From: Robin Hanson (rhanson@gmu.edu)
Date: Fri Jul 04 2003 - 06:31:24 MDT
At 12:00 AM 7/4/2003 -0400, Eliezer S. Yudkowsky wrote:
>Damien Broderick wrote:
>>On the topic of the MWI, I put forward the following, from a crotchety
>>quantum mechanic on another list who inveighs against relative state
>>interpretations. Here's one nub of his case. I'd like to hear a reasoned
>>defence of MW from someone up to the task:
>>=================
>>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. ...
>
>One explanation is to accept the probabilities as primordial, and prior to
>a frequency interpretation of probability. Various explanations have been
>put forth that try to derive frequencies from amplitudes, including one by
>our good friend Robin Hanson. I think the "standard" answer would be: "I
>don't know why the probabilities go as the squared amplitudes, but it's
>equally a mystery in classical and many-worlds theory - this is not where
>the argument for many-worlds rests." Though it's noteworthy that if Robin
>Hanson is correct, for example, many-worlds *would* be necessary to
>explain the observed frequencies.
Damien's critic is right; reproducing the Born probabilities is a serious
problem with many worlds. In a stochastic reduction theory, you can just
posit the probabilities; you haven't explained them, but at least they
don't contradict anything. In many worlds, you have a straightforward way
to calculate probabilities, namely counting worlds, that gives a
*different* answer, which is a much more serious problem. You can deal
with this problem by positing an infinity of "minds" per "world", which
then split during measurements due to some unknown process. Or you can
state decision theory axioms that declare that we do not care about
counting worlds. Neither of these is very satisfactory in my opinion.
My solution (published this month in Foundations of Physics) is described
at http://hanson.gmu.edu/mangledworlds.html .
Robin Hanson rhanson@gmu.edu http://hanson.gmu.edu
Assistant Professor of Economics, George Mason University
MSN 1D3, Carow Hall, Fairfax VA 22030-4444
703-993-2326 FAX: 703-993-2323
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