Implications of a New Axiom Set for Quantum Logic

  • A. R. Marlow
Part of the Boston Studies in the Philosophy of Science book series (BSPS, volume 13)


A recent work on the many-body problem in modern physics begins with the following paragraph:

A reasonable starting point for a discussion of the many-body problem might be the question of how many bodies are required before we have a problem. Prof. G. E. Brown has pointed out that, for those interested in exact solutions, this can be answered by a look at history. In eighteenth-century Newtonian mechanics, the three-body problem was insoluble. With the birth of general relativity around 1910 and quantum electrodynamics in 1930, the two- and one-body problems became insoluble. And within modern quantum field theory, the problem of zero bodies (the vacuum) is insoluble. So, if we are out after exact solutions, no bodies at all is already too many.1


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  1. 1.
    R. D. Mattuck, A Guide to Feynman Diagrams in the Many-Body Problem, McGraw-Hill, New York, 1967.Google Scholar
  2. 2.
    J. S. Bell, D. Bohm and J. Bub, Reviews of Modem Physics 38 (1966) (series of three papers).Google Scholar
  3. 3.
    J. M. Jauch and C. Piron, Helvetica Physica Acta 37 (1964) 293.Google Scholar
  4. 4.
    Cf. Letters to the Editor, Reviews of Modern Physics 40 (1968) 228ff.CrossRefGoogle Scholar
  5. 5.
    A. R. Marlow, Journal of Mathematical Physics (submitted for publication).Google Scholar
  6. 6.
    A. R. Marlow, Journal of Mathematical Physics (submitted for publication).Google Scholar
  7. 7.
    G. Birkhoff and J. von Neumann, Annals of Mathematics 37 (1936), 823.CrossRefGoogle Scholar
  8. 8.
    G. W. Mackey, The Mathematical Foundations of Quantum Mechanics, Benjamin, New York, 1963.Google Scholar
  9. 9.
    Piron, Helvetica Physica Acta 37 (1964), 439.Google Scholar
  10. 10.
    See note 8, p. 66.Google Scholar
  11. 11.
    For the further development of the quantum mechanical model, cf. note 8, pp. 71 ff.Google Scholar
  12. 12.
    For a full discussion of this point, see S. P. Gudder, Journal of Mathematical Physics 8 (1967), 1848 and our note 5, footnote 1.CrossRefGoogle Scholar
  13. 13.
    Due to a suggestion of Dr. Abner Shimony, the general proof of the existence of embedding is independent of the countability assumption (A).Google Scholar
  14. 14.
    At least some of this multiplicity is removed in the C*-algebra approach to quantum theory; for an account of this approach, see D. Kastler, pp. 179–191 in the volume edited by W. Martin and I. Segal, Analysis in Function Space, MIT Press, Cambridge, Mass., 1964.Google Scholar
  15. 15.
    This modifies and sharpens somewhat an interesting comparison offered by D. Bohm and J. Bub, Reviews of Modern Physics 40 (1968), 235.CrossRefGoogle Scholar

Copyright information

© D. Reidel Publishing Company, Dordrecht, Holland 1974

Authors and Affiliations

  • A. R. Marlow
    • 1
  1. 1.Loyola UniversityNew OrleansUSA

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