Current algebra, as a hypothesis about hadron physics, offers a set of algebraic relations relating one physically measurable quantity to another, although it cannot be used to calculate any from first principles. Presumably, the assumed validity of a hypothesis should first be tested before it can be accepted and used for further explorations. However, any exploration of the implications or applications of the hypothesis, within the general framework of hypothetic-deductive methodology, if its results can be checked with experiments, functions as a test.

The test of current algebra, however, requires delicate analyses of hadronic processes and effective techniques for identifying relevant measurable quantities in a justifiable way. For this reason, there was no rapid progress in current algebra until Sergio Fubini and Giuseppe Furlan (1965) suggested certain techniques that can be used, beyond its initial applications, to derive various sum rules from current algebra, which can be compared with experimental data. The importance of the sum rules thus derived, however, goes beyond testing the current algebra hypothesis. In fact, they had provided the first conceptual means for probing the constitution and internal structure of hadrons, and thus had created a new situation in hadron physics and opened a new direction for the hadron physics community to move, as we shall see in the ensuing sections and chapters.

In the 1950s, all hadrons, namely particles that are involved in strong interactions, including the proton and neutron (or nucleons) and other baryons, together with pions and kaons and other mesons, were regarded as elementary particles. Attempts were made to take some particles, such as the proton, neutron and lambda particle, as more fundamental than others, so that all other hadrons could be derived from the fundamental ones (Fermi and Yang, 1949; Sakata, 1956). But the prevailing understanding was that all elementary particles were equally elementary, none was more fundamental than others. This general consensus was summarized in the notion of “nuclear democracy” or “hadronic egalitarianism” (Chew and Frautschi, 1961a, b; Gell-Mann, 1987).

As to the dynamics that governs hadrons' behavior in the processes of strong interactions, early attempts to model on the successful theory of quantum electrodynamics (or QED, a special version of quantum field theory, or QFT, in the case of electromagnetism), namely the meson theory, failed, and failed without redemption (cf. Cao, 1997, Section 8.2). More general oppositions to the use of QFT for understanding strong interactions were raised by Landau and his collaborators, on the basis of serious dynamical considerations (Landau, Abrikosov, and Khalatnikov, 1954a, b, c, d; Landau, 1955). The resulting situation since the mid 1950s was characterized by a general retreat from fundamental investigations to phenomenological ones in hadron physics.

The underlying idea of current algebra, light-cone current algebra included, was to exploit the broken symmetry of strong interactions. The idea was pursued through abstracting physical predictions, as the consequences of the symmetry and in the form of certain algebraic relations obeyed by weak and electromagnetic currents of hadrons to all orders in strong interactions, from some underlying mathematical field theoretical models of hadrons and their interactions, more specifically from models of quark fields universally coupled to a neutral gluon field.

When current algebra was initially proposed, the symmetry was defined with respect to static properties of hadrons, such as mass, spin, charge, isospin, and strangeness. However, over the years, especially after the confirmation of scaling, in the changed theoretical and experimental context, the notion of symmetry underlying the current algebra project had undergone a transmutation. A new component of symmetry, that is, a dynamic symmetry, was brought into the scheme. The result was not only some adaptations in algebraic relations and corresponding physical predictions, but also a radical change in the nature of the underlying field theoretical model. More precisely, the result was the emergence of a gauge invariant quark–gluon model for strong interactions, or the genesis of quantum chromodynamics (QCD).

Murray Gell-Mann's proposal of current algebra in 1962 (Gell-Mann,1962) was an important step in the conceptual development of particle physics. In terms of insights, imagination, and consequences, this strategic move ranks among the highest scientific creativity in the history of fundamental physics. When the proposal first appeared, however, because of its mathematical complication and conceptual sophistication, it was perceived by most particle physicists to be too esoteric to understand or see its relevance and applicability. Even today, more than four decades later, with the advantage of hindsight, it remains difficult to properly assess its role in the history and understand why and how it played the role it did.

The difficulty lies not so much in Gell-Mann's idiosyncratic ingenuity but in, first, the puzzling situation of particle physics to which Gell-Mann's proposal was a response, and, second, in the bewildering trajectory of the subsequent development, which was shaped mainly by the competition between various speculative ideas and, ultimately, by the interplays between experiments and theorizing. The aim of this chapter is to address the first aspect of the difficulty, postponing the second to subsequent chapters.

Context

When Gell-Mann proposed his current algebra to deal with hadron physics, there was no accepted theory of strong interactions. Worse, there was no theory of how hadrons interacted with each other at all.

Writing a conceptual history of QCD is exciting. The materials of the project are not natural phenomena of nuclear forces, which are inherently meaningless occurrences; not quasi-independent abstract ideas, whose causal effectiveness in moving history forward only idealist historians would believe; but human activities, in which meaning was radically changing with the change of perspective, and whose long-term significance for physics, metaphysics, and culture in general is to be discerned and interpreted by historians of science.

Historians' interpretations, however, are conditioned and constrained by the wide cultural milieu. Broadly speaking, at the center of contemporary cultural debate on issues related to science, such as objectivity and progress in science or the nature of scientific knowledge and its historical changes, sit two closely related questions. First, can science provide us with objective knowledge of the world? Second, is the evolution of science progressive in nature in the sense that it involves the accumulation of objective knowledge? The old wisdom that science aims at discovering truths is seriously challenged by such prominent commentators as Richard Lewontin and Arthur Fine. According to Lewontin (1998), taking science as a reality-driven enterprise has missed the essential point of science as a social activity, namely, its ambiguity and complexity caused by the socio-historical setting that has put severe constraints on the thought and action of scientists. In his Presidential Address at the Central Division of the American Philosophical Association, Fine (1998) has skillfully dissolved the notion of objectivity and reduced it to a democratic procedure, which may contribute to enhance our trust in the product of scientific endeavor, but has nothing to do with the objective knowledge the product may provide.

This volume is the first part of a large project which has its origin in conversations with Cecilia Jarlskog and Anders Barany in December 1999, in which the difficulties and confusions in understanding various issues related to the discovery of QCD were highly appreciated.

While the forthcoming part will be a comprehensive historical study of the evolution of various conceptions about the strong interactions from the late 1940s to the late 1970s, covering the meson theory, Pauli's non-abelian gauge theory, S-matrix theory (from dispersion relation, Regge trajectories to bootstrap program), current algebra, dual resonance model and string theory for the strong interactions, QCD, lattice gauge theory, and also briefly the supersymmetry approach, the D-brane approach, and the string–gauge theory duality approach, titled The Making of QCD, this volume is a brief treatment, from a structural realist perspective, of the conceptual development from 1962 to 1972, covering the major advances in the current algebraic approach to QCD, and philosophical analysis of the historical movement.

The division of labor between the two parts of the project is as follows. This volume is more philosophically oriented and deals mainly with those conceptual developments within the scope of current algebra and QCD that are philosophically interesting from the perspective of structural realism; while the whole history and all the historical complexity in the making of QCD will be properly dealt with in the longer historical treatise. They will be mutually supportive but have minimal overlap and no repetition.

The notion of scaling conceived and proposed by Bjorken in 1968 played a decisive role in the conceptual development of particle physics. It was a bridge leading from the hypothetical scheme of current algebra and its sum rules to predicted and observable structural patterns of behavior in deep inelastic lepton–nucleon scattering. Both its underlying assumptions and subsequent interpretations had directly pointed to the notion of constituents of hadrons, and its experimental verifications had posed strong constraints on the construction of theories about the constituents of hadrons and their interactions.

The practical need for analyzing deep inelastic scatterings planned and performed at SLAC in the mid to late 1960s had provided Bjorken the general context and major motivation to focus on the deep inelastic kinematic region in his constructive approach to the saturation of sum rules derived from local current algebra. The deep inelastic experiments themselves, however, were not designed to test Bjorken's scaling hypothesis. Rather, the experimenters, when designing and performing their experiments, were ignorant, if not completely unaware, of the esoteric current algebra and all those concepts and issues related with it. They had their own agenda. This being said, the fact remains that the important implications of their experiments would not be properly understood and appreciated without being interpreted in terms of scaling and subsequent theoretical developments triggered by it.

The experimental confirmation of the approximate scaling from SLAC stimulated intensive theoretical activities for conceptualizing the observed short-distance behavior of hadron currents and for developing a self-consistent theory of strong interactions, starting from and constrained by the observed scaling. At first, the most prominent among these efforts was the parton model that was originated from Bjorken's thinking on deep inelastic scattering and Feynman's speculations on hadron–hadron collision, and made popular by Feynman's influential advocacy.

The assumption adopted by the parton model that the short-distance behavior of hadron currents should be described by free field theory, however, was immediately challenged once the scaling results were published. The theoretical framework the challengers used was the renormalized perturbation theory. Detailed studies of renormalization effects on the behavior of currents, by Adler and many others, reinforced the conviction about the limitations of formal manipulations in the PCAC and current algebra reasoning, which made these physical effects theoretically invisible, and discovered, first, the chiral anomaly and, then, the logarithmic violation of scaling. The theoretically rigorous argument for scaling violation was soon to be incorporated into the notion of broken scale invariance by Kenneth G. Wilson, Curtis Callan, and others, which was taken to be the foundation of such approaches as Wilson's operator product expansion and Callan's scaling law version of the renormalization group equation for conceptualizing the short-distance behavior of hadron currents, for giving a more detailed picture of these behaviors than current algebra could offer, and even for a general theory of strong interactions.

Gell-Mann's idea of current algebra as a physical hypothesis was rendered testable by Adler's sum rules. The success of the Adler–Weisberger zero momentum transfer sum rule testing the integrated algebra gave credit to Gell-Mann's general idea. But what about Adler's nonzero momentum transfer sum rules testing local current algebra? When Bjorken raised the issue of how the nonzero momentum transfer sum rule might be satisfied to Adler, at the Varenna summer school in July 1967 when both Adler and Bjorken were lecturers there, it seemed to be a very serious problem to Adler, since all the conceptual development up till then left undetermined the mechanism by which the nonforward neutrino sum rules could be saturated at large q2. After the Solvay meeting in October, 1967, Adler discussed this issue with his mentor Sam Treiman, and “then put the saturation issue aside, both because of the press of other projects and concerns, and a feeling that both shared that how the sum rule might be saturated ‘would be settled by experiment’ ” (Adler, 2003, 2009, private communications).

The response by Adler and Treiman to Bjorken's question seemed to be natural. How could anything else but experiments be the ultimate arbitrator for a physical hypothesis? However, as we will show, solely relying on experiments missed an opportunity to use the exploration of mechanisms for saturating the sum rule as a way to go beyond the conservative philosophy of the current algebra program, which was to abstract from field theory relations that might hold in general field theories, rather than searching for particular attractive field theory models that might underlie the general relations.

The importance of underlying fundamental entities in theoretical sciences, which in most cases are hypothetical, unobservable, or even speculative in nature, such as quarks and gluons in QCD, from the realist perspective, and also from the hypothetic-deductive methodology, is clear and understandable. It has deep roots in human desire for explanation. However, it might be argued that the stress on the importance of underlying entities, which ground a reductive analysis of science, is in direct opposition to the holistic stance of structuralism. According to this stance, the empirical content of a scientific theory lies in the global correspondence between the theory and the phenomena in the domain under investigations at the structural level, which is cashed out with mathematical structures without any reference to the nature of the phenomena, either in terms of their intrinsic properties, or in terms of the underlying unobservable entities. Thus for structuralists no ontological interpretation of structure would be possible or even desirable. A structuralist, such as Bas van Fraassen (1997), would argue that if you insist to interpret the mathematical structure anyway, then different ontological interpretations would make no difference to science. That is, no ontological interpretation should be taken seriously.