Equivalence principle and electromagnetic field: no birefringence, no dilaton, and no axion

The coupling of the electromagnetic field to gravity is discussed. In the premetric axiomatic approach based on the experimentally well established conservation laws of electric charge and magnetic flux, the Maxwell equations are the same irrespective of the presence or absence of gravity. In this sense, one can say that the charge “substratum” and the flux “substratum” are not influenced by the gravitational field directly. However, the interrelation between these fundamental substrata, formalized as the {\it spacetime relation} H=H(F) between the 2-forms of the electromagnetic excitation H and the electromagnetic field strength F, is affected by gravity. Thus the validity of the equivalence principle for electromagnetism depends on the form of the spacetime relation. We discuss the nonlocal and local linear constitutive relations and demonstrate that the spacetime metric can be accompanied also by skewon, dilaton, and axion fields. All these premetric companions of the metric may eventually lead to a violation of the equivalence principle.

💡 Research Summary

The paper revisits the coupling between electromagnetism and gravity using a pre‑metric framework that rests on two experimentally solid conservation laws: electric charge conservation (∂J = 0) and magnetic flux conservation (∂B = 0). Because these laws are independent of the spacetime structure, the Maxwell equations dH = J and dF = 0 retain exactly the same form whether a gravitational field is present or not. In this sense the “charge substratum” and the “flux substratum” are not directly altered by gravity.

The true point of interaction, however, lies in the spacetime (constitutive) relation that links the electromagnetic excitation H to the field strength F. In the most general linear, local, and possibly non‑local case one writes H_{ij}=½ χ_{ijkl} F^{kl}, where the constitutive tensor χ has 36 independent components. χ can be decomposed into three irreducible pieces: (i) a 20‑component principal part that is fully determined by the spacetime metric g_{μν}, (ii) a 15‑component skewon part that introduces non‑reciprocal, anisotropic behavior and can produce birefringence, and (iii) a single axion component α that contributes a pseudoscalar term α F∧F, affecting only the phase of electromagnetic waves.

If a skewon field were present, different polarizations would propagate with different effective light cones, leading to observable birefringence. High‑precision optical experiments have not detected such effects, which places very stringent limits on the skewon amplitude. The axion, by contrast, does not modify the energy‑momentum tensor and therefore does not violate the weak equivalence principle (WEP) in the classical sense, but it can generate subtle quantum‑interference phenomena such as an Aharonov‑Bohm‑type phase shift.

A further possible companion is the dilaton φ, a scalar that rescales the metric contribution in χ as φ g_{i