Are the Laws of Physics Inevitable?
Are the laws of nature discovered or invented? Scientists have given varying answers to this question. For Albert Einstein laws were the “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 the social constructionists, such as Harry Collins, Andrew Pickering, and others, who believe that experimental evidence plays a minimal role in the production of scientific knowledge, from the rationalists, including myself, who believe that evidence is crucial. 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 constructionists. Hacking1 illustrates this with Pickering=s account of high-energy physics during the 1970s during which the quark model came to dominate.2
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 physics would be equivalent to present physics. The physicist denies that.3 To sum up Pickering=s doctrine: there could have been a research program as successful (Aprogressive@) as that of high-energy physics in the 1970s, but with different theories, phenomenology, schematic descriptions of apparatus, and apparatus, and with a different, and progressive, series of robust fits between these ingredients. Moreover B and this is something badly in need of clarification B the Adifferent@ 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 this 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.4
Much depends here on what Hacking means by Adetermined.@ 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, 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, 1Barry 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 epistemologies that empower reality.”5
At the other extreme are the Ainevitablists,@ among whom Hacking classifies most scientists. He cites Sheldon Glashow, a Nobel Prize winner in physics, AAny intelligent alien anywhere would have come upon the same logical system as we have to explain the structure of protons and the nature of supernovae.@6 1On 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 theory of weak interactions by E.C. George Sudarshan and Robert Marshak and by Richard Feynman and Murray Gell-Mann (to be discussed in detail below); the proposal of quantum electrodynamics by Feynman, by Julian Schwinger, and by Sin-ItiroTomonaga; the proposal of quantum mechanics by Erwin Schrodinger 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 that presented 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. There are many factors which influence theory formation which, whereas they don’t entail a particular theory, 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 also build on what is already known and often use hypotheses similar to those that have previously 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 the effect, 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 β decay and the problem of determining the correct mathematical form of the weak interaction led to 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 are also several requirements that need to be satisfied in order for a theory to be considered seriously. These factors do not, of course, prevent the proposal of a totally new theory which 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. Similarly, a theory must be renormalizable, there must be a way of systematically removing infinities, for it to be a possibility as a 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. The theory was published in 1967. The number of citations 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? In that year Gerard t’Hooft showed 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 be 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.
I. The Road to the V-A Theory of Weak Interactions*8 A) Fermi’s Theory of β Decay
The above discussion has been rather abstract. To make it more concrete I will discuss, as one example, the investigation, both theoretical and experimental, of β decay** from the proposal of the first successful theory of β decay by Enrico Fermi9 to the simultaneous suggestion of the V-A theory of weak interactions by Sudarshan and Marshak10 and by Feynman and Gell-Mann11 nearly a quarter century later. The history is not one of an unbroken string of successes, but rather one which 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 conclusion.
Fermi’s theory 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 this perturbation takes the form
Hif = G [U*f Фe(r)Фν(r)] OxUi
where Ui and U*f describe the initial and final states of the nucleus, Фe and Фν are the electron and neutrino wavefunctions, respectively, G is a coupling constant, r is the position variable, and Ox is a mathematical operator.
Wolfgang Pauli12 had previously shown that Ox can take on only five forms if the Hamiltonian that describes the system is to be relativistically invariant. 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 with electromagnetic theory, and because his calculations were in agreement with experiment, he chose to use only the vector form of the interaction. It was the search for the correct mathematical form of the weak interaction that would occupy work on β decay for the next twenty five years.
To summarize the story in advance, we will find that by the early 1950s experimental results and theoretical analysis had limited the possible combinations for the form of the β-decay interaction to either some combination of S, T, and P or V and 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 Marshak13 and Feynman and Gell-Mann14 suggested that the form of the interaction was explicitly V-A. The only problem was that there were, at the 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 redone. They were. The new results supported the V-A theory, which became the Universal Fermi Interaction, applying to all weak interactions, both to β 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 would also exist.* The rate of such transitions would be greatly reduced and the shape of the energy spectrum would differ from that of the allowed transitions. Konopinski later found that the shape of the energy spectrum for allowed transitions was independent of the choice of interaction.15 Fermi also found that for allowed transitions certain selection rules would apply. These included no change in the angular momentum of the nucleus (ΔJ = 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 the work of B.W. Sargent on both the shape of the β decay energy spectrum and on decay constants and maximum electron energies.16 Sargent had found that if he plotted the logarithm of the decay constant (inversely proportional to the lifetime of the state, τo) against the logarithm of the maximum decay energy (which increases with increasing the maximum decay energy), the results for all measured decays fell into two distinct groups in which the product of the two logarithms, and thus the product of the lifetime and the energy integral, was approximately constant (Figure 1. Fermi’s theory predicted this result, namely that Fτo would be approximately constant for each type of transition, allowed, first forbidden, etc., where F is the integral of the energy spectrum and τo is the lifetime of the transition. (The two curves were associated with allowed and forbidden transitions). Thus, the Sargent curves, although not explicitly involving F and τo, argued that Fτo was approximately constant for each type of decay transition. The general shape of the observed energy spectra also agreed with Fermi’s theory.
It was quickly pointed out by Emil Konopinski and George Uhlenbeck17 that more detailed examination of the energy spectra revealed that Fermi’s theory predicted too few low-energy electrons and an average decay energy that was too high. They proposed a modification of the theory, which included the derivative of the neutrino wavefunction. Their modification gave a better fit to the observed spectra (Figure 2) and also predicted the approximate constancy of Fτo. The Konopinski-Uhlenbeck (K-U) modification was accepted as superior by the physics community. In a review article on nuclear physics, which remained a standard reference until the 1950s and was referred to as the “Bethe Bible,” Hans Bethe and Robert Bacher remarked, “We shall therefore accept the Konopinski-Uhlenbeck theory as the basis of future discussions.”18
A further modification of both Fermi’s original theory and of the Konopinski-Uhlenbeck modification was proposed by George Gamow and Edward Teller.19 They included possible effects of nuclear spin and obtained different selection rules namely ΔJ = ± 1, 0 with no 0 → 0 transitions. This required the presence of either axial vector or tensor terms in the decay interaction and was supported by a detailed analysis of the decay ThB [212Pb] → ThD [208Pb]. “We can now show that the new selection rules help us to remove the difficulties which appeared in the discussion of nuclear spins of radioactive elements using the original selection rule of Fermi(Gamow and Teller 1936, p. 897).”20
The Konopinski-Uhlenbeck theory received further support from the work of Franz Kurie and collaborators,21 who found that the spectra of 13N, 17F, 24Na, 31Si, and 32P all fit that model better than did the original Fermi theory. It was in this paper that the Kurie plot, which would prove very useful in the study of β decay, made its first appearance. The Kurie plot is a mathematical function, which differs for the Fermi and K-U theories, and is linear when plotted against the electron decay energy for whichever theory is correct.* Kurie and his collaborators plotted the function for both the Fermi and K-U theories and, as shown in Figure 3, the Konopinski-Uhlenbeck theory gave the 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 follow a straight line as they clearly do not.”22
Problems soon began to develop for the K-U theory. It was found that the maximum decay energy extrapolated from the K-U theory differed from that obtained from the measured energy spectrum and that “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.”23 This was closely related to the fact that the K-U theory required a mass for the neutrino of approximately 0.5 me, the mass of the electron, whereas the limits on the neutrino mass from nuclear reactions was about 0.1 me.
Toward the end of the 1930s experimental evidence from spectra began to favor the original Fermi theory over the K-U theory. Experiments using thinner radioactive sources favored the Fermi theory. It appeared that the decay electrons had been losing energy in leaving the source, giving rise to too many low energy electrons and too low an 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.”24
In addition, as pointed out by Lawson and Cork, “However, in all the cases so far accurately presented, experimental data for ‘forbidden’ transitions have been compared to theories for ‘allowed’ transitions. The theory for forbidden transitions has not been published .”25 Their measured spectrum of 114In, an allowed transition, for which a valid experiment-theory comparison could be made, clearly favored the Fermi theory (Figure 5). (The straight-line Kurie plot was obtained with Fermi’s theory.) Ironically, the energy spectrum for forbidden decays in the Fermi theory was calculated by Konopinski and Uhlenbeck (1941),26 and when it was the experimental results favored Fermi’s original theory. As Konopinski remarked in a review article on β decay, “Thus, the evidence of the spectra, which has previously comprised the sole support for the K-U theory, now definitely fails to support it.”27 Konopinski and Uhlenbeck applied their new theoretical results to the spectra of 32P and RaE and found that they could be fit by Fermi’s theory with either a vector or tensor interaction. They favored the tensor interaction because that gave rise to the Gamow-Teller selection rules.
One important piece of work done in the 1930s, whose importance was not realized until later, was that of Markus Fierz.28 He showed that if both the S and V terms were present in the β-decay interaction, or both the T and A terms, then there would be an interference term in the allowed energy spectrum, which vanished in the absence of such admixtures. The failure to observe such interference was cited by later writers as a major step toward deciding the form of the β-decay interaction. (See Figure 5. The graph would not be a straight line if interference terms were present.) It does not appear to have been cited at all in this period.
Thus, at the end of World War II, the situation could be summed up as follows. There was strong support for the Fermi theory of β decay, with some preference for the Gamow-Teller selection rules and the tensor interaction. The evidence from the decay energy spectra and the analysis provided by Konopinski and Uhlenbeck of the spectra of 32P and RaE along with the original analysis of the transition ThB → ThD by Gamow and Teller supported this view.
B) Toward a Universal Fermi Interaction: Muons and Pions
In 1935 Hideki Yukawa 29 hypothesized a new elementary particle, with mass intermediate between that of the electron and that of the proton, to explain the nuclear force. In the mid 1930s Carl Anderson and Seth Neddermeyer30 and Jabez Street and Edward Stevenson31 found a penetrating cosmic-ray particle with a mass approximately two hundred times that of the electron, later called the muon, which was initially identified with Yukawa’s particle. It was soon realized that the particle did not have the right properties for such an identification. Yukawa’s particle should have interacted very strongly with matter, whereas the muon penetrated considerable amounts of matter without interacting. It was then hypothesized that the muon was the decay product of Yukawa’s particle and in 1947 Cesar Lattes and collaborators32 presented evidence for the two-meson hypothesis and for the existence and decay of Yukawa’s particle (the pion) into a muon.
Even before the discovery of the pion, considerable effort had been devoted to studying the decay of the muon and its interaction with matter. Experiment showed that the muon decayed into an electron and two neutrinos (μ → e + ν + ν, or μ → e + 2ν, or μ → e + 2ν, where ν is the neutrino and ν, is its antiparticle, the antineutrino) with a lifetime of approximately 10-6s. (The pion was later shown to decay into a muon and a neutrino with a lifetime of about 10-8s.) It was also shown that the strengths of the interactions responsible for β decay, for the absorption of muons by matter, and for the decay of the muon were all approximately equal, suggesting that they might all be due to the same interaction. In a paper on the absorption of muons, J. Tiomno and John Wheeler33 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 x 10-49 erg cm3 for beta-decay and gμ ≈ 3 x 10-49 erg cm3 for the 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 processes with phenomena having a much closer relationship than we can now visualize.”34
Louis Michel35 showed that for the decay of the muon into an electron and two neutrinos the decay energy spectrum of the electron would be
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 which is a function of the particular form of the decay interaction (S, V, T, A, P), the way in which the particles are paired in the decay interaction, and on whether the two neutrinos are identical. The value of ρ did not uniquely determine the correct form of the interaction but, as discussed below, it did serve to eliminate some combinations.
There was, however, a clear-cut prediction for the decay of the pion. M. Ruderman and R. Finkelstein showed “that any theory which couples π-mesons to nucleons also predicts the π → (e, ν) decay.”36 They calculated that the ratio of the decays (π → (e, ν))/(π → (μ, ν)) was either zero, the decay was not possible, or of order unity, with the exception of the combination of a pseudoscalar pion and an axial vector decay interaction, for which the ratio would be 1.0 x 10-4. Because the electron decay of the pion had not yet been observed they concluded, “the symmetric coupling scheme is in agreement with experimental facts only if the π-meson is pseudoscalar (with either pseudoscalar or pseudovector coupling to the nucleons) and the β-decay coupling contains a pseudovector [axial vector] term.”37 During the early 1950s there were several unsuccessful searches for the electron decay of the pion. H. Friedman and James Rainwater38 (1951) showed that not more than one pion in 1400 decays into an electron, supporting the conclusion of Ruderman and Finkelstein. F.M. Smith39 set an upper limit of 0.3 ± 0.4 percent for electron decay, and S. Lokanathan and Jack Steinberger40 lowered that limit to 2 x 10-5. This was, in fact, lower than the prediction of Ruderman and Finkelstein and remained a problem for several years, and will be discussed below.
During the first half of the decade of the 1950s there were no fewer than twelve measurements of the Michel ρ parameter in muon decay. The results favored a value of ρ of approximately 0.5 or perhaps slightly larger. Theoretical analysis by Michel and Arthur Wightman,41 restricted to combinations of S, T, and P, which was then, as discussed below, the favored choice for the β-decay interaction, concluded that muon decay was consistent with such a combination.
C) Beta-Decay Theory After World War II
The search for the correct mathematical form of the decay interaction in β decay intensified after World War II. In 1943, Konopinski42 had noted that there was general support for Fermi’s theory with a preference for the tensor or axial vector interactions. By 1953, Konopinski and L.M. Langer could state, “As we shall interpret the evidence here, the correct theory must be what is known as the STP combination.”43 I will begin by discussing how they arrived at this incorrect, but plausible, conclusion.
Following the war physicists recognized the importance of Fierz’s 193744 work for clarifying the nature of the β-decay interaction. Fierz had shown that if the interaction contained both S and V terms or both A and T terms then certain interference terms would appear in allowed β-decay spectra. The Kurie plot shown in Figure 5 would not be a straight line, as it is, if such interference terms were present. This result argues against the presence of such interference terms. The presence of either the T or A terms in the β-decay interaction was further supported by M. Mayer et al.45 They used decay data from nuclei with odd mass to support their assignments of nuclear spins and parities. Based on these assignments they found twenty five decays for which ΔJ = ± 1, with no parity change. These decays required the presence of either the T or A terms. There was an element of uncertainty in this conclusion because it depended on the assignment of nuclear spins and parities which, although reliable, were somewhat uncertain. Evidence for the presence of these terms, which did not depend on a knowledge on nuclear spins, came from the examination of the energy spectra of unique forbidden transitions. These were n-times forbidden transitions for which ΔJ = n + 1. These transitions require the presence of A or T and, in addition, only a single term in the interaction makes any appreciable contribution to the decay. This allows the calculation of the spectral shape for the transition. Konopinski and Uhlenbeck46 showed that for such an n-times forbidden transition the energy spectrum would be that for an allowed transition multiplied by an energy-dependent factor that could be calculated. Figure 6 shows the Kurie plot for 91Y obtained by Langer and Price.47 It demonstrates that the correction factor provides a good fit to the spectrum, whereas the uncorrected spectrum is not a good fit, and that T or A terms must be present in the decay interaction.* The presence of either the S or V terms in the interaction was provided by the analysis of the decays of 10C and 14O by Sherr and collaborators.48
Further progress in isolating the particular form of the β-decay interaction was made by examining the spectra of once-forbidden transitions. A.M. Smith49 and D. Pursey50 showed that these spectra would contain energy-dependent interference terms, similar to those predicted for allowed spectra by Fierz, if the decay interaction included both V and T, A and P, or S and A terms. The failure to observe such terms further restricted the forms of the interaction.
We have seen that the S or V terms or the A or T terms must be included in the decay interaction. The failure to observe the Fierz interference terms restricted the choice of interaction to the triplets STP, SAP, VTP, or VAP, or doublets taken from these combinations. The absence of the interference terms in the spectra of once-forbidden transitions eliminated the VT, SA, and AP combinations. The VP and SP doublets were eliminated because they did not contain the required T or A terms and the TP doublet was eliminated because it did not contain either S or V. Thus, one was left with either the STP triplet or the VA doublet.
The decisive evidence came from a theoretical analysis of the spectrum of RaE (210Bi) by Albert Petschek and Marshak.51 Assuming that the RaE nucleus had spin = 0, and that there was both a parity change and a spin change, ΔJ = 0 or 2, in the decay, they attempted to fit the spectrum using all possible linear combinations of the five interactions, S, T, V, A, and P. They concluded that, “Within the errors noted previously, the linear combination of tensor and pseudoscalar [P] interactions… can be regarded as giving a satisfactory fit. Moreover it is the only linear combination which can explain the forbidden shape of the RaE spectrum…. Our calculation provides the first clear-cut evidence for the admixture of the pseudoscalar interaction to explain all β-ray phenomena.”52 This was the sole evidence that led Konopinski and Langer to choose the STP combination rather than the VA doublet.
Because of its importance, there was considerable theoretical discussion of the work of Petschek and Marshak. This became moot when K. Smith measured the spin of RaE directly and found a value of one.* This removed the only evidence supporting the presence of the pseudoscalar interaction in the theory of β decay. The demise of the RaE evidence removed only the necessity of including P. The STP combination remained the preference of most of the physics community because of the evidence provided angular-correlation experiments, discussed below. These experiments clearly favored S and T rather than V and A.
Angular-correlation experiments are those β-decay experiments in which both the decay electron and the recoil nucleus are detected in coincidence and their energies and decay angles measured. This allowed a calculation of the angle between the electron and the neutrino emitted in β decay. These experiments became quite important in the late 1940s. Donald Hamilton53 calculated the form of the angular distribution for both allowed and first-forbidden decays, if the decay involved only a single term. S.R. De Groot and H.A. Tolhoek54 found a more general form for the angular distribution allowing for a combination of terms in the interaction.
The most important of these angular-correlation experiments was done by Bryce Rustad and Stanley Ruby55 on the decay of 6He. Their results are shown in Figure 7. The tensor interaction is clearly favored. Further work on angular-correlation experiments in the 1950s, however, disturbed the agreeable consistency of the experimental results with the predictions of the STP interaction. Several experiments were consistent with both ST and VA. Experiments on 6He, the neutron, and 19Ne were consistent with ST, whereas experiments on 19Ne, the neutron, 15N, and 35A were consistent with VA. “It seems too early to choose between them.”56 Evidence from muon decay was consistent with ST, although no one seems to have attempted a fit to the VA combination.
D) The Discovery of Parity Nonconservation
In late 1956 and early 1957 the situation changed dramatically. Following a suggestion by Lee and Yang57 that parity conservation, or mirror symmetry, might be violated in the weak interactions, which included β decay, a series of experiments by Chien-Shiung Wu and her collaborators58, by Richard Garwin, Leon Lederman, and Marcel Weinrich59, and by Jerome Friedman and Valentine Telegdi 60 showed conclusively that this was the case. This discovery raised questions concerning the previous analyses of β decay, suggested new experiments, and pointed the way toward a new theory of β decay.
During the 1950s the physics community was faced with what was known as the “τ-θ puzzle.” On one set of accepted criteria, that of identical masses and lifetimes, the θ and τ particles appeared to be the same particle. On another set of accepted criteria, that of spin and parity, they appeared to be different. The spin and parity analysis was performed on the decay products, two pions for the θ and three pions for the τ. Parity conservation was assumed in these decays and the spin and parity of the τ and θ were inferred from the decay products. There were several attempts to solve this puzzle within the framework of currently accepted theories, but all of these 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 that the θ and τ would merely be two different decay modes of the same particle. This led them to examine the existing 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 evidence in favor of parity conservation in the weak interactions. It had never been tested.
Lee and Yang suggested several possible tests of their hypothesis. The most important of these were the β decay of oriented nuclei and the sequential decay π →μ→e. I will discuss only the former. Lee and Yang described the experiment as follows: “A relatively simple possibility is to measure the angular distribution of the electrons coming from the β decay 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 β decay.”61 This is made clear in Figure 8. Suppose the electron is always emitted in the direction opposite to the nuclear spin. In a mirror the electron momentum stays the same whereas the nuclear spin reverses so that the decay electron is now emitted along the spin direction. There is a difference between the real experimental result and its mirror image. This violates parity conservation or mirror symmetry.
This experiment was performed by C.S.Wu and her collaborators.62 It consisted of a layer of oriented, radioactive 60Co nuclei and a single electron counter, which was fixed in space, either parallel to or antiparallel to the orientation of the nuclei. The direction of the nuclear spins could be reversed and any difference in counting rate in the fixed electron counter observed. Their results are shown in Figure 9. There is a clear asymmetry. The counting rate with the electron emitted antiparallel to the nuclear spin is larger than that with the electron emitted parallel to the 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 β decay. This asymmetry has been observed in the case of oriented 60Co.”63 Two other experiments on the decay of pions and muons also clearly demonstrated parity nonconservation.64
Although this discovery complicated the previous analyses of β decay, it effected no significant change on the previous conclusions reached in the search for the correct form of the weak interaction. Even before the experimental results that demonstrated the nonconservation of parity were published, theoretical physicists attempted to incorporate that discovery into the theory of weak interactions. This was done independently by Lee and Yang65, by Lev Landau, 66 and by Abdus Salam.67 All three papers proposed a two-component theory of the neutrino. In ordinary relativistic physics the neutrino wavefunction contained four components: Two for the neutrino with spin either parallel or antiparallel to its momentum and two for an antineutrino with the same properties. In the two-component theory the neutrino had only a spin parallel to its momentum and the antineutrino antiparallel, or vice versa. This theory clearly violated parity conservation. We may see this as follows. A three-dimensional space reflection reverses each of the components of the momentum so that the momentum vector is reversed. The spin vector, however, remains unchanged. Thus, the reflected image differs from the original and parity is not conserved.
There were several important experimental implications of this new theory. It predicted both the asymmetry in the β decay of oriented nuclei and that the electron emitted in β decay would have a polarization equal to v/c, where v is the electron velocity and c is the speed of light. Perhaps most important for our discussion was the analysis of muon decay. All three papers reached the same conclusion. They considered three possibilities for muon decay:
1. μ → e + ν + ν
2. μ → e + 2ν
3. μ → e + 2ν
In case (1) the two-component theory required that the S, T, and P couplings all be equal to 0 and that the Michel parameter in the decay spectrum be ρ = 0.75. For cases (2) and (3) ρ = 0. This was inconsistent with the experimental results of C.P. Sargent et al.68 of ρ = 0.64 ± 0.10 and of A. Bonnetti et al.69 of ρ = 0.57 ± 0.14, a point noted by both Landau and by Lee and Yang.*70 Thus, by a process of elimination, the decay interaction for muons had to be a combination of the vector (V) and axial vector (A) forms. Recall that previous work had restricted the forms of the decay interaction in β decay to the STP triplet or the VA doublet.
During 1957 both parity conservation and the two-component theory of the neutrino received additional confirmation from both replications of the original parity-violating experiments and from other experiments. This made the situation with regard to a Universal Fermi Interaction that would apply to all weak interactions unclear. As Lee remarked, “Beta decay information tells us that the interaction between (p,n) and (e,ν) is scalar and tensor [based primarily on the angular correlation result of Rustad and Ruby discussed earlier], while the two-component neutrino theory plus the law of the conservation of leptons implies that the coupling between (e,ν) and (μ,ν) is vector. This means that the Universal Fermi Interaction cannot be realized in the way we have expressed it….Nevertheless, at this time it is very desirable to recheck even the old beta interactions to see whether the coupling is really scalar….”71
The situation at the end of the summer of 1957 was as follows. Parity nonconservation had been conclusively demonstrated and there was strong experimental support for the two-component theory of the neutrino. That theory plus the conservation of leptons led to the conclusion that the weak interaction responsible for the decay of the muon had to be a VA combination. Although most of the evidence from nuclear β decay was consistent with such a VA interaction, the seemingly conclusive evidence from the 6He angular correlation experiment of Rustad and Ruby gave T as the β-decay interaction. The failure to observe the electron decay of the pion also argued against a VA interaction. The situation was uncertain.
E) The V-A Theory of Weak Interactions and Its Acceptance
Despite the confusing situation noted at the end of the last section, several theorists, Sudarshan and Marshak and Feynman and Gell-Mann, proposed that a Universal Fermi Interaction (UFI), one that would apply to all weak interactions, was a linear combination of the vector (V) and axial vector (A) terms.72 Sudarshan and Marshak examined the available evidence from studies of the weak interactions and concluded that the only possible choice for a Universal Fermi Interaction was a linear combination and V and A, even though there was evidence apparently in conflict with this choice. The four experiments they cited in opposition to the V-A theory were
1. The electron-neutrino angular-correlation experiment on 6He performed by Rustad and Ruby.
2. The frequency of the electron mode in pion decay.
3. The sign of the electron polarization in muon decay.
4. The asymmetry in polarized neutron decay, which was smaller than predicted.
The first two were regarded as more significant problems. The latter two had less evidential weight and later experiments removed the difficulty. 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.”73 They also pointed out that the 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 allowed a similar treatment of pions and kaons and had the added feature that the neutrino emitted in all β decays had the same handedness, or helicity, which was not true for either the VT or SA combinations. This theoretical elegance was also emphasized by Feynman and Gell-Mann . “It is amusing to note that this interaction satisfies simultaneously almost all of the principles that have been proposed on simple theoretical grounds to limit the possible β couplings. It is universal, it is symmetric, it produces two-component neutrinos [and thus violates parity conservation], it conserves invariance under CP [combined particle-antipartcle and space-reflection symmetry] and T [time reversal symmetry]….”74 These theoretical arguments led Feynman and Gell-Mann to an even stronger statement concerning the experimental anomalies. “These theoretical arguments seem to the authors to be strong enough to suggest that the disagreement with the 6He recoil experiment and with some other less accurate experiments indicate that these experiments are wrong [emphasis added]. The π → e + ν may have a more subtle solution.”75
Note here the importance of the theoretical principles discussed at the beginning of the paper. Both sets of theorists were willing to question seemingly well-done experiments on the basis of a theory that satisfied those principles. This is not to say that evidential considerations were absent. As Feynman and Gell-Mann noted, “After all the theory also has had a number of successes. It yields the rate of μ decay to 2% and the asymmetry in the π → μ → e decay chain. For β decay, it agrees with the recoil experiments in 35A indicating a vector coupling, the absence of Fierz interference terms distorting the allowed spectra, and the more recent electron spin polarization measurements in β decay.”76 Nevertheless, the attractive theoretical features of the theory were important in both its suggestion and reception.
1) The angular correlation in 6He
Perhaps the most important piece of evidence favoring the tensor (T) interaction and arguing against the V-A theory was the angular-correlation experiment on 6He done by Rustad and Ruby.77 As we see in Figure 7, the results of that experiment clearly favored the tensor interaction. Following the suggestion of the V-A theory both Wu and Schwarzschild78 and Rustad and Ruby, themselves, began critical reexaminations of the Rustad-Ruby experiment.
One of the important factors in the calculation of the Rustad-Ruby result was the assumption that all of the 6He decays came from the source volume (Figure 10). If, however, there had been a significant amount of gas present in the collimating chimney below the source volume then both their measured angular correlation and their conclusion of tensor dominance might have had to be modified. The argument offered by Wu and Schwarzschild was as follows. First, the efficiency of the β counter, the β scintillation spectromenter in the upper portion of Figure 10, changes considerably with the angle between the counter and the recoil detector, the recoil ion multiplier shown in the lower portion of Figure 10. In addition, depending on the decay angle, the amount of material through which the decay electron passes is quite different. These two effects create a considerable change in the electron detection efficiency. Wu and Schwarzschild performed an approximate calculation of this effect and found that the gas pressure at the lower end of the first diaphragm had to be greater that 12 percent of that in the source volume. A better estimate was obtained by constructing a physical analogue of the gas system. Because the gas pressure in the system was so low, one could neglect collisions between the molecules and consider only reflections from the walls in estimating the gas pressure gradient. This is similar to optical diffusion from a perfectly reflecting surface. Wu and Schwarzschild constructed a scale model ten times larger than the actual Rustad-Ruby apparatus. They made the inner walls of both the source volume and the collimating chimney of the model highly reflecting. They placed a diffuse light source in the arm of the source volume to simulate the entering gas and then measured the light intensity at various parts of the model as an indication of the gas pressure. They combined this with the calculation of the solid angle of the detector and concluded that, “the decay due to 6He gas in the chimney is not insignificant in the correlation results.”79 They combined this with estimates of energy loss and backscattering of the electrons from decays in the chimney and although a precise calculation was “obviously impossible” they found that the corrected results “are more in favor of axial vector than tensor contradictory to the original conclusion.” This work cast doubt on the original Rustad-Ruby conclusion. In a postdeadline paper presented at the January 1958 meeting of the American Physical Society, Rustad and Ruby agreed.*
The 6He angular correlation experiment was redone by James Allen and his collaborators.80 Figure 11 shows their “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.”81 “the angular correlation coefficient λ should be either +1/3 or -1/3 corresponding, respectively, to the tensor or axial vector interaction. Our experimental result, λ = - 0.39 ± 0.02, clearly indicates that the axial vector interaction is dominant.”82 One of the anomalies for the V-A theory was gone.
2) The electron decay of the pion
We recall that in 1949 Ruderman and Finkelstein had calculated that the ratio of π→e/π→μ decays was approximately 10-4 assuming that the decay interaction was axial vector. However, as noted by both Sudarshan and Marshak and by Feynman and Gell-Mann, the best measurements of that ratio were too low. S. Lokanathan and Jack Steinberger83 had found the ratio to be (-0.3 ± 0.9) x 10-4, with an upper limit of 0.6 x 10-4. Herbert Anderson and Cesar Lattes84 found no evidence at all for the electron decay of the pion. Their value for the ratio of electron to muon decays was (-0.4 ± 9.0) x 10-6 , with a probability of one percent that the value would be greater than 2.1 x 10-5. This was clearly lower than the V-A prediction.
There were various unsuccessful theoretical attempts to explain the absence of the electron decay.85 These speculations became moot when Steinberger and his collaborators86 found convincing evidence for the electron decay of the pion. Using a hydrogen bubble chamber they found six clear (emphasis in original) examples of the π→e decay. The pions were stopped in the hydrogen and the experimenters searched for events in which the stopped pion emitted a minimum ionizing track, presumably an electron, with no visible intermediate muon track. Figure 12 shows examples of both types of event. 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. The experimenters also measured the momentum of the decay particle. Although most of the events initially selected were examples of π→μ→e decay with a very short muon track, the electron decays could be separated from these using a momentum criterion. The maximum momentum for an electron from π→μ→e decay is 52.9 MeV/c, if both the pion and the muon decay at rest. For an electron from π→e decay the unique momentum is 69.8 MeV/c, which was the momentum observed for the putative π→e events. The experimenters fit the electron energy spectrum for events with no visible muon track using Michel’s calculation of the μ→e decay spectrum. They obtained a good fit to the spectrum and they found that there would be no events expected in the region near 70 MeV/c. As a check, the experimenters measured the momentum spectrum for electrons from the 2983 events with a muon track. No events were found above 62 MeV/c, indicating that μ→e contamination in the high-momentum region and decays in flight were negligible. They set an upper limit of 1/10800 ± 40 percent for the electron decay of the pion. This was to be compared with the V-A prediction of 1/8000. They concluded, “The method does not yield a precise measurement of the branching ratio and cannot reasonably be extended to do so. However, the results here offer a very convincing proof of the existence of this decay mode, and show that the relative rate is close to that expected theoretically.”87 The second anomaly had been resolved.
During this same period of time the other two, less significant problems for the V-A theory; the asymmetry in the decay of polarized neutrons and the polarization of the electron in muon decay were also resolved.88 Even before the resolution of all the anomalies the V-A theory had received strong support when Maurice Goldhaber et al.89 measured the helicity (whether the spin of the neutrino was parallel or antiparallel to its momentum) of the neutrino emitted in β decay. They concluded that, “our result indicates that the Gamow-Teller interaction is axial vector for positron emitters.”90
By early 1959 all of the experimental evidence from weak interactions — nuclear beta decay, muon decay, pion decay, and electron capture —was in agreement with the V-A theory. As Sudarshan and Marshak later remarked, “And so it came to pass – only three years after parity violation in weak interactions was hypothesized — that the pieces fell into place and 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.”91
The history of the development and articulation of the theory of β 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 inevitability. It is, I believe, only one of many examples that can be found in the history of physics that support the rationalist position. Beginning with Pauli’s proof that there were only five relativistically invariant forms of four-Fermion interactions to the discussion of the theoretical attractiveness of the V-A theory by Sudarshan and Marshak and by Feynman and Gell-Mann, we have seen the importance of theoretical principles that constrain the types of theories offered. We have also seen how both theoretical calculation and experimental results, dare one say Nature, reduced the number of possible forms from more than 30 down to two, STP or VA. The discovery of parity nonconservation then essentially required the VA combination. By 1957 it seemed almost inevitable that the theory of β decay was a combination of the vector and axial vector interactions.
This was not a history that contained an unbroken string of successes. Early, incorrect experimental results led to the Konopinski-Uhlenbeck modification of the Fermi theory and also made it seem to be a better fit to the results. That choice involved both incorrect experimental results and an incorrect experiment-theory comparison. When both were corrected the Fermi theory was supported. The STP triplet was initially selected because of an incorrect theoretical analysis of the RaE energy spectrum. When that error was corrected one was still left with the choice between the STP and VA interactions. The incorrect angular-correlation experiment on 6He by Rustad and Ruby made the situation more complex and supported STP until the error in that experiment was found. Finally the four experiments that were anomalous for the V-A theory when it was first proposed were all redone and the later results supported the V-A theory. Physicists can overcome errors.
Would it have been possible for a physicist to propose an alternative explanation of β decay? Logically, of course, the answer is yes. But, as we have seen, Nature and theoretical principles constrained things so that the V-A theory seems almost inevitable.
Figure 1. The logarithm of the decay constant (inversely proportional to the lifetime of the transition, τ0) plotted against the logarithm of the maximum decay energy. The integral of the energy spectrum F depends monotonically on the maximum decay energy. Thus if Fτ0 is a constant for each type of decay (allowed or first forbidden) as predicted by Fermi’s theory then the graph should show two groups, as is indeed shown in the figure. The two groups are allowed and first-forbidden transitions. From Sargent, “Maximum Energy” ( ref. 16).
Figure 2 Energy spectrum of RaE. P(W) is the probability of emission of an electron with energy W (the number of electrons) and W is the energy of the electron. S is the statistical factor, FS is the Fermi theory prediction, and Modified Theory is the prediction of the Konopinski-Uhlenbeck modification. EXP is the experimental result of Sargent “Maximum Energy,” ref. 16. One can see that the Konopinski- Uhlenbeck theory is a better fit to the result than is Fermi’s theory. From Konopinski and Uhlenbeck, “Fermi Theory” ( ref.17).
Figure 3. The Kurie plot for electrons from phosphorus. The left axis is the fourth root of N/f, the number of electrons divided by the Coulomb factor for the decay. If the Konopinski-Uhlenbeck theory is correct then this quantity plotted as a function of the decay energy (E + 1, is the decay energy plus the mass of the electon in units of mec2) should be a straight line. The right axis is the square root of N/f, and should be a straight line when plotted as a function of energy if the Fermi theory is correct. The “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 follow a straight line as they clearly do not.” From Kurie et al., “Radiations” (ref. 21).
Figure 4. Kurie plots for electrons from a thin source of phosphorus for both the Fermi and K-U theories. The better theory, clearly Fermi’s, is the one that gives the better fit to a straight line. Compare with Figure 3. From J.L. Lawson, "The Beta-Ray Spectra of Phosphorus, Sodium, and Cobalt," Physical Review