On Tue, Aug 26, 2025 at 2:03 PM Quentin Anciaux <allco...@gmail.com> 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

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