De Broglie relations, Gravitational time dilation and weak equivalence principle. (arXiv:1803.02822v1 [quant-ph])

Interplays between quantum physics and gravity has long inspired exciting
studies, which also reveals subtle connections between quantum laws and the
general notion of curved spacetime. One important example is the uniqueness of
free-falling motions in both quantum and gravitational physics. In this work,
we study, from a different perspective, the free motions of quantum test wave
packets that distributed over weakly curved spacetime backgrounds. Except for
the de Broglie relations, no assumption of priori given Hamiltonians or least
actions satisfied by the quantum system is made. We find that the mean motions
of quantum test wave packets can be deduced naturally from the de Broglie
relations with a generalized treatment of gravitational time dilations in the
quantum waves. Such mean motions of quantum test systems are independent of
their masses and compositions, and restores exactly the free-falling or
geodesic motions of classical test masses in curved spacetime. This suggests a
novel perspective that weak equivalence principle, which states the
universality of free-fall and serves as the foundations of gravitational
theories, may be deeply rooted in quantum physics and be a phenomena emergent
from the quantum world.

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