On Sun, Jan 5, 2025 at 12:44 AM Bruce Kellett <[email protected]> wrote:
> On Sun, Jan 5, 2025 at 7:46 AM John Clark <[email protected]> wrote: > >> >> *About a month ago Sean Carroll uploaded a very good video explaining the >> Many Worlds theory, but it's over an hour long so I know there's about as >> much chance of a dilettante such as yourself of actually watching it is >> there is of you reading a post of mine if it's longer than about 100 words. >> * >> >> *The Many Worlds of Quantum Mechanics | Dr. Sean Carroll >> <https://www.youtube.com/watch?v=FTmxIUz21bo&t=8s> * >> > > I watched this video, but it is not as comprehensive as Carroll's book > "Something Deeply Hidden". > > However, something came up in the question period that might warrant a > comment. Talking about the Born rule, Carroll justifies it by saying that > if you measure the spin of 1000 unpolarized particles, you get 2^1000 > different UP-DOWN sequences. However, the vast majority of these sequences > will show proportions of UP vs DOWN close to the Born rule prediction of > 50/50. In the limit, if such a limit makes sense, the proportion of > sequences that show marked deviations from the Born Rule proportions will > form a set of measure zero, and can be ignored. > > That is just the law of large numbers at work, and is all very well if the > amplitudes are such that the Born probabilities are equal to 0.5. But it is > easy to rotate your S-G magnets so that the Born probabilities are quite > different, say, 0.9-Up to 0.1-DOWN. Now take 1000 trials again. According > to Everett, you necessarily get the same 2^1000 sequences of UP-DOWN that > you had before. The law of large numbers will then tell you that the > majority of these will have approximately a 50/50 UP/DOWN split, which is > grossly in violation of the Born rule result of a 90/10 split. In other > words, MWI. or Everettian QM. has a problem reproducing the Born rule. It > works in the simple case of equal probabilities, but fails miserably once > one departs substantially from equal probabilities. > > Bruce > David Z Albert mentions that if you define a measurement operator that just tells you the *fraction* of spin-up vs. spin-down in a large sequence of identical measurements, then even without any collapse assumption, in the limit as # measurements goes to infinity the wavefunction will approach an eigenstate of this operator that matches the probability that would be predicted by the Born rule. See his comments on p. 238 of The Cosmos of Science at https://books.google.com/books?id=_HgF3wfADJIC&lpg=PP1&pg=PA238#v=onepage&q&f=false "Then, even though there will actually be no matter of fact about what h takes the outcomes of any of those measurements to be, nonetheless, as the number of those measurements which have already been carried out goes to infinity, the state of the world will approach (not as a merely probabilistic limit, but as a well-defined mathematical epsilon-and-delta-type limit) a state in which the reports of h about the statistical frequency of any particular outcome of those measurements will be perfectly definite, and also perfectly in accord with the standard quantum mechanical predictions about what the frequency out to be." Jesse > -- > 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 view this discussion visit > https://groups.google.com/d/msgid/everything-list/CAFxXSLR0eNrjuTi-8vt_jMsCe3H7qB4UF84H6n6%3Dp8MMYaY4Gg%40mail.gmail.com > <https://groups.google.com/d/msgid/everything-list/CAFxXSLR0eNrjuTi-8vt_jMsCe3H7qB4UF84H6n6%3Dp8MMYaY4Gg%40mail.gmail.com?utm_medium=email&utm_source=footer> > . > -- 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 view this discussion visit https://groups.google.com/d/msgid/everything-list/CAPCWU3JG8kKwVugfkVbdktwJ86fd2X7d1ZgU8y%2BWnEjOTPRKSA%40mail.gmail.com.
