From: Mitchell Porter (mitchtemporarily@hotmail.com)
Date: Sat Aug 17 2002 - 01:59:08 MDT
>Suppose a micro black hole could pass your two-slit apparatus as an
>experiment is being conducted. Now this black hole had 1 chance in 2 (or in
>5, or whatever) of doing so, because in our world it came past Jupiter, and
>we know planetary orbits are chaotic, so in some contiguous MW universes
>Jupiter is also where we see it but in many others it's not. Say in your
>cosmos the hole misses you, having been flung out of the solar system, but
>in half the other superposed universes that are otherwise identical (or
>even in most of them) it whizzed in and gobbled up the test photons (and
>perhaps the lab as well). Now what happens to the diffraction pattern? If
>Deutsch's `QT-as-literal-truth' model is right, I think it looks rather
>odd, but I'm not sure how exactly. Thinned out? Entirely suppressed? Or
>exactly as usual, because the `black holes passes' strands decohered days
>ago, at Jupiter?
>
>Damien Broderick
First I should explain how I conceive of the many worlds interacting.
For several years I've criticized Deutsch for his 'interactionist'
statements about many worlds (i.e. that things happen a certain way
here because of the way they are over there), on the grounds that there
is no exact formulation of QM in those terms. I was all set to write
another such missive here, but I did in fact think of a way that it
*might* be done, so I decided to go with that.
Start with the Bohmian perspective. There you have a 'pilot wave'
(which is just the QM wavefunction), and a pseudoclassical state
trajectory that is wholly determined by the wave. For example, you
might have a 3D wavefunction, and a point particle moving in 3
dimensions. Or, you might have a 'wavefunction of the universe',
stretching over all possible combinations of spacetime geometry
and field state, and a 'classical' space-time history in which
geometry and fields always take specific values, and their evolution
is determined by the universal wavefunction.
In Bohmian mechanics, specifying the wavefunction only tells half
the story, you also have to specify the state in which the guided
system begins (e.g., for a particle, that means location). A given
pilot wave corresponds to a *family* of histories. In an appendix
to his PHYSICS OF IMMORTALITY, Tipler takes this to show that the
Everett interpretation is hiding even inside the Bohm interpretation.
I think they're still worlds apart, but however that may be, there
would still remain a problem for someone trying to derive an
*interactionist* many worlds theory, because according to the
equations of motion, each of the Bohmian worlds takes its cue
solely from the shared pilot wave; the other worlds have no influence
at all.
So my answer is to suppose that the ensemble of Bohmian worlds alone
can substitute for the pilot wave, i.e. that it always contains enough
information to determine the pilot wave. If you can do that, then you
can rewrite the Bohmian equations of motion so that, where they refer
to the pilot wave, instead they refer to some aggregated property of
the ensemble of pseudoclassical worlds. If you can do that, then you
really can have a many-worlds theory in which the worlds are directly
influencing each other. On top of the usual Bohmian problem of finding
a relativistic formulation, there is now the added problem or novelty
of 'trans-world simultaneity', but at least we (or I) would be able
to say exactly what "inter-world interaction" refers to.
Now, back to the scenario of 'rogue black hole eats double-slit
apparatus in half the worlds, what happens to the interference
pattern in yours'. In this Bohm-derived framework, what happens
in your world depends only on your 'neighborhood in configuration
space', i.e. only on what happens in worlds that differ minutely
from yours. And another important feature is that 'the neighborhood
is always full'. As some worlds diverge from you, others will flow
in. (This all derives straightforwardly from the properties of
Bohmian trajectories and how they relate to the pilot wave.)
The worlds where the black hole ate the experiment have diverged
from your multiversal neighborhood (where the experiment still
gets to happen) and are no longer relevant, I'm confident of that
much... But as for what happens to the interference pattern, I'm
really not sure. 'Thinned out' seems plausible. I might get back
to you on this ... offlist.
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