On 2/20/2025 11:30 PM, Quentin Anciaux wrote:
Brent,
The Schroedinger equation governs the evolution of the wavefunction,
but decoherence determines the effective structure of branches.
A branch is defined the result of the measurement. If the electron spin
is UP, then that defined the UP branch. Decoherence presumably spreads
from the SG detector and makes a world around UP that's orthogonal to
the world around DWN. "Effective structure" beyond this is just your
invention.
When I say a branch isn’t a single discrete unit, I mean that what we
call a “branch” is an approximation—a macroscopic, emergent structure
from the underlying quantum evolution.
Why isn't it single in the sense that it is the branch that originated
from a single measurement value. "emergent structure from the
underlying quantum evolution" is just obfuscation.
The wavefunction never truly “splits” into countable, independent
worlds; rather, it evolves into a superposition of decohered,
non-interfering components, which we approximate as separate branches.
If they are non-interfering they are in a superposition. They're
orthogonal.
The fact that different results are orthogonal doesn’t mean each
result corresponds to exactly one observer copy.
The UP world originated from the single UP measurement. How many people
observe it is irrelevant. They're all in one world.
The amplitudes still dictate relative frequencies, just as they do in
standard QM. The mechanism isn’t imposed externally—it’s in the
structure of the wavefunction itself. You ask what equation determines
that branches aren’t uniform: the answer is the same equation that
governs quantum amplitudes. The measure of an outcome isn’t
arbitrary—it follows from the squared amplitude of that outcome, just
as it does in any quantum experiment.
Here you spend three sentences to say the Born rule is instantiated.
But why and how is nothing but assertion and hand waving. Bruce and I
have both challenged you to provide the mathematics. You say the
equation that governs quantum amplitudes. But in an SG experiment the
probability amplitude for UP is proportional to cos(phi) where phi is
the angle between the beam polarization and the instrument's "UP". The
electron however doesn't carry that information to the detector; the
electron just registers on the counter as 0 or 1. Which is Bruce's
point that the "a" and "b" in a|up>+b|dwn> are NOT part of information
available in the experimental record. The structure of the
wave-function just determines the sequence of 0s and 1s. You know the
answer you want, the Born rule, so you just suppose it must be in there
somewhere. But it's not as Bruce's example shows and also the many
failures by smart people to try to derive the Born rule.
Your example about performing an experiment in a Superbowl crowd vs.
an undergrad lab misunderstands what’s being discussed. The measure
isn’t about the number of classical humans performing an
experiment—it’s about how many instances of an observer are
instantiated in a given outcome due to the structure of the wavefunction.
Yes, I know what you meant, I'm just cautioning you against using
misleading language. What you meant is the SG detector, when
registering an electron UP instead of decoherence producing one
UP-branch it produces a whole lot, a bush of UP-branches */and the
number of branches in this bush is proportional the b^2 in Bruce's
example./* It's this last that is the problem. There is no mechanism
for it. It is just your gratuitous assumption to get the Born rule by
branch counting.
The classical analogy would be a lottery where some numbers are
printed in greater quantities than others; if you pick a ticket
randomly, you are overwhelmingly likely to pick a more common one.
If branch count alone determined probability, we wouldn’t see Born’s
rule in experiments.
We would if you just assume the right number of branches. But as JKC
pointed out, doing so requires retro-causation to change the past.
Since we do, that means any valid interpretation of QM must account
for why low-amplitude branches contribute less to observer
experiences. If you believe MWI fails to do this, then you need to
provide a counterargument that doesn’t assume what it wants to
prove—that all branches contribute equally regardless of amplitude.
You are the one claiming that the Born rule follows from the
Schroedinger equation. Above you just repeat that we know it applies.
Yes, we know it applies empirically and for more that two results is
implied by Gleason's theorem. But that's not a derivation or a proof.
You just repeating you it must be so because we know it workds doesn't
add anything.
Brent
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