We report here an analogue for the vacuum state in classical field theory and its Planckian nature with respect to uniformly accelerated observers. We find that when a real, monochromatic mode of a classical field is Fourier transformed with respect to the proper time of a uniformly accelerating observer, the resulting power spectrum has three separate terms none of which have a simple classical meaning. But they bear a striking resemblance to the quantum mechanical description. Specifically, the three terms are (i) a factor [Formula presented] that is typical of the ground state energy of a quantum oscillator, (ii) a Planckian distribution [Formula presented] and, most importantly, (iii) a term proportional to [Formula presented] which is the root mean square fluctuations about the Planckian distribution. The implications of this result are discussed. © 1997 The American Physical Society.