Conformal Symmetry and the Thermal Effects of Acceleration in Classical Physic

TL;DR

This work shows that classical, conformally invariant physics can reproduce relativistic equilibrium distributions for particles and waves in a box undergoing finite-time acceleration via a Rindler frame. By leveraging conformal symmetry, the author derives the relativistic Jüttner distribution for particles and, for two-dimensional waves, obtains the Planck spectrum with zero-point radiation, while clarifying how time in the Rindler frame governs whether a spectrum appears thermal to comoving observers. The analysis emphasizes the geodesic dependence of zero-point correlations and argues that uniform acceleration in classical zero-point radiation does not necessarily yield a thermal state, highlighting a key distinction from quantum-field expectations. The work also integrates a conformal-invariant constant to connect acceleration, time, and temperature, and discusses the role of an infinite mode spectrum in achieving equilibrium for relativistic waves. Overall, the paper advances a classical, conformal view of thermal effects under acceleration and clarifies the limitations of translating these results to quantum thermal phenomena.

Abstract

An accelerating Rindler frame in Minkowski spacetime acting for a finite time interval is used to carry a box of particles or waves between two relativistic inertial frames. The finite spatial extent of the box allows treatment of the equations of motion for particles or for waves, while the Rindler acceleration provides a substitute for scattering to test for thermal equilibrium. In the case of equilibrium for relativist particles, the Juttner distribution is derived. For relativistic waves, a full derivation of the Planck spectrum including zero-point radiation is obtained within classical theory. For relativistic waves, relativistic behavior and conformal symmetry are crucial. It is emphasized that the classical two-point correlation function for classical zero-point radiation depends upon the geodesic separation between the spacetime points and is independent of the coordinate system choice. The classical point of view here does not give any support for the idea that a system in uniform acceleration through classical zero-point radiation finds a thermal system.