  Bell's theorem rests on the following fundamental condition for a local
system: P(a,b|alpha, beta, lambda)= P(a|alpha, lambda)P(b|beta, lambda). Here a
and b are the outcomes respectively for measurements alpha on one side, and
beta on the other, of an experiment involving two entangled particles traveling
in opposite directions from a source. The parameter lambda (the set of "hidden
variables") represents a more complete description of the joint state of the
two particles. Because of lambda, the joint probability of detection is now
dependent only on lambda and the local measurement setting of alpha; similarly
for the other side and the setting beta. From this equation John Bell derived a
simple inequality that is violated by the predictions of quantum mechanics,
which is generally taken to imply that quantum mechanics is a nonlocal theory.
But, by combining Richard Feynman's formulation of quantum mechanics with a
model of particle interaction described by David Deutsch, we develop a system
(the "space of all paths," SP) that (1) is immediately seen to replicate the
predictions of quantum mechanics, (2) has a single outcome for each quantum
event (unlike MWI on which it is partly based), and (3) contains the set lambda
of hidden variables consisting of all possible paths from the source to the
detectors on each side of the two-particle experiment. However, the set lambda
is nonmeasurable, and therefore the above equation is meaningless in SP.
