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Equivalence Principles for Quantum Systems

We ask the question how the (weak) equivalence principle established in classical gravitational physics should be reformulated and interpreted for massive quantum objects that may also have internal degrees of freedom (dof). This is necessary because even an elementary concept like a classical trajectory is not well defined in quantum physics — trajectories originating from quantum histories become viable entities only under stringent decoherence conditions. For quantum composite particles freely falling in a homogeneous gravitational field we calculate the interaction between the internal dof and the translational dof and try to identify observable consequences. Concerning the effects on the translational dof, for a particular class of initial states, we show that the internal dof can lead to the dephasing, namely, the suppression of the off-diagonal terms of the density matrix, in the position basis. Contrary to a recent claim, this phenomenon is not universal and the process is not decoherence, because it does not involve irreversible loss of information. Concerning the effects on the internal dof of a free-falling atom, we found a gravitational phase shift in the reduced density matrix of the internal dof. While this phase shift is a fully quantum effect, it has a natural classical interpretation in terms of gravitational red-shift and special relativistic time-dilation. From this investigation we posit two statements of the equivalence principle for quantum systems: Version A: The probability distribution of position for a free-falling particle is the same as the probability distribution of a free particle, modulo a mass-independent shift of its mean. Version B: Any two particles with the same velocity wave-function behave identically in free fall, irrespective of their masses. Based on the recent paper by C. Anastopoulos and B. L. Hu, “Equivalence Principle for Quantum Systems: Dephasing and Phase Shift of Free-Falling Particles” arXiv:1707.04526