Pilgrims’ progress in search of the fundamental constants

OCT 01, 1965

The fundamental constants of nature are so interrelated that a measurement affecting one affects them all. The author became interested when Millikan’s oil‐drop value of the electron charge was different from the value given by x‐ray determination of crystal spacings. To assist in finding the true values, he invented a method for plotting various functions of the constants in a space of as many coordinates as there are constants. If all measurements are consistent, the plotted functions intersect in a point. When they do not intersect, one examines standard deviations, which correspond to thicknesses of surfaces, in an effort to find out what is wrong. In three decades, searches of this kind have reduced uncertainties in the constants from a fraction of a percent to, at most, tens of parts per million.

DOI: 10.1063/1.3046944

Jesse W. M. DuMond

The practice of making broadly inclusive surveys, from time to time, of the status of our knowledge of the fundamental constants of physics and chemistry may be said to have started with a famous paper by Raymond T. Birge, of Berkeley, published in Reviews of Modem Physics in 1929. To Professor Birge, also, is due the credit for being the first, as far as I know, to apply the method of least squares in order to determine most probable values of three of the constants; e, the electronic charge m, the electron rest mass; and h, Planck’s constant, using a highly overdetermined set of experimental data on functions of these three quantities.

References

1. J. A. Bearden, Phys. Rev. 37, 1210 (1931); https://doi.org/PHRVAO
J. A. Bearden, J. Appl. Phys. 12, 395 (1941).https://doi.org/JAPIAU
2. E. Bäcklin, Z. Physik 93, 450 (1935).https://doi.org/ZEPYAA
3. M. Söderman, Nature 135, 67 (1935); https://doi.org/NATUAS
Dissertation, Uppsala (1934).
4. F. Tyrén, Z. Physik 109, 722 (1938); https://doi.org/ZEPYAA
Dissertation, Uppsala (1940).
5. J. W. M. DuMond and V. L. Bollman, Phys. Rev. 50, 524 (1936).https://doi.org/PHRVAO
6. J. W. M. DuMond, Phys. Rev. 56, 153 (1939).https://doi.org/PHRVAO
7. J. W. M. DuMond, Phys. Rev. 58, 457 (1940).https://doi.org/PHRVAO
8. J. W. M. DuMond and E. R. Cohen, Revs. Modern Phys. 20, 82 (1948).https://doi.org/RMPHAT
9. J. W. M. DuMond and E. R. Cohen, report to the National Research Council Committee on Constants and Conversion Factors of Physics: “A Least‐Squares Adjustment of the Atomic Constants as of December 1950” (unpublished).
10. E. R. Cohen, J. W. M. DuMond, T. W. Layton and J. S. Rollett, Revs. Modern Phys. 27, 363 (1955).https://doi.org/RMPHAT
11. A. Petermann, Helv. Phys. Act. 30, 407 (1957);
C. M. Sommerfield, Phys. Rev. 107, 328 (1957); https://doi.org/PHRVAO
E. R. Cohen and J. W. M. DuMond, Phys. Rev. Letters 1, 291 (1958).https://doi.org/PRLTAO
12. A discussion of error statistical‐correlation is given in Chapter 7 of E. R. Cohen, K. M. Crowe, and J. W. M. DuMond, Fundamental Constants of Physics (Interscience Publishers, Inc. New York, 1957). For the generalized formula of error propagation see Section 7.4.
13. I. Henins and J. A. Bearden, Phys. Rev. 135, A890 (1964).https://doi.org/PHRVAO
14. J. A. Bearden, Phys. Rev. 38, 2089 (1931); https://doi.org/PHRVAO
A. levins and M. E. Straumanis, Z. Physik 116, 194 (1940).https://doi.org/ZEPYAA
15. J. A. Bearden, “X‐Ray Wavelengths”, Technical Report No. NYO‐10586. AEC Division of Technical Information, Oak Ridge, Tenn., 1964 (unpublished).
16. J. W. Knowles, Can. J. Phys. 40, 257 (1962); https://doi.org/CJPHAD
Proceedings of the Second International Conference on Nuclidic Masses, Vienna, July 1963 (Springer‐Verlag, Vienna, 1964).
17. S. Hagström, Dissertation, Uppsala (1964):
S. Hagström, O. Hornfeldt, C. Nordling and K. Siegbahn, Arkiv Fysik 23, 145 (1962).https://doi.org/AFYSA7
18. J. J. Spijkerman and J. A. Bearden, Phys. Rev. 134, A871 (1964).https://doi.org/PHRVAO
19. J. A. Bearden, Phys. Rev. 137, B181 (1965).https://doi.org/PHRVAO
20. A. Smakula and V. Sils, Phys. Rev. 99, 1744 (1955); https://doi.org/PHRVAO
A. Smakula, J. Kalnajs, and V. Sils, Phys. Rev. 99, 1747 (1955).https://doi.org/PHRVAO
21. B. Edlén and L. K. Svensson, Arkiv Fysik 28, 427 (1965).https://doi.org/AFYSA7
22. J. W. M. DuMond and E. R. Cohen, Phys. Rev. 103, 1583 (1956); https://doi.org/PHRVAO
J. W. M. DuMond, Proc. Nat. Acad. Sci. 45, 1052 (1959).https://doi.org/PNASA6
23. These tests are explained in both references 24 and 25 under the heading “Measures of Incompatibility of an Input Datum”.
24. E. R. Cohen and J. W. M. DuMond, report to National Research Council Committee on the Fundamental Constants of Physics and Chemistry: “An Analysis of Variance of the Data Available in 1962” Feb. 28, 1963 (unpublished). Copies available from A. G. McNish, Committee Chairman, National Bureau of Standards, or from authors.
25. E. R. Cohen and J. W. M. DuMond, “Present Status of our Knowledge of the Numerical Values of the Fundamental Physical Constants,” Proceedings of the Second International Conference on Nuclidic Masses, Vienna, July 1963 (Springer‐Verlag, Vienna 1964). Copies obtainable from authors.
26. S. Triebwasser, E. S. Dayoff, and W. E. Lamb, Jr., Phys. Rev. 89, 98 (1953).https://doi.org/PHRVAO
27. S. B. Crampton, D. Kleppner and N. Ramsey, Phys. Rev. Letters II, 338 (1963).https://doi.org/PRLTAO
28. C. K. Iddings, Phys. Rev. 138, B446 (1965).https://doi.org/PHRVAO
29. P. L. Bender and R. L. Driscoll, Trans. I.R.E. I‐7, 176 (1958).
30. P. Vigoureux, Proc. Roy. Soc. (London) A270, 72 (1962).https://doi.org/PRLAAZ
31. H. Sommer, H. A. Thomas and J. A. Hipple, Phys. Rev. 82, 697 (1951).https://doi.org/PHRVAO
32. J. H. Sanders and K. C. Turberfield, Proc. Roy. Soc. (London) A272, 79 (1962).https://doi.org/PRLAAZ
33. H. S. Boyne and P. A. Franken, Phys. Rev. 123, 242 (1961).https://doi.org/PHRVAO
34. B. A. Mamyrin and A. A. Frantsuzov, Dokl. Akad. Nauk SSSR 159, 777 (1964).https://doi.org/DANKAS
35. D. N. Craig, J. I. Hoffman, C. A. Law and W. J. Hamer, Nat. Bur. Std. J. Res. 64A, 381 (1960).
36. R. T. Robiscoe, PhD thesis in Physics, University of Chicago, 1964; present address of author, Physics Department, Yale University.

More about the Authors

Jesse W. M. DuMond. California Institute of Technology.