From: Lee Corbin (lcorbin@tsoft.com)
Date: Fri Jul 04 2003 - 13:46:32 MDT
Damien had written (quoting his crotchety acquaintance on another list)
"Many Universes: originally/more correctly, Relative State Interpretation
that fundamentally cannot reproduce the probabilities (Everett introduced
the artifact that the branching is probabilistic!). Try out the branching
problem.
"[This refers to a scientist in each state trying to do experiments to test
out the predicted probabilities of his QM manyworld. with a state
vector that has 2 components with coefficients at psi1*psi1 = 0.9 and the
second at psi2*psi2 = 0.1. After three experiments, there would be 11 of the
16 branches in which the scientist(s) would be saying there is less than a
0.05 chance that this quantum mechanics is correct. With time, the percent
of universes in which the scientist(s) could still vouch for his(their) QM
would approach zero. The chance that we could live in a universe that
accepts QM is zero.]"
I do not see how the numbers come about. After three
experiments, one should have by the Bernoulli distribution:
1 3 3 1
.9^3 .9^2 .9 1
1 .1 .1^2 .1^3
with products respectively
.729 .3(.81) .03(.9) .001
or
.729 .243 .027 .001
and (whew!) these do sum to one. So out of say 37 worlds,
27 would have got the more probable outcome three times, 9
would have got two of the more probable and one of the
less probable, one would have got the less probable twice,
and a negligible number would have got the less probable
outcome 3 times.
Hal writes
> A simpler approach just occurred to me. Let's consider a photon which is
> emitted in a polarized state and encounters a polarizer tilted to give
> a 10% chance of passing. As Damien describes, if each photon splits
> the world into two, then the fraction of worlds that see the 10/90
> probabilities becomes vanishingly small.
Well, I would say that sees *three* such is vanishingly small (only
one in a thousand). But I fear I misunderstand you.
> But does it really split like this? In focusing on just the absorption
> aspect of the experiment, we are ignoring many other quantum mechanical
> variables. That's appropriate for experimental purposes, but not,
> perhaps, for philosophy.
>
> The photon emission itself is a quantum mechanical process. It was
> emitted by an excited electron dropping to a lower orbital. This quantum
> transition is more correctly modeled as a continuous process. The excited
> atom emits a constant, steady-state photon wave, and at some point the
> wave function collapses when we measure the photon as a particle.
Yes; but not when "we" do something in particular---when it decoheres
(all on its own). Yes, I know that this is what you meant, but such
talk spooks me still.
> Therefore even a single emission and polarization-measurement of a photon
> does not actually split the universe into two parts; it splits it into
> an infinite number of parts. Even if it turns out that photon emission
> is not truly continuous, that it can only happen at multiples of the
> Planck time or whatever, that's still a truly enormous number of parts.
>
> And the point is that among this humongous split, 10% of the universes
> will see the photon pass through the polarizer, and 90% will see it
> be absorbed. Given this reality, a simple counting rule does in fact
> reproduce the Born probabilities. It was only because we abstracted away
> the enormous additional complexity of the world in order to focus on the
> polarizer interaction that we thought the universe split into two just
> two branches.
This seems quite wonderful and simple to me. Too simple, unfortunately.
Might you be begging the question here? That is, people are wondering
how to go from amplitudes (given by the almighty QM) to probabilities,
and there is this funny rule: you square the moduli. The unwashed infidels
who have rejected our True MWI still point with glee to a missing step here,
no?
> Now, this is of course just one specific example. I don't know if it can
> be generalized, or if we could create quantum systems which literally
> have exactly two states, with no additional parameters or dimensions
> that can fatten things up and give us the Born rules. But at least I
> think this shows that these simple counting arguments are more suspect
> than they seem.
Maybe I just don't know what kind of heretical "counting arguments"
they're guilty of. Surely it's not so simple as them lumping together
identical branches in the count as just "one", failing to take measure
into account. What's going on?
Thanks,
Lee
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