A Material Frame: Hard Recoils from Slow Force Carriers

Abstract

We modify the Standard Model by making the longitudinal component of the photon physical, propagating with small speed $c_L \ll 1$. This modification breaks gauge invariance and Lorentz symmetry, defining a preferred reference frame. No new fields or scales are introduced, and the photon mass is protected by a Galilean higher-form symmetry. The theory has a smooth $c_L\to0$ limit: the new modes decouple from standard matter and ordinary gauge theory predictions are recovered. Experimental constraints are severe. Charged particles Cherenkov-emit these slow modes, experiencing hard recoils against the preferred frame. The recoil rate decreases with $c_L$, but the momentum transfer remains of the order of the particle's momentum. Dark matter detectors, sensitive to keV-scale nuclear recoils, imply an order-of-magnitude bound $c_L \lesssim 10^{-60}$, tens of orders of magnitude stronger than speed-difference bounds. At such values, $c_L$ is better understood as a recoil-rate factor rather than a physically relevant speed. The slow modes, practically fixed in space, make the reference frame a material medium capable of absorbing momentum from charged particles.