  We describe a quantum mechanical measurement as a variational principle
including interaction between the system under measurement and the measurement
apparatus. Augmenting the action with a nonlocal term (a double integration
over the duration of the interaction) results in a theory capable of describing
both the measurement process (agreement between system state and pointer state)
and the collapse of both systems into a single eigenstate (or superposition of
degenerate eigenstates) of the relevant operator. In the absence of the
interaction, a superposition of states is stable, and the theory agrees with
the predictions of standard quantum theory. Because the theory is nonlocal, the
resulting wave equation is an integrodifferential equation (IDE). We
demonstrate these ideas using a simple Lagrangian for both systems, as proof of
principle. The variational principle is time-symmetric and retrocausal, so the
solution for the measurement process is determined by boundary conditions at
both initial and final times; the initial condition is determined by the
experimental preparation and the final condition is the natural boundary
condition of variational calculus. We hypothesize that one or more hidden
variables (not ruled out by Bell's Theorem, due both to the retrocausality and
the nonlocality of the theory) influence the outcome of the measurement, and
that distributions of the hidden variables that arise plausibly in a typical
ensemble of experimental realizations give rise to outcome frequencies
consistent with Born's rule. We outline steps in a theoretical validation of
the hypothesis. We discuss the role of both initial and final conditions to
determine a solution at intermediate times, the mechanism by which a system
responds to measurement, time symmetry of the new theory, causality concerns,
and issues surrounding solution of the IDE.
