On Tue, Feb 18, 2020 at 9:46 AM 'Brent Meeker' via Everything List < [email protected]> wrote:
> On 2/17/2020 2:11 AM, Bruce Kellett wrote: > > 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. > > > Yes, I agree with that > Thanks, that's progress at least. It's another way of expressing my objection that while alpha=0.5 produces a > split into two worlds, alpha= 0.499 produces a split into a thousand worlds. > You are harking back to the branch counting idea. I agree that that is a natural way to think of outcomes having different weights -- by being associated with different numbers of branches. The problem, of course, is that this is not compatible with linear evolution according to the Schrodinger equation. Since the selling point of Everett was supposed to be "The SWE and nothing else!", anything along these lines is contrary to the hype. > But proponents of MWI like Sean Carroll and Bruno, essentially assume > there are already (infinitely?) many branches which, prior to the > measurement, are identical at the macroscopic level, but which get > projected (split) onto orthogonal subspaces by a measurement. > I know that Bruno talks in these terms, but I may have missed something in Carroll's book because I don't see that idea coming to the fore there. However, something similar has been suggested by other Everettians -- think of David Deutsch -- but since it departs even further from the original Everettian ideal, I don't think the idea has become very popular. I have been looking again at Sean's account of the origin of the Born rule in his new book. He gives an argument against branch counting as the basis for probability which I think is very weak, bordering on the imbecilic. David Wallace gives essentially the same argument in his book on the Emergent Multiverse. Sean's account goes like this: "Let's first dispatch the wrong idea of branch counting before turning to a strategy that actually works. Consider a single electron whose vertical spin has been measured by an apparatus, so that decoherence and branching has occurred. ... Let's imagine that the amplitudes for spin-up and spin-down aren't equal, but rather we have an unbalanced state |Psi>, with unequal amplitudes for the two directions. |Psi> = sqrt(1/3)|spin-up> + sqrt (2/3)spin-down>. Since the Born rule says the probability equals the amplitude squared, we should have a 1/3 probability of seeing spin-up and a 2/3 probability of seeing spin-down. "Imagine that we didn't know about the Born rule, and were tempted to assign probabilities by simple branch counting. Think about the point of view of the observers on the two branches. From their perspective (1p view, Ed.), those amplitudes are just invisible numbers multiplying their branch in the wave function of the universe. Why should they have anything to do with probabilities? (Good question, Ed.) Both observers are equally real, and they don't even know which branch they're on until they look. Wouldn't it be more rational, or at least more democratic, to assign them equal credences? "The obvious problem with that is that we're allowed to keep on measuring things. Imagine that we agreed ahead of time that if we measured spin-up, we would stop there, but if we measured spin-down, an automatic mechanism would quickly measure another spin. This second spins is in a state of spin-right, which we know can be written as a superposition of spin-up and spin-down. Once we've measured it (only on the branch where the first spin was down), we have three branches: one where the first spin was up, one where we got down and then up, and one where we got down twice in a row. The rule of 'assign equal probabilities to each branch' would tell us to assign a probability of 1/3 to each of these possibilities. "That's silly. If we followed that rule, the probability of the original spin-up branch would suddenly change when we did a measurement on the spin-down branch, going from 1/2 to 1/3. ....." (pp.142-4) That argument is about as silly as me saying that I don't know the colour of my car today because I might have it re-sprayed tomorrow! So I don't think Sean is into branch counting. His actual argument is little more than a decision to put the Born rule in by hand, since it is clear that linear evolution cannot give results that are sensitive to the coefficients (amplitudes). It is very difficult to make sense of his idea of branch 'weights' or 'thicknesses' when these do not change the actual nature of a branch, and are not visible to the 1p view from within the branch. 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/CAFxXSLSBO_SU84vVuMM2Sx9MRhc0SUdVZp-xJ6qhyXK4YHWqiQ%40mail.gmail.com.
