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Optico-Mechanical Analogy: an Axiomatic Approach

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Abstract

An axiomatic characterization of a ‘two-level Hamiltonian structure’ is proposed, which expresses the optico-mechanical analogy by representing optics and mechanics as (disjoint) classes of models satisfying the axioms. There is the ‘Hamilton–Jacobi level’, which involves a differential manifold on which the characteristic function satisfying the Hamilton–Jacobi equation is defined; and the ‘symplectic level’, involving the Hamiltonian, defined on the cotangent bundle of the manifold. The two levels, with the (analogous) structures on them, concern both optics and mechanics.

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References

  1. Arnol’d, V.I.: Mathematical Methods of Classical Mechanics. Springer, Berlin (1997)

    Google Scholar 

  2. Balzer, W., Moulines, C.U., Sneed, J.D.: An Architectonic for Science. Kluwer, Dordrecht (1987)

    MATH  Google Scholar 

  3. de Broglie, L.: Recherches sur la théorie des quanta. Ann. Phys. 3, 22–128 (1925)

    Google Scholar 

  4. McKinsey, J.C.C., Sugar, A.C., Suppes, P.: Axiomatic foundations of classical particle mechanics. J. Ration. Mech. Anal. 2, 253–72 (1953)

    MathSciNet  Google Scholar 

  5. McKinsey, J.C.C., Suppes, P.: Transformations of systems of classical particle mechanics. J. Ration. Mech. Anal. 2, 273–89 (1953)

    MathSciNet  Google Scholar 

  6. Moulines, U.M., Sneed, J.D.: Suppes’ philosophy of physics. In: Bogdan, R. (ed.) Patrick Suppes. pp. 59–91. Reidel, Dordrecht (1979)

    Google Scholar 

  7. Schrödinger, E.: Quantisierung als Eigenwertproblem (zweite Mitteilung). Ann. Phys. 79, 489–527 (1926)

    Article  Google Scholar 

  8. Schrödinger, E.: Der Grundgedanke der Wellenmechanik. In: Schrödinger, E. (ed.) Was ist ein Naturgesetz?. Oldenbourg, Munich (1987)

    Google Scholar 

  9. Sneed, J.D.: The Logical Structure of Mathematical Physics. Kluwer, Dordrecht (1979)

    MATH  Google Scholar 

  10. Stegmüller, W.: Theorie und Erfahrung. Springer, Berlin (1973)

    MATH  Google Scholar 

  11. Stegmüller, W.: Neue Wege der Wissenschaftsphilosophie. Springer, Berlin (1980)

    MATH  Google Scholar 

  12. Suppes, P.: Introduction to Logic. Dover, New York (1999)

    MATH  Google Scholar 

  13. Suppes, P.: Representation and Invariance of Scientific Structures. CSLI, Stanford (2002)

    MATH  Google Scholar 

  14. Wessel, L.: Schrödinger’s route to wave mechanics. Stud. Hist. Philos. Sci. 10, 311–40 (1979)

    Article  Google Scholar 

Download references

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  1. Istituto di Filosofia, Università di Urbino, Via Timoteo Viti 10, 61029, Urbino, Italy

    Alexander Afriat

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  1. Alexander Afriat
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Correspondence to Alexander Afriat.

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Afriat, A. Optico-Mechanical Analogy: an Axiomatic Approach. Int J Theor Phys 46, 2669–2675 (2007). https://doi.org/10.1007/s10773-007-9379-1

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