  It is difficult to extract reliable criteria for causal locality from the
limited ingredients found in textbook quantum theory. In the end, Bell humbly
warned that his eponymous theorem was based on criteria that "should be viewed
with the utmost suspicion." Remarkably, by stepping outside the wave-function
paradigm, one can reformulate quantum theory in terms of old-fashioned
configuration spaces together with 'unistochastic' laws. These unistochastic
laws take the form of directed conditional probabilities, which turn out to
provide a hospitable foundation for encoding microphysical causal
relationships. This unistochastic reformulation provides quantum theory with a
simpler and more transparent axiomatic foundation, plausibly resolves the
measurement problem, and deflates various exotic claims about superposition,
interference, and entanglement. Making use of this reformulation, this paper
introduces a new principle of causal locality that is intended to improve on
Bell's criteria, and shows directly that systems that remain at spacelike
separation cannot exert causal influences on each other, according to that new
principle. These results therefore lead to a general hidden-variables
interpretation of quantum theory that is arguably compatible with causal
locality.
