Quantum formulation of the Einstein Equivalence Principle

TL;DR

This paper introduces a quantum formulation of the Einstein Equivalence Principle (EEP), highlighting that classical tests do not necessarily verify its validity in quantum regimes and proposing new ways to test it experimentally.

Contribution

It formulates a quantum version of the EEP based on internal energy operators and analyzes how existing experiments relate to this quantum formulation.

Findings

Classical EEP does not guarantee quantum EEP validity.

Existing experiments partially test quantum EEP aspects.

Quantum EEP requires independent experimental verification.

Abstract

Validity of just a few physical conditions comprising the Einstein Equivalence Principle (EEP) suffices to ensure that gravity can be understood as space-time geometry. EEP is therefore subject to an ongoing experimental verification, with present day tests reaching the regime where quantum mechanics becomes relevant. Here we show that the classical formulation of the EEP does not apply in such a regime. The EEP requires equivalence between the total rest mass-energy of a system, the mass-energy that constitutes its inertia, and the mass-energy that constitutes its weight. In quantum mechanics internal energy is given by a Hamiltonian operator describing dynamics of internal degrees of freedom. We therefore introduce a quantum formulation of the EEP -- equivalence between the rest, inertial and gravitational internal energy operators. We show that the validity of the classical EEP does not imply the validity of its quantum formulation, which thus requires an independent experimental verification. We reanalyse some already completed experiments with respect to the quantum EEP and discuss to which extent they allow testing its various aspects.