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The weak equivalence principle of gravity is examined at the quantum level
in two ways. First, the position detection probabilities of particles described
by a non-Gaussian wave packet projected upwards against gravity around
the classical turning point and also around the point of initial projection are
calculated. These probabilities exhibit mass dependence at both these points,
thereby reflecting the quantum violation of the weak equivalence principle.
Second, the mean arrival time of freely falling particles is calculated using the
quantum probability current, which also turns out to be mass dependent. Such
a mass dependence is shown to be enhanced by increasing the non-Gaussianity
parameter of the wave packet, thus signifying a stronger violation of the weak
equivalence principle through a greater departure from Gaussianity of the initial
wave packet. The mass dependence of both the position detection probabilities
and themean arrival time vanishes in the limit of largemass. Thus, compatibility
between theweak equivalence principle and quantum mechanics is recovered in
the macroscopic limit of the latter. A selection of Bohm trajectories is exhibited
to illustrate these features in the free fall case.
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