On 16 April 2015 at 07:42, meekerdb <meeke...@verizon.net> wrote: > On 4/15/2015 12:58 AM, LizR wrote: > > On 14 April 2015 at 14:05, meekerdb <meeke...@verizon.net> wrote: > >> On 4/13/2015 4:35 PM, Bruce Kellett wrote: >> >>> LizR wrote: >>> >>>> On 14 April 2015 at 00:42, Bruce Kellett <bhkell...@optusnet.com.au >>>> <mailto:bhkell...@optusnet.com.au>> 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 everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
