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Quantum mechanics and the equivalence principle

P C W Davies

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A 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.


PACS

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

04.20.-q Classical general relativity

MSC

81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other quantum-mechanical equations

81P15 Quantum measurement theory

Subjects

Gravitation and cosmology

Quantum information and quantum mechanics

Dates

Issue 11 (7 June 2004)

Received 11 December 2003

Published 4 May 2004



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