The Ensemble Interpretation of Probability

  • T. A. Brody
Conference paper
Part of the Fundamental Theories of Physics book series (FTPH, volume 24)


Current philosophical interpretations are shown to be unsatisfactory when applied to problems of scientific research. An alternative, based on the work of Einstein and Gibbs, is proposed: probability as a scientific concept, with a theoretical and an experimental component, the former based on the ensemble and averages over it, the latter on relative frequencies in (finite) sets of experimental data. The two will agree only to the extent that the theoretical background of the ensemble is satisfactory. This interpretation extends in a natural way to the time-dependent probabilities of stochastic processes. The relevance of the concept in other areas of physics is exhibited.


Chaotic System Ensemble Average Scientific Concept Probability Concept Experimental Component 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. R. Balescu (1975), ″Equilibrium and Non-Equilibrium Statistical Mechanics″, J. Wiley, New YorkGoogle Scholar
  2. L. E. Ballentine (1970), Revs. Mod. Phys. 42, 358CrossRefzbMATHADSGoogle Scholar
  3. D. I. Blochinzew (1953), ″Grundlagen der Quantenmechanik″, Deutscher Verlag der Wissenschaften, BerlinGoogle Scholar
  4. N. Bohr (1936), Erkenntnis 6, 263CrossRefGoogle Scholar
  5. N. Bohr (1948), Dialectica 2, 312CrossRefzbMATHGoogle Scholar
  6. T. A. Brody (1975), Rev. Mex. Fis. 24, 25Google Scholar
  7. T. A. Brody (1983), Rev. Mex. Fis. 29, 461MathSciNetGoogle Scholar
  8. T. A. Brody (1984), Comp. Phys. Comm. 34, 39CrossRefADSMathSciNetGoogle Scholar
  9. P. Cvitanović (1984),″Universality in Chaos″, Adam Hilger, BristolzbMATHGoogle Scholar
  10. F. J. Dyson (1958), Scientific American 199(9), 74CrossRefGoogle Scholar
  11. F. J. Dyson(1902), Ann. d. Phys., IV. Folge, 9, 417Google Scholar
  12. A. Einstein(1903), Ann. d. Phys., IV. Folge, 11, 170CrossRefADSGoogle Scholar
  13. A. Einstein(1904), Ann. d. Phys., IV. Folge, 14, 354CrossRefADSGoogle Scholar
  14. A. Einstein(1936), J. Franklin Inst. 221, 349CrossRefADSGoogle Scholar
  15. A. Einstein (1953), in ″Scientific Papers Presented to Max Born″, Oliver & Boyd, Edinburgh, p. 33.zbMATHGoogle Scholar
  16. A. Einstein, B. Podolsky & N. Rosen (1935), Phys. Rev. 47, 111CrossRefGoogle Scholar
  17. B. de Finetti (1970), ″Teoria delle probabilta″ , Einaudi, TorinoGoogle Scholar
  18. R. H. Fowler & E. A. Guggenheim (1939), ″Statistical Thermodynamics″, Cambridge University Press, CambridgezbMATHGoogle Scholar
  19. J. W. Gibbs (1902), ″Elementary Principles in Statistical Mechanics″ , Yale University Press, Yale, ConnecticutzbMATHGoogle Scholar
  20. I. M. Hacking (1966), ″The Logic of Statistical Inference″ , Cambridge University Press, LondonGoogle Scholar
  21. Hao Bai-Lin (1984), ″Chaos″, World Scientific, SingaporezbMATHGoogle Scholar
  22. W. Heisenberg (1951), Naturwissenschaften 38, 49CrossRefADSMathSciNetGoogle Scholar
  23. W. A. Houston, Amer. J. Phys. 34, 351Google Scholar
  24. H. Jeffreys (1948), ″The Theory of Probability″, Oxford University Press, OxfordGoogle Scholar
  25. P. Jordan (1938), ″Die Physik des zwanzigsten Jahrhunderts″, Vieweg, BraunschweigGoogle Scholar
  26. M. Kac (1959), ″Probability and Related Topics in Physical Sciences″, Interscience, London and New York, p. 23zbMATHGoogle Scholar
  27. J. M. Keynes (1921), ″A Treatise of Probability″, Macmillan, LondonGoogle Scholar
  28. A. N. Kolmogorov (1933), “Grundbegriffe der Wahrscheinlich- keitsrechnung”, J. Springer Verlag, BerlinGoogle Scholar
  29. A. N. Kolmogorv (1969), Probl. Inf. Trans. 5, No. 3, 1Google Scholar
  30. W. E. Lamb, Jr. (1969), Phys. Today 22(4), 23CrossRefGoogle Scholar
  31. W. E. Lamb, Jr. (1978), in S. Fujita (ed.), “The Ta-You Wu Festschrift”, Gordon & Breach, London, p. 1Google Scholar
  32. E. N. Lorenz (1963), J. Atmos. Sci. 20, 130CrossRefADSGoogle Scholar
  33. B. J. Mason (1968), Contemp. Phys. 27, 463CrossRefADSGoogle Scholar
  34. R. V. Mises (1919), Math. Zeits. 5, 52CrossRefGoogle Scholar
  35. R. V. Mises (1931), “Wahrscheinlichkeitsrechnung und ihre Anwendung”, F. Deuticke, WienGoogle Scholar
  36. W. Pauli (1954), Dialectica 8, 112CrossRefMathSciNetGoogle Scholar
  37. K. R. Popper (1959), “The Logic of Scientific Discovery”, Hutchinson, LondonzbMATHGoogle Scholar
  38. F. P. Ramsey (1926), in R. B. Braithwaite (ed.), “Truth and Probability in the Foundations of Mathematics”, Routledge and Kegan Paul, LondonGoogle Scholar
  39. E. Rédei & P. Szegedi (1988), these proceedingsGoogle Scholar
  40. H. Reichenbach (1935), “Wahrscheinlichkeitslehre”, A. W. Sijthoff, Leiden Wissenschaften, BerlinGoogle Scholar
  41. A. A. Ross-Bonney, Nuovo Cim. 30B, 55Google Scholar
  42. J. C.Slater (1929), J. Franklin Inst. 207, 449CrossRefGoogle Scholar
  43. P. Suppes (1968), J. Phil. Sci. 65, 651Google Scholar
  44. R. C.Tolman (1938), “The Principles of Statistical Mechanics”, Oxford University Press, OxfordGoogle Scholar

Copyright information

© Kluwer Academic Publishers 1989

Authors and Affiliations

  • T. A. Brody
    • 1
  1. 1.Instituto de FisicaUNAM ApdoMexico, D.F.Mexico

Personalised recommendations