Yes, given a device that calculates the Born probability, almost all
worlds will agree on the probability.
Brent
On 8/27/2025 3:17 PM, Jesse Mazer wrote:
Also, even without invoking the Born rule there is a result that if
you consider a "pointer state" that records the relative fractions of
different possible measurement results in a *series* of N systems
prepared in the same initial state, and consider the limit as N
approaches infinity, in this limit all the amplitude gets concentrated
on the pointer state with the fractions that correspond to the
probabilities for individual measurements predicted by the Born
rule--see David Z Albert's comments at
https://books.google.com/books?id=_HgF3wfADJIC&lpg=PP1&pg=PA238
<https://books.google.com/books?id=_HgF3wfADJIC&lpg=PP1&pg=PA238> and
the paper discussing Mittelstaedt’s theorem at
https://www.academia.edu/6975159/Quantum_dispositions_and_the_notion_of_measurement
Jesse
On Wed, Aug 27, 2025 at 2:39 AM Quentin Anciaux <[email protected]>
wrote:
Bruce,
Everett’s original formulation describes a universal wavefunction
evolving unitarily, not discrete worlds with one observer per
branch. Your argument assumes this mapping, but it is an
interpretative choice, not a result derived from the Schrödinger
equation.
Also, your claim that all 2^N sequences have equal measure only
holds if amplitudes are treated as irrelevant. In standard quantum
mechanics, amplitudes directly determine observed frequencies via
the Born rule, which has strong experimental support. Ignoring
amplitudes means you are no longer analyzing Everett’s framework
but a different model where the Born rule indeed fails.
To refute Everett with Born included, you would need to show that
even when squared amplitudes define a natural measure, the
predicted observed frequencies still fail. Assuming uniform
sampling over sequences does not establish that.
This is why your derivation is not accepted: it relies on a hidden
premise, one observer per branch with uniform sampling, which is
not part of Everettian quantum mechanics.
Quentin
All those moments will be lost in time, like tears in rain. (Roy
Batty/Rutger Hauer)
Le mer. 27 août 2025, 07:32, Bruce Kellett <[email protected]>
a écrit :
On Wed, Aug 27, 2025 at 3:26 PM Quentin Anciaux
<[email protected]> wrote:
Bruce,
If your derivation is as solid as you claim, then a
skeptical referee is exactly who you should want to
convince. Repeating the same argument here without
engaging with the role of amplitudes will not make it any
stronger. You cannot dismiss amplitudes entirely and then
claim to have explained why measure must be uniform, that
is circular.
If you truly believe your reasoning refutes the Born rule
within Everett’s framework, then publishing it is the only
way to settle the matter. Otherwise, endlessly asserting
it here looks less like confidence and more like avoidance.
Your entire argument hinges on assuming uniform observer
sampling by postulating one observer per branch.
The argument does not depend on this. This shows nothing more
than that you have not understood the argument.
But that is precisely the point under debate, not a
derived result. If you ignore the role of amplitudes in
defining the structure of the wavefunction, you're not
engaging with Everett's formulation, only with your own
simplified model.
Until you demonstrate why amplitudes should be irrelevant
within unitary evolution, claiming equal weights is just
assuming your conclusion.
I think, rather, that you should show how the argument I have
made depends on amplitudes when it clearly does not. It
depends merely on the proportion of zero outcomes in each
sequence. And that does not depend on the amplitudes.
Bruce
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