  A relativistic classical field theory with zero-point radiation involves a
vacuum corresponding to a scale-invariant spectrum of random classical
radiation in spacetime with the overall constant chosen to give an energy
(1/2)\hbar\omega per normal mode in inertial frames. Classical field theory
with classical zero-point radiation gives the same field correlation functions
as quantum field theory for the symmetrized products of the corresponding free
massless fields in inertial frames; however, the interpretations in classical
and quantum theories are quite different. Quantum field theory has photons in
thermal radiation but not in the vacuum state; classical theory has radiation
in both situations. The contrast in interpretations is most striking for the
Rindler coordinate frame accelerating through zero-point radiation; classical
theory continues tensor behavior over to the Rindler frame, whereas quantum
theory introduces a new Rindler vacuum state. The classical interpretation of
thermal behavior rests on two fundamental principles. i) A scale-invariant
distribution of random radiation cannot correspond to thermal radiation at
non-zero temperature. ii) A scale-invariant distribution of random radiation
can acquire a correlation time which reflects the parameters of a spacetime
trajectory through the scale-invariant radiation. Based on these principles,
classical theory finds no basis for an accelerating observer to reinterpret
zero-point radiation in terms of thermal radiation. In contrast, quantum field
theory claims that an observer uniformly accelerated through zero-point
flucturations of the Minkowski vacuum encounters a thermal bath at the
temperature T=\hbar a/(2\pi ck).
