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Towards a Constructive Foundation of Quantum Mechanics

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Abstract

I describe a constructive foundation for quantum mechanics, based on the discreteness of the degrees of freedom of quantum objects and on the Principle of Relativity. Taking Einstein’s historical construction of Special Relativity as a model, the construction is carried out in close contact with a simple quantum mechanical Gedanken experiment. This leads to the standard axioms of quantum mechanics. The quantum mechanical description is identified as a mathematical tool that allows describing objects, whose degree of freedom in space–time has a discrete spectrum, relative to classical observers in space–time. This description is covariant with respect to (continuous) coordinate transformations and meets the requirement that the spectrum is the same in every inertial system. The construction gives detailed answers to controversial questions, such as the measurement problem, the informational content of the wave function, and the completeness of quantum mechanics.

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References

  1. Heisenberg, W.: Über quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen. Zeitschrift für Physik 33, 879 (1925)

    Article  ADS  Google Scholar 

  2. Born, M., Jordan, P.: Zur Quantenmechanik. Zeitschrift für Physik 34, 858 (1925)

    Article  ADS  Google Scholar 

  3. Born, M., Heisenberg, W., Jordan, P.: Zur Quantenmechanik II. Zeitschrift für Physik 35, 8 (1926)

    Article  Google Scholar 

  4. Schrödinger, E.: Quantisierung als Eigenwertproblem. Annalen der Physik 79, 361, 489, 734 (1926), and 81, 109 (1926)

  5. Dirac, P.A.M.: The Principles of Quantum Mechanics. Oxford University Press, Oxford (1930)

    MATH  Google Scholar 

  6. von Neumann, J.: Mathematische Grundlagen der Quanten Mechanik. Springer, Berlin (1932)

    Google Scholar 

  7. Rovelli, C.: Relational quantum mechanics. Int. J. Theor. Phys. 35, 1637 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  8. Einstein, A.: Zur Elektrodynamik bewegter Körper. Annalen der Physik 17, 891 (1905)

    Article  ADS  Google Scholar 

  9. Michelson, A.A., Morley, E.W.: On the relative motion of the earth and the luminiferous ether. Am. J. Sci. 34, 333 (1887)

    Article  MATH  Google Scholar 

  10. Poincaré, H.: L’état actuel et l’avenir de la physique mathématique. Bulletin des Sciences Mathématiques 28, 302 (1904)

    MATH  Google Scholar 

  11. Gerlach, W., Stern, O.: Der experimentelle Nachweis der Richtungsquantelung im Magnetfeld. Zeitschrift für Physik 9, 349 (1922)

  12. Gleason, A.M.: Measures on the closed subspaces of a Hilbert space. J. Math. Mech. 6, 885 (1957)

    MathSciNet  MATH  Google Scholar 

  13. Born, M.: Zur Quantenmechanik der Stoßvorgänge. Zeitschrift für Physik 37, 863 (1926)

    Article  ADS  MATH  Google Scholar 

  14. Schweber, S.S.: An Introduction to Relativistic Quantum Field Theory. Harper & Row, New York (1962)

    MATH  Google Scholar 

  15. 2014 CODATA recommended values

  16. O’Hara, P.: Bell’s Inequality, the Pauli Exclusion Principle and Baryonic Structure. In: Spin 96 Proceedings, World Scientific, Singapore (1997) arXiv:hep-th/9701089

  17. Lecture notes, ocw.mit.edu/courses

  18. Smilga W.: Momentum entanglement in relativistic quantum mechnanics J. Phys.: Conf. Ser. 597, 012069 (2015) iopscience.iop.org/1742-6596/597/1/012069

  19. Wheeler, J.A.: Information, physics, quantum: the search for links. In: Zurek, W. (ed.) Complexity, Entropy, and the Physics of Information. Addison-Wesley, Reading, MA (1990)

    Google Scholar 

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Correspondence to Walter Smilga.

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Smilga, W. Towards a Constructive Foundation of Quantum Mechanics. Found Phys 47, 149–159 (2017). https://doi.org/10.1007/s10701-016-0050-7

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