I see it now. Yes, I am aware of that solution, and while clever, it doesn't seem satisfactory. The whole Sleeping Beauty problem class seems to be misused in a lot of physics scenarios, IMO, in part because rational agent based models aren't reversible. For example, this is where Tegmark's first book (mentioned ITT) begins to start going off the rails. He starts talking about the Doomsday Problem, and "what are the chances that you would randomly be the nth member of X sentient species ," in terms of frequencies.
This is an area where frequentism starts to become incoherent if you apply it this way. MWI is deterministic. The person you are and the time you exist in history isn't random or independent, it is entirely determined in MWI. You can apply frequentism in plenty of physics cases and get away with it, but using it here in the context of cosmic inflation or MWI makes absolutely no sense.
In the Doomsday Scenario for instance, any early human would have been just as justified in thinking humanity will die out before even 5 billion people are born as Tegmark is today worrying about humanity going extinct before 250 billion people. But obviously, when one lives is not i.i.d. He's obviously a smart guy, and I enjoyed most of the book, but this and some Born Rule explanations could be part of a public awareness campaign called "this is your brain on frequentism. Just say no! (to calling probability and frequency identical)"
You can turn the Born Rule into an argument about which bets a person should place, but that doesn't answer why those bets are likely to be good ones except in terms of empiricism when the derivations of the Born Rule are circular (e.g. when using axioms originally added just for the Born Rule). It becomes a sort of hybrid frequentist-QBism in some solutions, which I don't even think is coherent if it is unpacked.
Or, to let someone else say it:
From these axioms they conclude that rational agents should bet on the outcomes of a quantum experiment with probabilities given by the Born rule. Who cares? Should we really believe that the statistics of an experiment will be constrained by rationality axioms? And conversely, if you can show that the statistics of a quantum experiment follow the Born rule, doesn’t it become obvious that rational agents should bet that they do, making the whole decision-theoretic argument superfluous? It’s worth noting that this same criticism applies to my derivation, as it is just a cleaned up version of the Deutsch-Wallace argument...
Let’s move on to Vaidman, Carroll, and Sebens. Their derivations differ on several important points, but I’m interested here in their common point: they passionately argue that probability is about uncertainty, that a genuine source of uncertainty in Many-Worlds is self-locating uncertainty, and that locality implies that your self-locating uncertainty must be given by the Born rule. Arguing about whether probability is uncertainty is a waste of time4, but their second point is well-taken: after a measurement has been done and before you know the outcome, you are genuinely uncertain about in which branch of the wavefunction you are. I just don’t see how could this be of fundamental relevance. I can very well do the experiment with my eyes glued to the screen of the computer, so that I’m at first aware that all possible outcomes will happen, and then aware of what the outcome in my branch is, without ever passing through a moment of uncertainty in between. Decoherence does work fast enough for that to happen.5 What now? No probability anymore? And then it appears when I close my eyes for a few seconds? That makes sense if probability is only in my head, but then you’re not talking about how Nature works, and I don’t care about your notion of probability.
https://mateusaraujo.info/2021/03/12/why-i-am-unhappy-about-all-derivations-of-the-born-rule-including-mine/
I don't have these same concerns, but I think it is important than many proponents of MWI do list similar concerns about other theories in quantum foundations.
I like MWI for itself elegance; no ad hoc collapse. But there is a problem where theory is elevated above empirical results (i.e. the observation of apparent collapse), but then a crucial element of collapse, is then explained in terms of epistemology. Why prefer shifting the
squishy part of the theory from one place to another?
This is also the issue of "splitting" versions of MWI. In these, there isn't one universal wave function that we see part of, but instead the universe actually "splits," during measurement. The problem is that, while physics is time asymmetrical as a whole, parts under consideration are not, making the "causal" relationship between measurement and "splitting" another thing that begs explanation (and this is true even if you argue "cause" is just another name for description). Splitting then seems as ad-hoc as collapse, whereas a seeming benefit of non-splitting versions is that such collapse/splitting is only an appearance.
Furthermore, because MWI is fully deterministic, it seems like we should have a block universe. But do we have a growing block universe where splits occur in the direction of time's passage? That is what the splitting versions of MWI seems to suggest. But if each world is its own four dimensional object then it seems we need a new, fifth, "time" dimension for the multiverse in which splitting occurs, this being true even if we take an eternalist view of such splits as having already occured/existing eternally. There is a state of the multiverse M1 before a split occurs where it has fewer branches than M2, the multiverse at a later time, but this change cannot occur across the same time dimension as the time dimension that each individual universe has, since a split is necessarily the spawning of a new, complete four dimensional object.
Then we have to consider that, if we have an eternalist view of things, why is it that, by reversing the direction of time, we have a universe where many universes begin to merge into a smaller number of universes? Is the direction of splitting the true arrow of time? If so, why (and why are there so many physicists who embrace eternalism, claim physics is ultimately reversible, and embrace MWI?) If the physics in question is reversible, why do we posit a splitting universe instead of a merging one, aside from the fact that having it split in both directions (forwards and backwards in time) is incoherent?
Perhaps whenever we make a measurement we merge universes, such that we progress by such merges to one of many potential end points, final conditions, of the universe, assuming ad hoc that it has an end? This might work, but it blows up the rational-agent based derivations of the Born Rule. Rational agent models are not reversible, we don't say, "given what I observe now, what must have happened in the future, what endpoint must I be most likely to be converging on?"
The problem might be worse, since splits occur vis-á-vis a parent, such that we can arbitrarily pick any starting point and then see a family tree descending from that current universe. If we have two such family trees, does it work to say that splitting in both occurs across the same dimension? I'm not sure it does, given the "multi-fingered" nature of time in our one observable universe, in which case you need even more time dimensions.