# How Maxwell made his mark: O. Darrigol’s

Electrodynamics from Ampère to Einstein

Among the more enduring legacies of 19th-century science, Maxwell’s Equations have long held a preferred position among physicists. One of today’s more outspoken physicists, Steven Weinberg has argued that the Equations constitute a noncontingent fact, without which contemporary physics would be unimaginable. Little more than a century ago, however, other, non-Maxwellian futures were still imaginable, and not only by poets and science-fiction writers, but by the likes of Kelvin and Helmholtz, for whom all known electrodynamic effects were the result of forces acting at a distance, in contradistinction to Maxwell’s field theory. The non-Maxwellian alternatives put up stiff competition, and while Helmholtz conceded the superiority of Maxwell’s theory in the mid-1870’s, Kelvin never gave in, even after Hertz demonstrated electromagnetic wave propagation in air. As Oliver Darrigol shows in his latest book, at crucial junctures in the 19th century, leading physicists held conceptually incompatible views of the nature of electricity and magnetism, and by extension, of the future direction of physics.

During the past twenty years, historical investigations of the origins, discovery and reception of Maxwell’s theory have transformed our image of a moribund Victorian science, building bizarre mechanical models to satisfy what Kelvin referred to as “fits of ether dipsomania,” into one of high-stakes intellectual adventure, pursued by physicists in scientific centers across Europe. Darrigol’s book is the first to draw on this work on a large scale, and is the first comprehensive history of electrodynamics since E.T. Whittaker’s A History of the Theories of Æther and Electricity (1910). It covers the period from 1820 to 1905, and stands as a chronological sequel to John Heilbron’s Electricity in the 17th and 18th Centuries (1979), although the author is obliged by the explosion of scientific activity in the late 19th century to forego Heilbron’s exhaustive treatment, in favor of a selective approach focusing on the leading edge of fundamental electrodynamics, represented by several hundred articles and books from 180 authors. Major developments and turning points discussed here include Ampère’s law, Faraday’s notions of charge and current, the emergence of new quantitative methods in Germany, Maxwell’s Equations, Hertz’s experiments, and the advent of the electron. Each of these topics has been addressed by monographs, but it is to Darrigol’s credit not only to have brought this research together in a synthetic narrative (which draws in addition on literature from the research annals, including the author’s own scholarly contributions over the past ten years), but also to have filled in the gaps. For example, Darrigol discusses Helmholtz’s investigations of $RL$ and $RLC$ circuits, because they effectively guided the latter’s transition from physiology to physics. Informed by manuscripts recently discovered in Berlin, the author’s subsequent analysis of Helmholtz’s theory of electrodynamics holds particular interest, as it shows how Helmholtz, after reinterpreting Maxwell’s theory in terms of electric actions at a distance and an infinitely polarizable vacuum, convinced himself that the latter theory represented the only viable alternative for future research.

Darrigol’s synthetic approach gives rise to new insights into the temporal continuity of certain research traditions in the theoretical and experimental realms. At the same time, it reveals remarkable spatial discontinuities, for instance, in the interpretation of Maxwell’s Equations in Britain and on the Continent. Most notably, the Maxwellian notions of electric displacement and current were misunderstood by continental physicists, including Hertz, who after failing to make sense of Maxwell’s potentials and hypothetical fluids, famously concluded that Maxwell’s theory is Maxwell’s system of equations.

For Darrigol, the historical unity of electrodynamics derives from a chain of ideas and events running from Ampère to Einstein, the links of which he patiently lays out for the reader. Surprisingly, only two of nine chapters have much mathematics; one is on Maxwell’s theory, the other on electron theory. Anyone referring to the original texts in these areas is faced with a bewildering array of terms and symbols, along with some strange mathematics. Nineteenth-century physicists, Darrigol observes, were often just as baffled, but to reduce reader discomfort he imposes standard units and notation, while noting the resulting anachronisms. Even with familiar notation, of course, many exercises are left to the reader, but for once there is no compromise with substantial facts or issues. Derivations and extended technical explanations are relegated to the appendix, but technical or not, opinions are well-documented, with appendices, bibliography and index accounting for nearly a quarter of the volume.

One of the recurring themes of Darrigol’s history concerns the close intertwining of theory and experiment in 19th-century electrodynamics, which is distinguished by the fact that all leading theorists were active in the laboratory. Observing how individual electrodynamicists coordinated their theoretical and experimental activity, Darrigol presents evidence that the same methodological principles were applied to both theory and experiment. In this way, Darrigol explains the profound harmony between the theoretical and experimental practice of Ampère, Faraday, F. Neumann, W. Weber, Kelvin, Maxwell, Helmholtz and Hertz.

Historians have lately accorded a degree of autonomy not only to individuals, but to certain experimental laws as well; Wien’s displacement law had, as E. Nagel put it, “a life of its own,” not contingent upon the continued validity of classical electrodynamics. Likewise, certain instruments and apparatus, and a number of physico-mathematical arguments have been shown to be robust across theory change. Sympathetic to this view, Darrigol includes, instead of portraits, more than a few equations, and dozens upon dozens of instrumental schemata and explanatory diagrams, many of the latter copied from the original memoirs under discussion.

Darrigol’s guided tour of the “lofty summits of the history of electrodynamics” will appeal to historians and philosophers of science, as well as to physicists, mathematicians, and engineers interested in the origins and evolution of field theory. Regardless of how one may feel about the chances for success of non-Maxwellian alternatives a century ago, Darrigol’s informed analysis of the evolution of electromagnetic theory and experiment effectively illustrates the subtle ways by which Maxwell’s Equations came to shape visions of the future.