  Causality and the relativity of simultaneity seem at odds with the apparently
sudden, acausal state-vector changes ("collapses") characteristic of quantum
phenomena. The problem of how physical phenomena can be causally determined,
have the probabilities predicted by quantum theory, and be consistent with
special relativity appears to be solved by the assumption, essentially the same
as one first used by Aharonov, Bergmann, and Lebowitz to address a different
problem, that the "initial" and "final" state vectors of a phenomenon or
observation, along with certain other state vectors, all represent the system's
state at all times. Each member of such an aggregate of state vectors is
postulated to represent a different aspect of a physical state rather than a
state, so that most of the state vectors in effect constitute a set of nonlocal
hidden variables. Various implications of this assumption are illustrated
through several physical situations. Among the results is a somewhat surprising
resolution of a paradox in a three-spin Greenberger-Horne-Zeilinger experiment
(a "three-particle EPR" experiment), which involves a logical consequence that
differs from familiar ideas of quantum physics that has no practical
experimental consequence, and the prediction of new experimental phenomena
related to the Zou-Wang-Mandel superposed-idler system. The potential value of
the concepts described as heuristics for new predictions and for developing
physical intuition by clarifying the interrelation and coherence of physical
principles that would otherwise seem contradictory is briefly discussed.
