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From: gwyn@brl-tgr.ARPA (Doug Gwyn )
Newsgroups: net.math
Subject: Re: a piece of folk-lore - really on randomness
Message-ID: <1844@brl-tgr.ARPA>
Date: Tue, 1-Oct-85 21:18:20 EDT
Article-I.D.: brl-tgr.1844
Posted: Tue Oct  1 21:18:20 1985
Date-Received: Sat, 5-Oct-85 02:19:52 EDT
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Organization: Ballistic Research Lab
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This quibbling over the distinction between randomness and
probabilities is beside the point.  Quantum mechanics has
the additional feature, not found in classical probability
theory, of addition of complex probability amplitudes when
possible alternative system states are considered.  This
makes the real probabilities not obey the classical (Bayes)
rules, which raises some real questions about what it all
means.  (I hope I can forestall responses that do no more
than state an operationalist frequency interpretation of the
resulting probabilities; I know that already, thank you.)
The interesting questions are "Why probability AMPLITUDES?"
or more generally "Why aren't the classical laws of probability
being obeyed?"  The reason for asking the latter is that the
classical laws are a direct result of counting alternative
outcomes, which somehow doesn't work for QM (quite apart from
the issue of whether identical particles are distinguishable).

Note that I am not asking whether it works, but why it works.
The trouble with the prevalent attitude that every theory is
just a mathematical model is that such an attitude makes one
quit trying to understand things; instead one just starts
cataloging their behavior.