We investigate the experimental feasibility of a null test probing possible gradient-dependent contributions to gravitational redshift using controlled electromagnetic energy density gradients. In standard general relativity, the fractional frequency gradient between two vertically separated clocks is given by d(lnf)/dh=g/c2. We test for an additional phenomenological contribution of the form η dχ/dh, where χ ≡uEM is the electromagnetic energy density and η is an effective coupling parameter. The proposed setup compares two configurations with identical gradient magnitude but opposite sign, providing a robust experimental signature: a genuine gradient-dependent effect reverses sign under configuration inversion, while most systematic effects do not. Using realistic laboratory field strengths (E ∼106 V/m) and meter-scale geometries, we estimate achievable energy density gradients dχ/dh∼1–10Jm−4 and corresponding signal levels. Combined with state-of-the-art frequency measurements at the 10-18 level, this allows direct experimental sensitivity to the coupling parameter. We find that the proposed null test is experimentally accessible with existing or near-term precision measurement technologies and can establish quantitative bounds on gradient-dependent extensions of gravitational redshift, even in the absence of a detected signal.
Remzi Öztürk (Sun,) studied this question.