  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.
