# Re: The Fuzzy Logic of Quantum Mechanics

Jim Carr (jac@ibms48.scri.fsu.edu)
Mon, 20 Apr 1998 21:51:44 +0200 (MET DST)

meron@cars3.uchicago.edu wrote:
}
} ca314159@bestweb.net writes:
} >Michael Weiss <columbus@nifty.camb.opengroup.org> wrote:
} >>
} >> ca314159 <ca314159@bestweb.net> writes:
} >> Hmm. A mixture, can be separetd uniquely into some fundemental
} >> objects composing that mixture. A superposition also.
} >>
} >> Nope--- the separation for a superposition is not unique, and is
} >> not into objects more fundamental than the original superposition.

...

} > If this extremal decomposition was not unique, you couldn't
} > determine what a 'pure' state was, it would be anything you wanted.
}
} I wrote already few times that pure state is unambiguosly defined in
} QM.
}
} > The problem is the 'pure' state was that it was defined in
} > statistical mechanics
}
} Pure state is defined in QM, not in statistical mechanics, and it is
} not defined statistically.

ca314159@bestweb.net writes:
>
> I don't know why you are aloof though to the more impressive
> statement that Young's apparatus, (Feynman vol 3.) a exemplar of
> all that is QM is simply a Fuzzy logical "OR" operation.

Because your statement is wrong, perhaps?

> Feynman gives
>
> I12 = I1 + I1 + 2*sqrt(I1*I2)* cos(theta) (1)
>
> which is modelling to the probability equation:
>
> P(A or B) = P(A) + P(B) - P(A and B) (2)
>
> the interference term of (1) is simply the dot product of the
> amplitudes |A|*|B|*cos(theta) and is therefore a measure of
> their degree of orthogonality.

Except that you don't normally get a negative number for P(A and B)
in probability theory, particularly in the kind used in fuzzy logic.
That is why QM is an _exotic_ probability theory, and why you cannot
un-mix a superposition as Mati and others correctly point out.

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