The inability, in the 1950s and 1960s, of traditional quantum field theory to provide a basis for reliable calculations in strong-interaction physics led to quite diverse theoretical responses, just as had the previous divergence problems for QFT in the 1930s. We have already discussed dispersion relations and the mass-shell field theory programs. Another attempt has been the axiomatic field theory approach begun by Arthur Wightman at Princeton. Freeman Dyson has recently even made the claim:

Wightman (1989) has written an historical outline of this program and a thorough discussion of it would require an entire, highly technical case study of its own. That particular axiomatic approach has not had a strong impact on high-energy theory and we shall not discuss it further. We mention it just as an example of one reaction to the impasse encountered by standard Lagrangian quantum field theory. Our story is of another reaction, the S-matrix program. In this chapter we examine the autonomous S-matrix program some envisaged once Chew had made a radical break with quantum field theory.

Landau had argued that the only directly observable variables were those associated with essentially asymptotically free particles (before or after a scattering process), such as their initial or final momenta.

In recent years there has been a move to ‘naturalize’ the philosophy of science. This has meant basing work in the philosophy of science upon the actual historical record of real scientific practice and stressing (in varying degrees) the use of the methods of science in studying the scientific enterprise. This attention to actual scientific practice has been supported by traditional realists, an example being Ernan McMullin (1984) who early on (1976a) argued for a central role for the history of science in the philosophy of science; by philosophers of various anti-theoretical bents, such as Nancy Cartwright (1983) and Ian Hacking (1983); and by empiricists, like Bas van Fraassen (1980, 1985). In the early 1960s, it was attention to the historical record that led Thomas Kuhn (1970), in his The Structure of Scientific Revolutions, to stress the importance of social factors in the practice of real science. The spirit of the present work is that careful and detailed study must be made of the actual development of science before conclusions are drawn about the appropriateness of any particular methodology of science. Ours is mainly a story about theory, but not one uncoupled from its relation to experiment.

We claim that many of the philosophically interesting questions in science, especially in regard to possible changes in the methodology and goals of science, can be seen and appreciated only upon examination of the technical details of that practice.

Particularly important sources for this and subsequent chapters are correspondence with Professor Chew and Chew's own recent recollections (Chew, 1989), as well as the Festschrift for him (De Tar, Finkelstein and Tan, 1985), especially the interview it contains with Chew (Capra, 1985). Let us give an overview of the next few chapters. Geoffrey Chew is a central figure in this chapter because he was extremely important for the early development of this program and because he provides an example of how one person came to propose a radically new theoretical approach.

As we stated previously in Chapter 2, Chew at Chicago became aware of Heisenberg's S-matrix proposal from some lectures given by Wentzel (cf. Wentzel's (1947) review article). However, Heisenberg's ideas seem to have played no direct role in Chew's work leading to the modern S-matrix program. (Only around 1960 did Chew appreciate that he was working with what was essentially Heisenberg's S-matrix.) His publications from the late 1940s to the 1960s can be grouped into three fairly distinct phases:

1. a. 1948–1952: analysis of hadron scattering data within the framework of potential theory. Chew became an expert in that business.

2. b. 1953–1955: field-theory calculations, to various orders or in certain approximations, again for hadron processes.

3. c. 1956–1960: his work with Low, Mandelstam and Frautschi. This marked a transition to problems of greater scope and foundational importance.

All of this theoretical work received major impetus from the rapidly expanding data base provided by the large and active high-energy experimental programs existing after World War II.

A major, overarching cluster of problems central to the philosophy of science and certainly underlying much of the debate in the recent literature is how scientific theories are constructed, how they are judged or selected, and what type of knowledge they give us. There are two aspects of answers to any of these three questions: what has actually occurred according to the historical record and what is the rational status of each of these activities or of the knowledge produced. A simple schema, that is based on induction and the hypothetical-deductive method and that provides answers to the above queries, is the sequence: observation, hypothesis, prediction, confirmation. This model or picture of science has a long tradition. We can see its roots already in Bacon's (1620 (1960, pp. 43–4 and 98-100)) advocating a slow and careful ascent from particulars to generalities (Aphorisms, Bk. I, XIV, XXII, CIII–CVII). He urged use of a combination of induction and deduction in arriving at knowledge. In Bacon's ladder of axiom, one is to make modest generalizations based on specific observations and data, check these modest theories by comparing their predictions with facts once again, then combine these generalizations into more general ones, check their predictions against observations, and in this way carefully proceed to the most general axioms, theories or laws. Whewell (1857, Vol. I, p. 146) speaks of the epochs of induction, development, verification, application and extension.

There exist some excellent technical reviews of relativistic dispersion relations (Goldberger, 1960, 1961; Jackson, 1961), as well as Goldberger's (1970) own informal recollections of the period from about 1954–69. In addition, Cini (1980) and Pickering (1989a) have written about some of the sociological influences on that program. We shall comment on these later in this chapter and in the concluding chapter. However, let us begin with a few general observations about the mood of theoretical physics in the United States just after the Second World War, at least in one Physics Department, namely the University of Chicago. This is relevant for what follows, since that Department became a center of activity for the dispersion theory program. Wentzel and Fermi were on the faculty then and Goldberger and Chew were graduate students there. One frequent attendee at the theory seminars at Chicago during those years recalls that at that time (around 1948) the general spirit of many of the younger, exceptionally gifted theorists was that physics was something to do (never mind studying the works of the great masters) and that nothing significant had been done (in their areas of interest) prior to this. In fact, many other people had worked on these problems (e.g., fixed-source field theory) before, but there was little sense of history among the younger generation. Wentzel's comments (say, from the audience at a talk) on the previous literature were typically received with impatience.

For those who view the S-matrix program as being independent of (and perhaps even opposed to) field theory, we have now arrived at what they might take to be the beginning of the S-matrix program. However, considering the field theory roots of nearly all the successful applications of the dispersion-theory and analytic S-matrix program, as well as the failure to date of the more revisionary form of S-matrix theory to attain a coherent abstract formulation and a large base of empirical confirmation, we do not use the term ‘S-matrix program’ as anything necessarily antithetical to field theory. Both field theory and S-matrix theory have been enormously fruitful, often in different areas, and we can consider them as complementary approaches. We shall see, though, that the developments of this chapter did lead to a proposal for a completely independent S-matrix theory, one that has not been refuted. That autonomous S-matrix program is the subject of the next chapter.

In this chapter we focus on the bootstrap, both its origin and some details of its applications. Pomeranchuk had given various arguments – some based on a simple physical model of scattering processes, others based on apparently reasonable asymptotic properties of an analytic scattering amplitude – that led to certain expectations about the asymptotic behavior of total cross sections and about relations among total cross sections for different processes. In particular, there were what appeared to be reasonably convincing theoretical arguments for the belief that total cross sections should approach constant values at high energy (as opposed to vanishing or continuing to increase indefinitely).

In order to be able to illustrate the central concepts in subsequent developments in the main body of this case study, we establish a certain technical background against which we can discuss the origins of Wheeler's and of Heisenberg's scattering matrix. This outline will provide a brief and selective summary of nonrelativistic Schrödinger scattering theory, classical electromagnetic wave theory and the theory of the interaction of a quantized atomic system with the radiation field. The material presented here I take to be given and unproblematic by the mid to late 1930s. As a justification for this assumption let me point out that the essentials of all these topics can be found in the 1933 edition of Mott and Massey's The Theory of Atomic Collisions, in the 1933 edition of Slater and Frank's Introduction to Theoretical Physics and in the 1936 edition of Heitler's The Quantum Theory of Radiation. These were all standard reference works at the time so that their contents can be assumed to have been known to practicing theoretical physicists of that era. The order of presentation here is not necessarily the historical one and very few specific references will be given for this background material. Also, a unified notation and a fairly modern presentation will be used to facilitate reading and subsequent reference for illustrations. The technical details given for this introductory background will be more complete than for most of the historical presentation in the main body of the text.

A common perception of Heisenberg's S-matrix program of the 1940s is that it encountered difficulties quite early on and then quickly died out. One can easily get the impression that the original Heisenberg program was irrelevant for the theoretical developments that provided the background out of which the dispersion-theory and later S-matrix theory program emerged. In this chapter we wish to show that Heisenberg's original program posed a set of questions the criticism of and response to which led to the dispersion-theory program of Goldenberger and Gell-Mann. It is not our purpose to review all of the elementary particle physics of the 1950s, or even all of what today, in retrospect, is judged to have been the ‘best’ or most important physics of that period.

In correspondence or in direct conversations, Geoffrey Chew, Marvin Goldberger, and Murray Gell-Mann all recall that Heisenberg's old S-matrix program had essentially no direct influence on their own work which led to the dispersion-theory and S-matrix theory programs of the late 1950s and of the 1960s. All had known of Heisenberg's general ideas from some lectures given at the University of Chicago by Gregor Wentzel or possibly from reading Heisenberg's papers. It was only later that they became aware of any relevance of their work to Heisenberg's S-matrix program.

We begin by reviewing Heisenberg's program (Cushing, 1982,1986a; Grythe, 1982; Oehme, 1989; Rechenberg, 1989) and the considerable theoretical activity related to it during the period from the mid-1940s to the early 1950s.

In this chapter we examine the origins of a program that emerged from the S-matrix formalism but that soon took on a quite independent existence. Its greatest interest for present high-energy physics is that it led to superstring theories. This evolution is also of interest methodologically, as an example of an abandoned research program giving rise to a possibly ‘correct’ theory that might otherwise never have been formulated.

The concept of duality was an outgrowth of the Regge program. The simple Regge-pole form for the scattering amplitude arises from the exchange (in the crossed channel) of a Regge pole and is valid at high energy. When that form is extended (or extrapolated) to low energies, it gives the same result as the average value of an amplitude generated by the exchange of resonances in the direct channel (see the ‘pictoral’ representation of Eq. (8.1) below). More specifically, when sum rules (an example of which we have seen in Eq. (6.31)) that are integrals over differences of total cross sections are evaluated once numerically using experimental data and once ‘theoretically’ using the simple Regge form (at all energies), the results agree. This type of equivalence between direct-channel resonance and crossed-channel Regge exchange became known as duality and was a self-consistency form of the bootstrap. Veneziano offered a specific and simple analytical model that provided a concrete instantiation of the duality conjecture. This example was important both for subsequent theoretical progress and for immediate phenomenological applications.

Collaborations 1893-1894

Hurter did, in fact, accept the Presidency, when Lodge formally resigned at the meeting of 23 October; Lodge was elected one of the Vice-Presidents. Five more resignations of members were accepted at this meeting and sixteen members (including George Tate) were recorded as being in two seasons' arrears with their subscriptions. “The Secretary read a list of members who had sent in resignations, and another of persons whose Annual Subscriptions were two Sessions in arrears.

“It was resolved that these names be removed from the list of members. The list, after this revision, contained 55 names.” 40 members and friends were present.

Hurter drew on his background in the chemical industry in giving his Presidential address on “Electrolysis”, paying special attention to the conversion of brine into caustic soda, a problem of great commercial importance in a region where salt supplies were plentiful and caustic soda a product in great demand. He first discussed Faraday's law, and its applications in cases of electrolytes giving rise to secondary reactions, before progressing on to the migration of ions, with special attention paid to the electrolysis of common salt. Here he showed the efficiency to be expected in the electrolytic conversion of brine into caustic soda. Lodge noted how Hurter, in such investigations, “earnestly strove to realise with his mind's eye the inner workings of things beyond even the aided organs of sense” and endeavoured “to picture to himself as clearly as possible what it was that was really happening in the molecular domain”.