Last week’s post about the Many-Worlds variant in “Divided by Infinity” prompted the usual vigorous discussion about the merits of the Many-Worlds Interpretation. This included the common objection that we don’t know how to obtain the probability of measurement outcomes in the Many-Worlds Interpretation.
This is one of those Deep Questions that lots of people expend lots of time talking about, and I can never quite understand what the problem is. How do we obtain the probability of events in the Many-Worlds Interpretation? Using the Born rule, of course: the probability of a particular measurement result is related to the squared norm of the wavefunction associated with that result. It’s the same rule that you use to get the probability in any other interpretation.
Now, it’s true that there isn’t a generally accepted way of deriving the Born rule in Many-Worlds– some people have claimed to be able to do it, but these claims remain highly controversial (as usual, the Stanford Encyclopedia of Philosophy entry includes a pretty good discussion). I’m not sure how this is a killer objection to Many-Worlds, though, because none of the other interpretations provide a generally accepted means of deriving the Born rule, either. If there were a way to get it from your favorite collapse interpretation, that’d be one thing, but arguing that Many-Worlds doesn’t allow you to do something that none of the other interpretations can manage to do doesn’t strike me as especially devastating.
A lot of the arguments go farther than that, though, in ways that don’t particularly make sense to me. The general argument seems to be that since all outcomes exist somewhere, the whole concept of probability is meaningless, and mere anarchy is loosed upon the world. I’ve posted about this before, and I continue to be baffled by it. This line seems to me to implicitly rely on assigning equal weight to each of the possible outcomes, and I don’t see how that’s significantly different from the crazy person’s argument in this Daily Show segment about the LHC (around 3:20 in).
Anyway, I continue to be unimpressed by this line of attack on Many-Worlds. If anything, a lot of these arguments make me more favorably disposed toward it, because I end up finding the counterarguments kind of silly. I’ve tried reading some of the papers about this stuff, but nothing I’ve read is terribly convincing. If there’s a definitive summary of this stuff out there, I’d be happy to be pointed to it. If there’s a convincing derivation of the Born rule in some non-MWI context, I might even change my mind. Short of that, though, I just don’t find this to be a devastating rebuke.