On Mon, Feb 17, 2020 at 6:04 PM 'Brent Meeker' via Everything List < [email protected]> wrote:
> On 2/16/2020 9:48 PM, Bruce Kellett wrote: > > On Mon, Feb 17, 2020 at 4:13 PM 'Brent Meeker' via Everything List < > [email protected]> wrote: > >> >> But exactly the same reasoning applies for any given true value of p. >> There will be different estimates by different experimenters and they can't >> all be right. Each will infer that any proportion other than the one he >> observed will have zero measure in the limit N->oo. >> > > Exactly right. That is what my example of spin measurements on an ensemble > of equally prepared spin states comes into play. If all 2^N bit strings are > realized for one orientation of the S-G magnet, then exactly the same 2^N > bit strings are realized for every other orientation. > > > ?? Suppose the ensemble is equally prepared in spin-up. What does it mean > to say all 2^N bit strings are realized for the S-G oriented left/right? > We may expect they will be for any number of trials >>N. But certainly > not for the S-G oriented up/down. > I think we are beginning to argue at cross-purposes, and I may not have understood you correctly. Let me try to restate the position clearly, and see if you can agree. Take a spin-half state, and prepare a linear combination in the x-basis: |psi> = (alpha*|x-spin up> + beta*|x-spin down>), where we assume that neither alpha nor beta is equal to zero. We can now measure this state in the x-direction and assume Everett, so that every result is obtained in a separate branch on every trial. Coding these results as zero and one, a run of N experiments will give 2^N binary strings of results, consisting of the set of all 2^N binary strings of length N. Now rotate the S-G magnet from the x-direction by, say, 10 degrees. Your results are again the set of all binary strings of length N. Similarly for any other angle (except those for which alpha or beta rotates to zero). Since the set of results is the same in all cases, even though rotation of the S-G magnet is equivalent to changing alpha and beta in the superposition, the individual sets of results must be independent of alpha and beta. However, the Born rule states that the probabilities depend on |alpha|^2 and |beta|^. But we have seen that the many-worlds data are actually independent of alpha and beta. The Born rule for probabilities is thus disconfirmed in this Everettian case. That is the crux of what I am trying to get across -- Everettian QM is disconfirmed by experiment, since experiments show results that depend on the coefficients alpha and beta, in accordance with the Born Rule. There are other points that I have been making, but let's get this straight first. 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 on the web visit https://groups.google.com/d/msgid/everything-list/CAFxXSLQM-O%3DjP9MOjKuny5%3DWJ2h%3D9fPKqZsaqDibgss0ugRziw%40mail.gmail.com.
