Quantum formulation of the Einstein equivalence principle


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.

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Fig. 1: Testing quantum formulation of the WEP.
Fig. 2: Internal state oscillations for testing quantum formulation of LLI and LPI.
Fig. 3: Interferometric test of the quantum formulation of LPI.


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We thank I. Pikovski and F. Costa for comments on early drafts of this manuscript; and C. Kiefer, D. Giulini and G. Tino for discussions. We acknowledge support from the ARC Centre EQuS CE110001013, the University of Queensland (UQ Fellowship grant no. 2016000089), the Templeton World Charity Foundation (TWCF 0064/AB38), the ÖAW Innovationsfonds ‘Quantum Regime of Gravitational Source Masses’, the Doctoral Programme CoQuS and the research platform TURIS. This publication was made possible through the support of a grant from the John Templeton Foundation. The opinions expressed in this publication are those of the authors and do not necessarily reflect the views of the John Templeton Foundation. M.Z. acknowledges the traditional owners of the land on which the University of Queensland is situated, the Turrbal and Jagera people.

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M.Z. and Č.B. contributed to all aspects of the research, with the leading input from M.Z.

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Correspondence to Magdalena Zych.

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Zych, M., Brukner, Č. Quantum formulation of the Einstein equivalence principle. Nature Phys 14, 1027–1031 (2018). https://doi.org/10.1038/s41567-018-0197-6

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