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
SN - 1355-2198
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
IS - 4
ER -