Specific Heat of a Classical, Plane, Rigid, Dipole Rotator in Electromagnetic Zero-Point Radiation

A semiquantitative calculation is performed for the specific heat of a plane, rigid, electric-dipole rotator having classical interactions with thermal electromagnetic radiation including electromagnetic zero-point radiation. The calculation is termed semiquantitative because of the introduction of an unevaluated parameter to account for the failure (at low frequencies) of a familiar approximation. The calculation seems of interest for three reasons: (i) It provides a rough classical understanding of qualitative behavior which is usually attributed to quantum interactions. (ii) It again emphasizes that in statistical thermodynamics a consistent classical theory including electromagnetism must include electromagnetic zero-point radiation. (iii) It is another step in a general program attempting to use electromagnetic zero-point radiation as an alternative hypothesis to quanta. From the calculation, the specific heat of the rotator is found to vanish with vanishing slope as the temperature $T\to 0$, and to go smoothly over to the traditional classical value $\frac{1}{2}k$ at high temperatures. Moreover, the rotator probability distribution with frequency, which departs from the traditional classical theory at absolute zero, becomes the usual Boltzmann distribution in the limits of high temperature or large moment of inertia. These results are in contrast to the classical calculation of Fokker in 1914 involving the Planck spectrum without zero-point radiation, which found behavior in complete contradiction with experiment—including infinite slope for the specific heat at $T=0\mathrm{}$ and a failure to approach $\frac{1}{2}k$ at high temperatures. Despite some qualitative features in agreement with experiment, it is suggested that the new results cannot be compared directly with quantum theory or with molecular specific heats, because the calculation involving classical radiation damping does not assure a separation of variables from the internal molecular variables, which would also be influenced by electromagnetic zero-point radiation.