Why a Femtometre Spacetime Lattice Need Not Violate Lorentz Invariance

Abstract

For decades, the notion of a discrete vacuum lattice at the femtometre scale has been dismissed on a single ground: it must violate Lorentz invariance catastrophically.This despite the idea's pedigree --- Dirac's quantum aether, Sakharov's induced gravity, Volovik's superfluid vacuum, Kleinert's defect--gauge correspondence --- and the deep structural parallels between crystalline defects and the field content of general relativity. The dismissal, however, assumes the simplest possible model: a rigid array of motionless point scatterers. We show that the lattice becomes fully compatible with current astrophysical bounds once the substrate is modelled as a relativistic quantum supersolid whose nodes are spatially extended bound states delocalised by zero-point motion. Two well-established crystallographic mechanisms --- the Peierls--Nabarro form factor and the Debye--Waller factor --- then combine to suppress coherent Bragg scattering by at least eighteen orders of magnitude, placing the predicted dispersion comfortably below the Fermi-LAT bound. A Peach--Koehler analysis separates this periodic-background transparency from stress-field coupling to topological defects, which survives undiminished --- consistent with the Kleinert programme in which gauge fields and gravity emerge precisely from such defect interactions.The primary phenomenological obstacle to lattice-based models of fundamental physics is, at minimum, substantially weakened.