Speaker
Description
The relative fractional change of resonance frequency equals the fractional change in stored energy. This relation predicts the change of EM frequency when the walls of a metallic cavity are deformed or small objects inserted. J.M. Mueller derived this formula in 1939 by conceptual and mathematical errors. Casimir corrected those errors in 1949. The formula is also associated with J.C. Slater, published in 1946. Similar formulae were derived by Kahan in 1946 and by Papas in 1954. The Kahan version was reported, influentially, by Borgnis & Papas in the 1958 Handbook of Physics. Nevertheless, the relation is often called Slater's theorem. The Mueller, Slater and Casimir versions rely only on the properties of eigenfunctions, and electromagnetic boundary conditions at a metallic surface. The Kahan and Papas short cut to the formula relies on thermodynamics, the adiabatic theorem, perfect thermal isolation and infinite time, and that the cavity contains EM oscillations in quadrature. The latter derivation relies on assumptions that are artificial and unnecessary, and fails completely if there is no EM field present while the cavity is deformed. The situation of multiple derivations and attributions has led to some confusion. The time to set the record straight is overdue!
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