Foucault Pendulum Experiment by Kamerlingh Onnes and Degenerate Perturbation Theory

Abstract

The paper pays homage to H. Kamerlingh Onnes by pointing out that he constructed the first properly functioning model of the Foucault pendulum. His success was largely due to an analysis which takes into account the unavoidable mechanical asymmetry of the pendulum. Based on the analysis he was able to eliminate the asymmetry and to obtain the desired performance which earlier workers had realized only to a limited extent. Onnes' analysis is reproduced with more modern tools such as vector notation and, especially, the concept of eigenfunctions. His analysis is probably one of the earliest examples of a particular type of doubly degenerate perturbation theory. Two different effects compete for lifting the degeneracy, one favoring “circular polarization,” the other “linear polarization.” The resulting eigenfunctions represent “elliptical polarization.” The tutorial significance of this perturbation theory is emphasized by mentioning other fields where it is applied if perhaps disguised by a different jargon and analytic technique. Examples include electromagnetic theory (microwave cavities for circular polarization), laser optics (mode analysis of ring lasers for rotation sensing), and quantum theory (quenching of orbital angular momentum by crystalline field).