On 14 April 2015 at 14:05, meekerdb <[email protected]> wrote: > On 4/13/2015 4:35 PM, Bruce Kellett wrote: > >> LizR wrote: >> >>> On 14 April 2015 at 00:42, Bruce Kellett <[email protected] >>> <mailto:[email protected]>> wrote: >>> >>> The expansion of the wave function in the einselected basis of the >>> measurement operator has certain coefficients. The probabilities are >>> the absolute magnitudes of these squared. That is the Born Rule. MWI >>> advocates try hard to derive the Born Rule from MWI, but they have >>> failed to date. I think they always will fail because, as has been >>> pointed out, the separate worlds of the MWI that are required before >>> you can derive a probability measure already assume the Born Rule. >>> The argument is at best circular, and probably even incoherent. >>> >>> In an article published in the 60s (I think) Larry Niven pointed out >>> that the MWI lead to the following situation - if you throw a dice you have >>> 6 outcomes, i.e. 6 branches. But a loaded dice should favour (say) the >>> branch where it lands on 6. Hence the MWI doesn't work. >>> >>> My reaction to this (when I first read it, probably several decades ago >>> now) was that you only have 6 MACROSCOPIC outcomes - like derivations of >>> the second law of thermodynamics, Niven's description of the system relies >>> on microstates being indistinguishable /to us/. But once you take this into >>> account there are more microstates ending with a 6 uppermost - and hence a >>> lot more than 6 branches - the MWI again makes sense using branch counting, >>> at least for non-quantum dice (I may not have known terms like microstates >>> at the time, nor was it called the MWI, but that was basically what I >>> thought). >>> >> >> I do not think that classical analogies can ever get to the heart of >> quantum probabilities. >> >> Can't the same be true of any quantum event? The essential requirement >>> is that any quantum event leads to results which can be assigned a rational >>> number, rather than an irrational one. This gives us a finite number of >>> branches, and counting to get the probability. Or do quantum events lead to >>> results with irrational numbered probabilities? >>> >> >> Quantum probabilities are not required to be rational: any real value >> between 0 and 1 is possible. For example, if you prepare a Silver atom in a >> spin up state then pass it through another S-G magnet oriented at an angle >> alpha to the original, the probability that the atom will pass the second >> magnet in the up channel is cos^2(alpha/2). This can take on any real value >> in the range. >> > > One argument against branch counting is that if you have two equally > likely outcomes (which can be judged by symmetry) there are two branches; > but if a small perturbation is added then there must be many branches to > achieve probabilities (0.5-epsilon) and (0.5+epsilon) and the smaller the > perturbation the larger the number required. Of course the number required > is bounded by our ability to resolve small differences in probability, but > in principle it goes as 1/epsilon. > > I think Bruno's answer to this is that for every such experiment there are > arbitrarily many threads of the UD going throught at experiment and this > provides the order 1/epsilon ensemble. But this somewhat begs the question > of why we should consider the probabilities of all those threads to be > equal since we have lost the justification of symmetry. I think this is > "the measure problem". >
I believe it's an open question as to whether these systems (angle of rotation of a magnet for example) are continuous or quantised. If quantised then there are merely a (perhaps) very large number of branches but no measure problem. -- 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.
