Shifting Standards: Experiments in Particle Physics in the Twentieth Century

Chapter 6 An Uncertain Interlude

• 55 Dunnington’s (1933) caution in assigning an experimental uncertainty to his measured value of e/m was no doubt influenced by the fact that the value of this quantity previously obtained by different methods differed by far more than the stated experimental uncertainties. Using the ratio of external to internal uncertainties, as advocated by Birge (1932), Dunnington argued that because the calculated ratio was approximately one, there were no large systematic effects in his measurements. In fact, his value for e/m = 1.7571 ± 0.0015 is in reasonable agreement, slightly more than one quoted uncertainty away, with the modern value of 1.75882. Nevertheless the question of the accuracy of both the values and the uncertainties of the fundamental physical constants has remained an issue until the present. In a 1943 letter to the editor of the Physical Review, Frank Benford (1943) complained that the values of many of the physical constants contained in Raymond Birge’s latest compilations (1929, 1941a)1 had changed by far more than the stated probable errors. (Table 6.1 lists a few of these changes. Figure 6.1 shows a graph of the recommended values of c, the velocity of light, as a function of time.) Benford noted that these constants were connected in many ways and that there were different ways of both measuring and calculating these constants. He further remarked that the main contributing factor to the changes between the 1929 and 1941 list is the new value assigned to the electronic charge. In 1929 it was 4.7700 ± 50 and in 1941 it was 4.8025 ± 10, a difference of 325 as compared to the probable error of 50. The change is 6.5 times as great as the probable error, and the chances against such a change are 100,000 to 1, on the basis of the 1929 figures. It is here again evident that the assigned limits refer to the consistency of the data from which 4.7700 ± 50 was derived, and the present value would, in 1929 have seemed impossible from the internal evidence. (212)2 CHAPTER 6 An Uncertain Interlude 56 • An Uncertain Interlude Table 6.1 Some changes in fundamental constants (from Benford 1943) 1929 1941 Change 1929 P.E.a Chance 1 to Velocity of light c 2.99796 ± 4 299776 ± 4 5.0 1.3 × 103 Electronic charge e 4.7700 ± 50 4.8025 ± 10 6.5 1.0 × 105 Planck constant h 6.5470 ± 80 6.6242 ± 24 9.6 1.0 × 1010 Avogadro’s number N0 6.0644 ± 60 6.0228 ± 11 7.0 4.0 × 105 Boltzmann constant K 1.37089 ± 140 1.38047 ± 26 6.8 1.0 × 105 a Probable error Figure 6.1. Speed of light as a function of the year that it was measured. From Henrion and Fischoff (1986). An Uncertain Interlude • 57 He chided Birge as follows: “The debt of chemists and physicists to Dr. Birge is great, and I hope he will, in future lists, increase this indebtedness by pointing out the distinction between consistency and accuracy” (212). Birge (1943) replied that this was a real problem and that he was responding only to Benford’s personal comment: “In the preceding paper by Dr. Frank Benford, attention is called to the important distinction between consistency and accuracy. The recent large and wholly unanticipated changes in the measured values of many of the general physical constants have been noted and discussed in many papers and it would be superfluous to make further comments were it not for the fact that Dr. Benford’s paper concludes with the remark, ‘I hope he will, in future lists, increase this indebtedness by pointing out the distinction between consistency and accuracy’” (213). Birge responded, correctly (see the discussion of internal and external consistency earlier), that “for many years now I have attempted to emphasize just this distinction. Unfortunately the true value of any physical magnitude can never be known. Hence the absolute accuracy of a measured result cannot be determined and we can only note the difference , if any, between the internal and external consistency of the data. In 1932 [Birge is referring to Birge (1932)], I initiated a discussion of these important concepts and noted certain relations and facts that had hitherto been overlooked” (213). He further noted that “as a result of the diversity of methods now used in determining most of the...