Re: The Fuzzy Logic of Quantum Mechanics
meron@cars3.uchicago.edu
Mon, 20 Apr 1998 22:18:50 +0200 (MET DST)
In article <6ha8st$d75$1@nnrp1.dejanews.com>, ca314159@bestweb.net writes:
>In article <6h8pf9$du9$1@news.fsu.edu>,
>jac@ibms48.scri.fsu.edu (Jim Carr) wrote:
>> ca314159@bestweb.net 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:
> http://www.seanet.com/~ksbrown/kmath309.htm
>
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,
meron@cars.uchicago.edu | chances are he is doing just the same"