Classical Correspondence of Unruh Effect

Derived from semi-classical quantum field theory in curved spacetime, Unruh effect was known as a quantum effect. We find that there does exist a classical correspondence of this effect in electrodynamics. The thermal nature of the vacuum in correlation function for the uniformly accelerated detector is coming from the non-linear relationship between the proper time and the propagating length of the electromagnetic wave. Both the Coulomb field of the detector itself and the radiation supporting the detector's uniformly accelerating motion contribute to the non-vanishing vacuum energy. From this observation we conclude that Unruh temperature experienced by a uniformly accelerated classical electron has no additional effects to Born's solution for laboratory observers far away from the classical electron.