The Fuzzy Logic of Quantum Mechanics

ca314159@bestweb.net
Mon, 20 Apr 1998 14:55:41 +0200 (MET DST)

In article <EqzyFL.DAq@midway.uchicago.edu>,
meron@cars3.uchicago.edu wrote:
>
> In article <6gaap5$tcf$1@nnrp1.dejanews.com>, ca314159@bestweb.net writes:
> >In article <ys0vhsom0fp.fsf@nifty.camb.opengroup.org>,
> > 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.
> >
> > Right, the decomposition is arbitrary, like coordinate systems.
> > Unless we happen to be in some fundemental 'coordinate system'
> > in which the statement of the decomposition is in some sense
extremal.
>
> There is no fundamental coordinate system.

In physics, there is always the implicit coordinate system.

>
> > 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.

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

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.

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.

Orthogonality maps over into the set intersection of (2) in terms of
the degree of overlap of the sets A and B.

The degree of orthogonality in (1) and the degree of set intersection
in (2) get interpreted as the correlation between the amplitudes of
I1 and I2 in (1) or the sets A and B in (2).

Hence, the distribution of Young's experiment is modelling a
fuzzy logical OR operation where the classically expected pattern
(no interference) is displayed when A and B are orthogonal (theta = 90)
and the probabilities simply add (non-identical particles).

While the quantum mechanical result is when (A and B) are partially
correlated or coherent yielding the partial interference pattern.
And at the other extreme where A and B are totally intersected (theta=0)
there is total interference (identical particles).

--
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