the probabilities of each distinct observable outcome are equal according to the Born rule. But it cannot account for cases where the Born rule says there are non-equal probabilities for the possible outcomes.
This is a fairly common problem which critics of the multiverse interpretation raise. See [1] for another example where a critic raises that problem in more detail (with examples).
Deutsch and others have responded. In short, the reply is that the mathematics of the Schrodinger equation describes a density of universes in the continuum which is the multiverse, not a finite set of distinct, interacting single universes. This undercuts the critics' argument. See [2] for an example of this kind of response.
[1] https://arxiv.org/pdf/0810.2657.pdf [2] https://www.pnas.org/doi/pdf/10.1073/pnas.1324238111
Further, the author of that paper, Frank Tipler, is a notorious nutjob: https://en.wikipedia.org/wiki/Frank_J._Tipler.
I don't have time at the moment to review the paper in detail to locate any potential flaws, but I wanted to flag this for others. I think there is substantial reason to be skeptical.
I also agree there is no consensus that the problem of getting Born's rule from the Schrodinger equation has been solved to everyone's satisfaction.
Andrew Gelman calls it a "tabloid": https://statmodeling.stat.columbia.edu/2014/06/17/hurricanes....
I will check the paper out though.
[0] https://www.science.org/content/blog-post/no-more-prearrange...
Edit: I read the paper. It is borderline crank work. There are decent arguments for the Born rule in MWI but this is not one of them. (I like David Wallace's book, for example.)
One basic problem is that using symmetry arguments to justify the assignment of subjective probabilities (cf. page 4, right column) is going to fail when there isn't a symmetry available, for example for irrational probabilities.
A deeper issue is the implicit assumption that one can coarse-grain into discrete "effectively distinguishable universes" for the purpose of doing these counting arguments. There are significant conceptual difficulties doing this, and this claim is much stronger than the bare MWI. Wallace discusses this at length; see for instance the citations in the blog post you responded to.
> This undercuts the critics' argument.
No, it doesn't, for all of the reasons given in the blog post and the subsequent discussion. The Born rule is an observable fact of nature, and you cannot derive it from the Schroedinger equation, Duetsch and Wallace's claims to the contrary notwithstanding.
Edited to add my understanding: if the cardinality of the multiverse is uncountable, one has to talk about densities of branches. In that scheme, the problems which branch counting introduce do not arise.
It doesn't (see below) but even if it did...
> doesn't that undercut the argument in the blog post?
No. It's really very simple: the SE is linear. The BR is not. You can't derive a non-linear result from a linear equation.
The only thing that is even a tiny bit complicated about this is figuring out where the Deutsch-Wallace argument fails, because Deutsch and Wallace are not idiots and they hid their questionable assumption very well.
So... why does the SE not describe a "density of universes"? It's because the SE does not describe universes at all! Deutsch and Wallace specifically acknowledge this, which makes their argument all that much more untenable. The SE describes the behavior of a function called "the wave function". The wave function is not a description of anything physical. The domain of the wave function is not physical space, it is configuration space. This is the reason entanglement seems weird to us, because we live in physical space and the wave function does not.
In order to get anything physical out of the wave function -- particles, universes, anything resembling our classical reality -- you have to add some additional assumption, and any additional assumption that you add will be in some sense isomorphic to the Born rule. There is no way around this. Trying to derive the BR from the SE is like trying to prove Euclid's fifth postulate.
This is circular: you're assuming that realism about the wave function is incorrect to argue against the (tragically misnamed) many-worlds interpretation, but the only substantive claim the MWI makes is that realism about the wave function is true.
No, I'm not assuming it. I simply observe that the SR by itself does not describe the outcomes of experiments. And I'm not even talking here about quantum experiments. The SR cannot by itself even account for the fact that we live in a three-dimensional space or that there is an arrow of time. And it certainly cannot account for the Born rule, which is also an experimentally observed fact.
> the only substantive claim the MWI makes is that realism about the wave function is true.
Yes, I know. The problem with this is that it is violently at odds with observations that every human makes every moment of their lives, and it does not account for the Born rule.
Other than that there's no problem with it.
No formalism describes the outcome of experiments by itself. There always needs to be an interpretation attached, and our choice of interpretation is always underdetermined by observation.
> The problem with this is that it is violently at odds with observations that every human makes every moment of their lives
Like all other interpretations of all other physical theories, MWI isn't and can't be at odds with our observations alone, because our observations alone aren't enough to imply any particular relationship between observations in general. And like all other interpretations, it is and must be at odds with competing interpretations, and in particular with the folk-physics model we're naturally inclined to use. But this means very little, because folk-physics is wrong, and this far from the paleolithic savanna, it's wrong in ways that matter. Intuition is evidence, but it's not particularly strong evidence, and it's certainly not proof.
> and it does not account for the Born rule.
Sure, it still needs a separate account of subjective probability. But so does everything else: it's just a little harder to notice in the classical regime, since the relevant probabilities are always either 1 or 0.
That is so wrong as to border on the ridiculous. The quantum mechanics formalism, i.e. the SE plus the BR together describe the outcomes of experiments. No interpretation is required. You just turn the crank on the math and predictions pop out. There is a reason that "shut up and calculate" is a thing.
The only reason people talk about interpretations at all is that the structure of the math is violently at odds with our intuitions and subjective experience, and this leaves some people feeling queasy and wanting an explanation. There's nothing wrong with that. But it has absolutely nothing to do with the power of the formalism to make predictions, which is completely independent of any interpretation. (And this is true of classical mechanics as well.)