On Tue, Jan 7, 2025 at 8:42 AM Russell Standish <li...@hpcoders.com.au> 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. > 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. 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 everything-list+unsubscr...@googlegroups.com. To view this discussion visit https://groups.google.com/d/msgid/everything-list/CAFxXSLQNreitHDWG6k-qrBDHWKN5JMfFYLY0AjPLzN13kpzCHw%40mail.gmail.com.
