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Scattering Times of Quantum Particles from the Gravitational Potential, and Equivalence Principle Violation

Universality of motion under gravity, the equivalence principle, is violated for quantum particles. Here, we study time it takes for a quantum particle to scatter from the gravitational potential, and show that the scattering time, formulated here using the opportune Bohmian formulation, acts as an indicator of the equivalence principle violation. The scattering times of wavepackets are distinctive enough to distinguish between the Bohmian and Copenhagen interpretations. The scattering time of mono-energetic stationary states, formulated here as a modification of the Bohmian time by probability undercurrents, turns out to be a sensitive probe of the equivalence principle violation. We derive the quantum scattering times, and analyze equivalence principle violating terms systematically. We discuss the experimental setup needed for measuring the violation, and describe implications of a possible measurement for time in quantum theory, including the tunneling time.