Speaker
Description
Even before his 1890 appointment at LMU Munich, Ludwig Boltzmann had ordered his mechanical engineer in Graz, Anton von Gasteiger, to build a mechanical model that was then further developed in Munich 1890 as the “Bizykel”—an “inexplicable apparatus with a gear mechanism”. Both the Graz and Munich original models were lost, so that only replicas exist in historical museums today. Following the undoubted success of Maxwell’s theory of electromagnetism, Boltzmann turned his attention to illustrating the analogy between cyclic (periodic) electromagnetic phenomena and simple mechanical constructions. It served as a didactic approach [1] to visualizing electromagnetic phenomena such as Faraday’s law of self-induction and the transport of energy in lumped electrical circuits. Today, the path to understanding electromagnetic circuits has been reversed: Physicists are more familiar with electric networks (since they are easier to construct). Boltzmann’s bicycle demonstrates how a two-coil arrangement (known as an electric transformer) can be simulated as a “Zahnradgetriebe mit 3 Konusrädern”. To the best of the author’s knowledge, and despite a wealth of descriptive articles on Boltzmann’s bicycle [2] and Paul Ehrenfest’s obituary for Ludwig Boltzmann [3], a comprehensive explanation of the bicycle’s principle from a modern perspective is missing. This will be addressed here using the example of an open and short-circuited electric transformer.
[1] L. Boltzmann: Vorlesungen über Maxwell’s Theorie der Elektricität
und des Lichts, 1. Theil, Leipzig: Johann Ambrosius Barth 1891
[2] H. Ebert: Mechanisches Modell zur Erläuterung der Inductionsgesetze
= Bizykelmodell, Annalen der Physik und Chemie, Bd. XLIX, Leipzig:
Johann Ambrosius Barth 1893, 642-650.
[3] P. Ehrenfest: Ludwig Boltzmann’s mechanische Deutungen, Necrology,
Mathematisch-Naturwissenschaftliche Blätter 1906, No. 12.