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arXiv:2602.21001

Internal dynamics and guided motion in general relativistic quantum interferometry

Thomas B. Mieling

gr-qcquant-phSubmitted Feb 24, 2026• Announced Feb 25, 2026
v1 · Feb 24, 2026v2 · Mar 3, 2026
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Abstract

The coupling between internal degrees of freedom of quantum systems and their overall motion in an external gravitational field plays a central role in multiple extensions of Einstein's equivalence principle to quantum physics. While previous models of such effects were predominantly restricted to linearized gravity and often required the motion of quantum particles to follow prescribed world-lines, this letter shows how such phenomena can be understood using generally covariant semiclassical approximations in the framework of quantum field theory in curved space-times. This method provides a unification and generalization of previously established results, but also predicts new effects such as an influence of internal energies on field amplitudes, as well as correction terms to the internal Schrödinger equation that give rise to Berry phases.

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10 pages

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The coupling between internal degrees of freedom of quantum systems and their overall motion in an external gravitational field plays a central role in multiple extensions of Einstein's equivalence principle to quantum physics. While previous models of such effects were predominantly restricted to linearized gravity and often required the motion of quantum particles to follow prescribed world-lines, this letter shows how such phenomena can be understood using generally covariant semiclassical approximations in the framework of quantum field theory in curved space-times. This method provides a unification and generalization of previously established results, but also predicts new effects such as an influence of internal energies on field amplitudes, as well as correction terms to the internal Schrödinger equation that give rise to Berry phases.
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Abstract In this paper, we study the phenomenon of quantum interference in the presence of external gravitational fields described by alternative theories of gravity. We analyze both non-relativistic and relativistic effects induced by the underlying curved background on a superposed quantum system. In the non-relativistic regime, it is possible to come across a gravitational counterpart of the Bohm–Aharonov effect, which results in a phase shift proportional to the derivative of the modified Newtonian potential. On the other hand, beyond the Newtonian approximation, the relativistic nature of gravity plays a crucial rôle. Indeed, the existence of a gravitational time dilation between the two arms of the interferometer causes a loss of coherence that is in principle observable in quantum interference patterns. We work in the context of generalized quadratic theories of gravity to compare their physical predictions with the analogous outcomes in general relativity. In so doing, we show that the decoherence rate strongly depends on the gravitational model under investigation, which means that this approach turns out to be a promising test bench to probe and discriminate among all the extensions of Einstein’s theory in future experiments.
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In a recent work \cite{Shaikh:2026nsi}, it was shown that for a non-relativistic particle, the operator equations of motion can be cast in the same differential form as Newton's equation of motion. This establishes a correspondence between quantum operator dynamics and classical mechanics at the level of the equations of motion. In this work, we investigate whether this correspondence extends to quantum field theory and linearized gravity. We explicitly show that the Heisenberg equations of motion for quantum field operators reproduce the corresponding classical equations of motion for a broad class of field theories. The Klein-Gordon equation, Maxwell's equations, Yang-Mills equations, and linearized Einstein equations are shown to arise at the operator level without taking the limit ℏ→0\hbar\rightarrow0ℏ→0. We then extend the analysis to curved spacetime and show that the quantum field operators satisfy the corresponding covariant field equations at the operator level. In the weak-field approximation, we show that the Heisenberg evolution of the metric-perturbations reproduces the linearized Einstein equations at the operator level. For a quantum particle in curved spacetime, the Heisenberg equations for position and momentum reproduce classical geodesic motion in the semiclassical limit, thereby extending the operator-level quantum-classical correspondence from fields to particle dynamics.
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