Morbert said:
As an aside: Does Vaidman or anyone explain how to exclude worlds with zero weights when pursuing these equal-amplitude terms? E.g. If we can rewrite a term ##\sqrt{\frac{2}{3}}|\psi\rangle## as ##\sqrt{\frac{1}{3}}|\psi\rangle + \sqrt{\frac{1}{3}}|\psi\rangle## what stops us from rewriting ##0|\psi\rangle## as ##|\psi\rangle - |\psi\rangle##
I can boil down my argument to this:
If you are doing a Markov chain in a equally likely scenario (coin toss, roll of a die etc.), then you can drop the probabilitity calculations at every branch and just count the final outcomes. I've often used this trick myself. Three rolls of a die, means ##6^3 = 216## equally likely outcomes and you simply count how many add up to 17, say, and that's your final probability: ##N(17)/216##.
A Markov chain is usually interpreted as a model of all the possibilities in a probabilistic setting. Only one line through the chain will actually happen. But, of course, it could be interpreted as an MWI-type model of everything that happens.
But, you can only replace probabilities with counting if everything has the same equal likelihood at every stage. For example, suppose we toss a coin to get us started. If it's heads we toss it again. If it's tails we roll a die. That gives us 8 final outcomes. But, these outcomes are not equally likely anymore. Even though each branch was an equally likely split. If we tried the MWI interpretation, we would find six worlds where the first toss was a tail and only two where it was a head. This won't do.
To fix this, we would have to split the second coin toss into six worlds: three being a head and three a tail. Now, we do have twelve equally likely final outcomes.
To do this counting trick for Markov chains requires some sleight of hand to keep the number of outcomes representative of the probabilies. And, in general, this counting trick cannot be made to work in all scenarios.
This idea, I believe, is at the heart of the idea that "probability is an illusion from the number of worlds" presented in these papers. They complicate the matter by reference to observers and macroscopic devices. But, these complications effectively obscure the fundamental problems with the idea:
1) You would need a superdeterministic sleight of hand to keep the number of worlds in all cases aligned with the quantum mechanical probabilities.
2) There is an immediate problem with any branching that is itself not an equally likely model. Addition of angular momentum using the Clebsch-Gordan coefficients is one example where the fundamental branching is not equally likely.
I just don't see how one could possibly pull off this trick in general.