Can We Measure The External Field Effect On Earth?

Color me skeptical. 

The External Field Effect can be understood as basically a swamping of a second order MOND effect by first order Newtonian effects, so I'm very doubtful that it could be measured experimentally in the solar system anywhere near Earth. Also, a 0.1 fm precision measurement, i.e. a fraction of the size of a proton or neutron, starts to run into definitional issues about what the object your measuring even is due to quantum mechanics and the parton makeup of hadrons. And, the uncertainty regarding the functional form of a MOND interpolating function further muddies the waters and makes any measurement model dependent.

Despite compelling evidence, the absence of a confirmed dark matter particle has sustained interest in modified gravity as an alternative explanation for the observed phenomenology. One prominent example is Modified Newtonian Dynamics (MOND), which predicts that the internal dynamics of a system depends on the external gravitational field in which it is embedded. This so-called External Field Effect violates the strong equivalence principle (SEP) and is absent in canonical mechanics, making it a promising avenue for experimental tests of modified gravity. 

Motivated by this, we investigate the dynamics of two spherical masses arranged such that their symmetry axis is either parallel or orthogonal to the local gravitational field. We derive solutions describing the internal dynamics of such systems in both strong uniform and radial external fields. In particular, for a radial external field, if the non-relativistic gravitational field is free to have non-vanishing curl, we find that the mutual attraction of the masses in the perpendicular configuration is not strictly aligned with their symmetry axis. It acquires a small transverse component, even when the external gravitational field is everywhere balanced by non-gravitational forces. 

Using these solutions, we determine the spatial and temporal sensitivities required to distinguish the two configurations and systematically assess experimentally relevant effects, including air drag, object size, and surface interactions. As an example, detecting the prediction of the simple MOND interpolating function requires a spatial sensitivity of order 0.1 fm for sub-millimeter masses evolving over approximately 30 minutes. Such times may be achievable with levitated particles or in space-based environments. Experiments operating at lower resolutions are also interesting as independent tests of SEP and place constraints on modified-gravity theories.

Ankit Kumar, et al., "Probing the Strong Equivalence Principle through the External Field Effect. How Do Two Masses Fall?" arXiv:2607.10247 (July 11, 2026).