On Fri, Aug 29, 2025 at 2:47 AM Jesse Mazer <[email protected]> wrote:
> > You were discussing a case of this form: "This is easily seen if one > considers a wave function with a binary outcome, |0> and |1> for example. > After N repeated trials, one has 2^N strings of possible outcome sequences. > One can count the number of, say, ones in each possible outcome sequence." > > If we are interested in statistics for N trials, let's define a > "supertrial" as a sequence of N trials of the individual measurement, and > say that we are repeating many supertrials and recording the results of all > the individual trials in each supertrial using some kind of physical memory > (persistent 'pointer states'). Each supertrial has 2^N possible outcomes, > and for a given supertrial outcome O (like up, down, up, up, up, down for > N=6) you can define a measurement operator on the pointer states whose > eigenvalues correspond to what the records would tell you about the > fraction of supertrials where the outcome was O. If I'm understanding the > result in those references correctly, then if one models the interaction > between quantum system, measuring apparatus, and records using only the > deterministic Schrodinger equation, without any collapse assumption or Born > rule, one can show that in the limit as the number of supertrials goes to > infinity, all the amplitude for the whole system including the records > becomes concentrated on state vectors that are parallel to the eigenvector > of the measurement operator with the eigenvalue that exactly matches the > frequency of outcome O that would have been predicted if you *had* used the > collapse assumption and Born rule for individual measurements. And this > should be true even if the probability for up vs. down on individual > measurements was not 50/50 given the experimental setup. > I haven't looked into this in any detail, but it seems to be a recasting of an idea that has been around for a long time. This idea hasn't made it into the mainstream because the details failed to work out. There are all sorts of problems with the idea, and it doesn't appear to translate well to the argument I am making. The 2^N sequences that result from repeated measurements on the basic binary system do not form a measurement in themselves. There is no operator for this, and no eigenfunctions and there is no obvious outcome. The results that one wants are the counts of zeros, say, in each sequence, so there is no single well-defined outcome. So I don't think it is worth worrying too much about the sort of argument you refer to -- it is not going anywhere. 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/CAFxXSLTN_P_8fZXMJOgmypO5zD0voia2XJfeBfowugkGwUy8ow%40mail.gmail.com.
