Phys. perspect. 10 (2008) 182–211
1422-6944/08/020182–30
DOI 10.1007/s00016-006-0309-z
Are the Laws of Physics Inevitable?
Allan Franklin*
Social constructionists believe that experimental evidence plays a minimal role in the production
of scientific knowledge, while rationalists such as myself believe that experimental evidence is crucial in it. As one historical example in support of the rationalist position, I trace in some detail the
theoretical and experimental research that led to our understanding of beta decay, from Enrico
Fermi’s pioneering theory of 1934 to George Sudarshan and Robert Marshak’s and Richard Feynman and Murray Gell-Mann’s suggestion in 1957 and 1958, respectively, of the V–A theory of weak
interactions. This is not a history of an unbroken string of successes, but one that includes incorrect experimental results, incorrect experiment-theory comparisons, and faulty theoretical analyses. Nevertheless, we shall see that the constraints that Nature imposed made the V–A theory an
almost inevitable outcome of this theoretical and experimental research.
Key words: Enrico Fermi; Richard P. Feynman; Markus Fierz; Murray Gell-Mann; Emil
J. Konopinski; Tsung-Dao Lee; Robert E. Marshak; Louis Michel; Wolfgang Pauli; E.C.
George Sudarshan; George E. Uhlenbeck; Chien-Shiung Wu; Chen Ning Yang; Hideki
Yukawa; beta decay; radioactivity; neutrinos; pions; muons; nuclear physics; particle
physics; Sargent curves; Konopinski-Uhlenbeck theory; Gamow-Teller selection rules;
angular-correlation experiments; nonconservation of parity; V–A theory of weak interactions; Universal Fermi Interaction; philosophy of physics; philosophy of experiment.
Introduction
Are the laws of nature discovered or invented? Scientists have given varying answers
to this question. For Albert Einstein laws were “free creations of the human mind.”
Isaac Newton, however, claimed that he “feigned no hypotheses,” and using his own
laws of motion, derived the inverse-square law of gravitation from Johannes Kepler’s
Third Law,** arguing for discovery.
A closely related issue, contingency, is one that divides those whom Ian Hacking has
called social constructionists, such as Harry Collins, Andrew Pickering, and others, who
believe that experimental evidence plays a minimal role in the production of scientific
* Allan Franklin is Professor of Physics at the University of Colorado. He works on the history
and philosophy of physics, particularly on the roles of experiment.
** Kepler’s Third Law states that the cube of the semimajor 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.
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knowledge, from rationalists, including myself, who believe that experimental evidence
is crucial in it. Contingency is the idea that science is not predetermined, that it could
have developed in any one of several successful ways. This is the view adopted by social
constructionists. Hacking illustrates this with Pickering’s account of high-energy
physics during the 1970s,1 when the quark model came to dominate.
The constructionist maintains a contingency thesis. In the case of physics, (a)
physics (theoretical, experimental, material) could have developed in, for example, a nonquarky way, and, by the detailed standards that would have evolved with
this alternative physics, could have been as successful as recent physics has been
by its detailed standards.* Moreover, (b) there is no sense in which this imagined
alternative physics would be equivalent to present physics. The physicist denies
that.2
…
To sum up Pickering’s doctrine: there could have been a research program as successful (“progressive”) as that of high-energy physics in the 1970s, but with different
theories, phenomenology, schematic descriptions of apparatus, and apparatus, and a
different, and progressive, series of robust fits between these ingredients. Moreover
– and this is something badly in need of clarification – the “different” physics would
not have been equivalent to present physics. Not logically incompatible with, just
different.
The constructionist about (the idea) of quarks thus claims that the upshot of the
process of accommodation and resistance is not fully predetermined. Laboratory
work requires that we get a robust fit between apparatus, beliefs about the apparatus, interpretations and analyses of data, and theories. Before a robust fit has been
achieved, it is not determined what that fit will be. Not determined by how the world
is, not determined by technology now in existence, not determined by the social practices of scientists, not determined by interests or networks, not determined by genius,
not determined by anything.3
Much depends here on what Hacking means by “determined.” If he means “entailed,”
then I agree with him. I doubt that the world, or more properly, what we can learn
about it, entails a unique theory. If not, as seems more plausible, and he means that the
way the world is places no constraints on successful science, then I disagree strongly. I
would certainly wish to argue that the way the world is constrains the kinds of theories
that will fit the phenomena, the kinds of apparatus we can build, and the results we can
obtain with such apparatuses. To think otherwise seems silly. I doubt whether Kepler
would have gotten very far had he suggested that the planets move in square orbits.
Nevertheless, at the extreme end of the contingency spectrum, Barry Barnes has stated that, “Reality will tolerate alternative descriptions without protest. We may say what
we will of it, and it will not disagree. Sociologists of knowledge rightly reject realist
epistemologies that empower reality.” 4
* 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.
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At the other extreme are the “inevitablists,” among whom Hacking classifies most
scientists. He cites Sheldon Glashow, a Nobel Prize winner in physics: “Any intelligent
alien, anywhere, sooner or later, would have come upon the same logical system as we
have to explain the structure of protons and the nature of supernovae.” 5 On a scale
from 1 to 5, where a score of 5 is a strong constructionist position and 1 is a strong rationalist position, Hacking and I both rate ourselves as 2 on contingency.
One reason for leaning toward inevitability is the independent and simultaneous
suggestion of theories or hypotheses. This includes the suggestion of the V–A (V minus
A) theory of weak interactions by E.C. George Sudarshan and Robert Marshak and by
Richard Feynman and Murray Gell-Mann (which I will discuss in detail below); the
proposal of quantum electrodynamics by Feynman, by Julian Schwinger, and by SinItiroTomonaga; the proposal of quantum mechanics by Erwin Schrödinger and by
Werner Heisenberg; the suggestion of the two-component neutrino by Tsung-Dao Lee
and Chen NingYang, by Lev Landau, and by Abdus Salam; and the independent suggestion of quarks by George Zweig and by Gell-Mann. There are numerous other similar instances. I believe that detailed examination of these episodes, similar to what I
will present below for the V–A theory of weak interactions, would provide additional
support for the rationalist position.
There are several reasons that make these simultaneous suggestions plausible. Thus,
many factors influence theory formation which, whereas they do not entail a particular theory, they do place strong constraints on it. The most important of these is, I
believe, Nature. Pace Barry Barnes, it is not true that any theory can be proposed and
that valid experimental results or observations will be in agreement with it. Regardless
of theory, objects denser than air fall toward the center of the earth when dropped. A
second important factor is the existing state of experimental and theoretical knowledge. Scientists read the same literature. They thus build upon what is already known
and often use hypotheses similar to those that previously have proven successful. Thus,
when faced with the anomalous advance of the perihelion of Mercury, some scientists
proposed that there was another planet in the solar system that caused it, a suggestion
similar to the successful hypothesis of Neptune previously used to explain discrepancies in the orbit of Uranus.* What are considered important problems at a given time
will also influence the future course of science. Thus, the need to explain ß (beta) decay
and the problem of determining the correct mathematical form of the weak interaction
prompted the extensive work, both theoretical and experimental, that led to the simultaneous suggestion of the V–A theory of weak interactions. The mathematics available
also constrains the types of theories that can be offered.
There also are several requirements that need to be satisfied for a theory to be considered seriously. These factors do not, of course, prevent the proposal of a totally new
theory that does not satisfy these requirements, but they do influence its reception. The
first of these is relativistic invariance. If a theory does not have the same mathematical
form for all inertial observers it is not likely that it will be further investigated. Simi-
* In this case, that suggestion failed and a new theory, namely, Einstein's general theory of relativity, was required to explain the observation.
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larly, a theory must be renormalizable: There must be a way of systematically removing infinities for it to be a possible theory that can be applied to Nature. This is graphically illustrated by the citation history of Steven Weinberg’s paper on the unification
of the electromagnetic and weak interactions.6 Weinberg published his theory in 1967.
The number of citations to it by year was 1967, 0; 1968, 0; 1969, 0; 1970, 1; 1971, 4; 1972,
64; 1973, 162. It went on to become one of the most cited papers in the history of elementary-particle physics, but as Sidney Coleman remarked, “Rarely has so great an
accomplishment been so widely ignored.” 7 What happened in 1971 that changed
things? Gerard ’t Hooft showed that year that the electroweak theory was renormalizable. It then became a serious contender.* Theories must also satisfy certain symmetries. These days most physicists believe that a theory must exhibit gauge symmetry,
that it must be possible to add an arbitrary phase to the wavefunction at any point in
space. Theories must also be translationally invariant and time symmetric.
The Road to the V–A Theory of Weak Interactions8
Fermi’s Theory of ß Decay** and the Konopinski-Uhlenbeck Modification
The above discussion has been rather abstract. To make it more concrete I will discuss
in detail, as one example, the investigation, both theoretical and experimental, of β
decay from Enrico Fermi’s proposal of the first successful theory of ß decay in 1934,9
to George Sudarshan and Robert Marshak’s and Richard Feynman and Murray GellMann’s simultaneous suggestion of the V–A theory of weak interactions nearly a quarter-century later.10 This history is not one of an unbroken string of successes, but rather
one that includes incorrect experimental results, incorrect experiment-theory comparisons, and faulty theoretical analyses. Nevertheless, at the end of the story the proposal of the V– A theory will seem to be an almost inevitable outcome.
Fermi’s theory of β decay assumed that the atomic nucleus was composed solely of
protons and neutrons and that the electron and the neutrino were created at the instant
of decay. He added a perturbing energy due to the decay interaction to the energy of the
nuclear system. In modern notation the Hamiltonian of this perturbation takes the form
Hif = G[U*f Φe(r)Φν (r)]OxUi ,
where Ui and U*f describe the initial and final states of the nucleus, Φe(r) and Φν (r)
are the electron and neutrino wavefunctions, respectively, G is a coupling constant, r is
the position variable, and Ox is a mathematical operator.
* 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.
** Beta (ß) decay is the spontaneous radioactive transformation of one atomic nucleus into another
with the simultaneous emission of an electron and a neutrino.
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Wolfgang Pauli had shown previously that the mathematical operator Ox can take
on only five forms if the Hamiltonian that describes the system is to be relativistically
invariant.11 We identify these as S, the scalar interaction; P, pseudoscalar; V, polar vector; A, axial vector; and T, tensor. Fermi knew this, but, in analogy to electromagnetic
theory, and because his calculations were in agreement with experiment, he chose to
use only the vector (V) form of the interaction. The search for the correct mathematical form of the weak interaction would occupy work on ß decay for the next twentyfive years.
To summarize the story in advance, we will find that by the early 1950s experimental results and theoretical analyses had limited the possible combinations for the form
of the ß-decay interaction to either some combination of scalar S, tensor T, and pseudoscalar P, or of vector V and axial vector A. In 1957 the discovery of parity nonconservation, the violation of space-reflection symmetry in the weak interactions, strongly
favored the V and A combination, and both Sudarshan and Marshak and Feynman and
Gell-Mann suggested explicitly that the form of the interaction was V–A.12 The only
problem was that there were, at that time, several experimental results that seemed to
rule out the V–A theory. Both sets of authors suggested that the empirical successes of
the theory, combined with its desirable theoretical properties, strongly argued that the
experiments should be repeated. They were. The new results supported the V–A theory, which became the Universal Fermi Interaction, applying to all weak interactions,
both to ß decay and to the decay of elementary particles.
Fermi initially considered only what he called “allowed” transitions, those for which
the electron and neutrino wavefunctions could be considered constant over nuclear
dimensions. He recognized that “forbidden” transitions also would exist,* those whose
decay rate would be greatly reduced and whose energy spectrum would differ from
that of the allowed transitions. Emil Konopinski later found that the shape of the ß-particle energy spectrum for allowed transitions was independent of the choice of interaction.13 Fermi also found that for allowed transitions certain selection rules would
apply. These included no change in the angular momentum of the nucleus (∆ J = 0) and
no change in the parity (the space-reflection properties) of the nuclear states.
Fermi cited already published experimental results in support of his theory, in particular B.W. Sargent’s, both on the shape of the ß-particle energy spectrum and on
decay constants and maximum electron (ß-particle) energies.14 Sargent had found that
if he plotted the logarithm of the decay constant λ (which is inversely proportional to
the lifetime τo of the state) against the logarithm of the maximum decay energy, all
measured maximum decay energies fall into two distinct groups (figure 1) in which the
product of the two logarithms, and thus the product of the integral F of the energy
* Because the neutrino interacts so weakly with matter we can describe it as a particle traveling
in free space, which is a plane wave Φν(r) = Aei(kr), which can be expanded as A[1 + i(kr) + …].
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 higher-order terms, which are much smaller and
lead to a reduced decay rate.
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Fig. 1. The logarithm of the decay constant λ (which is inversely proportional to the lifetime τo of the
state) for various radioactive nuclei plotted against the logarithm of the maximum decay energy. The
integral F of the energy spectrum varies monotonically with the maximum decay energy. Thus, if the
product Fτo is a constant for each type of ß decay (allowed or first-forbidden transitions) as predicted
by Fermi’s theory, then these two types of transitions should produce two separate curves, as indeed
they do. Source: Sargent, “Maximum Energy” (ref. 14), p. 671.
spectrum and the lifetime τo, was approximately constant. Fermi’s theory predicted this
result, namely, that the product Fτo would be approximately constant for each type of
transition, allowed, first-forbidden, and so forth. Thus, the two Sargent curves, which
were associated with allowed and first-forbidden transitions, although they did not
explicitly involve F and τo, they argued that the product Fτo was approximately constant for each type of transition. The general shape of the observed ß-particle energy
spectra also agreed with Fermi’s theory.
Emil Konopinski and George Uhlenbeck quickly pointed out that a more detailed
examination of the ß-particle energy spectra revealed that Fermi’s theory predicted too
few low-energy ß particles (electrons) and a too high average decay energy.15 They proposed a modification of the theory, which included the derivative of the neutrino wavefunction, and that gave a better fit to the observed ß-particle energy spectra (figure 2)
and also predicted the approximate constancy of the product Fτo. The KonopinskiUhlenbeck (K-U) modification was accepted as superior by the physics community. In a
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Phys. perspect.
Fig. 2. The electron (ß-particle) energy spectrum of RaE (83Bi210). P(W) is the probability of emission of an electron (ß-particle) of energy W (that is, the number emitted of that energy). The curves of
P(W) versus W are plotted for S, the statistical factor in the interaction; F-S, the Fermi theory; and Modified Theory, the Konopinski-Uhlenbeck modification of the Fermi theory. The experimental curve
(EXP) is plotted from Sargent’s data. The Konopinski-Uhlenbeck modified theory clearly fits Sargent’s
experimental data better than the Fermi theory. Source: Konopinski and Uhlenbeck, “Fermi Theory”
(ref. 15), p. 8.
classic review article on nuclear physics that remained a standard reference until the
1950s, the “Bethe Bible,” Hans A. Bethe and Robert F. Bacher declared: “We shall therefore accept the Konopinski-Uhlenbeck theory as the basis of our future discussions.” 16
George Gamow and Edward Teller proposed a further modification of both Fermi’s
original theory and of Konopinski and Uhlenbeck’s modified theory.17 They included
possible effects of nuclear spin and obtained different selection rules, namely, ∆ J = ± 1
or 0 with no J = 0 → J = 0 transitions permitted. This required the presence of either
axial vector (A) or tensor (T) terms in the decay interaction and was supported by a
detailed analysis of the decay of ThB (82Pb212) → ThD (82Pb208). “We can now show,”
they wrote, “that the new selection rules help us to remove the difficulties which
appeared in the discussion of nuclear spins of radioactive elements by using the original selection rule of Fermi.” 18
The Konopinski-Uhlenbeck theory received further support from the work of Franz
Kurie and his collaborators, who found that the spectra of 7N13, 9F17, 11Na24, 14Si31, and
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32
15P
all fit the K-U theory better than the original Fermi theory.19 The Kurie plot,
which would prove very useful in the study of ß decay, made its first appearance in this
paper. The Kurie plot is a mathematical function, which differs for the Fermi and K-U
theories, but when plotted against the electron (ß-particle) decay energy yields a
straight line for whichever of the two theories is correct.* Kurie and his collaborators
plotted this function for both the Fermi and K-U theories and, as shown in figure 3, the
Konopinski-Uhlenbeck theory gave a better fit to a straight line, indicating its superiority. “The (black) points marked ‘K-U modification’ should fall as they do on a
straight line.… If the Fermi theory is being followed the (white) points should fall on a
straight line as they clearly do not.” 20
Problems soon began to develop for the K-U theory. The maximum decay energy
extrapolated from the K-U theory was found to differ from that obtained from the
measured ß-particle energy spectrum, and “in those few cases in which it is possible to
predict the energy of the beta-decay from data on heavy particle reactions…, the visually extrapolated limit has been found to fit the data better than the K-U value.” 21 This
was closely related to the requirement of the K-U theory that the mass of the neutrino
was approximately half the mass of the electron, 0.5 me, whereas its upper limit as
determined from nuclear reactions was about 0.1 me.
Toward the end of the 1930s experimental evidence from ß-particle energy spectra
using thin radioactive sources began to favor the original Fermi theory over the modified K-U theory. The decay electrons (ß particles) appeared to be losing energy in leaving the source, giving rise to too many low-energy electrons and thus reducing their
average energy (figure 4). “The thin source results in much better agreement with the
original Fermi theory of beta-decay than with the later modification introduced by
Konopinski and Uhlenbeck.” 22
In addition, as pointed out by James L. Lawson and James M. Cork in 1940, “in all
of the cases so far accurately presented, experimental beta-ray spectra for ‘forbidden’
transitions have been compared to theories which have been developed for ‘allowed’
transitions. The theory for forbidden transitions is not yet published.” 23 They measured
the spectrum of 49In114, an allowed transition, for which a valid experiment-theory
comparison could be made, and found that it clearly favored the Fermi theory, because
it yielded the straight-line Kurie plot shown in figure 5. Ironically, the ß-particle energy spectrum for forbidden decays on Fermi’s theory was calculated by Konopinski and
Uhlenbeck in 1941,24 and the experimental results then also favored Fermi’s theory. As
Konopinski remarked in a review article on ß decay, “Thus, the evidence of the spectra, which has previously comprised the sole support for the K-U theory, now definite-
* Fermi’s theory predicted that P(W) = G2⏐M2⏐f(Z,W)(Wo – W)2 (W2 – 1)WdW, where M is the
matrix element for the transition, G is a coupling constant, W is the decay energy of the electron or ß particle (in units of mec2, where me is the mass of the electron and c the speed of light),
Wo is the maximum decay energy, P(W) is the probability of the emission of an electron of energy
W, and f(Z,W) is a function giving the effect of the Coulomb field of the nucleus on the emis1
sion of electrons. We see that [P(W)/f (Z,W)(W2 – 1)W] /2 is a linear function of W. For the KU theory, an exponent of 1/4 gives a linear function of W. In the original papers, P(W) is called
N, the number of electrons.
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Fig. 3. The Kurie plot for electrons (β-particles) from phosphorus. The left and right vertical axes are
the fourth and square roots of N/f, the number N of electrons divided by the Coulomb factor f for the
decay, both of which are plotted as a function of the decay energy E + 1 (the decay energy E plus the
mass of the electon me in units of mec 2, where c is the speed of light). If the Konopinski-Uhlenbeck
(K-U) theory is correct, then the fourth root of N/f versus E + 1 should be a straight line; if the Fermi
theory is correct, then the square root of N/f versus E + 1 should be a straight line. The K-U modification clearly does yield a straight line while the Fermi theory does not. Source: Kurie, Richardson, and
Paxton, “Radiations” (ref. 19), p. 377.
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Fig. 4. The Kurie plots for electrons (ß-particles) from a thin source of phosphorus-32 for both the
Fermi (F) theory (left vertical axis versus energy) and the Konopinski-Uhlenbeck (K-U) theory (right
vertical axis versus energy). The Fermi theory now is clearly better, because it yields a straight line,
whereas the K-U theory does not. Source: J.L. Lawson, “The Beta-Ray Spectra of Phosphorus, Sodium
and Cobalt,” Physical Review 56 (1939), 131–136; plot on 135.
ly fails to support it.” 25 Konopinski and Uhlenbeck applied their new theoretical
results to the spectra of 15P32 and RaE (83Bi210) and found that they fit Fermi’s theory
with either a vector (V) or tensor (T) interaction. They favored the tensor (T) interaction because that one gave rise to the Gamow-Teller selection rules.
Markus Fierz published an important analysis in 1937,26 but its significance was
not recognized until later. He showed that if both the scalar (S) and vector (V) terms
were present in the ß-decay interaction, or both the tensor (T) and axial vector (A)
terms were, then there would be an interference term in the allowed ß-particle energy spectrum that vanished in their absence. The failure to observe such interference
terms was later cited as a major step toward deciding the form of the ß-decay interaction. (The plot shown in figure 5 would not be a straight line if such interference
terms were present.) But Fierz’s analysis appears not to have been cited at all at this
time.
In sum, by the end of World War II there was strong support for Fermi’s original theory of ß decay, with some preference for the Gamow-Teller selection rules and the tensor (T) interaction. The evidence from the ß-particle energy spectra and Konopinski
and Uhlenbeck’s analysis of the spectra of 15P32 and RaE (83Bi210), along with Gamow
and Teller’s earlier analysis of the transition ThB (82Pb212) → ThD (82Pb208), supported
this view.
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Fig. 5. The Kurie plot for electrons (ß particles) from indium-114. The vertical axis is the square root
of N/p2f, which is plotted as a function of the electron-decay energy, where N is the number of electons
(ß particles) emitted at a given energy, p is the electron’s momentum, and f is the Coulomb factor in the
decay. If the Fermi theory is correct, then this should be a straight line, as it is. Source: Lawson and Cork,
“Radioactive Isotopes” (ref. 23), p. 994.
Toward a Universal Fermi Interaction: Muons and Pions
In 1935 Hideki Yukawa hypothesized a new elementary particle, with mass intermediate between that of the electron and proton, to explain the nuclear force.27 In 1936 Carl
D. Anderson and Seth H. Neddermeyer, and in 1937 Jabez Street and Edward Stevenson, found a penetrating cosmic-ray particle, later called the muon (µ), with a mass
approximately two hundred times that of the electron,28 which was initially identified
with Yukawa’s particle, but this identification was soon abandoned. Yukawa’s particle
should have interacted strongly with matter, whereas the muon did not; it penetrated
considerable amounts of matter without interacting. Physicists then hypothesized that
the muon was the decay product of Yukawa’s particle, later called the pion (π). In 1947
Cesar Lattes and his collaborators presented evidence for the existence of the pion and
its decay into a muon.29
Even before the discovery of the pion, considerable effort had been devoted to studying the decay of the muon and its interaction with matter. Experiments showed that the
muon decayed into an electron and two neutrinos with a lifetime of approximately 10–6
second according to the reactions µ → e+ν +⎯ ν , or µ → e+2ν, or µ → e+ 2⎯ ν, where µ is the
muon, ν is the neutrino, and ⎯ ν is its antiparticle, the antineutrino. (The pion was later
shown to decay into a muon and a neutrino with a lifetime of about 10–8 second.) It was
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also shown that the strengths of the interactions responsible for ß decay, for the absorption of muons by matter, and for the decay of the muon were all approximately equal,
suggesting that they all might be due to the same interaction. Thus, in a paper of 1949 on
the absorption of muons, Jayme Tiomno and John A. Wheeler remarked:
[We] conclude that it is reasonable to assign a value near 10–49 erg cm3 to this quantity [the coupling constant, or strength, of muon absorption]…. We compared this
result with the coupling constants gβ ~ 2.2 × 10–49 erg cm3 for beta-decay and gµ ~ 3
× 10–49 erg cm3 for decay of the µ-meson on the hypothesis of three end products.
We note that the three coupling constants determined quite independently agree with
one another within the limits of error of experiment and theory. We apparently have
to do in all three reaction processes with phenomena having a much closer relationship than we can now visualize.30
Louis Michel showed in 1952 that for the decay of the muon into an electron and two
neutrinos the electron-decay energy spectrum would be given by
P(W) ~ (W2/Wo4){3[Wo – W] + 2ρ [(4/3)W – Wo]},
where W is the electron energy, Wo is the maximum electron energy, and ρ is a parameter that is a function of the particular form of the decay interaction (S, V, T, A, P), and
also depends upon the way in which the particles are paired in the decay interaction
and whether the two neutrinos are identical.31 The value of Michel’s ρ parameter did
not determine the correct form of the decay interaction uniquely, but it did serve to
eliminate some of its combinations (see below).
There was, however, a clear-cut prediction for the decay of the pion. Malvin A. Ruderman and Robert J. Finkelstein had shown in 1949 “that any theory which couples πmesons to nucleons also predicts the π → (e, ν) decay.” 32 They calculated that the ratio
of the pion-to-electron-and-neutrino decays to pion-to-muon-and-neutrino decays,
that is, the ratio [π → (e, ν)]/[π → (µ, ν)], was either zero (the decay was not possible)
or of order unity – except if the pion decay interaction was a combination of a pseudoscalar (P) and an axial vector (A) interaction, for which the ratio would be 1.0 × 10–4.
Because the decay of the pion into an electron had not yet been observed, however,
they concluded that, “The symmetric coupling scheme is in agreement with experimental facts only if the π-meson is pseudoscalar [P] (with either pseudoscalar [P] or
pseudovector [axial vector A] coupling to nucleons) and the ß-decay coupling contains
a pseudovector [axial vector A] term.” 33 During the early 1950s there were several
unsuccessful searches for the electron decay of the pion. Helen L. Friedman and James
Rainwater showed in 1951 that not more than one pion in 1400 decays into an electron,34 supporting the conclusion of Ruderman and Finkelstein. That same year
Frances M. Smith set an upper limit of 3 × 10–3 ± 0.4 percent for the decay of a pion
into an electron,35 and in 1955 S. Lokanathan and Jack Steinberger lowered that limit
to 2 × 10–5.36 That limit, in fact, was lower than the one that Ruderman and Finkelstein
had predicted, which remained a problem for several years (see below).
During the first half of the 1950s there were no less than twelve measurements of
the Michel ρ parameter in muon decay. The results favored a value of ρ of approxi-
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mately 0.5 or perhaps slightly larger. Theoretical analysis by Michel and Arthur Wightman in 1954,37 which was restricted to a combination of the scalar (S), tensor (T), and
pseudoscalar (P) interactions – the favored combination for the ß-decay interaction at
that time (see below) – led to the conclusion that the muon-decay interaction was consistent with the triplet STP combination.
Beta-Decay Theory after World War II
The search for the correct mathematical form of the ß-decay interaction intensified
after World War II. In 1943 Konopinski had noted that there was general support for
Fermi’s theory with a preference for the tensor (T) or axial vector (A) interactions.38
By 1953, however, Konopinski and Lawrence M. Langer could state that: “As we shall
interpret the evidence here, the correct law must be what is known as an STP combination.” 39 I begin by discussing how they arrived at this plausible conclusion, but one
that was later shown to be incorrect.
After the war, physicists recognized the importance of Fierz’s work of 1937 for clarifying the nature of the ß-decay interaction.40 Recall that Fierz had shown that if the
interaction contained both scalar (S) and vector (V) terms, or both axial vector (A) and
tensor (T) terms, then certain interference terms would appear in the ß-decay interaction
for allowed transitions. (The Kurie plot shown in figure 5 would not be a straight line, as
it is, if such interference terms were present.) The presence of either axial vector (A) or
tensor (T) terms in the ß-decay interaction, however, was supported by Maria Goeppert
Mayer and her collaborators in 1951, who used ß-decay data from nuclei of odd mass
number to support their assignments of nuclear spins and parities.41 They found twentyfive ß decays for which ∆ J = ± 1, with no parity change, which required the presence of
either axial vector (A) or tensor (T) terms in the interaction. (There was an element of
uncertainty in their conclusion, however, because it depended upon their somewhat
uncertain assignment of nuclear spins and parities.) Evidence for the presence of axial
vector (A) or tensor (T) terms that did not depend upon a knowledge of nuclear spins
came from the ß-particle energy spectra of unique forbidden transitions, ones that were
n-times forbidden, for which the change in spin is ∆ J = n + 1. These n-times forbidden
transitions require the presence of axial vector (A) or tensor (T) terms in the interaction,
and since each of them makes an appreciable contribution to the decay interaction, the
spectral shapes of these transitions could be calculated. Konopinski and Uhlenbeck
showed that the ß-particle energy spectrum for an n-times forbidden transition would be
that for an allowed transition multiplied by an energy-dependent factor a1 that could be
calculated.42 Langer and H. Clay Price obtained the Kurie plot for 39Y91 shown in figure
6,43 which demonstrates that the correction factor a1 yields a straight line (lower curve)
and provides a good fit to the spectrum, whereas the uncorrected spectrum (a1 → 1) does
not fit a straight line (upper curve), and hence axial vector (A) and tensor (T) terms must
be present in the decay interaction.* Rubby Sherr and his collaborators also demon* Many other such spectra were measured, all of which were consistent with the presence of axial
vector (A) or tensor (T) terms; see Franklin, Experiment, Right or Wrong (ref. 8), pp. 42–53.
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Fig. 6. The Kurie plot for the unique, once-forbidden ß-particle energy spectrum of yttrium-91. The
vertical axis is the square root of N/a1pWF, which is plotted as a function of the electron (ß-particle)
decay energy W in units of mc2 (m is the mass of the electron), where N is the number of electrons, p
is the electron’s momentum, and F is the Coulomb factor in the decay. The curve for the correct theory should be a straight line. The Fermi theory, for which a1 → 1, does not fit a straight line, while introducing the correction factor a1 = C[(W2 – m2c4) + (Wo – W)2], where C is a constant and Wo is the maximum electron energy, which Konopinski and Uhlenbeck calculated in 1941, does fit a straight line.
Source: Konopinski and Langer, “Experimental Clarification” (ref. 39), p. 290.
strated the presence of either scalar (S) or vector (V) terms in the interaction by analyzing the ß decays of 6C10 and 8O14.44
Further progress in isolating the particular form of the ß-decay interaction was
made by examining the spectra of once-forbidden transitions. In 1951 both A.M. Smith
and D.L. Pursey showed that these spectra would contain energy-dependent interference terms, similar to those that Fierz had predicted for allowed spectra, if the decay
interaction included both vector (V) and tensor (T) terms, or axial vector (A) and pseudoscalar (P) terms, or scalar (S) and axial vector (A) terms.45 The failure to observe
such terms further restricted the forms of the interaction.
We have seen that the scalar (S) or vector (V), or the axial vector (A) or tensor (T)
terms must be included in the ß-decay interaction. The failure to observe interference
terms restricted the choice of the interaction to the triplet STP, SAP, VTP, or VAP
combinations, or to doublet combinations formed from them. The absence of the Fierz
interference terms in the spectra of once-forbidden transitions eliminated the doublet
VT, SA, and AP combinations. The doublet VP and SP combinations were eliminated
because they did not contain the required axial vector (A) or tensor (T) terms, and the
doublet TP combination was eliminated because it did not contain either scalar (S) or
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vector (V) terms. The result was that, of the more than thirty possible forms of the ßdecay interaction, only two were left, namely, either the triplet STP or the doublet VA
combination.
In 1952 Albert Petschek and Robert Marshak provided what was then regarded as
the decisive evidence for choosing between these two combinations as a result of their
theoretical analysis of the spectrum of RaE (83Bi210).46 They assumed that the RaE
(83Bi210) nucleus had spin J = 0 and that both a parity change and a spin change, ∆ J =
0 or 2, occurred in the decay, and they then attempted to fit its ß-particle energy spectrum using all possible linear combinations of the five interactions S, T, V, A, and P.
They concluded:
Within the errors noted previously, the linear combination of tensor [T] and pseudoscalar [P] interactions… can be regarded as giving a satisfactory fit of the RaE
spectrum. Moreover it is the only linear combination which can explain the forbidden shape of the RaE spectrum.… [Our] calculation provides the first clearcut evidence for an admixture of the pseudoscalar [P] interaction to explain all ß-ray phenomena.47
This was the sole evidence that led Konopinski and Langer in 1953, as I noted above,
to choose the triplet STP instead of the doublet VA combination for the ß-decay interaction.
Because of its importance, Petschek and Marshak’s analysis generated considerable
theoretical discussion, but it all became moot when K. Smith measured the spin of the
RaE (83Bi210) nucleus directly and found a value of J = 1,* which removed the only evidence that Petschek and Marshak had cited in support of the presence of the pseudoscalar (P) term in the ß-decay interaction. That left the triplet STP combination,
however, which remained the preference of most of the physics community owing to
the evidence provided by angular-correlation experiments (see below), which clearly
favored the scalar (S) and tensor (T) terms rather than the vector (V) and axial vector
(A) terms in the ß-decay interaction.
In angular-correlation experiments, which became important in the late 1940s, the
decay electron (ß particle) and the recoil nucleus are detected in coincidence, and their
energies and the angle between the direction of emission of the electron and that of the
recoil nucleus are measured, which allows one to calculate the angle between the direction of emission of the decay electron and that of the emitted neutrino. In 1947 Donald Hamilton calculated the form of the angular distribution of the decay electrons
both for allowed and for first-forbidden transitions under the assumption that the ßdecay interaction involved only a single term.48 In 1950 S.R. de Groot and H.A. Tolhoek found a more general form for the angular distribution that allowed a combination of ß-decay interaction terms.49
In 1953 Brice Rustad and Stanley Ruby carried out the most important of these
angular-correlation experiments, on the ß decay of 2He6.50 Their results are shown in
* I have not been able to find a published reference to Smith’s work. It is cited as a private communication in several review articles at the time.
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Fig. 7. The coincidence counting rate plotted as a function of the angle θ between the direction of
emission of the electron (ß particle) and that of the recoil nucleus in the ß decay of 2He6 for (left) electrons in the energy range from 4.5–5.5 mc2 (m is the mass of the electron) and (right) electrons in the
energy range from 5.5–7.5 mc2. The theoretical curves predicted on the basis of the various forms of the
ß-decay interaction, vector (V), tensor (T), axial vector (A), and scalar (S), clearly show that the tensor
(T) interaction is favored. Source: Rustad and Ruby, “Gamow-Teller” ( ref. 50), pp. 999–1000.
figure 7, where the theoretical coincidence rate is plotted against the electron-recoil
angle θ, the angle between the direction of emission of the decay electron and that of
the recoil nucleus, for the vector (V), tensor (T), axial vector (A), and scalar (S) interactions for electron energies in two different energy ranges, 4.5–5.5 mc2 (left) and
5.5–7.5 mc2 (right). Their experimental data clearly favored the tensor (T) interaction.
Further angular-correlation experiments in the 1950s, however, disturbed the agreeable consistency of the experimental results with the predictions of the triplet STP
combination for the ß-decay interaction. Several experiments were consistent with the
doublet ST and VA combinations: Experiments on 2He6, the neutron, and 10Ne19 were
consistent with the doublet ST combination, whereas other experiments on the neutron, 10Ne19, 7N15, and 18A35 were consistent with the doublet VA combination. “It
seems too early to choose between these,” Konopinski wrote in 1958.51 Evidence from
muon decay was consistent with the doublet ST combination, although no one seems
to have attempted an experimental fit to the doublet VA combination.
The Discovery of Parity Nonconservation
In late 1956 and early 1957 the situation changed dramatically. Following a suggestion
by Tsung-Dao Lee and Chen Ning Yang that parity conservation, or mirror symmetry,
might be violated in the weak interactions,52 which included ß decay, a series of experiments by Chien-Shiung Wu and her collaborators, by Richard Garwin, Leon Leder-
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man, and Marcel Weinrich, and by Jerome Friedman and Valentine Telegdi, showed
conclusively that parity was not conserved.53 This discovery raised fundamental questions about the earlier analyses of ß decay, suggested new experiments, and pointed the
way toward a new theory of ß decay.
During the 1950s the physics community was faced with what was known as the “θτ puzzle.” On one set of accepted criteria, that of identical masses and lifetimes, the θ
(theta) and τ (tau) particles appeared to be the same particle. On another set of accepted criteria, that of spin and parity, they appeared to be different particles. The spin and
parity analysis focused on the decay products, two pions for the θ particle, and three
pions for the τ particle. Parity conservation was assumed in these decays, and the spin
and parity of the θ and τ particles were inferred from the decay products. Several
attempts were made to solve this puzzle within the framework of currently accepted
theories, but all were unsuccessful.
In 1956 Lee and Yang realized that if parity was not conserved in the weak interactions, then the spin and parity analysis of the θ and τ decays would be incorrect, and the
θ and τ particles merely would be two different decay modes of the same particle. This
led them to thoroughly examine the existing experimental evidence in favor of parity
conservation. They found, to their surprise, that although earlier experiments strongly
supported the conservation of parity in the strong and electromagnetic interactions to
a high degree of accuracy, there was, in fact, no experimental evidence in favor of the
conservation of parity in the weak interactions. It had never been tested experimentally.
Lee and Yang suggested several possible tests of their hypothesis. The two most
important ones concerned the ß decay of oriented nuclei and the sequential decay of a
pion into a muon and the muon into an electron (π → µ → e). I will discuss only the
former, which Lee and Yang described as follows:
A relatively simple possibility is to measure the angular distribution of the electrons
coming from ß decays of oriented nuclei. If θ is the angle between the orientation of
the parent nucleus and the momentum of the electron, an asymmetry of distribution
between θ and 180° – θ constitutes an unequivocal proof that parity is not conserved
in ß decay.54
This is made clear in figure 8. Suppose that in real space the direction of the electron
momentum is opposite to that of the nuclear spin. In a mirror the direction of the electron momentum remains unchanged, but the direction of rotation of the nucleus and
hence the nuclear spin is reversed, so that the decay electron is now emitted in the
same direction as that of the nuclear spin. There is thus a difference between the real
experimental result and its mirror image, which violates mirror symmetry or the conservation of parity.
Chien-Shiung Wu and her collaborators carried out this experiment.55 It consisted
of a layer of oriented radioactive 27Co60 nuclei and a single electron counter that was
fixed in space and detected the electrons (ß particles) as they were emitted either parallel or antiparallel to the direction of the nuclear spins as they were reversed by an
external magnetic field H. They found a clear asymmetry in the two counting rates at
low temperatures (small counting times), as shown in figure 9: The counting rate when
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Fig. 8. The ß decay of an oriented nucleus in both real space and mirror space. The direction of rotation of the nucleus is reversed in the mirror image, and hence the spin vector now points downward,
which shows that parity or mirror symmetry is not conserved in ß decay. Sketch by the author.
the electrons were emitted antiparallel to the nuclear spin was larger than when the
electron was emitted parallel to the nuclear spin.
If an asymmetry in the distribution between θ and 180° – θ (where θ is the angle
between the orientation of the parent nuclei and the momentum of the electrons) is
observed, it provides unequivocal proof that parity is not conserved in beta decay.
This asymmetry effect has been observed in the case of oriented Co60.56
Two other experiments on the decay of pions and muons also clearly demonstrated
parity nonconservation.57
Although the discovery of nonconservation of parity complicated the previous
analyses of ß decay, it did not significantly affect the earlier conclusions on the correct
form of the ß-decay interaction. Indeed, even before the above experimental results
were published, Lee and Yang, Lev Landau, and Abdus Salam attempted to incorporate nonconservation of parity into the theory of weak interactions by proposing a twocomponent theory of the neutrino.58 This was in contrast to ordinary relativistic physics
where the neutrino wavefunction contained four components, two for the neutrino
with spin either parallel or antiparallel to its momentum, and two for the antineutrino
with the same properties. In the two-component theory, the neutrino only had a spin
parallel to its momentum, and the antineutrino antiparallel to its momentum, or vice
versa, which violated parity conservation. Thus, a three-dimensional space reflection
reverses each of the components of the momentum, so that the momentum vector is
reversed, but the spin vector remains unchanged, and thus the reflected image differs
from the original, and parity is not conserved.
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Fig. 9. The ratio of the observed counting rate to the counting rate obtained when the sample is
warmed up as a function of time for electrons (ß particles) emitted in the decay of oriented 27Co60
nuclei. At low temperatures (small counting times), more electrons are emitted opposite to the direction of the nuclear spin (external magnetic field H) than in that direction, but as the sample warms up
(counting time increases), the orientation of the spins of the nuclei is washed out and the relative counting rate becomes unity. Source: Wu, Ambler, Hayward, Hoppes, and Hudson, “Experimental Test” (ref.
53), p. 1414.
Two important experimental implications followed from this new theory: It predicted
the asymmetry in the ß decay of oriented nuclei, and it predicted that the electron emitted in ß decay would have a polarization equal to v/c, where v is the velocity of the electron and c is the speed of light. Most important for our discussion, however, was its implications for the decay of the muon. There were three possibilities: The muon might decay
into (1) an electron, neutrino, and antineutrino (µ → e+ν +⎯ ν ); (2) an electron and 2 neutrinos (µ → e+2ν ); or (3) an electron and 2 antineutrinos (µ → e+2⎯ ν ). For case (1) the
two-component theory of the neutrino required that the scalar (S), tensor (T), and pseudoscalar (P) couplings all be equal to 0, and that the Michel ρ parameter be ρ = 0.75,
whereas for cases (2) and (3) ρ = 0. This value was inconsistent with the experimental
results of C.P. Sargent and his collaborators, who found that ρ = 0.64 ± 0.10,59 and of A.
Bonetti and his collaborators, who found that ρ = 0.57 ± 0.14,60 a point noted both by Lee
and Yang and by Landau. Walter F. Dudziak and his collaborators later reported a value
of ρ of approximately 0.75.61 This meant that the decay interaction for muons could not
involve the scalar (S), tensor (T), and pseudoscalar (P) terms, but had to be a combination of the vector (V) and axial vector (A) terms (recall that earlier work had restricted
the ß-decay interaction terms to the triplet STP or doublet VA combinations).
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During 1957 both parity nonconservation and the two-component theory of the
neutrino received further experimental confirmation, which suggested that there might
not be a Universal Fermi Interaction that would apply to all weak interactions. As Lee
remarked:
Beta decay information tells us that the interaction between (p, n) and (e, ν) [the
proton and the neutron and the electron and the neutrino] is scalar [S] and tensor
[T, as Rustad and Ruby’s angular-correlation experiments had indicated], while the
two-component neutrino theory plus the law of conservation of leptons [electrons,
neutrinos, muons] implies that the coupling between (e, ν) and (µ, ν) is vector [V].
This means that the Universal Fermi Interaction cannot be realized in the way we
have expressed it.... Nevertheless, at this moment it is very desirable to recheck even
the old beta interactions to see whether the coupling is really scalar [S].…62
In sum, by the end of the summer of 1957 parity nonconservation had been conclusively demonstrated and there was strong experimental support for the two-component theory of the neutrino. That theory, together with the conservation of leptons, led
to the conclusion that the weak interaction responsible for the decay of the muon had
to be a doublet VA combination. Although most of the evidence from ß decay was consistent with such a doublet VA interaction, Rustad and Ruby’s angular-correlation
experiment on 2He6 provided seemingly conclusive evidence that the ß-decay interaction was tensor (T). The failure to observe the decay of the pion into an electron also
argued against a doublet VA interaction. The situation was uncertain.
The V–A Theory of Weak Interactions and Its Acceptance
Despite this uncertain and confusing situation, Sudarshan and Marshak, and Feynman
and Gell-Mann, proposed that a Universal Fermi Interaction (UFI) – one that would
apply to all weak interactions – would be a linear combination of the vector (V) and
axial vector (A) terms.63 Sudarshan and Marshak reached this conclusion from an
examination of the experimental evidence on the weak interactions, although they
noted that four experiments stood in opposition to the V–A theory, as follows: (1) Rustad and Ruby’s electron-neutrino angular-correlation experiments on 2He6; (2) the frequency of the electron decay mode of the pion; (3) the sign of the polarization of the
electron in muon decay; and (4) the asymmetry in the decay of polarized neutrons,
which was smaller than predicted.
The first two cases were regarded as significant problems, whereas the second two
had less evidential weight and were eliminated by later experiments. Nonetheless,
Sudarshan and Marshak suggested that, “All of these experiments should be redone,
particularly since some of them contradict the results of other recent experiments on
the weak interactions.” 64 They also pointed out that the V–A theory had some very
attractive features. It provided a natural mechanism for parity violation in strange-particle decays leading to the θ and τ decay modes of the K meson. It also allowed a similar treatment of pions and kaons and had the added feature that the neutrino emitted
in all ß decays had the same handedness, or helicity, which was not true for either the
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doublet VT or SA combinations. Feynman and Gell-Mann also emphasized this theoretical elegance:
It is amusing that this interaction satisfies simultaneously almost all the principles
that have been proposed on simple theoretical grounds to limit the possible ß couplings. It is universal, it is symmetric, it produces two-component neutrinos [and thus
violates parity conservation], it conserves leptons, it preserves invariance under CP
[combined particle-antipartcle and space-reflection symmetry] and T [time-reversal
symmetry].…65
Feynman and Gell-Mann went even further in regard to the experimental anomalies.
These theoretical arguments seem to the authors to be strong enough to suggest that
the disagreement with the He6 recoil experiment and with some other less accurate
experiments indicates that these experiments are wrong [emphasis added]. The π →
e + ν problem may have a more subtle solution.66
Note the importance here of the theoretical principles that I discussed at the beginning
of my paper. On the basis of a theory that satisfied these principles, both teams of theorists were willing to question seemingly well-done experiments. This is not to say that
evidential considerations were absent. As Feynman and Gell-Mann noted:
After all, the theory also has a number of successes. It yields the rate of µ decay to
2% and the asymmetry in direction in the π → µ → e decay chain. For ß decay, it
agrees with the recoil experiments in A35 indicating a vector [V] coupling, the
absence of Fierz [interference] terms distorting the allowed spectra, and the more
recent electron spin polarization measurements in ß decay.67
The attractive theoretical features of the V–A theory, as we shall now see, also were
important in its reception.
The Removal of the Experimental Anomalies
The Angular-Correlation Experiment on 2He6
Rustad and Ruby’s angular-correlation experiment on 2He6 probably was the most
important piece of evidence, as we saw in figure 7, that favored the tensor (T) and
argued against the V–A interaction in ß decay.68 After Sudarshan and Marshak and
Feynman and Gell-Mann proposed the V–A theory, however, Rustad and Ruby themselves, and Wu and Arthur Schwarzschild, critically reexamined the Rustad-Ruby
experiment.69
One of the important factors in Rustad and Ruby’s calculation was their assumption
that all of the 2He6 that decays was confined to the source volume, as shown in figure 10. If, however, a significant amount of the 2He6 gas were present in the collimating chimney below the source volume, then the angular correlation they measured
between the emitted ß particle and recoil ion (nucleus), and their conclusion that the
interaction was tensor (T), might be affected. Wu and Schwarzschild argued as follows.
First, the efficiency of the ß-particle counter (the ß-scintillation spectromenter),
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Fig. 10. Schematic diagram of Rustad and Ruby’s experimental apparatus for their angular-correlation experiment of 1953 on 2He6. Source: Rustad and Ruby, “Correlation” (ref. 50), p. 880.
changes considerably as the angle between it and the recoil-ion detector (the recoil ion
multiplier) changes. Second, the amount of material through which the decay electron
(ß particle) passes changes as that angle changes. Together, these two factors will affect
the electron-detection efficiency.
Wu and Schwarzschild carried out an approximate calculation and found that the
gas pressure at the lower part of the pumping diaphragm had to be greater than 12 percent of the gas pressure in the source volume. They obtained a better estimate by constructing an optical analogue of the gas system. Thus, since the gas pressure was low,
collisions between the gas molecules could be neglected and the gas-pressure gradient
could be estimated by considering only their reflections from the walls of the source
volume, which was analogous to optical scattering from a perfectly reflecting surface.
Wu and Schwarzschild then constructed a scale model ten times larger than the Rustad-Ruby apparatus, making the inner walls of the source volume and collimating
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chimney highly reflecting. They placed a diffuse light source in the source volume to
simulate the entering gas and, as an analogue to the gas pressure, they measured the
light intensity at various places inside their model. They also took account of the finite
solid angle through which the ß particles entered the ß-particle detector after being
emitted both in the source volume and in the chimney, finding that “the decay due to
He6 gas in the chimney is not insignificant in the correlation results.” 70 They further
estimated the energy loss and backscattering of the decay ß particles in the chimney,
and although they realized that a precise calculation was “obviously impossible,” they
concluded, finally, that the corrected results “are more in favor of axial vector [A] than
tensor [T] contradictory to the original conclusion.” 71 Their work thus cast doubt on
Rustad and Ruby’s original conclusion, and in a postdeadline paper that Rustad and
Ruby presented at a meeting of the American Physical Society in January 1958, they
agreed with that assessment.*
James S. Allen and his collaborators repeated the 2He6 angular-correlation experiment in 1958.72 Figure 11 shows their “distribution of recoil ions observed in the decay
of He6 as a function of the recoil energy R. The solid curves are the computed distributions for the tensor (T) and axial vector (A) interactions.” 73 The “angular correlation coefficient λ should be either +1/3 or –1/3 corresponding, respectively, to the
tensor [T] or axial-vector [A] interaction. Our experimental result, λ = – 0.39 ± 0.02,
clearly indicates that the axial-vector [A] interaction is dominant.” 74 One of the experimental anomalies for the V–A theory had been removed.
The Electron Decay of the Pion
Recall that in 1949 Ruderman and Finkelstein had calculated that the ratio of pion-toelectron to pion-to-muon decays [(π → e)/(π → µ)] was approximately 10–4 assuming
that the decay interaction was axial vector (A). In 1957 Sudarshan and Marshak, and
in 1958 Feynman and Gell-Mann noted, however, that the best measurements of this
ratio were too low. Thus, in 1955 S. Lokanathan and Jack Steinberger had found the
ratio to be (–0.3 ± 0.9) × 10–4, with an upper limit of 0.6 × 10–4,75 and two years later
Herbert L. Anderson and Cesar Lattes had found no evidence at all for the electron
decay of the pion and had concluded that the ratio probably was as low as (0.4 ± 9.0)
× 10–6, with a probability of only one percent that it was greater than 2.1 × 10–5.76 This
was clearly lower than the ratio predicted by the V–A theory.
Various unsuccessful theoretical attempts were made to explain the absence or near
absence of the electron decay of the pion.77 All became moot, however, when Steinberger and his collaborators found convincing evidence for it in 1958.78 They used a
hydrogen bubble chamber and found six clear examples (their emphasis) of pion-toelectron (π → e) decay as well as other examples of pion-to-muon-to-electron (π → µ
→ e) decay. In the first case, the pions were stopped in the hydrogen and then emitted
* There are no abstracts of postdeadline papers. Ruby remembers, however, that the tone of their
paper was mea culpa; private communication, 1989.
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Fig. 11 The distribution of recoil ions observed in the ß decay of 2He6 as a function of the energy R
of the recoil ion. The solid curves are the computed distributions for the tensor (T) and axial vector (A)
interactions. The angular correlation coefficient λ should be +1/3 for the tensor (T) interaction and –1/3
for the axial vector (A) interaction. The experimental result, λ = –0.39 ± 0.02, clearly indicates that the
axial vector (A) interaction is dominant. Source: Hermannsfeldt, Burman, Stähelin, and Allen, “Determination” (ref. 71), p. 62.
an electron, which produced a low-ionization track without an intermediate muon
track, as shown at point A in figure 12. The two-track event at A shows a dark track
entering from the left (a pion) followed by a lighter track (an electron) heading
upward. This is an example pion-to-electron (π → e) decay. In the second case, as seen
in the three-track event shown at point B, a dark track enters from the left (a pion) and
is followed by a dark track heading up and to the left (a muon), which is followed by a
lighter track going to the right (an electron). This is an example of pion-to-muon-toelectron (π → µ → e) decay.
Steinberger and his collaborators also measured the momentum of the decay electron. Although most of the events they identified initially were examples of pion-tomuon-to-electron (π → µ → e) decay with a very short intermediate muon track, the
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Fig. 12. A hydrogen bubble-chamber photograph. 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 of
pion-to-electron (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 and to the left (a muon), followed by a lighter track going
to the right (an electron). This is an example of pion-to-muon-to-electron (π → µ → e) decay. Source:
Impeduglia, Plano, Prodell, Samios, Schwartz, and Steinberger, “ß-Decay” (ref. 78), p. 250.
electron decays could be separated from these using a momentum criterion. Thus, if
both the pion and the muon decay at rest, then the maximum momentum of the electron from the (π → µ → e) decay is 52.9 MeV/c (million electron volts divided by the
speed of light). For the pion-to-electron (π → e) decay, the unique momentum of the
electron is 69.8 MeV/c, which was the momentum they observed for their putative (π
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→ e) events. For events with no visible intermediate muon track, they fit the electron
energy spectrum using Michel’s calculation of the muon-to-electron (π → e) decay
spectrum, found a good fit, and calculated that no pion-to-electron (π → e) events were
to be expected in the region near 70 MeV/c. As a check, they measured the momentum
spectrum of the electrons from the 2983 events they identified that had a muon track,
finding none with an electron momentum above 62 MeV/c, which indicated that contamination in this high electron-momentum region was negligible. They set an upper
limit of (1/10,800) ± 40 percent for the ratio of pion-to-electron to pion-to-muon [(π →
e)/(π → µ)] decays, which was to be compared with the V–A prediction of 1/8000. They
concluded:
The method does not yield a precise measurement of the [above] branching ratio
and cannot reasonably be extended to do so. However, the results here offer a very
convincing proof of the existence of this [π → e] decay mode, and show that the relative rate is close to that expected theoretically.79
The second experimental anomaly for the V–A theory had been removed.
During this same period the other two, less significant problems for the V–A theory, the sign of the polarization of the electron in muon decay and the asymmetry in the
decay of polarized neutrons, were also resolved.80 Even before all four of the
anomolies for the V–A theory had been removed, however, it had received strong support in 1958 when Maurice Goldhaber and his collaborators had measured the helicity of the neutrino (whether its spin is parallel or antiparallel to its momentum) emitted in ß decay.81 They concluded that “our result indicates that the Gamow-Teller interaction is axial vector (A) for positron emitters.…” 82
In sum, by early 1959 all of the experimental evidence on the weak interactions –
nuclear beta decay, pion decay, muon decay, and electron capture – was in agreement
with the V–A theory. As Sudarshan and Marshak remarked later:
And so it came to pass – only three years after parity violation in weak interactions
was hypothesized – that the pieces fell into place and that we not only had confirmation of the UFI [Universal Fermi Interaction] concept but we also knew the basic
(V–A) structure of the charged currents in the weak interactions for both baryons
and leptons.83
Conclusions
The history of the development and articulation of the theory of ß decay from its inception in 1934 to the proposal and acceptance of the V–A theory in the late 1950s is an
example of what I mean by the inevitability of the laws of physics. From Pauli’s proof
that there are only five relativistically invariant forms of four-Fermion interactions to
Sudarshan and Marshak’s and Feynman and Gell-Mann’s discussions of the theoretical attractiveness of the V–A theory, we have seen how theoretical principles constrain
the types of theories that physicists propose. We also have seen how both theoretical
calculations and experimental results – dare I say Nature? – reduced the number of
possible forms of the ß-decay interaction from more than thirty down to only two, the
208
Allan Franklin
Phys. perspect.
triplet STP and the doublet VA combinations. Then the discovery of parity nonconservation essentially required the doublet VA combination. By 1957 it seemed almost
inevitable that the theory of ß decay was a combination of the vector (V) and axial vector (A) interactions. I believe that this is only one of many examples in the history of
physics that support the rationalist position.
This was not a history of an unbroken string of successes. Early, incorrect experimental results led Konopinski and Uhlenbeck to modify the Fermi theory of ß decay
in a way that seemingly fit the experimental results better – a modification that rested
upon both incorrect experimental results and an incorrect comparison of experiment
to theory. When both were subsequently corrected, the original Fermi theory was again
supported. The triplet STP combination then was initially selected as the form of the
interaction owing to an incorrect theoretical analysis of the RaE (83Bi210) ß-particle
energy spectrum. When that error was corrected, physicists still were left with the
choice between the triplet STP and the doublet VA interactions. Rustad and Ruby’s
angular-correlation experiment on 2He6 made the situation more complex and supported the triplet STP combination until their experiment was found to be in error.
Finally, the four experimental anomalies that emerged for the V–A theory after it was
proposed were all removed by subsequent experiments, thus lending convincing support to the V–A theory. Physicists can overcome errors.
Would it have been possible for some physicist or physicists to propose an alternative explanation of ß decay? Logically, of course, the answer is yes. But, as we have
seen, theoretical principles and calculations and experimental results – Nature – introduced constrains, so that the development of the V–A theory of the weak interactions
seems to have been almost inevitable.
Acknowledgment
I thank Roger H. Stuewer for his careful and thoughtful editorial work on my paper.
His work has improved my paper considerably.
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210
Allan Franklin
Phys. perspect.
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Laws of Physics
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Sudarshan and Marshak, “Four-Fermion Interaction” (ref. 10); Feynman and Gell-Mann, “Fermi
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Sudarshan and Marshak, “Four-Fermion Interaction” (ref. 10), p. 126.
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Ibid.
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Chien-Shiung Wu and Arthur Schwarzschild, “A Critical Examination of the He6 Recoil Experiment of Rustad and Ruby” (New York: Columbia University Report, 1958).
Ibid., p. 6.
Ibid., p. 8.
W.B. Hermannsfeldt, R. L. Burman, P. Stähelin, and J.S. Allen, “Determination of the GamowTeller Beta-Decay Interaction from the Decay of Helium-6,” Phys. Rev. Lett. 1 (1958), 61–63.
Ibid., p. 62, Fig. 1 caption.
Ibid., p. 61.
Lokanathan and Steinberger, “Search” (ref. 36).
H.L. Anderson and C.M. Lattes, “Search for the Electronic Decay of the Positive Pion,” Nuovo
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Giuseppe Morpurgo, “Possible Explanation of the Decay Processes of the Pion in the Frame of the
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G. Impeduglia, R. Plano, A. Prodell, N. Samios, M. Schwartz, and J. Steinberger, “ß Decay of the
Pion,” Phys. Rev. Lett. 1 (1958), 249–251.
Ibid., p. 251.
For details, see Franklin, Experiment, Right or Wrong (ref. 8), pp. 75–96.
M. Goldhaber, L. Grodzins, and A.W. Sunyar, “Helicity of Neutrinos,” Phys. Rev. 109 (1958),
1015–1017.
Ibid., p. 1017.
E.C.G. Sudarshan and R.E. Marshak, “Origins of the Universal V–A Theory” (Blacksburg, Virginia: Virginia Polytechnic and State University Report VPE-HEP-84/8, September 16, 1985), 25
pages; quote on p. 14; reprinted in Alfred K. Mann and David B. Cline, ed., Discovery of Weak Neutral Currents: The Weak Interaction Before and After [AIP Conference Proceedings 300] (New
York: American Institute of Physics, 1994), pp. 110–123; quote on p. 118.
Department of Physics
Campus Box 390
University of Colorado
Boulder, CO 80309-0390 USA
e-mail: [email protected]