On 2/24/2025 1:07 PM, Quentin Anciaux wrote:
Brent,
The issue is precisely that if you start with only unitary evolution
and no additional assumptions, you don’t get probabilities at all—just
a deterministic wavefunction. That’s why the Born rule must be
explained rather than assumed. The problem is not that MWI contradicts
the Born rule, but that it needs to derive it without assuming it.
Your argument boils down to saying, "The Born rule is empirically
confirmed, so MWI must explicitly postulate it."
No, you leave out the point that the Born rule can't be derived from
just the Schroedinger equation. As Bruce as explained repeatedly, MWI
alone provides no mechanism for changing the sequences generated by
measurements. You are of course free to postulate a probability measure
based on the wave-function amplitudes...which is assuming the Born
rule. It's what everybody did for 40yrs before Everett wrote his paper
and which everybody has continued doing sense.
But any interpretation of QM, including single-world ones, requires
some justification for why the squared amplitude determines
probability. If MWI needs additional reasoning to get there, that’s an
open question, not a refutation.
What if you can't get there from bare MWI? Many have tried and failed.
Why not just accept that it's a probabilistic rule that needs to be
added to the interpretation. Gleason's theorem shows that there's no
other way to apply a probabilistic measure if there are more than two
possible results. Although Gleason's theorem is independent of choice
of basis, so there's still the preferred basis problem; which we hope
decoherence can solve but I don't think anyone has shown it yet.
You say that different values of a and b still produce the same
sequences, but What you’re missing is that in MWI, observer instances
are not evenly distributed across all sequences—this is fundamental to
Everett’s relative state interpretation. If all sequences contributed
equally, there would be no need for measure at all, and MWI would have
been dismissed from the start. Everett’s entire motivation was to
account for probability within a deterministic framework, meaning your
argument misrepresents what MWI actually proposes. The number of
observer instances experiencing each sequence scales with the
amplitude squared
But that doesn't follow from the measurements which just produce one
branch for every possible result. It only follows from assuming the
branches have a probability measure equal to the square modulus of the
amplitude, aka the Born rule. The concept of "observer instances" and
their "experiences" is a fantasy. The number of observers of a
particular result can be anything once the result in recorded.
Brent
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