A longstanding issue in attempts to understand the Everett (Many-Worlds) approach to quantum mechanics is the origin of the Born rule: why is the probability given by the square of the amplitude? Following Vaidman, we note that observers are in a position of self-locating uncertainty during the period between the branches of the wave function splitting via decoherence and the observer registering the outcome of the measurement. In this period it is tempting to regard each branch as equiprobable, but we argue that the temptation should be resisted. Applying lessons from this analysis, we demonstrate (using methods similar to those of Zurek's envariance-based derivation) that the Born rule is the uniquely rational way of apportioning credence in Everettian quantum mechanics. In doing so, we rely on a single key principle: changes purely to the environment do not affect the probabilities one ought to assign to measurement outcomes in a local subsystem. We arrive at a method for assigning probabilities in cases that involve both classical and quantum self-locating uncertainty. This method provides unique answers to quantum Sleeping Beauty problems, as well as a well-defined procedure for calculating probabilities in quantum cosmological multiverses with multiple similar observers.
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Here's a blog post I wrote about this recently:
http://blog.rongarret.info/2019/07/the-trouble-with-many-wor...
The TL;DR is that the critics are correct. Deriving the Born rule begs the question because it makes an unjustified assumption (branching indifference) and also introduces an "invisible pink unicorn", i.e. a concept that, according to the theory, has physical significance but cannot be measured. In the case of MWI that concept is branch weights.
[UPDATE] The critique I wrote is based on Wallace (https://arxiv.org/abs/0906.2718). Carroll's argument appears to be somewhat different. I'm just now working my way through his paper (https://arxiv.org/abs/1405.7577) but I'd be very surprised if it did not also have some untenable assumption hidden in there somewhere.
Being able to count worlds in the manner you describe is apparently not easy to justify. If I recall correctly, this is actually a pretty thorny epistemological problem with the theory. IIRC the current response among Many Worlds people is that either (1) it doesn't really matter because there is no reason to believe that probabilities are "real" in the first place, or (2) attempting to show that if you did insist on finding a metric that looked like probability, it would provably have to be the Born probability (see https://arxiv.org/abs/1405.7577). All this stuff is way over my head so I have no way of evaluating whether it's persuasive or not, but it does at least seem to be contentious among physicists.
I agree that progress in experimental abilities and QC is really forcing physicists to think carefully about what QM means. In fact the month of May saw three papers by major physicists about these deeper issues in QM [1,2,3] In my own humble capacity as a graduate student in physics, my research is about clearly understanding the divide between classical and quantum physics.
On the rewriting of theory, I should have been clearer. I meant that when you rewrite the theory you should think about ontology. Differences in ontology between different rewrites, as well as interpretations of those rewrites, will point to how quantum theory can be generalized.
I agree completely…
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that quantum mechanics is taught horribly. Strangest of all are introductory quantum/modern physics courses that are meant to give students an intuition of quantum theory use the Copanhagen interpretation -the one that says the least about ontology and emphasizes calculations and empiricism.
I still stand behind my central claim. Let me be clearer. The mathematical model of classical physics says something about physical reality. The mathematical model of quantum mechanics says something very different about reality. Even if there are disagreements, we all agree that the ontology of classical physics is very much incorrect. Extrapolating from this I claim that the next theory of physics will have an ontology that will look nothing like that of quantum theory. As I have said previously, the ontology of quantum theory can be a means to an end (the next theory), but not the end itself.
[1] http://arxiv.org/abs/1405.1548
[2] http://arxiv.org/abs/1405.3483
[3] http://arxiv.org/abs/1405.7577
The Fermi paradox is the conflict between an expectation of a high {\em ex ante} probability of intelligent life elsewhere in the universe and the apparently lifeless universe we in fact observe.
Despite their massive size, successful deep artificial neural networks can exhibit a remarkably small difference between training and test performance.
In honor of Alan Turing's hundredth birthday, I unwisely set out some thoughts about one of Turing's obsessions throughout his life, the question of physics and free will.