# 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.