On Thu, Aug 28, 2025 at 5:16 AM Brent Meeker <[email protected]> wrote:
> I think some specificity would help this debate. Suppose N=6, so there > are 64 different sequences in 64 different worlds. The number of observers > is irrelevants; we can suppose the results are recorded mechanically in > each world. Further suppose that a=b so there is no question of whether > amplitudes are being respected. Then in one of the worlds we have 011000. > Per the Born rule its probability is 0.2344. In MWI it is 1/64=0.0156. > The difference arises because the observers applying the Born rule looks at > it as an instance of 2 out of 6 successes. > The trouble with this is that you are treating this as an instance of Bernoulli trials with probability p= 0.5. When every outcome occurs with every trial we no longer have a Binomial distribution The Binomial distribution assumes that you have x successes out of N trials. In the Everettian case you have one success on every trial. So your probability above for 2 successes applies to Bernoulli trials with one as the 'success'. The thing is that the probability of getting a zero is also 1/2, so we also have four successes out of six trials in your example. The Binomial probability for this result is also 0.2344. Actually, if we regard this experiment as a test of the Born rule, we have four zeros in 6 trials, which gives an estimate of the probability as 4/6 = 0.667, or as two ones in 6 trials which gives an estimate of the probability as 2/6 = 0.333, neither estimate is equivalent to |a|^2 = 0.5. The difference becomes more pronounced as N increases. The problem with your analysis is that you are assuming a binomial distribution. and we do not have any such distribution. Bruce So why can't the MWI observer do the same calculation? He certainly can. *He > can apply the Born rule.* But when he does so, it can't be interpreted > as a probability of his branch since such probabilities would add up to > much more than 1.0 when summed over the 64 different worlds. From the > standpoint of statistics 011000 is the same as 001010 and their > probabilities sum. Their difference is just incidental, but they are > different worlds in MWI and summing them makes no sense. > > 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/CAFxXSLRfM7Gh8pVsvwqT6cTiOGFavvRSXncFmhzTiAk7VAtvDA%40mail.gmail.com.
