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. 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. Please - lets focus on genuine problems of the MWI, rather than making up problems that don't exist. -- ---------------------------------------------------------------------------- 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/Z3xaIFoMga6LycqS%40zen.
