Special relativity description of the heat propagation in Minkowski spacetime

TL;DR

This paper examines heat propagation under intense laser beams in Minkowski spacetime, demonstrating that hyperbolic heat equations preserve causality while Fourier diffusion violates it at high energies.

Contribution

It shows that hyperbolic heat transport equations are valid for high-intensity laser-induced heat transfer, maintaining causality in Minkowski spacetime.

Findings

Fourier diffusion speed exceeds light speed, breaking causality.

Hyperbolic heat transport speed remains below light speed, preserving causality.

Linear hyperbolic heat equation is applicable up to 10^29 W/cm^2 intensity.

Abstract

In this paper we investigate the heat transport induced by continuous laser beams up to an intensity of about 1029 Watt/cm2. We maintain that up to this intensity nonlinear effects are negligible and that the application of the linear hyperbolic heat transport equation is fully justifiable. We show that the Fourier diffusion equation gives the speed of diffusion, v > c and breaks the causality of the thermal processes in Minkowski space-time. For hyperbolic heat transport v<c and causality is valid Key words: high energy continuous laser beams, causality, Minkowski space-time.