The Classical Roots of Wave Mechanics: Schrödinger's Transformations of the Optical-Mechanical Analogy (2009)
Joas, Christian (Author)
Lehner, Christoph (Author)
Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics
Volume: 40
Pages: 338--351
In the 1830s, W. R. Hamilton established a formal analogy between optics and mechanics by constructing a mathematical equivalence between the extremum principles of ray optics (Fermat's principle) and corpuscular mechanics (Maupertuis's principle). Almost a century later, this optical-mechanical analogy played a central role in the development of wave mechanics. Schrödinger was well acquainted with Hamilton's analogy through earlier studies. From Schrödinger's research notebooks, we show how he used the analogy as a heuristic tool to develop de Broglie's ideas about matter waves and how the role of the analogy in his thinking changed from a heuristic tool into a formal constraint on possible wave equations. We argue that Schrödinger only understood the full impact of the optical-mechanical analogy during the preparation of his second communication on wave mechanics: Classical mechanics is an approximation to the new undulatory mechanics, just as ray optics is an approximation to wave optics. This completion of the analogy convinced Schrödinger to stick to a realist interpretation of the wave function, in opposition to the emerging mainstream. The transformations in Schrödinger's use of the optical-mechanical analogy can be traced in his research notebooks, which offer a much more complete picture of the development of wave mechanics than has been previously thought possible.
...MoreArticle Dongen, Jeroen van; Dieks, Dennis; Uffink, Jos; Kox, A. J. (2009) On the History of the Quantum: Introduction to the HQ2 Special Issue. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics (p. 277).
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Revue des Questions Scientifiques
Physis: Rivista Internazionale di Storia della Scienza
Physics in Perspective
科学史研究 Kagakusi Kenkyu (History of Science)
Isis: International Review Devoted to the History of Science and Its Cultural Influences
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