On Sat, Apr 23, 2022 at 6:55 PM smitra <smi...@zonnet.nl> wrote: > On 23-04-2022 03:44, Bruce Kellett wrote: > > On Sat, Apr 23, 2022 at 11:18 AM George Kahrimanis > > <gekah...@gmail.com> wrote: > > > >> On Friday, April 22, 2022 at 1:54:36 AM UTC+3 Bruce wrote: > >> > >>> we now know that MWI is inconsistent with any sensible > >>> interpretation of probability; strict MWI is inconsistent with the > >>> Born rule. > >> > >> Dittos!!! At least, mostly. > >> > >> What do you mean "we now know"? Any citations, pretty please? > > > > This has been argued by people like Adrian Kent and David Albert. See > > Albert's "Mindscape" discussion with Sean Carroll, for example. Or > > Kent's contribution to the volume "Many Worlds? Everett, Quantum > > Theory, and Reality" (Oxford, 2010). > > > > In claiming that MWI is inconsistent with the Born rule, I point to > > the fact that MWI insists that every outcome occurs (in different > > branches) on every trial. > > This in itself cannot possibly lead to a problem,
But it does lead to a problem. As explained below. > because we may let Mr. > DATA from Star Trek do experiments with two possible outcomes with > probabilities of 1/3 and 2/3. A moment's thought should make it clear to you that this is not possible. If both possibilities are realized, it cannot be the case that one has twice the probability of the other. In the long run, if both are realized they have equal probabilities of 1/2. After each experiment where MR. DATA does > n trials, we reset Mr. DATA's internal state to that just before the > first experiment. Why would you want to reset his internal state to that of just before the experiment? > For Mr. DATA every outcome for the n trials occurs and > yet there is no contradiction with the notion of probabilities here. At > least, while one may invoke a problem here like in the Sleeping Beauty > paradox, this is then really an issue within the realm of probability > theory, it has nothing whatsoever to do with the MWI. > The Sleeping Beauty paradox is of no conceivable relevance to the argument. This means that for the state > > > > a|0> + b|1> > > > > there is a branch with result |0> and another branch with result |1> > > for every trial, independent of the coefficients a and b. The Born > > rule, on the other hand, says that the probability of obtaining |0> is > > |a|^2, and the probability of obtaining |1> is |b|^2. (Note that there > > is no branching with the application of the Born rule -- there is just > > one result, obtained with the specified probability.) > > Whether or not there is branching is independent of assuming the Born > rule. > You can't have branching with unequal probabilities for the formation of each branch when both branches are certainly formed. So if the Born rule gives unequal probabilities for the results, you cannot form a single branch for each result at the same time as satisfying the Born rule. You can (by fiat) give your branches different weights, but such weights are not probabilities. > > Over N trials, > > strict MWI (one example of each result, on different branches) implies > > that the relative frequency of |0> and |1> results tends to 0.5 for > > the majority of branches, regardless of the coefficients a and b. > > Whereas the Born rule says the the proportion of |0> results, for > > example, will tend to |a|^2 for large N. (Recall that |a|^2 + |b|^2 = > > 1). For general and and b, these predictions are incompatible. So MWI > > is inconsistent with the Born rule. > > > > That's MWI with branch counting instead of the Born rule, which is > indeed not the same as QM without collapse. > There is no branch counting involved. As usual, you seek to raise red herrings in an attempt to divert attention from the logic of the argument as presented. The probabilities for each result in Everettian QM do not, in general, agree with the Born rule, as has been pointed out by Kent and Albert among others. 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 on the web visit https://groups.google.com/d/msgid/everything-list/CAFxXSLSgxVO9rdmt5931OWFuONhEB6qM7riPKBVwvLB9FETPUA%40mail.gmail.com.
