Transit time of a freely falling quantum particle in a background gravitational ﬁeld
David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Using a model quantum clock, I evaluate an expression for the time of a nonrelativistic quantum particle to transit a piecewise geodesic path in a background gravitational ﬁeld with small spacetime curvature (gravity gradient), in the case that the apparatus is in free fall. This calculation complements and extends an earlier one (Davies 2004) in which the apparatus is ﬁxed to the surface of the Earth. The result conﬁrms that, for particle velocities not too low, the quantum and classical transit times coincide, in conformity with the principle of equivalence. I also calculate the quantum corrections to the transit time when the de Broglie wavelengths are long enough to probe the spacetime curvature. The results are compared with the calculation of Chiao and Speliotopoulos (2003), who propose an experiment to measure the foregoing effects.
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