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.
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
On 8/26/2025 11:39 PM, Quentin Anciaux 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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