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. Bruce -- 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/CAFxXSLRG-r%3DLwwO3a-%2BjJJB0uKs67QqboNMnJEVdMFQGOBq5pA%40mail.gmail.com.
