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In article <1992Jul19.202309.29157@galois.mit.edu> jbaez@cayley.mit.edu (John C. Baez) writes:

			...................

>There is an extensively investigated, beautiful, and (IMHO) perfectly
>satisfactory theory of quantum logic which physicists and mathematicians
>might find worth learning.  A good introduction is Jauch's "Foundations
>of Quantum Theory" (if I have the title right).  Basically, what
>distinguishes quantum logic from classical is the nondistributivity of
>"and" and "or".  I.e, what fails is

>		P & (Q v R) = (P & Q) v (P & R).

>For example, 

>P = the particle is moving to the right [i.e. its momentum is
>definitely positive]

>Q = the particle is on the left [i.e. its position is definitely
>negative]

>R = the particle is on the right

>makes the left-hand side true but the right side false.

>I.e. propositions form a nondistributive lattice.  This has the effect
>that a "state" is no longer just an assignment of "T" or "F" to each
>proposition, but a probability value ranging from 0 to 1, satisfying
>certain conditions.

It is not clear that the theory of quantum logic cited is useful for 
anything, or adequate.  I believe that a better view of the uncertainty
principle is that P&Q, for example, is utter nonsense; even making
things probabilistic does not help.

Also, there is no satisfactory truth value system which makes truth
values merely probabilities, but rather elements of a probability
space.  If A has probability .5, so does ~A.  But A&A has probability
.5, while A&~A has probability 0.

There have been many attempts to describe quantum mechanics within 
probability, but I know of no successful ones.  Quantum processes
are far more complicated than stochastic processes.
-- 
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
Phone: (317)494-6054
hrubin@pop.stat.purdue.edu (Internet, bitnet)  
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