Physical non-reality of electromagnetic potentials?

Robert Golub, J. P. Carrico, T. S. Stein +1 more

S. C. Tiwari

Shan Gao

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.

Alexander Afriat

The transformation properties of the electromagnetic four-potential can make one wonder whether it has any physical reality. But it is felt (with the Aharonov-Bohm effect in mind) that the reality in question has to be \emph{somewhere}, 'thereabouts'; if it is not in the potential itself, might it not be in the loops around which it is integrated? I argue that no ontological solidity is gained by retreating to the loops, which are just as flimsy as the potential.

Peter D. Noerdlinger

Richard Healey

Classically, a gauge potential was merely a convenient device for generating a corresponding gauge field. Quantum-mechanically, a gauge potential lays claim to independent status as a further feature of the physical situation. But whether this is a local or a global feature is not made any clearer by the variety of mathematical structures used to represent it. I argue that in the theory of electromagnetism (or a non-Abelian generalization) that describes quantum particles subject to a classical interaction, the gauge potential is best understood as a feature of the physical situation whose global character is most naturally represented by the holonomies of closed curves in space-time.