On Thu, Feb 6, 2025 at 9:16 AM Quentin Anciaux <[email protected]> wrote:
> Bruce,
>
> Quantum mechanics has explanatory power because it provides accurate
> predictions and a framework for modeling reality. The problem isn’t with
> quantum mechanics itself—it’s with trying to reconcile probability with a
> single-history universe where only one sequence of events ever occurs.
>
> In a framework where only one history unfolds, probability is purely
> descriptive—it does not explain why this history, rather than any other, is
> the one that exists.
>
You seem to have difficulty with the concept of a completely random event--
one that does not have a 'classical' mechanistic explanation. Sorry about
that, but quantum events have a tendency to be completely random (within a
well-defined probability distribution).
It assigns numbers to theoretical possibilities that never had a chance of
> being real. You keep asserting that probabilities are meaningful in a
> single-history view, but meaningful in what sense? If a certain event,
> despite being assigned a 30% probability, never happens in the one realized
> history, then in what sense was it ever a possibility?
>
In the sense that it will happen approximately 30% of the time in repeated
trials. You object to this answer because there can always be
low-probability events that never actually happen in any finite sequence of
trials. I agree, but that is just the nature of probability....
In contrast, in a framework where all possibilities are realized,
> probability maintains a clear meaning: it describes the relative measure of
> outcomes across the full set of realized possibilities. In that case,
> probability is tied to something real, rather than just being a tool we use
> to pretend that nonexistent possibilities matter.
>
Unfortunately, the idea that all possibilities are realized on every trial
is in direct conflict with the Born rule for probabilities. To demonstrate
this, let me spell out a specific example. Consider an experiment on a
two-state system, with a wave function of, say,
|psi> = a|0> + b|1>,
where a^2 + b^2 = 1 specifies the normalization of the state. If we now
measure this state according to the variable with eigenstates |0> and |1>
we get two branches, one with outcome '0', and the other with outcome '1'.
Now repeat the experiment in each branch, so we get four branches, with
outcomes '00', '01', '10', and '11', respectively. Repeat this N times and
you find 2^N branches, covering all possible binary sequences. Note that
this result does not depend on the coefficients 'a' and/or 'b' in the above
wave function. So you get the same 2^N branches whatever the coefficients.
But the Born rule says that the probability that you observe any particular
sequence depends on the squares of the coefficients, and the number of each
coefficient depends on the numbers of '0's and '1's in the branch you
happen to be on. Since, in the multiverse framework, the branch you happen
to be on is random (determined by some self-location probability -- uniform
probability over all branches in this case), it is very unlikely that the
relative numbers of '0's and '1's in your branch happens to agree with the
Born probabilities: In fact the probability that you will see the Born
probabilities vanishes as 1/{2^N }as N becomes large. The fact that
experiments in quantum mechanics universally obtain results that agree with
the Born probabilities is, therefore, inexplicable in the many-worlds model.
Bruce
The fact that quantum mechanics works well does not mean that a
> single-history interpretation is logically coherent when it comes to
> probability. You’re conflating the success of QM with the philosophical
> implications of trying to force probability into a framework where
> unrealized possibilities never had any reality at all. That’s the problem
> you’re not addressing.
>
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