Re: The Fuzzy Logic of Quantum Mechanics

Jim Carr (jac@ibms48.scri.fsu.edu)
Fri, 1 May 1998 14:35:49 +0200 (MET DST)

jac@ibms48.scri.fsu.edu (Jim Carr) wrote:
|
|> ca314159@bestweb.net writes:
|> >
|> > I12 = I1 + I2 + 2*sqrt(I1*I2)* cos(theta) (1)

>where I1, I2, I12 are intensities.

that is, non-negative quantities

| > 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.

ca314159@bestweb.net writes:
>
> Probability theory is not without it's deeper aspects:

Yes, like the use of definitions.

> There is no reason confine probabilities to positive numbers and
> Feynman (~1987) has already proposed using negative numbers.

There is if you are doing conventional probability theory. They
are not allowed. But you restate the obvious about there being
no reason not to extend probability theory to a different axiomatic
base. What I am trying to get across is the seemingly obvious
idea that when you do so you are now using an exotic probability
theory and the things you think you know from conventional theory
no longer apply.

> The reference above shows how negative probabilities bring on
> a nicer symmetry and how complex probabilities have some
> really interesting properties.

Yeah, like the use of complex probability amplitudes to explain
quantum mechanics.

> The interference term is not present (theta=90) when complete
> knowledge of which path the particle took through the two-slits
> is given (Maxwell-Boltzmann)

It is not present in any conventional probability theory. Note,
however, that "not present" does not mean it is present with a
fixed angle. It means it is not present, period.

> When no knowledge of the paths is available, the particles are
> called "identical" (theta=0) and the set overlap is complete.

This statement is simply wrong.

Please re-read past articles or learn some basic QM or wave theory.

```--
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