A Lorentz-Covariant Spectral Universality of Stochastic Fields

Abstract

We derive a Lorentz-covariant spectral universality for stationary stochastic fields in Minkowski spacetime. We show that no covariant local mapping can relate temporal and spatial power spectra in more than one spatial dimension. For Lorentz homogeneous spectra, the temporal index is symmetry protected, observer invariant, and offset from the spatial index by a universal geometric factor set by effective momentum space dimensionality. We show how spectral universality breaks down for anisotropic scaling and dispersion dominated spectra, establishing the necessity of a Lorentz-covariant formulation of relativistic spectral inference.