On Sun, Jan 5, 2025 at 5:35 PM Bruce Kellett <[email protected]> wrote:
> On Mon, Jan 6, 2025 at 9:14 AM Jesse Mazer <[email protected]> wrote: > >> 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." >> > > But then Albert goes on to say that there are all sorts of reasons why > this simple theory cannot be the answer to the origin of the Born rule. I > have pointed out one of the most cogent of these. If you perform similar > measurements on N identically prepared systems (say z-spin measurements on > systems prepared in an x-spin-left state), then according to Everett, you > get all 2^N possible sequences of UP/DOWN spins. This exhausts the > possibilities for the outcome of N trials, and, significantly, you must get > exactly the same 2^N sequences whatever the amplitudes of the initial > superposition might be. So you get these 2^N sequences if the amplitudes > are equal, and also if the amplitudes are in the ratio 0.9/0.1. This > behaviour is incompatible with the Born rule, and hence with ordinary > quantum mechanics. > You do get all these sequences but this tells us nothing about what their relative probabilities/frequencies are. I assume as an extension of his analysis, if we did repeated experiments where on each trial we performed exactly N measurements and this was repeated over many trials (approaching infinity), then you could define a measurement operator that would tell you the fraction with any specific N-sequence (for example, for N=3 there would be an operator giving the fraction of trials with result 000, likewise other operators for 001 and 010 and 011 and 100 and 101 and 110 and 111). If you had a setup where the relative probability of these sequences was not uniform according to the Born rule, then if the number of trials with that setup goes to infinity, it will presumably likewise be true that the state approaches the eigenstate of this operator with the frequency predicted by the Born rule, without ever actually invoking the Born rule. Albert would presumably say that this still doesn't resolve the measurement problem because it doesn't give an outcome on any particular trial, only a sort of aggregate over many trials, but this is different from the criticism you are making. Even if we do use the Born rule in the above scenario, it's still true that each of the specific outcomes that are possible for a given trial with N measurements (eg the outcomes 000, 001, 010, 011, 100, 101, 110, and 111) will occur in the long term, but that doesn't mean they are equiprobable. 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/CAPCWU3Jy2-7a_eXU19ms9opMn07buvXdL3VBgKagPEOr%3DdxhGA%40mail.gmail.com.
