Are the Laws of Physics Inevitable

56 (1939), 131-136.

Figure 5. Kurie plot for electrons from ¹¹⁴In. The y axis is the square root of N/p²f, where N is the number of electons, p is the electron momentum, and f is the Coulomb factor in the decay, plotted as a function of the electron decay energy. If the Fermi theory is correct this should be a straight line. It is. From Lawson and Cork, “Radioactive Isotopes” (ref. 25).

Figure 6. The Kurie plot for the unique, once-forbidden spectrum of ⁹¹Y. The y axis is the square root of Na₁pf, where N is the number of electons, p is the electron momentum, and f is the Coulomb factor in the decay, plotted as a function of the electron decay energy. The graph for the correct theory should be a straight line. The unmodified Fermi thory, a₁ = 1, does not fit a straight line. The correction factor a₁ = C[(W² – m²_oc⁴) + (W_o – W)²], calculated by Konopinski and Uhlenbeck, “-Radioactivity," (ref. 26) does give a linear fit. C is a constant. From Konopinski and Langer, “Experimental Clarification” (ref. 43).

Figure 7. Coincidence counting rate plotted as a function of angle between the electron and the recoil nucleus in the decay of ⁶He for (a) electrons in the energy range 4.5-5.5 mc² and (b) electrons in the energy range 5.5-7.5 mc². The predictions for the various forms of the decay interaction are shown. Tensor is clearly favored. From Rustad and Ruby, “Gamow-Teller” ( ref. 55).

Figure 8. The decay of an oriented nucleus in both real space and mirror space.

Figure 9. The counting rate relative to the counting rate obtained when the sample is warm as a function of time, for electrons from the decay of oriented ⁶⁰Co nuclei for different orientations (field directions). More electrons are emitted opposite to the nuclear spin. The nuclei are oriented only at low temperatures. The x axis is the time after the sample has been cooled down. As the sample warms up the orientation of the nuclei disappears and the relative counting rate is 1. From Wu et al., “Experimental Test” (ref. 58).

Figure 10. Schematic view of the experimental apparatus for the ⁶He angular-correlation experiment of Rustad and Ruby, “Correlation” (ref. 55).

Figure 11 The distribution of recoil ions observed in the decay of ⁶He as a function of the recoil energy R. The solid curves are the computed distributions for the tensor (T) and axial vector (A) interactions. The angular correlation coefficient λ should be either +1/3 or -1/3 corresponding, respectively, to the tensor or axial vector interaction. The experimental result, λ = - 0.39 ± 0.02, clearly indicates that the axial vector interaction is dominant. From Hermannsfeldt et al., “Determination” (ref. 80).

Figure 12. A bubble chamber photograph from Impeduglia et al., “β-Decay” (ref. 86). The two-track event at A has a dark track entering from the left (a pion) followed by a lighter track (an electron) heading upward. This is an example π→e decay. The three-track event at B has a dark track entering from the left (a pion), followed by a dark track heading up to the left (a muon), followed by a lighter track going to the right (an electron). This is an example of π→μ→e decay.

* Kepler’s Third Law states that the cube of the semi-major axis of a planet’s elliptical orbit divided by the square of its period is a constant for all planets in the solar system. It is reasonable to regard this as an empirical law.

* Hacking seems to believe that an alternative physics would necessarily have different standards of success. I don=t think this is correct. One can imagine an alternative physics that would be just as successful by the same standards.

* In this case that suggestion failed and a new theory, namely, Einstein’s General Theory of Relativity, was required to explain the observations.

* My colleague, Tom DeGrand, a theoretical particle physicist, has told me that renormalizability is now regarded as a desirable, but not a required, feature of theories. In performing calculations physicists now use theories with a limited range of applicability, called effective field theories. Renormalizable theories have a much broader range of applicability. He notes, however, that symmetries are still extremely important.

* For details see Franklin, Right or Wrong (ref.7 ), Chapters 1-5.

** Beta decay is the spontaneous transformation of one atomic nucleus into another with the simultaneous emission of an electron and a neutrino.

* Because the neutrino interacts so weakly with matter we can describe it as a particle traveling in free space, which is a plane wave Φ_v(r) = Ae^i(k.r) , which can be written as A[ 1 + i(k.r) + ...]. The electron wavefunction cannot be written as a plane wave because of the electron=s interaction with the Coulomb field of the nucleus. But it can also be expanded as a series of successively smaller terms. For allowed transitions, one keeps only the first, constant terms of the expansion. Forbidden transitions involve subsequent terms, which are much smaller and lead to a reduced decay rate.

* Fermi’s theory predicted that

P(W) = G² │M²│f(Z,W) (W_o – W)² (W² – 1) W dW

where M is the matrix element for the transition, G is a coupling constant, W is the energy of the decay electron (in units of m_ec²) W_o is the maximum decay energy, P(W) is the probability of the emission of an electron with energy W, and f(Z,W) is a function giving the effect of the Coulomb field of the nucleus on the emission of electrons. We see that [P(W)/ f(Z,W) (W² – 1) W]^1/2 is a linear function of W. For the K-U theory the exponent will be ¼ for the straight line. In the original papers P(W) is called N, the number of electrons.

* Many other such spectra were measured. They were all consistent with the presence of T or A.. For details see Allan Franklin, Right or Wrong (ref. 8).

* I have not been able to find a published reference to this work. It is cited as a private communication in several review articles at the time.

* Later experiments reported a value of ρ of approximately 0.75. Dudziak, “Positron Spectrum,” ref. 70.

* There are no abstracts of postdeadline papers. In a private communication, Ruby remembers the tone of the paper as mea culpa.

1

References

^ Ian Hacking, I. The Social Construction of What? (Cambridge, MA: Harvard UniversityPress,1999), Chapter 3.

2 Andrew Pickering, Constructing Quarks (Chicago: University of Chicago Press, 1984).

3 Hacking, Social Construction (ref.1), pp. 78-79.

4 Hacking, Social Construction (ref. 1), pp. 72-73, emphasis added.

5 Barry Barnes, "How Not to Do the Sociology of Knowledge, "Rethinking Objectivity, part1. Special Issue of Annals of Scholarship 8 (1991), 321-335, quote p. 331.

6 Sheldon Glashow, S. (1992), “The Death of Science!?” in R. J. Elvee, ed., The End of Science? Attack and Defense (Lanham, MD: University Press of America, 1992), p. 28.

7 Sidney Coleman, “The 1979 Nobel Prize in Physics,” Science 206 (1979), 1290-1292. Quote p. 1291.

8 Allan Franklin, Experiment, Right or Wrong (Cambridge: Cambridge University Press, 1990).

9 Enrico Fermi, "Attempt at a Theory of Rays," Il Nuovo Cimento 11 (1934), 1-21;

"Versuch einer Theorie der -Strahlen," Zeitschrift fur Physik 88 (1934), 161-177.

10 E.C. George Sudarshan and Robert. Marshak, “The Nature of the Four-Fermion Interaction,” in Padua Conference on Mesons and Recently Discovered Particles (Padua, 1957), pp. V-14 – V-24; "Chirality Invariance and the Universal Fermi Interaction," Physical Review 109 (1958), 1860-1862.

11 Richard Feynman and Murray Gell-Mann, "Theory of the Fermi Interaction," Physical Review 109 (1958), 193-198.

12 Wolfgang Pauli, "Die Allgemeinen Prinzipen der Wellenmechanik," Handbuch der Physik 24 (1933), 83-272.

13 Sudarshan and Marshak, “Fermi Interaction” (ref. 10).

14 Feynman and Gell-Mann, “Fermi Interaction” (ref. 11).

15 Emil Konopinski, "Beta-Decay," Reviews of Modern Physics 15 (1943), 209-245.

16 B.W. Sargent, "Energy Distribution Curves of the Disintegration Electrons," Proceedings of the Cambridge Philosophical Society 24 (1932), 538-553; "The Maximum Energy of the β-Rays from Uranium X and other Bodies," Proceedings of the Royal Society (London) A139 (1933), 659-673.

17 Emil Konopinski and George Uhlenbeck, "On the Fermi Theory of Radioactivity," Physical Review 48 (1935), 7-12

18 Hans Bethe and Robert. Bacher, "Nuclear Physics," Reviews of Modern Physics 8 (1936), 82-229.

19 George Gamow and Edward Teller, "Selection Rules for the -Disintegration," Physical Review 49 (1936), 895-899.

20 Ibid., p. 897.

21 Franz N.D. Kurie, J. R. Richardson, and H. C. Paxton, "The Radiations from Artificially Produced Radioactive Substances," Physical Review 49 (1936), 368-381.

22 Ibid., p. 377.

23 M. Stanley Livingston and Hans Bethe , "Nuclear Physics," Reviews of Modern Physics 9 (1937), 245-390, quote on p. 357.

24 A.W. Tyler, "The Beta- and Gamma- Radiations from Copper⁶⁴ and Europium ¹⁵²," Physical Review 56 (1939), 125-130, quote p. 125.

25 J.L. Lawson and J. M. Cork, "The Radioactive Isotopes of Indium," Physical Review 57 (1940), 982-994, quote, p. 994.

26 Emil Konopinski and George Uhlenbeck, "On the Theory of -Radioactivity," Physical Review 60 (1941), 308-320.

27 Konopinski, “Beta Decay” (ref. 15), p. 218.

28 Markus Fierz, "Zur Fermischen Theorie des -Zerfalls," Zeitschrift fur Physik 104 (1937), 553-565.

29 Hideki Yukawa, "On the Interaction of Elementary Particles," Proceedings of the Physico-Mathematical Society of Japan 17 (1935), 48-57.

30 Carl Anderson and Seth Neddermeyer, "Cloud Chamber Observation of Cosmic-Rays at 4300 Meters Elevation and Near Sea Level," Physical Review 50 (1936), 263-271.

31 Jabez Street and Edward Stevenson, "New Evidence for the existence of a Particle of Mass intermediate between the Proton and Electron," Physical Review 52 (1937), 1003-1004.

32 Cesar Lattes, H. Muirhead, Giuseppe Occhialini, et al., "Processes Involving Charged Mesons," Nature 159 (1947), 694-697.

33 J. Tiomno and John Wheeler, "Charge-Exchange Reaction of the -Meson with the Nucleus," Reviews of Modern Physics 21 (1949), 153-165.

34 Ibid., pp. 156-157.

35 Louis Michel, "Coupling Properties of Nucleons, Mesons, and Leptons," Progress in Cosmic Ray Physics 1 (1952), 127-190.

36 M. Ruderman, M. and R. Finkelstein, "Note on the Decay of the -Meson," Physical Review 76 (1949), 1458-1460.

37 Ibid., p. 1459.

38 H.L. Friedman and James Rainwater, "Experimental Search for the Beta-Decay of the ⁺ Meson," Physical Review 84 (1951), 684-690.

39 F.M. Smith, "On the Branching Ratio of the ⁺ Meson," Physical Review 81 (1951), 897-898.

40 S. Lokanathan and Jack Steinberger, "Search for the -Decay of the Pion," Nuovo Cimento 10 (1955), 151-162.

41 Louis Michel and Arthur Wightman, "-Meson Decay,  Radioactivity, and Universal Fermi Interaction," Physical Review 93 (1954), 354-355.

42 Konopinski, “Beta Decay” (ref. 15).

43 Emil Konopinski and L. M. Langer, "The Experimental Clarification of the Theory of -Decay," Annual Reviews of Nuclear Science 2 (1953), 261-304, quote p. 261.

44 Markus Fierz, “Fermischen Theorie” (ref. 28).

45 M.G. Mayer, S. A. Moszkowski, and L. W. Nordheim, "Nuclear Shell Structure and Beta Decay. I. Odd A Nuclei," Reviews of Modern Physics 23 (1951), 315-321.

46 Konopinski and Uhlenbeck, “β-Radioactivity” (ref. 26).

47 L.M. Langer and H. C. Price, "Shape of the Beta-Spectrum of the Forbidden Transition of Yttrium 91," Physical Review 75 (1949), 1109.

48 Ruby Sherr, R. and J. Gerhart, "Gamma Radiation of C¹⁰," Physical Review 86 (1952), 619; Ruby Sherr, R., H. R. Muether and Milton White, "Radioactivity of C¹⁰ and O¹⁴," Physical Review 75 (1949), 282-292.

49 A.M. Smith, "Forbidden Beta-Ray Spectra," Physical Review 82 (1951), 955-956.

50 D.L. Pursey, "The Interaction in the Theory of Beta Decay," Philosophical Magazine 42 (1951), 1193-1208.

51 Albert Petschek and Robert Marshak, "The -Decay of Radium E and the Pseudoscalar Interaction," Physical Review 85 (1952), 698-699.

52 Ibid., p. 698.

53 Donald Hamilton, "Electron-Neutrino Angular Correlation in Beta-Decay," Physical Review 71 (1947), 456-457.

54 S.R. de Groot and H. A. Tolhoek, "On the Theory of Beta-Radioactivity I: The Use of Linear Combinations of Invariants in the Interaction Hamiltonian," Physica 16 (1950), 456-480.

55 Bryce Rustad and Stanley Ruby, "Correlation between Electron and Recoil Nucleus in He⁶ Decay," Physical Review 89: (1953), 880-881; "Gamow-Teller Interaction in the Decay of He^6," Physical Review 97 (1955), 991-1002.

56 Emil Konopinski, “Theory of the Classical -Decay Measurements,”. Rehovoth Conference on Nuclear Structure, Rehovoth, Israel (1958), 319-335, quote p. 330.

57 Tsung-Dao Lee and Chen Ning Yang, "Question of Parity Nonconservation in Weak Interactions," Physical Review 104 (1956), 254-258.

58 Chien-Shiung Wu, Eric Ambler, R. W. Hayward, et al., "Experimental Test of Parity Nonconservation in Beta Decay," Physical Review 105 (1957), 1413-1415.

59 Richard Garwin, Leon Lederman and Marcel Weinrich, "Observation of the Failure of Conservation of Parity and Charge Conjugation in Meson Decays: The Magnetic Moment of the Free Muon," Physical Review 105 (1957), 1415-1417.

60 Jerome Friedman and Valentine Telegdi, "Nuclear Emulsion Evidence for Parity Nonconservation in the Decay Chain pi - mu-e," Physical Review 105 (1957), 1681-1682.

61 Tsung-Dao Lee and Chen Ning Yang, “Question” (ref. 57), p. 255.

62 Chien-Shiung Wu et al., “Experimental Test” (ref. 58).

63 Ibid., p. 1413.

64 Garwin et al., “Failure”( ref. 58) and Friedman and Telegdi, Nuclear Emulsion” (ref. 59).

65 Tsung-Dao Lee and Chen Ning Yang, "Parity Nonconservation and a Two-Component Theory of the Neutrino," Physical Review 105 (1957), 1671-1675.

66 Lev Landau, "On the Conservation Laws for Weak Interactions," Nuclear Physics 3 (1957), 127-131.

67 Abdus Salam, "On Parity Conservation and the Neutrino Mass," Nuovo Cimento 5 (1957), 299-301.

68 C.P. Sargent, M. Rinehart, L. M. Lederman, et al, "Diffusion Cloud-Chamber Study of Very Slow Mesons. II. Beta Decay of the Muon," Physical Review 99 (1955) 885-888.

69 A. Bonnetti, R. Levi Setti, M. Panetti, et al., "Lo spettro di energie degli elettroni di decadimento dei mesoni mu in emulsione nucleare," Nuovo Cimento 3 (1956), 33-50.

70 W.F. Dudziak, R. Sagane and J. Vedder, "Positron Spectrum from the Decay of the  Meson," Physical Review 114 (1959), 336-358.

71 Tsung-Dao Lee, T. D., Introductory Survey, Weak Interactions, High Energy Nuclear Physics, Rochester, Interscience, VII-1 – VII-12, quote p. VII-7.

72 E.C. George Sudarshan and Robert Marshak, “Four Fermion,” ref. 10 and Richard Feynman and Murray Gell-Mann, “Fermi Interaction,” ref. 11.

73 Sudarshan and Marshak, “Four-Fermion” (ref. 10), p. 126.

74 Feynman and Gell-Mann, “Fermi Interaction” (ref. 11), p. 198.

75 Ibid., p. 198.

76 Ibid., p. 198.

77 Rustad and Ruby, “Helium⁶” (ref. 55).

78 Chien-Shiung Wu and Arthur Schwarzschild, “A Critical Examination of the He⁶ Recoil Experiment of Rustad and Ruby,” New York, Columbia University Report, (1958).

79 Ibid., p.6.

80 W.B. Hermannsfeldt, R. L. Burman, P. Stahelin, et al., "Determination of the Gamow-Teller Beta-Decay Interaction from the Decay of Helium-6," Physical Review Letters 1 (1958), 61-63.

81 Ibid., p. 62.

82 Ibid., p. 61.

83 S. Lokanathan and Jack Steinberger, "Search for the -Decay of the Pion," Nuovo Cimento 10 (1955), 151-162.

84 Herbert Anderson and Cesar Lattes, "Search for the Electronic Decay of the Positive Pion," Nuovo Cimento 6 (1957), 1356-81.

85 Giuseppe Morpurgo, "Possible Explanation of the Decay Processes of the Pion in the Frame of the 'Universal' Fermi Interaction," Nuovo Cimento 5 (1957), 1159-65; John Taylor, "Beta Decay of the Pion," Physical Review 110 (1958), 1216.

86 G. Impeduglia, R. Plano, A. Prodell, et al., " Decay of the Pion," Physical Review Letters 1 (1958), 249-251.

87 Ibid., p. 251.

88 Franklin, Right or Wrong, ref. 7, Chapter 5.

89 Maurice Goldhaber, Lee Grodzins and Andrew Sunyar, "Helicity of Neutrinos," Physical Review 109 (1958), 1015-1017.

90 Ibid, p. 1017.

91 E.C. George Sudarshan and Robert Marshak, “Origins of the V-A Theory,” Blacksburg, VA, Virginia Polytechnic and State University Report (unpublished), (1985), quote p. 14.