On 16 April 2015 at 07:42, meekerdb <[email protected]> wrote: > On 4/15/2015 12:58 AM, LizR wrote: > > 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. > > > I'm quite willing to say that there can only be finite precision in any > physical measurement, so the measurements are effectively quantized even if > the theory is built on real numbers. But I don't think that solves the > measurement problem. It doesn't justify considering all the possible > values equi-probable; that requires some symmetry principle. >
That wasn't quite what I meant. If the situation is quantised and there is a rational number for each probability then we might for example have a probability of 12345 / 67890 for a given event "A" (one of two possibilities). This requires (somewhat weirdly, but the logic is OK) that there are 12345 branches in which event A happens, and 67890 - 12345 in which event B happens. All branches are equiprobable, which was my key point. PS I admit this is horrible, as stated! But if all events emerge as macroscopically similar but microscopically distinct, it does at least make sense and avoid the measure-on-infinity problem. PPS see Russell's reply for a different take on this (which I don't quite get, as yet). -- 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.
