On the quantum analogue of Galileo's leaning tower experiment

Details On the quantum analogue of Galileo's leaning tower experiment On the quantum analogue of Galileo's leaning tower experiment

2006-06-22

arxiv.org/abs/quant-ph/0606183v2

Class.Quant.Grav. 23 (2006) 6493-6502

Physics

Quantum Physics

Latex, 12 pages, 1 figure, uses IOP style, clarifications and references added

Scientific paper

10.1088/0264-9381/23/22/024

The quantum analogue of Galileo's leaning tower experiment is revisited using wave packets evolving under the gravitational potential. We first calculate the position detection probabilities for particles projected upwards against gravity around the classical turning point and also around the point of initial projection, which exhibit mass dependence at both these points. We then compute the mean arrival time of freely falling particles using the quantum probability current, which also turns out to be mass dependent. The mass dependence of both the position detection probabilities and the mean arrival time vanish in the limit of large mass. Thus, compatibility between the weak equivalence principle and quantum mechanics is recovered in the macroscopic limit of the latter.

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