Conformal Symmetry and the Thermal Effects of Acceleration in Classical Physic

TL;DR

This paper explores how conformal symmetry and acceleration influence thermal effects in classical physics, deriving distributions like Juttner and Planck spectra within a classical framework, emphasizing the role of relativistic and conformal invariance.

Contribution

It provides a classical derivation of thermal spectra for relativistic particles and waves, highlighting the importance of conformal symmetry and acceleration effects.

Findings

Derivation of the Juttner distribution for relativistic particles.

Full classical derivation of the Planck spectrum including zero-point radiation.

Classical zero-point radiation correlation functions depend on geodesic separation, not coordinate choice.

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.