On Tue, Jan 7, 2025 at 4:23 PM Brent Meeker <[email protected]> wrote:
> On 1/6/2025 2:33 PM, Russell Standish wrote: > > On Tue, Jan 07, 2025 at 09:12:26AM +1100, Bruce Kellett wrote: > > On Tue, Jan 7, 2025 at 8:42 AM Russell Standish <[email protected]> > <[email protected]> wrote: > > On Mon, Jan 06, 2025 at 09:50:47PM +1100, Bruce Kellett wrote: > > > We are not doing branch counting as an explanation of probability here. > > I thought that is exactly what we're doing. The aim is to reproduce > the Born rule. > > > Then you have misunderstood what I am arguing here. I am not trying to derive > the Born rule; I am just pointing out that if every outcome occurs for any > measurement, then you get results that contradict the Born rule probabilities. > > > So you're trying to do the opposite - that the theory cannot reproduce > the Born rule. It is still the same thing - Proof by contradiction is > still a valid form of proof. > > > > My point about S-G magnets to measure spin values was that they can > easily be > > rotated away from the 50/50 position. The exact values do not matter in > this > > context. You still get either an UP or a DOWN result along the axis of > the > > magnet in its final position. The only thing that changes are the > probabilities > > for each outcome. > > > > Yes - and my point is that branch counting will probably explain the > variation in probability in this experiment too. But my main point is > that your argument fails, and that is most clearly seen when creating > outcomes that are simple logical functions of the 50/50 case. > > > You have not understood the argument. It has nothing to do with branch > counting, although you seem to be insisting that that is what this is all > about. > > > > Let us consider a more realistic experimental situation. We set up a > source of > > spin-half particles in the x-spin-left state, (easily done by a > preliminary > > state preparation magnet.) Then pass these prepared particles through a > further > > S-G maget in some orientation and record the result -- either UP or > DOWN. Do > > this N times and look at the records of all copies of the > experimentalist. > > According to the Everettian theory, each copy will have recorded some > sequence > > of UP/DOWN results, but each copy will have a different sequence. In > total, > > there are 2^N copies and 2^N different output records. In fact, these > 2^N > > records will cover all possible binary sequences of length N. The > additional > > branches coming from decoherence do not come into play here. We are > considering > > only the records of recorded measurement results. The final point to be > made is > > that regardless of the orientation of the S-G magnet, we must get the > same set > > of 2^N possible sequences. Each set of results will converge to 50/50 > UP vs > > DOWN as N becomes very large. This contradicts the Born probability for > all but > > a very limited number of magnet orientations. > > > > But the setup is _not_ symmetric with respect to the set of possible > outcomes. You have to further subdivide the measured "worlds" (by > adding in additional unobserved observables) until you end with a set > of symmetric outcomes, which you can then apply > branch-counting. Summing over the unobserved observables leads to the > nonuniform probability distribution. > > > That is not what is going on here. I do not have to "further subdivide the > measured worlds (by adding in additional unobserved observables) until you end > with a set of symmetric outcomes". I have no interest in symmetric outcomes or > branch counting. You are confusing my argument with obscure thoughts of your > own. > The point is that, according to Everett, if there are two possible outcomes > for > each trial, then each is realized on any measurement. This leads to the same > 2^ > N sequences for any magnet orientation, contradicting the expectation from the > Born rule which is that the proportion of, say, UP results, should follow a > cos > ^2(theta/2) distribution, where theta is the angle between the x-direction and > the magnet orientation. The probability of an UP result depends on the magnet > orientation, which is not what is found if every outcome is realized in every > trial. > > > You are applying an "indifference principle" as Sebens and Carroll > call it when you say that each world of distinct N bit sequence is > equally likely. And you are applying it inappropriately, as that is > only justified when each outcome corresponds to physically symmetric > situations. > > No. He's not saying each bit sequence is equally likely. Probabilities > have not been introduced. He's saying that in every measurement of UP or > DWN, *both* results occur per MWI, and so in N repetitions there will be > N occurrences of UP and N occurrences of DWN and this obtains independent > of the probability of UP. Then for every observer who sees p*N Ups then > there will also be an observer who sees (1-p)*N UPs (by simple symmetry). > And if p has a Born rule value other than 0.5 then one observer will find > QM confirmed and the other will see it contradicted. > That is more or less the situation.That no "indifference principle" is required is obvious from the fact that the N trials at each orientation of the S-G magnet results in 2^N sequences of UP/DOWN results, one such sequence for each observer or branch. These 2^N sequences cover all possible binary sequences of UP/DOWN results. So, clearly, the same set of sequences must result at every orientation -- there are no other possibilities. So no assumption about equal probabilities is necessary. All the sets of sequences are identical. And, for the majority of cases, the probabilities resulting from the data contradict the quantum expectation of the Born frequencies. Any given observer at any magnet orientation gets some sequence of UP/DOWN results. To estimate the probability of say UP, he or she simply counts the UPs and divides by N; p = n_up/N. This estimate of the probability will generally be at odds with the Born estimate, which is given by the modulus squared of the amplitude, a_up. These will generally be at odds since, by the law of large numbers, as N becomes large, there tends to be equal numbers of UPs vs DOWNs on a typical branch, which would give a probability p = 0.5 for UP, regardless of the magnet orientation and the Born probability. Bruce In order to generalise to non-symmetric situations, then you need to > some sort of branch counting, contra your claim this has nothing to do > with branch counting. > > My example above shows branch counting can't work. To make MWI work you > must either have something different than both UP and DWN occurring at > every measurement, OR you must have weights assigned to the UP and DWN > instead of just counting the numbers. > > Please - lets focus on genuine problems of the MWI, rather than making up > problems that don't exist. > > What do you consider the genuine problems? > > Brent > > > -- > 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/33f63c2a-644f-4a04-a81c-f35b882ac2a5%40gmail.com > <https://groups.google.com/d/msgid/everything-list/33f63c2a-644f-4a04-a81c-f35b882ac2a5%40gmail.com?utm_medium=email&utm_source=footer> > . > -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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