Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Quantum Evidence for the Reality of Electromagnetic Potentials and the Gravitational Field

Shan Gao

Published Jul 29, 2026• 0 citations
OpenAlex

Abstract

The ontological status of the fundamental fields appearing in gauge theories and general relativity has been one of the deepest conceptual questions in modern physics. In electromagnetism, the central issue concerns whether the electromagnetic potential \(A_\mu\), rather than only the gauge-invariant field strength \(F_{\mu\nu}\), represents a physically real structure. In general relativity, the analogous question concerns whether the gravitational field \(g_{\mu\nu}\), despite its dependence on coordinate choices, should be regarded as a physically real field or merely as a mathematical representation of invariant spacetime relations. In this paper, we present a comprehensive argument for the reality of both \(A_\mu\) and \(g_{\mu\nu}\). For the electromagnetic case, we show that when the source is treated as a fully quantized dynamical system with backreaction, the closed-loop Aharonov--Bohm phase acquires a gauge-dependent contribution that is the sum of two open-path integrals of \(A_\mu\). Since this phase contributes to observed interference patterns, it must correspond to a unique physical quantity, forcing the conclusion that \(A_\mu\) is a real physical field. We further argue that the Lorenz condition is the additonal physical law that, together with boundary conditions, determines \(A_\mu\) uniquely. For the gravitational case, we extend this analysis to both closed-loop and open-path phases. First, we show that closed-loop gravitational phases, such as those measured in the Colella-Overhauser-Werner (COW) experiment and the Overstreet et al. experiment, become gauge dependent under diffeomorphisms when source backreaction is properly accounted for. Second, we show that existing quantum optical experiments using local homodyne tomography already measure open-path relative phases of photons in spatially separated modes, which contain a gravitational contribution—the open-path gravitational phase. Since both closed-loop and open-path gravitational phases are gauge dependent under diffeomorphisms, their measurability entails the reality of the gravitational field \(g_{\mu\nu}\). We further argue that the harmonic (de Donder) gauge is the additional physical law that, together with boundary conditions, determines \(g_{\mu\nu}\) uniquely. These results establish that both electromagnetic potentials and the gravitational field are real physical fields, not mere mathematical auxiliaries. They challenge the conventional identification of gauge invariance with physical reality and have profound implications for non-Abelian gauge theories and quantum gravity.

Related papers

Reality and Measurability of Gauge Potentials

Shan Gao

Gauge invariance is conventionally interpreted as a fundamental redundancy of description, implying that gauge potentials represent the same physical situation and that only gauge-invariant quantities, such as the electromagnetic field strengths and closed-loop holonomies, are physically observable. Within this orthodox view, the gauge potential \(A_\mu\) in quantum electrodynamics possesses no independent ontological status. In this paper we re-examine this interpretation by treating the electromagnetic source in the Aharonov--Bohm (AB) effect as a fully quantized dynamical system whose backreaction on the test particle is explicitly included. We show that, once source dynamics are incorporated, the standard proof of gauge invariance no longer applies. The observable AB phase acquires an additional contribution that can be expressed as the sum of two open-path integrals of the gauge potential and is generally gauge dependent. Since this contribution affects measurable interference, it must correspond to a unique physical quantity, suggesting that the gauge potential itself is physically real rather than merely a redundant mathematical representation. We then argue that the Lorenz condition, $\partial_\mu A^\mu = 0$, should be interpreted not as a gauge choice but as a fundamental physical constraint which, together with the appropriate initial and boundary conditions, uniquely determines the gauge potential. Within this framework, the open-path relative phase of a charged particle, \(\int_{\gamma_1} A_\mu dx^\mu - \int_{\gamma_2} A_\mu dx^\mu\), becomes a well-defined observable, even though it is formally gauge dependent under transformations that do not preserve the Lorenz condition or boundary conditions. To establish the operational significance of this quantity, we propose a Spatial-to-Internal Phase Transfer (SIPT) protocol that coherently transfers the open-path phase of a single fermion into localized internal quantum memories, allowing the phase to be reconstructed through local correlation measurements without recombining the original spatial branches. We discuss possible implementations based on atomic electron capture and semiconductor--superconductor hybrid systems, and argue that such an experiment would constitute an \emph{experimentum crucis}, analogous to the Michelson--Morley experiment, capable of distinguishing experimentally between gauge redundancy and gauge-potential realism. Finally, we show that the conventional gauge-fixed formulation of quantum electrodynamics is mathematically equivalent to a formulation in which the Lorenz condition is imposed as a fundamental law. We further argue that local gauge invariance of the interaction follows from current conservation and the structure of the matter–field coupling rather than representing an independent physical symmetry, and that the gauge-parameter independence of physical amplitudes does not uniquely establish gauge redundancy. These results call for a reexamination of the conceptual foundations of quantum gauge theories and open the door to experimental tests that could transform our understanding of the ontological status of gauge potentials.

•Jul 22, 2026•0 citations

Gauge Dependence and Physical Reality: Open-Path Gravitational Phases as a Probe

Shan Gao

The gravitational phase accumulated by a quantum particle along an open path depends directly on the gravitational potential---which in general relativity is represented by the metric field---rather than solely on spacetime curvature. Although such open-path phases are gauge dependent and therefore usually regarded as unobservable, we show that this conclusion is incorrect. First, we argue that existing quantum optical experiments based on local homodyne tomography already reconstruct the open-path relative phase of spatially separated single-photon modes. Since the two photon paths experience different gravitational potentials, these measurements already contain an unnoticed gravitational open-path contribution. Second, we propose a modification of the large-scale fiber interferometer of Hilweg et al. that directly isolates and reads out the gravitational open-path phase without recombining the optical paths. The predicted signal is of the same order as the gravitational phase considered by Hilweg et al. but is obtained through quantum-state tomography rather than closed-loop interference. These results establish a direct operational method for measuring the gravitational potential through open-path quantum phases, providing strong evidence that the gravitational potential is a directly measurable physical quantity.

•Jul 26, 2026•0 citations

Does the Aharonov-Bohm Effect Imply the Reality of Electromagnetic Potentials?

Shan Gao

The Aharonov--Bohm (AB) phase for a closed interferometric loop is widely regarded as gauge invariant. This conclusion is usually obtained by treating the electromagnetic source as a fixed background that is unaffected by the test charge. We investigate whether this conclusion remains valid when backreaction is included within the standard gauge-fixed formulation of quantum electrodynamics (QED). Our analysis indicates that, when the interfering branches become entangled with distinct electromagnetic field configurations, changes of the gauge-fixing condition can induce a non-vanishing shift of the total phase. This result gives rise to an apparent paradox: the total phase predicted by the QED formalism appears gauge dependent, whereas experiments robustly exhibit a definite interference shift. We examine two possible resolutions of this paradox. The standard approach attributes the observed interference only to a gauge-invariant component of the total phase and treats the remaining gauge-dependent contribution as physically irrelevant. We argue, however, that the QED formalism itself predicts the total phase governing the interference outcome and does not provide a dynamical prescription that extracts a gauge-invariant component while discarding the remaining terms. We then explore an alternative perspective in which the electromagnetic potential $A_\mu$ is regarded as a physical field whose configuration is determined by the Lorenz condition together with appropriate causal and boundary conditions. From this viewpoint, the total phase can be interpreted as a well-defined physical quantity within the QED formalism. We conclude by discussing a possible experimental test based on direct measurements of open-path relative phases, which may help clarify the ontological status of electromagnetic potentials.

•Aug 6, 2026•0 citations

The Aharonov-Bohm Effect Explained: Reality of Gauge Potentials and Its Implications

Gao, Shan

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 $A_\mu$, 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 $g_{\mu\nu}$ 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.

•Mar 16, 2025•0 citations

A New Approach for Testing the Quantum Nature of Gravity

Shan, Gao

The quantum nature of gravity is one of physics' greatest unsolved problems, with existing experimental proposals facing formidable challenges in maintaining spatial superpositions of massive objects against decoherence. We propose a fundamentally different approach that bypasses these difficulties. The central insight is that a quantum gravitational field can imprint a gauge-invariant phase on a particle's wavefunction even along an open trajectory, arising from the quantum backreaction of the source. This phase, which manifests prior to the final recombination stage of an interferometer and cannot be generated by a classical gravitational field, provides an operationally direct witness to the quantumness of gravity. Our experimental design uses a single photon whose accumulated gravitational phase due to the Earth is transferred via absorption to auxiliary atoms near the end of the interferometer sequence, preserving the open-path character essential for the test. We scale the interferometer to yield a detectable phase of order $10^{-3}$ rad and show how non-local correlation measurements on the atoms can access this gauge-invariant signature. Leveraging established quantum optical and atomic techniques, this proposal offers a feasible path to distinguish quantum from classical gravity. A positive result would provide the first experimental evidence for the quantum nature of gravitational fields, with profound implications for quantum gravity theories.

•Nov 8, 2025•0 citations

Failure of Gauge Invariance or Necessity of Quantum Gravity?

Shan Gao

We analyse the gravitational Aharonov-Bohm (AB) phase within the semiclassical framework. We first review the traditional non-relativistic approximation, where a particle of rest mass \(m\) couples to the Newtonian potential via \(H_{\rm int}=m\Phi\), yielding a gauge-invariant phase analogous to the electromagnetic AB effect. We then show that this approximation fails when the particle's total energy varies between interferometer branches. A rigorous derivation from linearised general relativity reveals that in the weak-field, non-relativistic limit, gravity couples to the local energy density, not merely the rest mass. In a laser-driven atom interferometer, the two branches of the superposition differ by the location of an excitation energy \(\delta E\): either stored in the laser apparatus at \(\mathbf{x}_L\) or carried by the atom at \(\mathbf{x}_A(t)\). Under a gauge transformation $\delta h_{\mu\nu} = -\partial_\mu \xi_\nu - \partial_\nu \xi_\mu$, the gravitational AB phase acquires a residual \(\delta(\Delta \phi_{\rm grav}) = -\frac{\delta E}{\hbar c^2}[\xi_0(\mathbf{x}_L,t_f)-\xi_0(\mathbf{x}_A(t_f),t_f)]\) for a purely temporal generator, which is generically nonzero. Since experiments such as Overstreet et al. (2022) measure a stable, reproducible gravitational AB phase, we are compelled to choose between two mutually exclusive possibilities. If gauge invariance (diffeomorphism invariance) is a fundamental principle, then the semiclassical framework is incomplete and a quantum theory of gravity is necessary. If, on the other hand, gauge invariance fails, then semiclassical gravity can be a complete theory. In this case, the gravitational potentials must be understood as real physical fields, and the gauge-dependent phase is a genuine observable, consistent with experiment. These two resolutions are mutually exclusive, and their implications for the nature of gravity and gauge symmetry are profound.

•Jul 18, 2026•0 citations
The ontological status of the fundamental fields appearing in gauge theories and general relativity has been one of the deepest conceptual questions in modern physics. In electromagnetism, the central issue concerns whether the electromagnetic potential (A_\mu), rather than only the gauge-invariant field strength (F_{\mu\nu}), represents a physically real structure. In general relativity, the analogous question concerns whether the gravitational field (g_{\mu\nu}), despite its dependence on coordinate choices, should be regarded as a physically real field or merely as a mathematical representation of invariant spacetime relations. In this paper, we present a comprehensive argument for the reality of both (A_\mu) and (g_{\mu\nu}). For the electromagnetic case, we show that when the source is treated as a fully quantized dynamical system with backreaction, the closed-loop Aharonov--Bohm phase acquires a gauge-dependent contribution that is the sum of two open-path integrals of (A_\mu). Since this phase contributes to observed interference patterns, it must correspond to a unique physical quantity, forcing the conclusion that (A_\mu) is a real physical field. We further argue that the Lorenz condition is the additonal physical law that, together with boundary conditions, determines (A_\mu) uniquely. For the gravitational case, we extend this analysis to both closed-loop and open-path phases. First, we show that closed-loop gravitational phases, such as those measured in the Colella-Overhauser-Werner (COW) experiment and the Overstreet et al. experiment, become gauge dependent under diffeomorphisms when source backreaction is properly accounted for. Second, we show that existing quantum optical experiments using local homodyne tomography already measure open-path relative phases of photons in spatially separated modes, which contain a gravitational contribution—the open-path gravitational phase. Since both closed-loop and open-path gravitational phases are gauge dependent under diffeomorphisms, their measurability entails the reality of the gravitational field (g_{\mu\nu}). We further argue that the harmonic (de Donder) gauge is the additional physical law that, together with boundary conditions, determines (g_{\mu\nu}) uniquely. These results establish that both electromagnetic potentials and the gravitational field are real physical fields, not mere mathematical auxiliaries. They challenge the conventional identification of gauge invariance with physical reality and have profound implications for non-Abelian gauge theories and quantum gravity.
Gauge invariance is conventionally interpreted as a fundamental redundancy of description, implying that gauge potentials represent the same physical situation and that only gauge-invariant quantities, such as the electromagnetic field strengths and closed-loop holonomies, are physically observable. Within this orthodox view, the gauge potential AμA_\muAμ​ in quantum electrodynamics possesses no independent ontological status. In this paper we re-examine this interpretation by treating the electromagnetic source in the Aharonov--Bohm (AB) effect as a fully quantized dynamical system whose backreaction on the test particle is explicitly included. We show that, once source dynamics are incorporated, the standard proof of gauge invariance no longer applies. The observable AB phase acquires an additional contribution that can be expressed as the sum of two open-path integrals of the gauge potential and is generally gauge dependent. Since this contribution affects measurable interference, it must correspond to a unique physical quantity, suggesting that the gauge potential itself is physically real rather than merely a redundant mathematical representation. We then argue that the Lorenz condition, ∂μAμ=0\partial_\mu A^\mu = 0∂μ​Aμ=0, should be interpreted not as a gauge choice but as a fundamental physical constraint which, together with the appropriate initial and boundary conditions, uniquely determines the gauge potential. Within this framework, the open-path relative phase of a charged particle, ∫γ1Aμdxμ−∫γ2Aμdxμ\int_{\gamma_1} A_\mu dx^\mu - \int_{\gamma_2} A_\mu dx^\mu∫γ1​​Aμ​dxμ−∫γ2​​Aμ​dxμ, becomes a well-defined observable, even though it is formally gauge dependent under transformations that do not preserve the Lorenz condition or boundary conditions. To establish the operational significance of this quantity, we propose a Spatial-to-Internal Phase Transfer (SIPT) protocol that coherently transfers the open-path phase of a single fermion into localized internal quantum memories, allowing the phase to be reconstructed through local correlation measurements without recombining the original spatial branches. We discuss possible implementations based on atomic electron capture and semiconductor--superconductor hybrid systems, and argue that such an experiment would constitute an \emph{experimentum crucis}, analogous to the Michelson--Morley experiment, capable of distinguishing experimentally between gauge redundancy and gauge-potential realism. Finally, we show that the conventional gauge-fixed formulation of quantum electrodynamics is mathematically equivalent to a formulation in which the Lorenz condition is imposed as a fundamental law. We further argue that local gauge invariance of the interaction follows from current conservation and the structure of the matter–field coupling rather than representing an independent physical symmetry, and that the gauge-parameter independence of physical amplitudes does not uniquely establish gauge redundancy. These results call for a reexamination of the conceptual foundations of quantum gauge theories and open the door to experimental tests that could transform our understanding of the ontological status of gauge potentials.
The gravitational phase accumulated by a quantum particle along an open path depends directly on the gravitational potential---which in general relativity is represented by the metric field---rather than solely on spacetime curvature. Although such open-path phases are gauge dependent and therefore usually regarded as unobservable, we show that this conclusion is incorrect. First, we argue that existing quantum optical experiments based on local homodyne tomography already reconstruct the open-path relative phase of spatially separated single-photon modes. Since the two photon paths experience different gravitational potentials, these measurements already contain an unnoticed gravitational open-path contribution. Second, we propose a modification of the large-scale fiber interferometer of Hilweg et al. that directly isolates and reads out the gravitational open-path phase without recombining the optical paths. The predicted signal is of the same order as the gravitational phase considered by Hilweg et al. but is obtained through quantum-state tomography rather than closed-loop interference. These results establish a direct operational method for measuring the gravitational potential through open-path quantum phases, providing strong evidence that the gravitational potential is a directly measurable physical quantity.
The Aharonov--Bohm (AB) phase for a closed interferometric loop is widely regarded as gauge invariant. This conclusion is usually obtained by treating the electromagnetic source as a fixed background that is unaffected by the test charge. We investigate whether this conclusion remains valid when backreaction is included within the standard gauge-fixed formulation of quantum electrodynamics (QED). Our analysis indicates that, when the interfering branches become entangled with distinct electromagnetic field configurations, changes of the gauge-fixing condition can induce a non-vanishing shift of the total phase. This result gives rise to an apparent paradox: the total phase predicted by the QED formalism appears gauge dependent, whereas experiments robustly exhibit a definite interference shift. We examine two possible resolutions of this paradox. The standard approach attributes the observed interference only to a gauge-invariant component of the total phase and treats the remaining gauge-dependent contribution as physically irrelevant. We argue, however, that the QED formalism itself predicts the total phase governing the interference outcome and does not provide a dynamical prescription that extracts a gauge-invariant component while discarding the remaining terms. We then explore an alternative perspective in which the electromagnetic potential AμA_\muAμ​ is regarded as a physical field whose configuration is determined by the Lorenz condition together with appropriate causal and boundary conditions. From this viewpoint, the total phase can be interpreted as a well-defined physical quantity within the QED formalism. We conclude by discussing a possible experimental test based on direct measurements of open-path relative phases, which may help clarify the ontological status of electromagnetic potentials.
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.
The quantum nature of gravity is one of physics' greatest unsolved problems, with existing experimental proposals facing formidable challenges in maintaining spatial superpositions of massive objects against decoherence. We propose a fundamentally different approach that bypasses these difficulties. The central insight is that a quantum gravitational field can imprint a gauge-invariant phase on a particle's wavefunction even along an open trajectory, arising from the quantum backreaction of the source. This phase, which manifests prior to the final recombination stage of an interferometer and cannot be generated by a classical gravitational field, provides an operationally direct witness to the quantumness of gravity. Our experimental design uses a single photon whose accumulated gravitational phase due to the Earth is transferred via absorption to auxiliary atoms near the end of the interferometer sequence, preserving the open-path character essential for the test. We scale the interferometer to yield a detectable phase of order 10−310^{-3}10−3 rad and show how non-local correlation measurements on the atoms can access this gauge-invariant signature. Leveraging established quantum optical and atomic techniques, this proposal offers a feasible path to distinguish quantum from classical gravity. A positive result would provide the first experimental evidence for the quantum nature of gravitational fields, with profound implications for quantum gravity theories.
We analyse the gravitational Aharonov-Bohm (AB) phase within the semiclassical framework. We first review the traditional non-relativistic approximation, where a particle of rest mass mmm couples to the Newtonian potential via Hint=mΦH_{\rm int}=m\PhiHint​=mΦ, yielding a gauge-invariant phase analogous to the electromagnetic AB effect. We then show that this approximation fails when the particle's total energy varies between interferometer branches. A rigorous derivation from linearised general relativity reveals that in the weak-field, non-relativistic limit, gravity couples to the local energy density, not merely the rest mass. In a laser-driven atom interferometer, the two branches of the superposition differ by the location of an excitation energy δE\delta EδE: either stored in the laser apparatus at xL\mathbf{x}_LxL​ or carried by the atom at xA(t)\mathbf{x}_A(t)xA​(t). Under a gauge transformation δhμν=−∂μξν−∂νξμ\delta h_{\mu\nu} = -\partial_\mu \xi_\nu - \partial_\nu \xi_\muδhμν​=−∂μ​ξν​−∂ν​ξμ​, the gravitational AB phase acquires a residual δ(Δϕgrav)=−δEℏc2[ξ0(xL,tf)−ξ0(xA(tf),tf)]\delta(\Delta \phi_{\rm grav}) = -\frac{\delta E}{\hbar c^2}[\xi_0(\mathbf{x}_L,t_f)-\xi_0(\mathbf{x}_A(t_f),t_f)]δ(Δϕgrav​)=−ℏc2δE​[ξ0​(xL​,tf​)−ξ0​(xA​(tf​),tf​)] for a purely temporal generator, which is generically nonzero. Since experiments such as Overstreet et al. (2022) measure a stable, reproducible gravitational AB phase, we are compelled to choose between two mutually exclusive possibilities. If gauge invariance (diffeomorphism invariance) is a fundamental principle, then the semiclassical framework is incomplete and a quantum theory of gravity is necessary. If, on the other hand, gauge invariance fails, then semiclassical gravity can be a complete theory. In this case, the gravitational potentials must be understood as real physical fields, and the gauge-dependent phase is a genuine observable, consistent with experiment. These two resolutions are mutually exclusive, and their implications for the nature of gravity and gauge symmetry are profound.