17:56
I think you might be misunderstanding me. I agree with you (and Sean Carroll) and have actually read quite a bit of philosophy surrounding the Born rule (as well as Everett's thesis), and I agree there has been much progress surrounding explaining the Born rule. I also think the criticism I'm describing doesn't have a lot of "bite" because ultimately if the branch counting measure is taken as an axiom it is ultimately no worse than assuming the Born rule as an axiom in Copenhagen, etc.
But what I'm trying to get at is the specific point that is even not always understood by MWI proponents, which is just that one of the superficially beautiful and compelling features of the MWI is that the probabilities are just what you get from "counting up the number of worlds." Ie if you have a wave function with two delta functions with equal coefficients then you have the same number of "worlds" in each one, so the probability is going to be 50-50 based on the principle of indifference.
But supposedly (and as best as I can tell this is pretty much agreed on by everyone, including Sean etc) this doesn't actually work, at least not naively. The reason is basically the one I described far above, that you run into trouble when you superpose wave function so that, for example, it looks like the number of worlds are in a 2:1 ratio, but the actual probability is 1:4 because of the square in the Born rule.
The problem is that I just can't find an example of this happening in reality, so it slowly started to dawn on me that maybe this criticism, which seems to be agreed on by everyone, actually might not hold up in a subtle way, ie that whenever you come up with these 1:2 vs 1:4 examples, they are contrived and if you were to actually follow backwards how you ended up with those amplitudes, they would only come from situations where you couldn't do naive branch counting because the apparatus...
...just split up the wave function in some non-50-50 proportion, in which case you can no longer trust that that proportion corresponds to some ratio of worlds, because for all you know the "measure" is built into how the amplitude is divided in the first place. This is why starting with a 50-50 branching and the re-combining I think is crucial. The above is difficult to explain, sorry if it comes across as muddled.
In any case I hope that explains why your proposed question wouldn't actually be answering what I want answered. It's not whether the MWI has a problem assigning probabilities (that can be axiomatized), it is whether the naive intuitive branch counting is really in conflict with Born.
This is important philosophically, because I think one of the most compelling aspects of MWI derives from the fact that if you just assume unitary evolution (ie a classical theory), all of the great mysteries and paradoxes of QM, the non-intuitive stuff that lead Feynman to say no one understands QM, it is all solved by just counting up branches. This is so compelling that I think philosophically a lot of people are completely convinced it cannot possibly be a wrong ontology, it would just...
...be too much of a coincidence. The same goes for me, and it all hinges on this question of whether the Born rule is really derived from unitary evolution alone, or that you need to add in a totally arbitrary axiomatic measure on the branches into order to get the Born rule. At the end of the day most people like Sean "derive" Born but still manage to make an assumption the ruins the above philosophical payoff, which is why no one exclaims that Sean et all have "solved the measure problem"
OK sorry that was long...
