NetNews Usenet Archive 1992 #31/NN_1992_31.iso/spool/sci/math/17370

Internet Message Format | 1992-12-23 | 2.4 KB

Xref: sparky sci.math:17370 sci.physics:21675
Path: sparky!uunet!mtnmath!paul
From: [e-mail] (Paul Budnik)
Newsgroups: sci.math,sci.physics
Subject: Re: Bayes' theorem and QM
Message-ID: <[e-mail]>
Date: 23 Dec 92 17:27:22 GMT
References: <[e-mail]> <[e-mail]>
Followup-To: sci.math
Organization: Mountain Math Software, P. O. Box 2124, Saratoga. CA 95070
Lines: 37

In article <[e-mail]>, [e-mail] (John C. Baez) writes:
] In article <[e-mail]> [e-mail] (Daryl McCullough) writes:
] > [...]
] >When you say that quantum mechanics is fundamentally probabilistic, do
] >you mean (A) QM is a probabilistic theory with no known deterministic
] >completion, or (B) QM is a probabilistic theory that is known *not* to
] >have a deterministic completion?
]
] Neither, since I'm not interested in so-called "completions" of
] quantum mechanics, which is already complete enough for me.

This is an intriguing statement. Perhaps my proof that quantum mechanics
is an incomplete theory will change your mind assuming no one finds
any flaws in it.

] [...]
] Less tersely: in classical mechanics, in a pure state one can calculate
] a numerical value for every observable; an ideal measurement of this
] observable should give this number as an answer.  Probability
] distributions for the value of an observable are only different from
] delta functions in the case of mixed states (i.e., states in which one
] doesn't know a maximal amount of information about what's going on, as
] are used in statistical mechanics.)  We can say that probability theory
] is only needed classically if you have some ignorance about what the
] system is up to.  In quantum mechanics, even in a pure state one can
] only calculate a probability distribution for the value of an
] observable, and generically this is not a delta function, but has
] nonzero "dispersion" or standard deviation. [...]

The same thing effectively happens in chaotic classical systems.
In theory we can compute a value for every observable, but such a
computations is, from a practical standpoint, not possible even with
perfect information of the initial state. It seems likely
to me that some form of deterministic chaos also underlys the seemingly
fundamental nature of probability in quantum mechanics.

Paul Budnik