Re: The Fuzzy Logic of Quantum Mechanics
Mon, 20 Apr 1998 22:18:50 +0200 (MET DST)

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.
> Probability theory is not without it's deeper aspects:
Quoting from a web page is not a reference, just noise.

> There is no reason confine probabilities to positive numbers and
> Feynman (~1987) has already proposed using negative numbers.
There are very good reasons to confine probabilities to positive
numbers as they are defined in terms of measures on sets and measures
are non-negative. One may envision possibilities of extending the
definition but this is far from trivial. And, as an aside, name
dropping like "Feynman suggested", "Einstein suggested", "God
suggested" etc. is not a physical (or mathematical) argument.

Mati Meron | "When you argue with a fool, | chances are he is doing just the same"