P C W Davies 2004 Class. Quantum Grav. 21 2761 doi:10.1088/0264-9381/21/11/017
P C W Davies
Show affiliationsA quantum particle moving in a gravitational field may penetrate the classically forbidden region of the gravitational potential. This raises the question of whether the time of flight of a quantum particle in a gravitational field might deviate systematically from that of a classical particle due to tunnelling delay, representing a violation of the weak equivalence principle. I investigate this using a model quantum clock to measure the time of flight of a quantum particle in a uniform gravitational field, and show that a violation of the equivalence principle does not occur when the measurement is made far from the turning point of the classical trajectory. The results are then confirmed using the so-called dwell time definition of quantum tunnelling. I conclude with some remarks about the strong equivalence principle in quantum mechanics.
03.65.Xp Tunneling, traversal time, quantum Zeno dynamics
03.65.Ge Solutions of wave equations: bound states
03.65.Ta Foundations of quantum mechanics; measurement theory
Issue 11 (7 June 2004)
Received 11 December 2003
Published 4 May 2004
P C W Davies 2004 Class. Quantum Grav. 21 2761
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