On 2/10/2025 2:32 PM, Quentin Anciaux wrote:
Le lun. 10 févr. 2025, 23:21, Bruce Kellett <[email protected]> a
écrit :
On Mon, Feb 10, 2025 at 11:09 PM Quentin Anciaux
<[email protected]> wrote:
Bruce,
Your argument assumes that all measurement sequences are
equally likely, which is false in MWI. The issue is not about
which sequences exist (they all do) but about how measure is
distributed among them. The Born rule does not emerge from
simple branch counting—it emerges from the relative measure
assigned to each branch.
You really are obsessed with the idea that I am assuming that all
measurement sequences are equally likely. It does not matter how
many times I deny this, and point out how my argument does not
depend in any way on such an assumption, you keep insisting that
that is my error. I think you should pay more attention to what I
am saying and not so much to your own prejudices.
Each of the binary sequences that result from N trials of
measurements on a 2-component system will exist independently of
the original amplitudes. For example, the sequence with r zeros,
and (N - r) ones, will have a coefficient a^r b^(N-r). You are
interpreting this as a weight or probability without any evidence
for such an interpretation. If you impose the Born rule, it is the
Born probability of that sequence. But we have not imposed the
Born rule, so as far as I am concerned it is just a number. And
this number is the same for that sequence whenever it occurs. The
point is that I simply count the zeros (and/or ones) in each
sequence. This gives an estimate of the probability of getting a
zero (or one in that sequence). That estimate is p = r/N. Now that
probability estimate is the same for every occurrence of that
sequence. In particular, the probability estimate is independent
of the Born probability from the initial state, which is simply a^2.
The problem here is that we get all possible values of the
probability estimate p = r/N from the set of 2^ binary sequences
that arise from every set of N trials. This should give rise to
concern, because only very few of these probability estimates are
going to agree with the Born probability a^2. You cannot, at this
stage, use the amplitudes of each sequence to downweight anomalous
results because the Born rule is not available to you from the
Schrodinger equation.
The problem is multiplied when you consider that the amplitudes in
the original state |psi> = a|0> + b|1> are arbitrary, so the true
Born probabilities can take on any value between 0 and 1. This
arbitrariness is not reflected in the set of 2^N binary sequences
that you obtain in any experiment with N trials because you get
the same set for any value of the original amplitudes
You claim that in large N trials, most sequences will have an
equal number of zeros and ones, implying that the estimated
probability will tend toward 0.5. But this ignores that the
wavefunction does not generate sequences with uniform measure.
The amplitude of each sequence is determined by the product of
individual amplitudes along the sequence, and when you apply
the Born rule iteratively, high-measure sequences dominate the
observer’s experience.
Your mistake is treating measurement as though every sequence
has equal likelihood, which contradicts the actual evolution
of the wavefunction. Yes, there are 2^N branches, but those
branches do not carry equal measure. The vast majority of
measure is concentrated in the sequences that match the Born
distribution, meaning that nearly all observers find
themselves in worlds where outcomes obey the expected frequencies.
This is not speculation; it follows directly from the
structure of the wavefunction. The weight of a branch is not
just a number—it represents the relative frequency with which
observers find themselves in different sequences. The fact
that a branch exists does not mean it has equal relevance to
an observer's experience.
Your logic would apply if MWI simply stated that all sequences
exist and are equally likely. But that is not what MWI says.
It says that the measure of a branch determines the number of
observer instances that experience that branch. The
overwhelming majority of those instances will observe the Born
rule, not because of "branch counting," but because
high-measure sequences contain exponentially more copies of
any given observer.
If your argument were correct, QM would be falsified every
time we ran an experiment, because we would never observe
Born-rule statistics.
That is the point I am making. MWI is disconfirmed by every
experiment. QM remains intact, it is your many worlds
interpretation that fails.
Yet every experiment confirms the Born rule, which means your
assumption that "all sequences contribute equally" is
demonstrably false.
Since I do not make that assumption, your conclusion is wrong.
You are ignoring that measure, not count, determines what
observers experience.
When you do an experiment measuring the spin projection of some
2-component state, all that you record is a sequence of zeros and
ones, with r zeros and (N - r) ones. You do not ever see the
amplitude of that sequence. It has no effect on what you measure,
so claiming that it can up- or down-weight your results is absurd.
Bruce
Your argument is based on treating the measurement process as merely
counting sequences of zeros and ones, while dismissing the amplitudes
as “just numbers.”
No amplitudes show up in the sequence of zeros and ones. You are
implicitly assuming the Born rule attaches to those sequences of 0 and
1, but it doesn't without a separate axiom saying so.
But this ignores that the wavefunction governs the evolution of the
system, and the amplitudes are not arbitrary labels—they encode the
structure of reality.
But in MWI at every repetition of the experiment all the possible
results occur. And they don't have any weights attached to them.
The Schrodinger equation evolves the system deterministically, and
when measurement occurs, the measure of each branch determines how
many observer instances find themselves in it.
Now you're assuming branch counting instead of weights. But the same
objection applies. The Schroedinger equation doesn't not create
different numbers of branches. MWI assumes every possible outcome
occurs once per experiment. To get some different branching structure
you need the Born rule or some equivalent assumption (like Barbour's).
You claim that the amplitude of a sequence does not affect what is
measured, yet this is exactly what determines how many observers
experience a given sequence. The claim that “you do not ever see the
amplitude” misses the point: you do not directly observe measure, but
you observe its consequences. The reason we see Born-rule statistics
is that the measure dictates the relative number of observers
experiencing different sequences.
How does the measure appear in the multiple worlds? If you're going to
have every possibility occur, how in each world, where the only
observation is 1 or 0, does the measure occur?
Brent
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