Contrasting Classical and Quantum Vacuum States in Non-Inertial Frames

TL;DR

This paper compares classical and quantum vacuum states in non-inertial frames, showing classical zero-point radiation's invariance and questioning the quantum notion of vacuum differences like the Unruh effect.

Contribution

It demonstrates that classical zero-point radiation remains invariant under acceleration, contrasting with quantum vacuum state distinctions, and challenges the physical reality of acceleration-induced heating effects.

Findings

Classical zero-point radiation depends only on geodesic separations.

No physical difference between classical vacua in inertial and accelerated frames.

Questions the existence of Unruh-like heating effects in classical theory.

Abstract

Classical electron theory with classical electromagnetic zero-point radiation (stochastic electrodynamics) is the classical theory which most closely approximates quantum electrodynamics. Indeed, in inertial frames, there is a general connection between classical field theories with classical zero-point radiation and quantum field theories. However, this connection does not extend to noninertial frames where the time parameter is not a geodesic coordinate. Quantum field theory applies the canonical quantization procedure (depending on the local time coordinate) to a mirror-walled box, and, in general, each non-inertial coordinate frame has its own vacuum state. In complete contrast, the spectrum of random classical zero-point radiation is based upon symmetry principles of relativistic spacetime; in empty space, the correlation functions depend upon only the geodesic separations (and their coordinate derivatives) between the spacetime points. It makes no difference whether a box of classical zero-point radiation is gradually or suddenly set into uniform acceleration; the radiation in the interior retains the same correlation function except for small end-point (Casimir) corrections. Thus in classical theory where zero-point radiation is defined in terms of geodesic separations, there is nothing physically comparable to the quantum distinction between the Minkowski and Rindler vacuum states. It is also noted that relativistic classical systems with internal potential energy must be spatially extended and can not be point systems. Based upon the classical analysis, it is suggested that the claimed heating effects of acceleration through the vacuum may not exist in nature.