On Tuesday, August 11, 2015 at 6:08:31 PM UTC+10, Bruce wrote: > > Pierz wrote: > > Thanks Bruce, that actually makes a lot of sense ... and kind of > > completely trashes my previous understanding! It also makes QM weirder, > > and even makes me doubt MWI, which reading Deutsch had convinced me was > > the true account. > > MWI is popular, but it is not without its problems. > > > As an aside, quantum probabilities as given by the Born Rule do not > > come from branch counting -- the probability is not a measure > > of the underlying universe count. > > > > Then where do they come from? Without that notion of a measure, MWI > > seems not to be telling us all that much. > > That just the question! Deutsch and Wallace have devoted a lot of energy > trying to derive the Born rule from MWI, plus something like rational > decision theory. These attempts have been widely criticized, and I agree > with the criticism that the approach is basically circular: they get the > Born rule only by assuming that small amplitudes correspond to small > probabilities -- which is just another way of expressing the Born rule. > > > ....... > > > Sorry can you clarify why branch counting is ruled out on this, ah, > > basis? Do you mean that there are an uncountable infinity of possible > > values and therefore you can't count anything? Actually this was going > > to be another part of my original question - surely "worlds" have to at > > least be countable, even if infinite? How much sense does a "continuum > > of worlds" make? > > If space and time are continuous, there are an infinite number of > possible eigenvalues for position and momentum. So you need to consider > an infinite number of branches for most real-valued probabilities. And > the reals form an uncountable infinity. > > I think there are some technical arguments against branch counting that > I can't call to mind at the moment, but I think simple arguments > suffice. Consider the two-valued spin case. We only ever have at most > two components to the wave function, whatever the basis. If the > coefficients are such that one result has probability 1/3, and the other > 2/3, branch counting would require that there be two branches giving one > result with only one for the other result. Where did that extra branch > come from? It is not in the formalism. And since it is necessarily > identical to one of the other branches, the identity of indiscernibles > would say that we only have two distinct branches. In which case, all > probabilities would equal 0.5, whatever the measurement angle. And this > is absurd. >
That's the first objection one hears to MWI, but Deutsch's version of MWI makes that argument redundant. It's not that there is one universe per branch - that leads to the absurdity you describe. Rather there is an infinity of identical universes which differentiates into 'stacks' of differing size infinities. Deutsch explicitly repudiates the Identity of Indiscernibles, and I'm personally fine with that. The Identity of Indiscernibles seems to make sense logically, but it's a philosophical idea that predates QM by a few centuries. Leibniz could not have foreseen quantum logic either! I'm much more troubled by the basis problem. > > Bruce > > > -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
