Why Thomson and Maxwell Didn’t Like the Way Faraday “Spoke” About Physics

The author visiting Michael Faraday in London, July 2019
The author visiting "Michael Faraday" in London, July 2019

Let’s begin with some facts:

  1. In 1905, Albert Einstein published “On the Electrodynamics of Moving Bodies,” the paper that would reframe physics based on his special theory of relativity and ultimately render Victorian ether theories obsolete.
  2. Though he credits Maxwell, Einstein begins “On the Electrodynamics of Moving Bodies” with a description of Michael Faraday’s field theory, specifically his definition of electromagnetic induction [1].
  3. In 1907, Einstein declared that the “happiest thought of his life” was when he constructed an analogy between the electromagnetic field and the gravitational field. Victorian physics, and specifically the radical departure from Newtonian mechanics, catalyzed Einstein’s special theory of relativity.

After Einstein published his special theory of relativity in 1905, fields and field phenomena forcefully entered the twentieth-century mainstream. However, as Kieran Murphy has recently argued, Einstein’s rise to prominence obscured our treatment of nineteenth-century conceptualizations of electromagnetic fields in science (and in literature). We owe to Michael Faraday much of the massive imaginative leap from Newtonian physics to field theory.

Faraday’s work captivates me. He doesn’t have the kind of celebrity that Einstein and Maxwell do; yet he was an equally important contributor to physics, particularly through his unparalleled imaginative insights and experimental rigor. I am pictured above, grinning next to “Faraday” during a visit to London in July 2019. No short posting can do justice to Faraday’s work. Nevertheless, here I will gloss some key details of Faraday’s theory of fields, and of their reception in the mainstream scientific community. Specifically, I will focus on Faraday’s unorthodox approach to problem-solving, and his departure from the conventions of institutional science. Because Faraday lacked the classical education of his colleagues, his theories forged a new path away from traditional Newtonian force relations and their mathematically predictable, clockwork motions of matter. However, Faraday’s imaginative trailblazing was taken seriously by the scientific community only after his classically trained colleagues, most prominently William Thomson and James Clerk Maxwell, translated his theories into the language of conventional mathematics.

Electromagnetic Induction and Invisible Fields

Throughout the 1830s, a self-educated experimental physicist named Michael Faraday investigated a fascinating but perplexing link between electricity and magnetism.

Michael Faraday, Lithograph.
Michael Faraday. Lithograph. Photo by The Wellcome Collection

In 1819, the Danish physicist Hans Christian Oersted had discovered that a current-carrying wire deflected a magnetic compass needle nearby, a finding he published in 1820 [2]. Almost immediately afterward, Faraday launched into his career-long study of the interaction between electricity and magnetism, or what he later considered two linked manifestations of the same phenomenon.

Though Oersted was first to demonstrate a link between electricity and magnetism, it was Faraday who developed the theory of why a moving magnet generates an electric current in a nearby wire. This phenomenon is called “induction,” an electromagnetic effect that opened the doors for many of the technological transformations of the mid-to-late nineteenth century. In 1831, Faraday first reported his discovery of electromagnetic induction, arguing that electric currents were induced in a changing magnetic field, or when a conductor “cut” what he called magnetic “lines of force.” These lines of force, made visible by iron filings in the space around magnets, formed the backbone of Faraday’s theory. They demonstrated physical activity in the space around current-carrying wire, and around magnets.

Faraday Lines of Magnetic Force
Faraday's Lines of Magnetic Force, printed in [3], 1952

Faraday radically rejected several long-held Newtonian assumptions. First, he dismissed action at a distance, the notion that forces like gravity, electricity, and magnetism transmit apparently at a distance through ethereal mediation or some other agent whose action is obviated by mathematical accuracy. For example, when two planets exert a gravitational force on each other, nineteenth-century scientists could mathematically model those forces, but could not explain how gravity operated across the distance separating those planets. Where many scientists accepted the math without recourse to physical explanation, Faraday did not accept the blackboxing of such phenomena and therefore developed a physical explanation to support mathematical models.

Second, he eventually scrapped the need for the ether. The luminiferous ether was considered an invisible medium permeating all space through which “imponderable” phenomena like heat, light, and electromagnetism traveled. Faraday pictured electromagnetic action as a tension across space involving contiguous particle transmission. This might tempt us to conjure up a mental picture of ether, although Faraday was fairly convinced by the 1850s that his lines of force did not need ether mediation [5].

Third, he rejected the idea that electricity was a fluid. As Faraday’s theory of the field evolved, he increasingly insisted that the space around conductors was an active component of the electromagnetic energetic system. And, as we will see, Faraday’s interpretation of that active space differed substantially from those of his younger contemporaries, William Thomson and James Clerk Maxwell.

“Translating” Faraday

Despite Faraday’s insights, his background as a self-educated son of a blacksmith impeded his credibility in the mainstream scientific community. William Thomson and James Clerk Maxwell famously cast Faraday’s work into mathematical notation, yet their translation of Faraday’s field theory denatured some of his original intuitions, reinserting fluid analogy and mechanistic explanation where Faraday had removed it.

To better understand Faraday’s intervention in physics, let’s first cover the basics of Newtonian scientific convention, and the various schools of thought that upheld dominant theoretical methodologies during the Victorian era.

Energy science evolved out of a departure from traditional Newtonian physics, which was governed by two intellectual trends: mechanization and Neoplatonist mathematization.

  • Mechanization: mechanical philosophers such as Descartes held that physical phenomena were the clockwork motions of matter.
  • The Neoplatonists, like the astronomer Johannes Kepler, argued that the world was structurally representational, held together by mathematical law without need to defer to physical explanation [6]. In this view, math was the Platonic ideal: the pure, true reality. Physical structures were inferior to mathematical forms.

The sticking point of the Newtonian worldview was the problem of representing forces that are transmitted at a distance, like gravity, electricity, and magnetism. Newtonian scientists handled this problem variously. Cartesians argued for ether mediation and subtle fluids that transmitted forces across space. Alternatively, others argued that void space was still possible because the mathematical models were empirically successful without describing any agent of transmission [6].

The dawn of nineteenth-century energy physics ushered in a new era of scientific investigation during which action at a distance drew sharp controversy. Among its most relentless critics, Michael Faraday refused Newtonian action at a distance, which, as his contemporary John Tyndall explained, “perplexed and bewildered him” throughout his entire life [5]. Faraday refused to accept action at a distance on the premise that, basically, the math just worked out.

Faraday lacked the classical mathematical training that would have groomed him to accept math as metaphysics. He entered the scientific fold by working as Sir Humphrey Day’s assistant at the Royal Institution. Despite his humble beginnings, Faraday ultimately surpassed even Davy’s expertise and matured into one of the nineteenth century’s most imaginative thinkers. By the 1830s, he had challenged action at a distance, uncovered electromagnetic induction phenomena, and suggested that “lines of force” conveyed invisible influences between bodies.

And yet, despite his experimental successes, Faraday’s fresh approach to physics came at the price of his requiring “translators” for the benefit of the greater scientific community.

Joseph Turner describes Thomson’s and Maxwell’s treatment of Faraday as “compar[ing] Faraday’s lines of force to more familiar notions” [7], that is, assimilating his theory into well-accepted scientific and mathematical conventions. As Faraday’s younger and more educated contemporaries, Thomson and Maxwell were initially wary of the way Faraday “spoke” about physics [2]. In other words, the vestiges of his working-class background lingered in his unorthodox approach to science. Thomson even recalled that he had rejected the little he knew of Faraday’s ideas in the early 1840s [8], despite that Thomson is widely credited with understanding and employing Faraday’s theory during that period.

Maxwell addressed his own former skepticism in a contrite appeal to readers in the 1873 preface of his Treatise on Electricity and Magnetism, six years after Faraday’s death, explaining,

“I was aware that there was supposed to be a difference between Faraday’s way of conceiving phenomena and that of the mathematicians, so that neither he nor they were satisfied with each other’s language… As I proceeded with the study of Faraday, I perceived that his method of conceiving the phenomena was also a mathematical one, though not exhibited in the conventional form of mathematical symbols. I also found that these methods were capable of being expressed in the ordinary mathematical forms, and thus compared with those of the professed mathematicians… When I had translated what I considered to be Faraday’s ideas into a mathematical form, I found that in general the results of the two methods coincided, so that the same phenomena were accounted for, and the same laws of action deduced by both methods, but that Faraday’s methods resembled those in which we begin with the whole and arrive at the parts by analysis, while the ordinary mathematical methods were founded on the principle of beginning with the parts and building up the whole by synthesis” [9].

As Maxwell describes it here, Faraday’s methods were viable yet needed the coaxing of a trained mind into “ordinary mathematical forms.” What ultimately matters to Maxwell is the end result of his translation labors: that Faraday’s method agrees with the already accepted conventions of mathematics. Although he validates Faraday, he is less concerned with the imaginative differences language produces in arriving at the convergence, the solution.

This is a statement with which some readers may disagree, especially considering Maxwell’s famous argument for the power of knowledge creation by “Physical Analogy.” And it’s true that Maxwell, himself, was deeply invested in figurative language as a theoretical modality. Nevertheless, I maintain that this very heuristic of analogizing, on the parts of both Maxwell and Thomson, indirectly reinscribed the same conventional knowledge that it purported to transgress. Faraday was theorizing fields; they reinstated the dominant mechanistic fluid models to describe what Faraday “meant.”

Since Maxwell and Thomson applied fluid analogies to cast Faraday into standard mathematics, one way to approach their respective translations of Faraday is to ask what analogy meant to these scientists. Maxwell introduced physical analogy as a “mean” between pure mathematics and physical hypothesis. He believed that analogy closed the gap between two equally practical scientific methods, while simultaneously producing new knowledge [7]. Thomson, on the other hand, employed analogy where he needed to make sense of one branch of physics in terms of another.

Most historians of science accept that Thomson synthesized Faraday’s ideas with the theory of heat flow to describe how current travels along wires. Yet Thomson swept electrostatics into a heat transfer analogy because it provided a new way of seeing, or of knowing, a phenomenon that was not readily seeable or knowable to him. He was already involved in the study of heat transfer, and he used Faraday’s research as a creative tool to serve an established epistemological framework.

As language mattered to these scientists, the distinctive way Faraday “spoke” and wrote about physics matters a great deal to the interpretation of his theory. He articulated a clear need for mathematically trained scientists to deconstruct their theoretical conjectures in terms more concrete than symbolic representations of physical phenomena.

For instance, when André-Marie Ampère reduced magnetism to the motion of fluid currents, Faraday denounced Ampère’s conclusion as the ad hoc outcome of mathematical discovery without recourse to demonstrating his process of investigation [2]. By contrast, Faraday did provide extensive experimental demonstration and logical reasoning for his theory, which is why Thomson’s and Maxwell’s return to fluid analogy is, to my mind, somewhat perplexing.

In the course of translating Faraday, Maxwell turned Faraday’s description of the electromagnetic field into a flux analogy, which we still employ in a traditional physics education. Maxwell asserted that “in every case the motion of electricity is subject to the same condition as that of an incompressible fluid” [10], and further encouraged readers to consider dielectrics, or special materials that resist electric current, as elastic meshes that hold this liquid in place [11].

Thomson arrived at Faraday’s work earlier than Maxwell, and did not translate and extend Faraday so much as merely assimilate him into Thomson’s own projects. The traditional interpretation of Thomson’s work asks us to assume that he accepted Faraday’s theory by the early 1840s, while working on an analogy between electrostatic “flow” and heat “flow.” However, as Jed Buchwald compellingly demonstrates in his comparison of Thomson’s and Faraday’s work, “Thomson in 1845 was introducing theoretical notions foreign to Faraday’s theory, about which he was not altogether clear… Thomson’s new formulation was afterwards seen as the essence of Faraday’s electrostatics” [8].

Despite Thomson’s and Maxwell’s inarguably crucial roles in developing electromagnetic field theory, Faraday’s original ideas do differ markedly from their translations.

Science and Technology Studies (STS) scholars have thoroughly discussed the machinic tendency of western science to flatten varied and layered perspectives into convention [12]. Assimilating Faraday into an already-accepted scientific tradition hammered one mode of representation into another, dominant one. In other words, scientific credibility depends on a number of variables, including a scientist’s ability to follow institutional convention. Faraday was brilliant, and he thought “outside the box,” as we say, but none of that mattered to institutional circles until his theories could be made legible to the authorities of Victorian science.

In their book, Laboratory Life, Bruno Latour and Steve Woolgar argue that “cycles of credit” underpin the motivation for scientific advancement. “Credit as credibility” operates as a commodity that can be accumulated, circulated, and/or lost. Scientists’ projects are thus “investments” within a credibility economy where success of the project furthers the symbolic capital of the scientist [13]. Although we cannot make direct comparisons between the twentieth-century laboratories that Latour and Woolgar studied and Victorian institutional science, we can argue that knowledge production in the Victorian era was no less restricted by convention and the prestige economy than sciences of recent decades. In fact, Crosbie Smith has reinforced this argument by claiming that “the pursuit of national credibility” [14] was a core objective of the first framers of energy physics.

While Faraday’s work made space for the large-scale development of field theory, it was the translation of value from Faraday’s ideas to Maxwell’s and Thomson’s interpretations of those ideas that cemented field theory as legitimate institutional science. Faraday was indeed employed by the Royal Institution, and thus operated within the structure of institutional knowledge production, but it would be a misstep not to acknowledge that his original theory emerged as a rupture in institutional thinking. Moreover, had Faraday not made that giant imaginative leap about electromagnetic induction, Einstein might not have had his “happiest thought.” In a system that rewards investment in “the pursuit of national credibility,” we owe much to the perspectives that thoughtfully diverge from those conventions.  


[1] Einstein, Albert. “On the Electrodynamics of Moving Bodies.” Annalen der Physik 17. 1905.

[2] Purrington, Robert D. Physics in the Nineteenth Century. Rutgers University Press. 1997.

[3] Faraday, Michael. “On the Physical Character of the Lines of Magnetic Force,” Philosophical Magazine and Journal of Science, Fourth Series, 3, no. 20 (June 1852).

[4] Murphy, Kieran M. Electromagnetism and the Metonymic Imagination. The Pennsylvania State University Press, 2020.

[5] Jones, Bence. The Life and Letters of Faraday, vol. 2, 2nd Ed. Longmans, Green, and Co., 1870.

[6] Cao, Tian Yu. Conceptual Developments of 20th Century Field Theories, 2nd ed. Cambridge University Press, 2019.

[7] Turner, Joseph. “Maxwell on the Method of Physical Analogy.” The British Journal for the Philosophy of Science 6.23, 1955.

[8] Buchwald, Jed. “William Thomson and the Mathematization of Faraday’s Electrostatics.” Historical Studies in the Physical Sciences 8, 1977.

[9] Maxwell, James Clerk. Preface to A Treatise on Electricity and Magnetism, First ed., Vol. 1, 1873. Dover Publications, 2016.

[10] Maxwell, James Clerk. A Treatise on Electricity and Magnetism, First ed., Vol. 1, 1873. Dover Publications, 2016.

[11] McAulay, Alex. “On the Mathematical Theory of Electromagnetism.” Royal Society 183, 1892.

[12] Bruno Latour’s work is notable here. Latour argues that inscription devices translate and flatten transverse perspectives into written documents. See Latour, Bruno. Pandora’s Hope: Essays on the Reality of Science Studies. Harvard University Press, 1999.

[13] Latour, Bruno, and Steve Woolgar. Laboratory Life: The Construction of Scientific Facts. Princeton University Press, 1986.

[14] Smith, Crosbie. The Science of Energy: A Cultural History of Energy Physics in Victorian Britain. University of Chicago Press, 1998.

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