Quantum formulation of the Einstein equivalence principle

Abstract

The validity of just a few physical conditions comprising the Einstein equivalence principle (EEP) suffices to ensure that gravity can be understood as spacetime geometry. The EEP is therefore subject to ongoing experimental verification, with present-day tests reaching the regime in which quantum mechanics becomes relevant. Here we show that the classical expression of the EEP does not apply in such a regime. The EEP requires equivalence between the rest mass-energy of a system, the mass-energy that constitutes its inertia, and the mass-energy that constitutes its weight. In quantum mechanics, the energy contributing to the mass is given by a Hamiltonian operator of the internal degrees of freedom. Therefore, we introduce a quantum expression of the EEP—equivalence between the rest, inertial and gravitational internal energy operators. Validity of the classical EEP does not imply the validity of its quantum formulation, which thus requires independent experimental verification. We propose new tests as well as re-analysing existing experiments, and we discuss to what extent they allow quantum aspects of the EEP to be tested.