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Reconstruction of Quantum Mechanics

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Rational Reconstructions of Modern Physics

Part of the book series: Fundamental Theories of Physics ((FTPH,volume 174))

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Abstract

The historical development of quantum mechanics offers a rather heterogeneous picture, a large variety of interpretations, goals, and philosophical classifications. Quantum mechanics was understood as a theory in the spirit of positivism, operationalism, and empiricism, – to mention here only a few of numerous interpretations. None of the main protagonists of quantum mechanics, Bohr, Heisenberg, Schrödinger, and Pauli agreed completely about the understanding of the new theory, nor do individual scientists permanently represent the same philosophical position. As an outstanding example, we mention here Heisenberg, who changed his assessment of quantum mechanics several times.

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Notes

  1. 1.

    Bohr (1934), p. 53.

  2. 2.

    Bohr (1934), p. 8.

  3. 3.

    Bohr (1934), pp. 54–55.

  4. 4.

    Mittelstaedt (2005).

  5. 5.

    Mittelstaedt (1976) and Stachow (1976).

  6. 6.

    Mittelstaedt (1976).

  7. 7.

    Mittelstaedt (1978).

  8. 8.

    Mittelstaedt (1978).

  9. 9.

    Stachow (1980).

  10. 10.

    Busch et al. (1996).

  11. 11.

    Mittelstaedt (1978).

  12. 12.

    Stachow (1980).

  13. 13.

    Mittelstaedt (1978).

  14. 14.

    If two propositions are proof equivalent, then they are also value equivalent. The inverse is not generally true. However, in classical language the two equivalence relations coincide.

  15. 15.

    Stachow (1976).

  16. 16.

    Mittelstaedt (1978), p. 29, Kalmbach (1983).

  17. 17.

    Stachow (1984).

  18. 18.

    Cf. Piron (1964), MacLaren (1965), and Varadarajan (1968).

  19. 19.

    Keller (1980).

  20. 20.

    For more details cf. Dalla Chiara et al. (2001, pp.48–50, 2004, pp.72–74).

  21. 21.

    Solèr (1995).

  22. 22.

    Piron (1976) and MacLaren (1965).

  23. 23.

    Busch et al. (1996).

  24. 24.

    Mittelstaedt (1998).

  25. 25.

    Busch et al. (1996).

  26. 26.

    Mittelstaedt et al. (1987)

  27. 27.

    Busch (1985) and Busch et al. (2007).

  28. 28.

    Giuntini and Greuling (1989).

  29. 29.

    Dalla Chiara (1995).

  30. 30.

    Foulis and Bennett (1994).

  31. 31.

    Giuntini (1990).

  32. 32.

    Dalla Chiara et al. (1993).

  33. 33.

    Dalla Chiara and Giuntini (1994).

  34. 34.

    Busch and Shimony (1996).

  35. 35.

    Busch (1998).

  36. 36.

    Natanson (1911).

  37. 37.

    Bose (1924a, b).

  38. 38.

    Einstein (1924, 1925).

  39. 39.

    Adopted from Hund (1967), p. 154.

  40. 40.

    Pauli (1940).

  41. 41.

    Streater and Wightman (1964), Section 4.4.

  42. 42.

    Leibniz, G. W. Discours de Métaphysique, GP IV, p. 433.

  43. 43.

    Castellani and Mittelstaedt (2000).

  44. 44.

    Leibniz, G. W., Discours de Métaphysique, GP IV, p. 434.

  45. 45.

    Adopted from Hund (1967), p. 154.

  46. 46.

    G. W. Leibniz, GP V, p. 214. – (Engraving reproduction; Schubert 1796).

  47. 47.

    G. W. Leibniz, GP VII, p. 372.

  48. 48.

    Armstrong (1983), Mittelstaedt and Weingartner (2004) and Van Fraassen (1989).

  49. 49.

    von Neumann (1932).

  50. 50.

    Birkhoff and von Neumann (1936).

  51. 51.

    For a very detailed presentation of the history of quantum logic cf. Jammer (1974), pp. 341–616.

  52. 52.

    Feyerabend (1965) and Stegmüller (1970), pp. 438–461.

  53. 53.

    Putnam (1969).

  54. 54.

    Stachow (1976) and Mittelstaedt (1978).

  55. 55.

    Lorenzen (1955).

  56. 56.

    Curry (1952).

  57. 57.

    As mentioned in Section (3.4) a lattice of this kind is atomic and fulfils the covering law.

  58. 58.

    We will come back to this ontology O(Q U) in Sections (4.3.1) and (4.3.4).

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  1. Institut für Theoretische Physik, Universität zu Köln, Köln, Germany

    Peter Mittelstaedt

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Mittelstaedt, P. (2013). Reconstruction of Quantum Mechanics. In: Rational Reconstructions of Modern Physics. Fundamental Theories of Physics, vol 174. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-5593-2_3

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