Re: The Fuzzy Logic of Quantum Mechanics

Michael Weiss (columbus@nifty.camb.opengroup.org)
Mon, 20 Apr 1998 15:35:38 +0200 (MET DST)

ca314159:

Yes. But the Science Times section of the NY Times today
says QM is wrong :)

A reference, I presume, to "Physical Laws Collide in a Black Hole
Bet", and not "Applying Quantum Mechanics to Bees and Honey" ;>)

The article actually says, "For the information paradox seems to hint
that at least one of the two theories that lie at the foundation of
physics -- quantum mechanics and general relativity -- is subtly
flawed." The folks over on s.p.r. discuss this all time--- we don't
have a theory of quantum gravity yet, so it's anyone's guess what it
will look like when (and if) we do.

ca314159's other point is an analogy between the QM formula:

I12 = I1 + I1 + 2*sqrt(I1*I2)* cos(theta) (1)

and the standard probability formula:

P(A or B) = P(A) + P(B) - P(A and B) (2)

He omits to mention that P(A and B) is always non-negative in standard
probability theory, but cos(theta) takes on both positive and negative
values in the QM applications.

Perhaps this is why he says: "QM is simply a _Fuzzy_ logical `OR'
operation." (my emphasis)

I didn't think Fuzzy Logic (as introduced by Lofti Zadeh) worked that
way, but I'm not really up on it--- perhaps someone more knowledgeable
can comment. (The site http://www.law.umich.edu/thayer/fuzzy.htm has
some basic intro material on fuzzy sets.)

ca314159 has also referred in the past to a paper, "Quantum Theory as
an Exotic Probability Theory". (I must say, he does come up with
interesting refs!) I haven't been able to download this in a readable
form, but Jim Carr posted a few remarks. The idea of *formally*
extending (2) by allowing negative or even complex probabilities is
intriguing; I'm quite prepared to believe that QM could be recast in
these terms, and this might even prove enlightening. (Perhaps in the
same way that von Neumann's quantum logic provided new insights into
QM.)

All this has (IMHO) nothing to do with ca314159's "ultra pure states".