Damien forwards
> http://xxx.lanl.gov/abs/quant-ph/0003146
>
> Does Quantum Nonlocality Exist? Bell's Theorem and the
> Many-Worlds Interpretation
>
> Authors: Frank J. Tipler
It's been known for a long time that Bell's Theorem does not apply
to the MWI in terms of showing nonlocality. Tipler refers to a paper
from 1982 which makes that point.
The basic idea of Tipler's analysis echoes Mike Price's Many-Worlds
FAQ, Q32, "What about Bell's inequality?" See for example at
http://kuoi.asui.uidaho.edu/~kamikaze/documents/many-worlds-faq.html.
Mike follows the same reasoning, looking at the experiment in terms
of three local measurements, and counting the splits. Tipler does
go into more detail with the math, though.
Mike's conclusion:
: So where did Bell and Eberhard go wrong? They thought that all theories
: that reproduced the standard predictions must be non-local. It has been
: pointed out by both Albert [A] and Cramer [C] (who both support
: different interpretations of QM) that Bell and Eberhard had implicity
: assumed that every possible measurement - even if not performed - would
: have yielded a *single* definite result. This assumption is called
: contra-factual definiteness or CFD [S]. What Bell and Eberhard really
: proved was that every quantum theory must either violate locality *or*
: CFD. Many-worlds with its multiplicity of results in different worlds
: violates CFD, of course, and thus can be local.
Tipler's result is not fundamentally new at all, although as I said he
does work out some of the math in more detail.
One comment from Tipler struck me as odd:
> it is a presupposition of the MWI that only coefficients with rational
> squares are allowed since irrational squares would imply an irrational
> number of worlds
I think Tipler meant an "infinite number of worlds", since he is
apparently thinking that the coefficient squares represent ratios of
worlds, and irrationals could only be considered as ratios of infinite
values.
Of course the conventional mathematical formalism for QM does allow for
arbitrary irrational (in fact, complex) coordinates. If the MWI really
exerted this restriction then it would be more than an interpretation.
For example, given a vertically polarized photon, to express its state
in a basis tilted at angle alpha involves cos(alpha) and sin(alpha) as
coordinates. Apparently with the MWI we need to define new functions
that are like sin and cos but which always have rational outputs?
I don't think so.
Hal
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