Take two. (Damn DSL just crashed, wiping out my original reply.) Ahem!
Dan, since I clearly misunderstood your original example, I dug out my
copy of Gribbin's _In Search of Schrodinger's Cat_ and read his
description of the research surrounding Bell's Theorem. I think I have a
better idea of what you and he are talking about now, so I'm going to ask
you to indulge me as I back up a few steps and try again to get my
bearings.
The doctrine of "local realism" rests, as Gribbin describes it, on the
following assumptions. "First, that there are real things that exist
regardless of whether we observe them [basic realism]; second, that it is
legitimate to draw general conclusions from consistent obervations or
experiments [the laws of science and math hold true]; and third, that no
influence can propogate faster than the speed of light, which
[D'Espagnat] calls 'locality.'" In this context I interpret "locality"
as the doctrine that everything exists in its own location in space-time;
two things can't be in the same place at once, so the fastest an influence
can get from object A to object B is at the speed of light per special
relativity. Gribbin doesn't explicitly define the term, so I'm guessing a
little.
What the research regarding Bell's Inequality Theorem shows, however, is
that local realism and and QM don't mix. I'm not sure how to demonstrate
this without trying to rehash your original post, Dan, so I won't. In
short: when a particle splits and creates two particles A and B,
those particles remain parts of a system "AB," and when particle
A interacts with something, particle B responds *simultaneously* in
order to conserve spin, angular momentum, etc., no matter how far
apart those particles are. However, for a given property a
particle is always in a state of uncertainty--it has a spin along a
given axis of +1 and -1 simultaneously, and there is always some
randomness about which way the cookie will crumble at the moment of
observation, so normal set theory and statistics don't predict accurately
the correlations between spin combinations among the various axes of the
particles. The funky rules of QM, however, do accurately predict what we
observe.
The fact that A and B respond to each other instantly regardless of
distance undermines the assumption of locality. The fact that observed
correlations of particle spins don't match the predictions of "normal"
mathematics, which assume that an object's properties are either fixed or
will be changed according to fixed and predictable rules, undermines the
assumption that objects exist, with their attendant properties and
characteristics, independently of observation or interaction.
Does that sound about right? I think I should stop there before tacking
the metaphysical end of things.
Marvin Long
Austin, Texas
