A bilocal picture of quantum mechanics

A new, bilocal picture of quantum mechanics is developed. We show that Born's rule supports a virtual probability for a particle to arrive, as a wave, at any two locations (but no more). We discuss two ways to implement twin detectors suitable for detecting bilocal arrivals. The bilocal picture sheds light on currents in quantum mechanics. We find there are two types of bilocal current density, whose polar form and related mean velocities are given. In the bilocal context, the definitions of both current types simplify. In the unilocal case, the two types become the usual current and a fluctuation current. Their respective mean velocity fields are the usual de Broglie-Madelung-Bohm velocity and the imaginary (osmotic) velocity. We obtain a new, probabilistic Schrodinger equation for the bilocal probability by itself, solve the example of a free particle, develop the dyadic stationary states, and find that the von Neumann equation for time-varying density of states follows directly from the new equation. We also show how to include the electromagnetic potentials in this probabilistic Schrodinger equation.