Brownian motion of a mirror

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Abstract
Einstein's analysis of the Brownian motion of a mirror in a field of natural radiation played a crucial role, in the first decade of quantum theory, in persuading physicists that the Maxwell description of the electromagnetic field was inadequate, and that light quanta, with discrete momentum as well as energy, have a real existence. Here an alternative analysis is given of this motion. We see that, if the spectral density of the radiation field is given by the Planck spectrum plus the zero-point electromagnetic field, that is, by the spectral density of Planck's second theory, then the motion is correctly described in terms of the Maxwell theory, without any need for a quantum hypothesis. An essential step in this analysis is to include Boyer's correction to the Einstein model, whereby account is taken of the radiative energy loss each time the mirror collides with the walls of the cavity.