Re: The Fuzzy Logic of Quantum Mechanics
Mon, 20 Apr 1998 22:46:42 +0200 (MET DST)

In article <>, wrote:
> In article <6ha8st$d75$>, writes:
> >In article <6h8pf9$du9$>,
> > (Jim Carr) wrote:
> >> writes:
> >
> >Young's two-slit spatial probability density (Feynman Lectures vol 3.)
> >> >
> >> > I12 = I1 + I2 + 2*sqrt(I1*I2)* cos(theta) (1)
> >
> >where I1, I2, I12 are intensities.
> >
> >> > 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.

Except we do this when we un-mix the -superposition- of sound frequencies
in a Fourier transform or in radio waves. But radio waves are also,
considered as composed of many in-phase coherent photons. And from
this point of view the radio signal is considered a -mixture- of
photons of specific frequencies (pure states).

Depending on how you develop a basis of micro and macro states,
and the how the identicality and indistinguishablilty of the pure
states and "particles" is stated, determines when we view
something as a superposition or as a mixture. So a mixture can look
like a superposition if the arbitrarily bucketed pure states
(macrostates) are not orthogonal (do not compose an orthogonal
subspace of pure states)

Negative probabilities[1] were introduced by someone (Feynman) to
in an attempt to solve the renormalization (reorthogonalization)
problem in particle physics where the annoying infinities pop up.

[1] Quantum Implications, edited by Hiley and Peat, 1987, Routledge &
Kegan Paul

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