On 2/11/2025 2:28 PM, Bruce Kellett wrote:
On Tue, Feb 11, 2025 at 11:27 PM Quentin Anciaux <allco...@gmail.com>
wrote:
Bruce,
I'll still give it a try to get a discussion (dumb me).
If your response boils down to "this is nonsense" and "you’re not
clever enough," then you’re not engaging with the actual argument.
The question is not whether the Schrödinger equation explicitly
encodes the Born rule—it does not, just as it does not encode
classical probability either. The question is whether MWI can
recover the Born rule without adding collapse, and there are
multiple serious approaches to doing so.
Your claim that "MWI does not match experiments because it cannot
get the Born rule" is just an assertion. The Schrödinger equation
does evolve amplitudes, and those amplitudes do determine the
structure of the wavefunction. You dismiss measure as meaningless,
yet every quantum experiment confirms that the statistics follow .
If naive branch counting were correct, experiments would
contradict the Born rule—but they do not. That means something in
MWI must account for it.
Saying "all branches exist equally" ignores what "equally" even
means in a probabilistic context. Probability is not about "some
things happen while others don’t"—that’s a description, not an
explanation. Classical probability arises because there are more
ways for some outcomes to occur than others. In MWI, the weight of
a branch is not a degree of existence—it’s a statement about how
many copies of an observer find themselves in that outcome.
If you have a counterargument, provide one—just dismissing the
approach as "fantasy" without addressing the core point doesn’t
make your position stronger. If you want to argue that MWI cannot
recover the Born rule, then you need to explain why all proposed
derivations (Deutsch-Wallace, Zurek’s envariance, self-locating
uncertainty, etc.) are fundamentally flawed, not just assert that
they don’t count.
Many others have pointed out the deficiencies of the arguments by
Deutsch-Wallace, Zurek, and many others. The problems usually boil
down to the fact that these attempts implicitly assume the Born rule
from the outset. For example, as soon as you involve separate
non-interacting worlds, and rely on decoherence to give (approximate)
orthogonality, then you have assumed that small amplitudes correspond
to low probability -- which is just the Born rule. Similar
considerations apply to other arguments. The paper by Kent that I
referenced earlier looks at many of the arguments and points out the
many problems.
As far as your basic argument goes, there is no evidence that the
Schrodinger equation itself "evolves the amplitude", or that it gives
different numbers of observers on branches according to the
amplitudes. The idea of "branch weight" is just a made-up surrogate
for assuming a probabilistic interpretation; namely, the Born rule.
The position I am taking tries to avoid all these spurious additional
assumptions/interpretations. We take the Schrodinger equation with the
Everettian proposal that all outcomes occur on every trial, and see
where that takes us. In the binary case, with repeated trials on
similarly prepared systems, we get the 2^N binary strings. We get the
same 2^N strings whatever amplitudes the initial wave function started
with. There is only one copy of the initial observer on every such
binary sequence. That observer can count the number of zeros in
his/her string to estimate the probability. Since the string is
independent of the amplitudes, the same proportion of ones will be
found for the same string in every case. Since the Born probability
varies according to the original amplitude, we find that this simplest
version of many worlds is in conflict with the Born rule. Other
conflicts with the Born rule are evident in other ways -- I have
mentioned some of them previously. To go beyond this you have to
introduce complications that are not inherent in the original
Schrodinger equation and are largely incompatible with simple unitary
state evolution.
But are compatible with interpretations based on the density matrix as
proposed by Barandes, Wigner, and Pearle. So it's not as though we're
stuck with Everett v. Copenhagen.
Brent
Bruce
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