🚀 go-pugleaf

In article <1992Jul17.174536.514@kong.gsfc.nasa.gov> joslyn@kong.gsfc.nasa.gov (Cliff Joslyn) writes:
>
>The following is a quote from the section called "The It from Bit"
>from a recent Scientific American article on modern quantum philosophy.
>
>"Quantum theory may demmand a revamping of our concepts of rationality
>and logic. Boolean logic, which is based on either-or propositions,
>suffices for a world in which an atom goes through one slit or the
>other, but not both slits. Bub [Jeffery, U.MD philosophy] concedes,
>however, that none of the so-called quantum logic systems devised so
>far has proved very convincing."

>I'd like to know more. I am aware that a few physicists are advancing
>a Zadeh-Brower quantum logic (essentially the standard fuzzy logic) to
>quantum spaces, and are playing with relaxed excluded middles to
>account for quantum uncertainty ("Unsharp Particle-Wave Duality in a
>Photon Split-Beam Experiment", P. Mittelstaedt, A Prieur, R. Schieder,
>Foundations of Physics, 17:9, 1987, pp. 891-903).

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.