On 2/10/2025 3:45 AM, Bruce Kellett wrote:
On Mon, Feb 10, 2025 at 9:41 PM Quentin Anciaux <[email protected]>
wrote:
Bruce,
Yes, every possible experience is lived by some version of me in
MWI, but that does not mean all experiences are equally likely or
subjectively equivalent. The measure of a branch determines how
many copies of me experience a given outcome. In practice, my
conscious experience will overwhelmingly be shaped by the branches
with higher measure, not by the rare and improbable ones.
You cannot prove this. It is pure speculation.
For example, if a quantum event has a 1% probability, then there
will be branches where I observe it, but they will be
exponentially fewer than those where I do not. The measure is not
just an abstract number—it reflects the relative weight of
different outcomes in the wavefunction. This is why, as an
observer, I will almost always see frequencies matching the Born
rule, because the majority of my copies exist in branches where
this distribution holds.
No they don't.
Your argument assumes that since all branches exist, they must be
equiprobable, but this ignores the fact that measure determines
how many copies of an observer exist in each branch. In a lottery,
every ticket exists, but some are printed in larger quantities.
Saying "all branches exist, so they must be equal" is as flawed as
saying "all lottery tickets exist, so all should win equally."
Ultimately, my conscious experience is not determined by the mere
existence of branches, but by the relative number of copies of me
in each. Low-measure branches do exist, but they are not
representative of my experience. This is why MWI naturally leads
to the Born probabilities, without assuming collapse or
introducing an arbitrary rule.
Your reasoning collapses probability into mere branch-counting,
but probability is about where observers actually find themselves,
not about an abstract collection of sequences.
Like Russell, you have not even begun to understand the argument I am
making. It has nothing to do with weights or the number of observers
on each branch.
Let me recast the argument. We have a binary wave function: |psi> =
a|0> + b|1>. For convenience I have taken a spin-half system, or
photon polarizations. Then we can use a = cos(theta) and b=sin(theta)
so that a^ +b^2 = 1 is easily maintained and it is simple to rotate
things to alter the magnitudes of the coefficients.
Now we run N trials of measuring this system at some angle. Since the
basic MWI principle is that every possibility is realized on every
trial, we get 2^N sequences of results, covering all possible binary
sequences of length N. Note particularly that we get exactly the same
set of sequences for any angle theta. (We must, because there are only
2^N possible sequences.)
The procedure is now to estimate the probability coefficient of the
original wave function from our measured sequence (which is simply one
of the 2^N). We do this by counting the number of zeros and/or ones
in the sequence. Then p = n_zero/N The weight of the sequence,
whatever it is, does not enter into this calculation of the
probability, which is why I can reasonably take all sequences to have
the same weight (although I do not do this, and it is not necessary).
The point of this exercise is that the probability estimate that I get
(p), is unlikely to be the Born probability which is a^2. As N becomes
large, the law of large numbers implies that a large majority of the
sequences will have approximately equal numbers of zeros and ones
(independently of the coefficients a and b.). Consequently, the
estimated probability will be 0.5 in nearly every case. This is only
the Born probability for a set of angles of measure zero, so the
majority of experimenters are going to find results that do not
conform to the Born rule, and thus find that QM is disconfirmed. This
follows directly from the requirement that every result be found on
every trial ,which is an essential feature of MWI, so MWI is
disconfirmed -- it is not a viable interpretation of QM.
Bruce
There are ways MWI can be saved. For example Julian Barbour's idea that
a single macroscopic world consists of an enormous number of parallel
worlds that are microscopically distinct, and a measurement divides this
stream of microscopic worlds into macroscopically distinct worlds. Then
the division can reflect instantiating uneven probabilities. There's a
paper by Pearle which I cited in reply to JC which puts some mathematics
on a similar idea.
But is certainly not "just the Schroedinger equation". It's interesting
to think how the Born rule may be realized. Barandes, Weinberg, and
Pearle have ideas worked out in different degrees. Generally they begin
by rejecting the Hilbert space picture and adopting the density matrix
as fundamental, recognizing that that a real state is never completely
isolated.
Brent
--
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/d8a437c4-111b-4e09-8b89-b18b4ec7153f%40gmail.com.
