TY - JOUR

T1 - The classical roots of wave mechanics

T2 - Schrödinger's transformations of the optical-mechanical analogy

AU - Joas, Christian

AU - Lehner, Christoph

PY - 2009/12/1

Y1 - 2009/12/1

N2 - 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.

AB - 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.

KW - Hamilton, W. R.

KW - Optical-mechanical analogy

KW - Quantum mechanics

KW - Schrödinger, E.

KW - Wave mechanics

UR - http://www.scopus.com/inward/record.url?scp=71849097121&partnerID=8YFLogxK

U2 - 10.1016/j.shpsb.2009.06.007

DO - 10.1016/j.shpsb.2009.06.007

M3 - Journal article

AN - SCOPUS:71849097121

VL - 40

SP - 338

EP - 351

JO - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics

JF - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics

SN - 1355-2198

IS - 4

ER -