Re: The Fuzzy Logic of Quantum Mechanics

meron@cars3.uchicago.edu
Mon, 20 Apr 1998 15:26:42 +0200 (MET DST)

In article <6gd5pt$1u4$1@nnrp1.dejanews.com>, ca314159@bestweb.net writes:
>In article <EqzyFL.DAq@midway.uchicago.edu>,
> meron@cars3.uchicago.edu wrote:
>>
>> In article <6gaap5$tcf$1@nnrp1.dejanews.com>, ca314159@bestweb.net writes:
>> >In article <ys0vhsom0fp.fsf@nifty.camb.opengroup.org>,

>> > 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.
>
No, not always. And when there is a coordinate system, it is one
chosen for convenience, devoid of any deeper significance. When your
results depend on your choice of coordinate system, you know you've
made an error somewhere.
>>
>> > 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 :)
>
Ahh, the Science Times section of the NY Times, the people who (a
decade ago) wrote about creation and annihilation of antiprotons as a
solution to all future energy problems. A distinguished source
indeed:-)

> 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)
>
Feynman gives? You mean you can't calculate it yourself? As an
aside, (1) by itself has nothing to do with QM, only with wave
properties.

> which is modelling to the probability equation:
>
> P(A or B) = P(A) + P(B) - P(A and B) (2)
>
No, not quite.

> 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.
>
There is no "orthogonality of the amplitudes". There is Orhtogonality
of the Wave functions which is a global property. The above is a
local property.

> 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).
>
Boy, oh boy. Do you have things thoroughly mixed up:-)

Mati Meron | "When you argue with a fool,
meron@cars.uchicago.edu | chances are he is doing just the same"