Foundations of Physics

, Volume 18, Issue 5, pp 491–528 | Cite as

The foundations of quantum mechanics

  • P. J. Bussey
Article
Received:
Revised:

Abstract

Starting from a set of assumptions mainly of an “operational” or experimentally based nature, a derivation of quantum mechanics is presented, with the aim of clarifying the essential features of the theory and their interpretation. Various properties of quantum mechanics such as the addition of amplitudes, the calculation of probabilities, de Broglie's equations, and energy-momentum conservation are derived from first principles. It is investigated whether quantum amplitudes may be constructed from quantities of higher order than complex numbers. Measurable physical quantitics, as traditionally understood, are seen to play a role distinct from and supplementary to the behavior of the quantum amplitudes themselves. This is related to two distinct aspects of the nature of time in the context of quantum mechanics.

Keywords

Quantum Mechanic Complex Number Essential Feature Distinct Aspect Quantum Amplitude 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    P. A. M. Dirac,The Principles of Quantum Mechanics (Clarendon Press, Oxford, 1930).Google Scholar
  2. 2.
    J. von Neumann, “Mathematische Begründungen der Quantenmechanik,”Göttinger Nachrichten, 1927;Mathematical Foundations of Quantum Mechanics (Princeton University Press, Princeton, New Jersey, 1955).Google Scholar
  3. 3.
    E. P. Wigner,Group Theory and Its Applications to the Quantum Mechanics of Atomic Spectra (Academic Press, New York, 1959), pp. 233–236.Google Scholar
  4. 4.
    E. C. G. Stueckelberg,Helv. Phys. Acta 33, 727 (1960); E. C. G. Stueckelberg and M. Guenin,Helv. Phys. Acta 34, 621 (1961).Google Scholar
  5. 5.
    R. P. Feynman, R. B. Leighton, and M. Sands,The Feynman Lectures on Physics (Addison-Wesley, Reading, Massachusetts, 1965), Vol. 3, Eq. 11.49.Google Scholar
  6. 6.
    D. Finkelstein, J. M. Jauch, S. Schiminovich, and D. Speiser,J. Math. Phys. 3, 207 (1962).Google Scholar
  7. 7.
    A. Peres,Phys. Rev. Lett. 42, 683 (1979).Google Scholar
  8. 8.
    U. Timm,Fortschr. Phys. 17, 767 (1969).Google Scholar
  9. 9.
    H. P. Stapp, Lawrence Berkeley Laboratory Preprint LBL-17576, 1984; Proceedings, “Physics and the Ultimate Significance of Time,” Claremont, California.Google Scholar

Copyright information

© Plenum Publishing Corporation 1988

Authors and Affiliations

  • P. J. Bussey
    • 1
  1. 1.Department of Natural Philosophy (now Department of Physics and Astronomy)University of GlasgowUK

Personalised recommendations