The Exigencies of War and the Stink of a Theoretical Problem: Understanding the Genesis of Feynman's Quantum Electrodynamics as Mechanistic Modelling at Different Levels

1. A Question of Style

In 1949, Richard Feynman (1918–1988) published the essentials of his solution to the recalcitrant problems that plagued quantum theories of electrodynamics of his days (Feynman 1949a). The main problem was that the theory, that was considered to be correct and often led to correct observable consequences, also implied that some quantities should be infinite, while by common sense or empirical evidence they were finite. Feynman devised a method of solving the relevant theoretical equations in which particular combinations of elementary solutions yielded empirically adequate results even when applied to complex problems. The combination of the basic solutions was guided by relatively simple graphical considerations as to how the elements that represented elementary interactions of electrons and light quanta could be put together to form a complex diagram.

Much of Feynman's method relied on a diagrammatic representation of the physical processes as well as, at the same time, of the mathematical expressions used to describe the processes quantitatively. Ever since their first appearance, these Feynman diagrams (Figure 1), as they came to be known, have been extensively used in theoretical particle physics to calculate reaction rates and other observable, or otherwise relevant, quantities. After making their initial "leap" out of Feynman's head about the year 1948 they took the world in a rapid "dispersion" and were put to a wide variety of uses (Kaiser 2005).

It has been widely acknowledged that Feynman's approach to the difficulties in finding a quantum theory of electrodynamics was idiosyncratic, although it may be hard to say what the characteristics of his style exactly were (see, e.g., Schweber 1986a). A conspicuous feature of his approach certainly was his prominent use of diagrams in his publications on the topic and the way he used them in a peculiar mix of diagrammatic, physical, and mathematical reasoning.

Figure 1.

Feynman's first published "Feynman diagram" (Feynman 1949a, p.772)

One goal of the present article is to identify characteristic aspects of the way in which Feynman was developing his version of quantum electrodynamics (QED) at different stages of his early career (i.e., up to 1949). But I will also discuss the question of which circumstances or events might have been responsible for Feynman's exhibiting different characteristic methods at different times. Finally, I will contrast my findings with similar studies, especially with Peter Galison's, in which Feynman's war-related work takes center stage (Galison 1998). To a considerable extent, I will build on my own reconstruction of the genesis of Feynman diagrams, which in turn is based on my selection of documents from the Feynman Papers hosted at the California Institute of Technology (Wüthrich 2010).

2. The Main Problem and Feynman'sFirst AttempttoSolve It

In the early 1940s, when Richard P. Feynman was a graduate student, one of the most pressing problems facing theoretical physicists was the fact that infinite and, therefore, uninterpretable quantities arose from some of the principles of electrodynamics—in both classical electrodynamics as well as in the early attempts to establish a quantum version of it.¹ In classical electrodynamics, the difficulties of divergences had been known for some time, and it had been hoped that quantizing the theory would eliminate them. An alternative strategy was to first remove the infinite quantities in the classical theory before attempting to quantize it. It is in this theoretical context that Feynman wrote his Ph.D. thesis, with the removal of the divergences in electrodynamics being his superordinate objective (Feynman 2005, p. 2). In his thesis, he adopted the second strategy of first trying to establish a divergence-free classical theory and then proceeded to quantize it. Indeed, together with his supervisor John Archibald Wheeler, Feynman had already developed an alternative theory of classical electrodynamics with the desired feature that just awaited quantization.

The standard procedure for quantizing a classical theory was to interpret the classical Hamiltonian function H as an operator in...