Noncovariant parabolic theories of relativistic diffusion

TL;DR

This paper investigates a noncovariant relativistic diffusion theory that avoids instabilities by using observer-dependent equations, revealing how frame-dependent effects influence predictions at high velocities.

Contribution

It introduces a noncovariant approach to relativistic dissipation that addresses dynamical instabilities and analyzes the impact of observer-dependent anisotropies on diffusion predictions.

Findings

Disagreements between observers are due to relativity of simultaneity.

Frame-dependent anisotropic delays affect diffusion at high velocities.

Finite errors at infinite Lorentz factors allow regime where observers agree.

Abstract

A new first-order theory of relativistic dissipation has been recently proposed, where viscous effects are incorporated using the traditional Navier-Stokes framework. Its main novelty is the avoidance of dynamical instabilities by allowing different observers to use equations that are not related by exact Lorentz transformations. In this work, we explore the implications of this non-covariance in depth. In particular, we discuss how predictions differ between observers moving at nearly luminal speeds relative to each other. We find that all disagreements stem from the relativity of simultaneity, which introduces frame-dependent anisotropic delays in the diffusive process. These anisotropies significantly limit the applicability of the equation used by observers who move very fast relative to the medium. However, the magnitude of the related error remains finite at infinite Lorentz factors, meaning that it is possible to find a regime where all observers agree on the outcome of experiments.