Foundations of Physics

, Volume 16, Issue 9, pp 883–903 | Cite as

A probability law for the fundamental constants

  • B. Roy Frieden


If all the fundamental constants x of physics were expressed in one set of units (e.g., mks) and then used as pure numbers in one overall histogram, what shape would that histogram have? Based on some invariances that the law should reasonably obey, we show that it should have either an x−1 or an x−2 dependence. Empirical evidence consisting of the presently known constants is consistent with an x−1 law. This is independent of the system of units chosen for the constants. The existence of the law suggests that the fundamental constants may have been independently and randomly chosen, at creation, from it, and hence that at the next “big bang” randomly a different set will be produced. Also, because of the law, the number 1.0 has an interesting cosmological property: it is the theoretical median of all the fundamental constants. Finally, as a practical matter, the law predicts that current methods of evaluating the fundamental constants are biased toward overly large numbers. A correction term is given for each of three kinds of noise.


Empirical Evidence Current Method Correction Term Fundamental Constant Practical Matter 
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  1. 1.
    C. W. Allen,Astrophysical Quantities (Athlone Press, London, 1973), 2nd edn.Google Scholar
  2. 2.
    H. H. Jeffreys,Scientific Inference (Cambridge University Press, London, 1973), 3rd ed.Google Scholar
  3. 3.
    E. T. Jaynes, “Prior Probabilities”,IEEE Trans. Syst. Sci. Cybern. SSC-4, 227–241 (1968).Google Scholar
  4. 4.
    A. Papoulis,Probability, Random Variables and Stochastic Processes (McGraw-Hill, New York, 1965).Google Scholar
  5. 5.
    B. R. Frieden,Probability, Statistical Optics and Data Testing (Springer-Verlag, New York, 1983).Google Scholar
  6. 6.
    B. R. Frieden, “Unified Theory for Estimating Frequency-of-Occurrence Laws and Optical Objects,”J. Opt. Soc. Am. 73, 927–938 (1983).Google Scholar
  7. 7.
    Private communication, John Morgan, Aerospace Corporation, Los Angeles.Google Scholar
  8. 8.
    C. E. Shannon, “A mathematical Theory of Communication,”Bell Syst. Tech. J. 27, 379–423, 623–656 (1948).Google Scholar
  9. 9.
    P. A. M. Dirac, “A New Basis for Cosmology,”Proc. R. Soc. London Ser. A 165, 199–208 (1938).Google Scholar
  10. 10.
    F. J. Dyson, “The Fundamental Constants and Their Time Variation,” inAspects of Quantum Theory, A. Salam and E. P. Wigner, eds. (Cambridge University Press, Cambridge, 1972).Google Scholar
  11. 11.
    H. H. Jeffreys,Theory of Probability (Oxford University Press, London, 1961), 3rd. edn.Google Scholar
  12. 12.
    R. S. Pinkham, “On the Distribution of First Significant Digits,”Ann. Math. Stat. 32, 1223–1230 (1961).Google Scholar
  13. 13.
    B. H. Soffer, Hughes Research Laboratories, private communication.Google Scholar
  14. 14.
    E. T. Jaynes, “The Well-Posed Problem,”Found Phys. 3, 477–492 (1973).Google Scholar
  15. 15.
    Y. Tikochinsky, N. Z. Tishby, and R. D. Levine, “Consistent Inference of Probabilities for Reproducible Experiments,”Phys. Rev. Lett. 52, 1357–1360 (1984).Google Scholar
  16. 16.
    J. D. Barrow, in “Anthropic Definitions,”Q. J. R. Astron. Soc. 24, 146–153 (1983).Google Scholar
  17. 17.
    B. B. Mandelbrot,The Fractal Geometry of Nature (W. H. Freeman, San Francisco, 1982).Google Scholar
  18. 18.
    E. R. Cohen, J. W. M. Dumond, T. W. Layton, and J. S. Rollett, “Analysis of Variance of the 1952 Data on the Atomic Constants and a New Adjustment, 1955,”Rev. Mod. Phys. 27, 364 (1955).Google Scholar
  19. 19.
    E. Hille,Analytic Function Theory, Vol. 1 (Ginn and Company, Boston, 1959).Google Scholar

Copyright information

© Plenum Publishing Corporation 1986

Authors and Affiliations

  • B. Roy Frieden
    • 1
  1. 1.Optical Sciences CenterUniversity of ArizonaTucson

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