The Operational Approach to Quantum Mechanics

Part of the The University of Western Ontario Series in Philosophy of Science book series (WONS, volume 7)


The operational approach in the title of this paper refers to the primitive and fundamental status accorded to the concept of a physical experiment or operation by the authors. This emphasis on the operational approach should not be construed as an adoption of operationalism, logical positivism, or radical empiricism, as may initially appear to be the case. Our approach does not entail the rejection of subjective methods; in particular, it does not deny — and in fact readily accomodates — the unifying and explanatory power of idealized models.


Operational Approach Regular State Compact Open Subset Physical Operation Orthomodular Poset 
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.


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  1. [1]
    Alfsen, E. M., Compact Convex Sets and Boundary Integrals, Springer-Verlag, New York, 1971.Google Scholar
  2. [2]
    Alfsen, E. M. and Shultz, F. W., Non-Commutative Spectral Theory for Affine Function Spaces on Convex Sets, Part I, Preprint Series, Inst. of Math., Univ. of Oslo, Norway 1974.Google Scholar
  3. [3]
    Beaver, O. R. and Cook, T. A., ‘States on Quantum Logics and their Connection with a Theorem of Alexandroff’, Proc. A.M.S. 67 (1977), 133–134.CrossRefGoogle Scholar
  4. [4]
    Birkhoff, G. and von Neumann, J., ‘The Logic of Quantum Mechanics’, Ann. of Math., 37 (1936), 823–843.CrossRefGoogle Scholar
  5. [5]
    Collins, W. R. ‘A Category of Sample Spaces’, Unpublished Ph.D. dissertation, University of Massachusetts, Amherst, 1971.Google Scholar
  6. [6]
    Cook, T. A., ‘The Geometry of Generalized Quantum Logics’, Int. J. Theor. Phys., To appear (1977).Google Scholar
  7. [7]
    Cook T. A. and Rüttimann, G. T.,’ symmetries on Quantum Logics’, Submitted to Proc. A.M.S. Google Scholar
  8. [8]
    Dacey, J. C., Jr., ‘Orthomodular Spaces’, Unpublished Ph.D. dissertation, University of Massachusetts, Amherst, 1968.Google Scholar
  9. [9]
    Davies, E. B. and Lewis, ‘An Operational Approach to Quantum Probability’, Commun. Math. Phys. 17 (1970), 239–260.CrossRefGoogle Scholar
  10. [10]
    Dirac, P. A. M., The Principles of Quantum Mechanics, Clarendon, Oxford, 1930.Google Scholar
  11. [11]
    Dunford, N. and Schwarz, J., Linear Operators, Part I, Interscience Pub. Inc., New York, 1957.Google Scholar
  12. [12]
    Edwards, C. M., ‘The Operational Approach to Algebraic Quantum Theory I’, Commun. Math. Phys. 16 (1970), 207–230.CrossRefGoogle Scholar
  13. [13]
    Fischer, H. and Rüttimann, G. T., ‘Fields of Manuals’, To appear.Google Scholar
  14. [14]
    Foulis. D. J. and Randall, C. H., ‘Operational Statistics I, Basic Concepts’, J. Math. Phys. 13(1972), 1667–1675.CrossRefGoogle Scholar
  15. [15]
    Foulis, D. J. and Randall, C. H., ‘Empirical Logic and Quantum Mechanics’, Synthese 29 (1974), 81–111.CrossRefGoogle Scholar
  16. [16]
    Foulis, D. J. and Randall, C. H. ‘The Stability of Pure Weights Under Conditioning’, Glasgow Math. J. 15 (1974), 5–12.CrossRefGoogle Scholar
  17. [17]
    Foulis, D. J. and Randall, C. H., ‘The Empirical Logic Approach to the physical Sciences’, in A. Hartkämper and H. Neumann (eds.), Foundations of Quantum Mechanicsand Ordered Linear Spaces, Springer-Verlag, New York, 1974, 230–249.CrossRefGoogle Scholar
  18. [18]
    Gleason, A. M., ‘Measures on the Closed Subspaces of a Hilbert Space’, J. Math. Mechanics 6 (1953), 885–893.Google Scholar
  19. [19]
    Haag, R. and Kastler, D., ‘An Algebraic Approach to Quantum Field Theory,’ J. Math. Phys. 5 (1964), 848–861.CrossRefGoogle Scholar
  20. [20]
    Hartkämper, A. and Neumann, H. (eds.), Foundations of Quantum Mechanics and Ordered Linear Spaces, Springer-Verlag, New York, 1974.Google Scholar
  21. [21]
    Heider, L. J., ‘A Representation Theory for Measures on Boolean Algebras’, Michigan Math. J. 5 (1958), 213–221.CrossRefGoogle Scholar
  22. [22]
    Hein, C, ‘The Poincare sample space’, Foundations of Phys. 7 (1977), 597–608.CrossRefGoogle Scholar
  23. [23]
    Jauch, J. M., Foundations of Quantum Mechanics, Addison Wesley Publ. Co., Reading, Mass., 1968.Google Scholar
  24. [24]
    Jordan, P., von Neumann, J. and Wigner, E., ‘On an Algebraic Generalization of the Quantum Mechanics Formalism’, Ann. Math. 35 (1934), 29–64.CrossRefGoogle Scholar
  25. [25]
    Kolmogorov, A. N., Foundations of the Theory of Probability, 2nd Edition, Chelsea Publ. Co., New York, 1956 (German ed. 1933.)Google Scholar
  26. [26]
    Ludwig, G., ‘Versuch einer axiomatischen Grundlegung der Quanten Mechanik und allgemeinerer physikalischer Theorien’, Z. Physik 181 (1964), 233–260.CrossRefGoogle Scholar
  27. [27]
    Mackey, G. W., Mathematical Foundations of Quantum Mechanics, W. A. Benjamin, Inc., New York, 1963.Google Scholar
  28. [28]
    Mackey, G. W., Induced Representations of Groups and Quantum Mechanics, W. A. Benjamin, Inc., New York, 1968.Google Scholar
  29. [29]
    Mielnik, B., ‘Geometry of Quantum States’, Commun. Math. Phys. 9(1968), 55–80.CrossRefGoogle Scholar
  30. [30]
    Nagel, R. J., ‘Order Unit and Base Norm Spaces’, in A. Hartkämper and H. Neumann (eds.), Foundations of Quantum Mechanics and Ordered Linear Spaces, Springer-Verlag, New York, 1974, 23–29.CrossRefGoogle Scholar
  31. [31]
    Pool, J.C.T., ‘Baer “”-Semigroups and the Logic of Quantum Mechanics’, Commun. Math. Phys. 9 (1968), 118–141.CrossRefGoogle Scholar
  32. [32]
    Piron, C, ‘Axiomatique quantique’, Helv. Phys. Acta 37(1964), 439–468.Google Scholar
  33. [33]
    Randall, C. H., ‘A Mathematical Foundation for Empirical Science’, Ph.D. dissertation, Rensselaer Polytechnic Institute, Troy, N.Y., 1966.Google Scholar
  34. [34]
    Randall, C. H. and Foulis D. J., ‘Operational Statistics II, Manuals of Operations and their Logics’, J. Math. Phys. 14 (1973), 1472–1480.CrossRefGoogle Scholar
  35. [35]
    Randall, C. H. and Foulis, D. J., ‘A mathematical setting for inductive reasoning’, in C. Hooker (ed.), Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Science, Vol. III, D. Reidei Publ. Co., Dordrecht: Holland, 1976, 169–205.Google Scholar
  36. [36]
    Rüttimann, G. T., ‘Jauch-Piron States’, J. Math. Phys. 18(1977), 189–193.CrossRefGoogle Scholar
  37. [37]
    Rüttimann, G. T. ‘Jordan-Hahn Decomposition of Signed Weights on Finite Orthogonality Spaces’, Comment. Math. Helvetica 52(1977), 129–144.CrossRefGoogle Scholar
  38. [38]
    Segal, I. E., ‘Postulates for General Quantum Mechanics’, Ann. Math. 48(1947), 930–948.CrossRefGoogle Scholar
  39. [39]
    Stone, M. H., ‘Postulates for the Barycentric Calculus’, Ann. Math. Pure Appl. 29(1949), 25–30.CrossRefGoogle Scholar
  40. [40]
    von Neumann, J., Mathematical Foundations of Quantum Mechanics, Princeton University Press, Princeton, N.J., 1955.Google Scholar
  41. [41]
    Wright, R., The Structure of Projection-Valued States; A Generalization of Wigner’s Theorem’, Int. J. Theor. Phys. 16 (1977), 567–573.CrossRefGoogle Scholar
  42. [42]
    Wright, R., ’spin manuals’: Empirical Logic Talks Quantum Mechanics,’ in A. R. Marlow (ed.) Mathematical Foundations of Quantum Theory, Academic Press, 1978, 177-254.Google Scholar

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© D. Reidel Publishing Company, Dordrecht, Holland 1978

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