The effects of general relativistic gravity on quantum mechanics are thoroughly investigated. The Schr\"odinger equation is derived for a nonrelativistic spinless particle and for a spin- $1/2$ particle, with the general relativistic corrections of Earth's gravity up to the first post-Newtonian order, ${O(1/c}^{2})$ . The phase differences due to the post-Newtonian corrections in quantum interferometer experiments are also calculated.The effects of general relativistic gravity on quantum mechanics are thoroughly investigated. The Schr\"odinger equation is derived for a nonrelativistic spinless particle and for a spin-$1/2$ particle, with the general relativistic corrections of Earth's gravity up to the first post-Newtonian order, ${O(1/c}^{2})$. The phase differences due to the post-Newtonian corrections in quantum interferometer experiments are also calculated.

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fieldsFeb 15, 199732 citations

On the Interpretation of Quantum Gravity

Mario Castagnino, C. D'Negri

Jan 1, 19901 citation

Relativity, states and quantum evolutions in atom interferometry

Stephan Kleinert

The physics of the 20th century was dominated by the fascinating effects of quantum mechanics and relativity. However, a satisfactory unification of both theories could never be achieved. Quantum gravity is still an open problem – not a theory. The purpose of this thesis is not to solve this problem, but to provide customized, theoretical tools which can model future experiments acting at the interface of gravity and quantum mechanics. Special attention is paid to a geometrical interpretation of the underlying physics. In particular, we study three different aspects: (i) we consider how Newtonian gravity enters into the quantum evolution of matter waves, (ii) we study relativistic quantum fields in the presence of arbitrary curved spacetime and (iii) we investigate the geometric effects of quantum state space on the evolution in interferometric setups – also including entanglement. For the analysis of quantum states we employ the instructive tool of quasi-probability distributions in phase space.The physics of the 20th century was dominated by the fascinating effects of quantum mechanics and relativity. However, a satisfactory unification of both theories could never be achieved. Quantum gravity is still an open problem – not a theory. The purpose of this thesis is not to solve this problem, but to provide customized, theoretical tools which can model future experiments acting at the interface of gravity and quantum mechanics. Special attention is paid to a geometrical interpretation of the underlying physics. In particular, we study three different aspects: (i) we consider how Newtonian gravity enters into the quantum evolution of matter waves, (ii) we study relativistic quantum fields in the presence of arbitrary curved spacetime and (iii) we investigate the geometric effects of quantum state space on the evolution in interferometric setups – also including entanglement. For the analysis of quantum states we employ the instructive tool of quasi-probability distributions in phase space.

Jan 1, 20180 citations

Bargmann-invariant witness of the graviton commutator

Hiroki Matsui

We identify the phase of a Bargmann invariant of two matter-wave interferometers as a quantum gravity signature that cannot be reproduced by any branchwise-definite classical gravitational field. For matter coupled linearly to linearized gravity, the interferometric coherence factorizes exactly into a conservative Newtonian phase, the characteristic functional of the graviton state, and a commutator phase. For Wigner-positive graviton states, the first two are classically reproducible; therefore, decoherence alone cannot certify that gravity is quantized. The Bargmann phase isolates the commutator, which is independent of the graviton state and of all Newtonian interactions and is bounded by which-path decoherence. For gravity, this radiation-reaction effect is sixty orders of magnitude below experimental reach, but trapped-ion analogs can test it at order unity.We identify the phase of a Bargmann invariant of two matter-wave interferometers as a quantum gravity signature that cannot be reproduced by any branchwise-definite classical gravitational field. For matter coupled linearly to linearized gravity, the interferometric coherence factorizes exactly into a conservative Newtonian phase, the characteristic functional of the graviton state, and a commutator phase. For Wigner-positive graviton states, the first two are classically reproducible; therefore, decoherence alone cannot certify that gravity is quantized. The Bargmann phase isolates the commutator, which is independent of the graviton state and of all Newtonian interactions and is bounded by which-path decoherence. For gravity, this radiation-reaction effect is sixty orders of magnitude below experimental reach, but trapped-ion analogs can test it at order unity.

gr-qcCross-listedarXiv:2610.35253Oct 27, 20260 citations

Measurement in Quantum Gravity

H.‐H. von Borzeszkowski, H.‐J. Treder

Springer eBooksJan 1, 19880 citations

The effects of general relativistic gravity on quantum mechanics are thoroughly investigated. The Schr\"odinger equation is derived for a nonrelativistic spinless particle and for a spin-

1/2

particle, with the general relativistic corrections of Earth's gravity up to the first post-Newtonian order,

{O(1/c}^{2})

. The phase differences due to the post-Newtonian corrections in quantum interferometer experiments are also calculated.