At the 11 May 1917 meeting of the German Physical Society, Albert Einstein, then a professor at the University of Berlin, presented the only research paper of his career that was written on the quantization of energy for mechanical systems. 1 The paper contained an elegant re-formulation of the Bohr–Sommerfeld quantization rules of the old quantum theory, a rethinking that extended and clarified their meaning. Even more impressive, the paper offered a brilliant insight into the limitations of the old quantum theory when applied to a mechanical system that is nonintegrable—or in modern terminology, chaotic. Louis de Broglie cited the paper in his historic thesis on the wave properties of matter, 2 as did Erwin Schrödinger in the second of his seminal papers on the wave equation for quantum mechanics. 3 But the 1917 work was then ignored for more than 25 years until Joseph Keller independently discovered the Einstein...
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1 August 2005
August 01 2005
Einstein’s Unknown Insight and the Problem of Quantizing Chaos Available to Purchase
Chaotic systems were beyond the reach of an ingenious coordinate-invariant quantization scheme developed by Albert Einstein, and to this day, their quantization remains a challenge.
Physics Today 58 (8), 37–43 (2005);