The Gravitational Drag

Gravity is conservative — a particle moving through a gravitational field gains and loses energy reversibly. No friction, no dissipation, no drag. This is axiomatic in Newtonian mechanics and carries over to general relativity. A photon passing through a gravitational potential undergoes a frequency shift (blueshift in, redshift out) that cancels exactly.

Ortiz and Khatiwada (arXiv:2502.07174) derive a gravitational friction effect for particles passing through a homogeneous low-density medium with non-holonomic constraints. Using d’Alembert’s principle — one of the oldest tools in classical mechanics — they compute the energy lost by particles, including photons, due to the gravitational interaction with the medium. The results agree with continuum mechanics calculations.

The structural point: the friction doesn’t violate energy conservation. It arises from the non-holonomic constraints — constraints that involve velocities, not just positions, and therefore can’t be incorporated into a potential energy. The least action principle, which governs most of classical mechanics, assumes holonomic constraints. When the constraints are non-holonomic (as they are in a medium where particle trajectories are constrained by local density fluctuations), the variational framework breaks down, and dissipation appears.

d’Alembert’s principle — published in 1743 — handles this case. The virtual work of the constraint forces is nonzero for non-holonomic constraints, producing genuine energy loss. The gravitational interaction is still conservative; the constraints are not. The friction lives in the boundary conditions, not the force law.