On Mon, Jan 06, 2025 at 09:23:50PM -0800, Brent Meeker 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]> 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).
But that simple symmetry only applies if you've included also those observers who have rotated their apparatus -θ as well as those who have rotated the apparatus θ. If you restrict the range of observers to just those who have rotated the apparatus to θ (as Bruce does), then it is no longer true that "for every observer who sees p*N Ups then there will also be an observer who sees (1-p)*N UPs". > 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. > -- ---------------------------------------------------------------------------- Dr Russell Standish Phone 0425 253119 (mobile) Principal, High Performance Coders [email protected] http://www.hpcoders.com.au ---------------------------------------------------------------------------- -- 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/Z3zH5JqAk2TAQzbG%40zen.
