From: Hal Finney (hal@rain.org)
Date: Fri Aug 01 1997 - 00:06:13 MDT
Damien Broderick, <damien@ariel.ucs.unimelb.edu.au>, writes:
> It's worse than this, if David Hodgson's objection is correct in THE MIND
> MATTERS (1991). He notes:
>
> `The absurdity is highlighted when one considers that in some situations
> quantum mechanical probabilities can be given by irrational numbers (not
> expressible as a fraction), so that in those cases... the determination of
> the number of worlds to be created would have to be the result of some
> approximation chosen by Nature.' (p. 338)
>
> I have never seen this objection met; on the other hand, Hodgson's book was
> well received by QT-canny people such as Paul Davies.
This is an objection to the popularized notion of "many worlds" rather
than to Everett's original idea of eliminating state function reduction.
IMO you can't take this "universe splitting" idea that literally. What I
prefer is to suggest that the effect of the decoherence (and resulting
independence) of branches of the state function is "as though" the universe
were splitting. But there is only one state function; what changes is
which part of it you can interact with.
So the problem with counting the "number of worlds" is not really a
serious objection against Everett's ideas. As I wrote in my other
message, Everett actually worked with the continuous form of the state
function throughout, so he would have had an infinite number of worlds
right off the bat, if he were using that term (he never says "worlds").
A good, accessible article comparing the popular many-worlds interpretation
with Everett's original relative-state formulation is Am. J. Phys 58 (9),
September 1990, p. 829. (Am. J. Phys. is a relatively non-technical journal
for physics teachers and students.) Among the arguments against MW in
the popular form is that it violates conservation of mass, since new
universes are being created all the time. This is really a matter of
misunderstanding Everett's key idea.
Hal
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