Gravity Looks Sideways express
A lead sphere hangs above another lead sphere. According to the usual laws of gravitation, they attract each other exactly along the vertical — along the line connecting their centers. But some theories, devised to explain galaxy motion without dark matter, predict an unexpected twist: the force between bodies depends on what happens outside. This is called the external field effect.
The authors considered the simplest case — two identical spheres whose symmetry axis is either parallel or perpendicular to the local gravitational field. It turns out that in the perpendicular orientation, the attraction is no longer strictly central: a tiny sideways component appears. The reason is that in modified gravity, the field can curl like a whirlpool rather than just spreading out in straight lines.
Such sensitivity sounds fantastic, but physicists haven't lost hope. Small particles suspended in vacuum using lasers or magnetic fields can float almost undisturbed for about half an hour. In space, where there are no vibrations or air currents, the experiment becomes even cleaner. Even less precise experiments will be useful: they will test the very principle — whether the fundamental rule of equivalence of all reference frames is violated.
Original abstract
as written by the authors arXiv:2607.10247
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.
A femtometer (10⁻¹⁵ m) is the scale of an atomic nucleus. And 0.1 femtometer is already ten times smaller than a proton. Measuring such displacements is like noticing that a needle tip has shifted by one millionth of a human hair's thickness.
In Liu Cixin's novel "The Dark Forest," droplet probes violate familiar laws of motion — possibly using exactly that "non-centrality" of forces that such experiments seek.