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American Journal of Physics

The gravitational Aharonov–Bohm effect with photons

Edward G. Harris

Published Apr 1, 1996• 20 citations
Publisher

Abstract

The analogy between general relativity and electromagnetism suggests that there is a gravitational analog of the Aharonov–Bohm effect. There is indeed such an effect. Since gravitation couples to all fields, the effect should exist for photons. There is a close connection with the Sagnac effect. Both the electromagnetic field and the gravitational field are classical fields, so the effect could have been predicted in the interval between the publication of the theory of general relativity in 1915 and the discovery of quantum mechanics in the mid 1920s.

DOI
10.1119/1.18251

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The analogy between general relativity and electromagnetism suggests that there is a gravitational analog of the Aharonov–Bohm effect. There is indeed such an effect. Since gravitation couples to all fields, the effect should exist for photons. There is a close connection with the Sagnac effect. Both the electromagnetic field and the gravitational field are classical fields, so the effect could have been predicted in the interval between the publication of the theory of general relativity in 1915 and the discovery of quantum mechanics in the mid 1920s.
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Aharonov–Bohm effect is a quantum mechanical phenomenon that attracted the attention of many physicists and mathematicians since the publication of the seminal paper of Aharonov and Bohm [1] in 1959. We consider different types of Aharonov–Bohm effects such as the magnetic AB effect, electric AB effect, combined electromagnetic AB effect, AB effect for the Schrödinger equations with Yang–Mills potentials, and the gravitational analog of AB effect. We shall describe different approaches to prove the AB effect based on the inverse scattering problems, the inverse boundary value problems in the presence of obstacles, spectral asymptotics, and the direct proofs of the AB effect.
The Aharonov-Bohm (AB) effect, wherein an electron acquires a phase shift in a field-free region due to electromagnetic potentials, poses a profound challenge to the ontology of quantum mechanics and gauge theories. This paper demonstrates that gauge-invariant explanations, which attribute the phase to measurable quantities, rely on nonlocal and discontinuous mechanism and fail to account for its continuous accumulation along the electron's path—a process evident in the generalized AB effect, where a time-varying magnetic flux induces a phase that builds gradually over time, as predicted by quantum mechanics. Through a new analysis spanning quantum mechanics and quantum electrodynamics, I argue that the electromagnetic potentials AμA_\muAμ​, fixed in the Lorenz gauge, emerge as the fundamental physical reality, offering a local, relativistically consistent account of the phase’s generation. This exclusion of gauge-invariant paradigms reverberates across gauge theories: it redefines the Higgs mechanism, favoring dynamic potentials over static invariants, and extends to general relativity, where gravitational potentials gμνg_{\mu\nu}gμν​ may anchor spacetime’s substantival reality via a gravitational AB effect. By unraveling the AB phase’s continuous generation—locally mediated by potentials—this study not only addresses a long-standing conundrum but also bridges electromagnetic, gravitational, and Yang-Mills frameworks, offering a unified potential-centric perspective with novel implications for physics and philosophy.
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.