Foundations of Physics

, Volume 9, Issue 9–10, pp 641–671 | Cite as

Measurement theory for physics

  • John F. Cyranski
Article

Abstract

A highly abstracted theory of measurement is synthesized from classical measurement theory, fuzzy set theory, generalized information theory, and predicate calculus. The theory does not require specific truth value concepts, nor does it specify what subsets of the reals can be observed, thus avoiding the usual fundamental difficulties. Problems such as the definition of systems, the significance of observations, numerical scales and observables, etc. are examined. The general logico-algebraic approach to quantum/classical physics is justified as a special case of measurement theory.

Keywords

Information Theory Measurement Theory Numerical Scale Classical Measurement Fundamental Difficulty 

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References

  1. 1.
    J. F. Cyranski, Measurement, Theory, and Information,Inf. Contr., to appear.Google Scholar
  2. 2.
    J. Pfanzagl,Theory of Measurement (Physica-Verlag, Wurzburg-Wien, 1971).Google Scholar
  3. 3.
    D. H. Krantz, R. D. Luce, P. Suppes, and A. Tversky,Foundations of Measurement (Academic, 1971), Vol. I.Google Scholar
  4. 4.
    J. M. Jauch,Foundations of Quantum Mechanics (Addison-Wesley, 1968).Google Scholar
  5. 5.
    C. Piron,Foundations of Quantum Physics (Benjamin, 1976).Google Scholar
  6. 6.
    N. J. Nilsson,Problem-Solving Methods in Artificial Intelligence (McGraw-Hill, 1971).Google Scholar
  7. 7.
    J. A. Goguen,J. Math. Anal. Appl. 18, 145 (1967).Google Scholar
  8. 8.
    S. D. Drell,Physics Today 31(6), 23 (1978).Google Scholar
  9. 9.
    S. T. Ali and E. Prugovecki,J. Math. Phys. 18, 219 (1977).Google Scholar
  10. 10.
    G. Birkhoff,Lattice Theory 3rd ed., (Am. Math. Soc., 1973).Google Scholar
  11. 11.
    A. Kaufmann,Introduction to the Theory of Fuzzy Subsets (Academic, 1975), Vol. 1.Google Scholar
  12. 12.
    S. C. Kleene,Introduction to Metamathematics (North-Holland, 1971).Google Scholar
  13. 13.
    J. F. Cyranski,Found. Phys. 8, 805 (1978).Google Scholar
  14. 14.
    M. M. Gupta, G. N. Saridis, and B. R. Gaines, eds.Fuzzy Automata and Decision Processes (North-Holland, 1977).Google Scholar
  15. 15.
    C. Møller,The Theory of Relativity (Oxford, 1952).Google Scholar
  16. 16.
    W. R. Tunnicliffe,Proc. London Math. Soc. 3, 13 (1974).Google Scholar
  17. 17.
    R. J. Greechie and S. P. Gudder, inThe Logico-Algebraic Approach to Quantum Mechanics, C. A. Hooker, ed. (Reidel, 1975), p. 545.Google Scholar
  18. 18.
    C. A. Hooker, ed.,The Logico-Algebraic Approach to Quantum Mechanics (Reidel, 1975).Google Scholar
  19. 19.
    M. D. MacLaren,Pac. J. Math. 14, 597 (1964).Google Scholar
  20. 20.
    S. Watanabe,Inf. Contr. 15, 1 (1969).Google Scholar
  21. 21.
    J. Sallantin,Journees Inform.-Questionnaires-Reconnaissance (Structures de l'Information Publications, C.N.R.S, Paris, 1977).Google Scholar
  22. 22.
    F. Gallone and A. Mania,Ann. Inst. H. Poincaré XVA, 37 (1971).Google Scholar
  23. 23.
    J. F. Cyranski, to appear.Google Scholar
  24. 24.
    F. Maeda and S. Maeda,Theory of Symmetric Lattices (Springer-Verlag, 1970).Google Scholar
  25. 25.
    G. A. Fraser,Trans. Am. Math. Soc. 217, 183 (1976).Google Scholar
  26. 26.
    F. Treves,Topological Vector Spaces, Distributions and Kernels (Academic, 1967).Google Scholar
  27. 27.
    A. Zecca,J. Math. Phys. 19, 1482 (1978).Google Scholar
  28. 28.
    B. de Finetti,Probability, Induction and Statistics, The art of guessing (Wiley, 1972).Google Scholar
  29. 29.
    A. De Luca and S. Termini,J. Math. Anal. App. 40, 373 (1972).Google Scholar
  30. 30.
    B. L. Wellman,Technical Descriptive Geometry (McGraw-Hill, 1957).Google Scholar
  31. 31.
    R. S. Ingarden and A. Kossakowski,Ann. Phys. 89, 451 (1975).Google Scholar
  32. 32.
    J. Sallantin, inThéories de l'Information, J. Kampé de Fériet and C. F. Picard, eds. (Springer-Verlag, 1974), p. 76.Google Scholar
  33. 33.
    J. Sallantin,Séminaires sur les Questionnaires (Structures de l'Information Publications, CNRS, Paris, 1977), pp. 141, 153.Google Scholar
  34. 34.
    G. Comyn and J. Losfeld,Journées Lyonnaises des Questionnaires (Structures de l'Information Publications, CNRS, 1976), p. 45.Google Scholar
  35. 35.
    R. Carnap,Logical Foundations of Probability (Chicago, 1950).Google Scholar
  36. 36.
    K. H. Norwich,Bull. Math. Biol. 39, 453 (1977).Google Scholar
  37. 37.
    K. Friedman and A. Shimony,J. Stat. Phys. 3, 381 (1971).Google Scholar
  38. 38.
    J. F. Cyranski,Found. Phys. 8, 493 (1978).Google Scholar
  39. 39.
    J. F. Cyranski, Entropy in Classical and Quantum Physics, submitted for publication.Google Scholar
  40. 40.
    E. T. Jaynes,Phys. Rev. 106, 620 (1957);108, 171 (1957).Google Scholar
  41. 41.
    J. Kampé de Fériet, inThéories de l'Information, J. Kampé de Fériet and C. F. Picard, eds. (Springer-Verlag, 1974), p. 1.Google Scholar
  42. 42.
    S. Guiasu,Information Theory and Applications (McGraw-Hill, 1977).Google Scholar
  43. 43.
    V. S. Varadarajan,Geometry of Quantum Theory (D. van Nostrand, 1968), Vol. 1.Google Scholar
  44. 44.
    M. E. Munroe,Introduction to Measure and Integration (Addison-Wesley, 1953).Google Scholar
  45. 45.
    A. M. Gleason, inThe Logico-Algebraic Approach to Quantum Mechanics, C. A. Hooker, ed. (Reidel, 1975), p. 123.Google Scholar
  46. 46.
    J. von Neumann,Mathematical Foundations of Quantum Mechanics (Princeton Univ. Press, 1955).Google Scholar
  47. 47.
    M. Jammer,The Philosophy of Quantum Mechanics (Wiley, 1974).Google Scholar
  48. 48.
    P. R. Halmos,Algebraic Logic (Chelsea, 1962).Google Scholar
  49. 49.
    B. Carter,Gen. Rel. Grav. 1, 349 (1971).Google Scholar
  50. 50.
    J. L. Park and H. Margenau,Int. J. Theor. Phys. 1, 211 (1968).Google Scholar
  51. 51.
    J. von Neumann,Ann. Math. 33, 587 (1932).Google Scholar

Copyright information

© Plenum Publishing Corporation 1979

Authors and Affiliations

  • John F. Cyranski
    • 1
  1. 1.Theoretical Chemistry InstituteThe National Hellenic Research FoundationAthensGreece

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