You’re conflating mathematical possibilities with experiential frequencies. Yes, all 2^N sequences exist in the wavefunction, but their measures are not equal. The Born rule emerges because observers are not uniformly distributed across these sequences: almost all self-locating observers end up in high-measure branches. If you assume equal weighting, you’re rejecting the very structure of the wavefunction and replacing quantum mechanics with branch counting.
Quentin All those moments will be lost in time, like tears in rain. (Roy Batty/Rutger Hauer) Le mar. 26 août 2025, 06:46, Bruce Kellett <[email protected]> a écrit : > On Tue, Aug 26, 2025 at 2:03 PM Quentin Anciaux <[email protected]> > wrote: > >> Not all possibilities are realized, but those with non-zero amplitude are >> realized somewhere in the superposition. In MWI, "possibility" refers to >> branches with different measures, not to mere logical abstractions. A >> "possible" event with zero measure is equivalent to non-existence. >> > > In quantum mechanics, the Born rule is confirmed in experiments by > counting the number of times a particular result is obtained in repeated > trials. The proportion of 'successes' gives an approximate measure of the > Born rule probability of that result. In other words, the observed > proportion is a reliable estimate of the absolute value squared of the > amplitude of that eigenfunction in the wave function (the Born rule). > > In any model (such as MWI) in which every possibility is realized on every > trial, the Born rule is not confirmed in the majority of cases. This is > easily seen if one considers a wave function with a binary outcome, |0> and > |1> for example. After N repeated trials, one has 2^N strings of possible > outcome sequences. One can count the number of, say, ones in each possible > outcome sequence. The proportion of ones takes on any value between zero > and unity, whereas these sequences are all generated from the same wave > function with a particular value for the amplitude of a |0> outcome. In > most cases, therefore, the observers who obtain each particular proportion > of zeros will fail to confirm the Born rule. This is more apparent as the > amplitude of the |0> component can be changed to any value between zero and > one, while the number of successes in each string remains unchanged. > > 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 [email protected]. > To view this discussion visit > https://groups.google.com/d/msgid/everything-list/CAFxXSLTSp0S5WjE4raWrURhm67a9Ost%3DuR_OKWh_E7WjkB8MYw%40mail.gmail.com > <https://groups.google.com/d/msgid/everything-list/CAFxXSLTSp0S5WjE4raWrURhm67a9Ost%3DuR_OKWh_E7WjkB8MYw%40mail.gmail.com?utm_medium=email&utm_source=footer> > . > -- 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/CAMW2kAqC5t%3DGjZA790qw_RLTuwPim99b8ozqVkq3GhMSE803Jg%40mail.gmail.com.
