Electrons rule our world, but not so long ago they were only an idea. This month marks the 120th anniversary of a profound and influential creation, the electron theory of Dutch physicist Hendrik Antoon Lorentz. His electron was not merely a hypothesized elementary particle; it was the linchpin of an ambitious theory of nature. Today physicists are accustomed to the notion that a complete description of nature can rise out of simple, beautiful equations, yet prior to Lorentz that was a mystic vision.

For most physicists the memorable peak of 19th-century physics is the theory of electrical and magnetic fields, capped by James Clerk Maxwell’s mathematical synthesis of 1864. Then a haze settles, until the 20th-century massifs of relativity and quantum theory poke through. That foggy folk history obscures the bridge between—itself a brilliant achievement, built through heroic labor.

To set the context, it is important to admit a blasphemy: Maxwell’s own exposition of his equations is a mess. You will not find, in his writings, the clean, compact, elegant structure that students learn as “Maxwell’s equations.” Instead you discover a torrent of symbols and a sprawl of words and equations. Maxwell, a profoundly humble man, did not consider that he was producing poetry for the ages, suitable for engraving. Rather he simply set out to summarize, in mathematical form, everything then known about electricity and magnetism. In his presentation, fundamental equations mingle with makeshift phenomenology.

Lorentz’s achievement was to purify the message of Maxwell’s equations—to separate the signal from the noise. The signal: four equations that govern how electrical and magnetic fields respond to electric charge and its motion, plus one equation that specifies the force those fields exert on charge. The noise: everything else!

Now one had definite equations for the behavior of tiny bodies with specified mass and charge. Could one use those equations to rebuild the description of matter on a new foundation, starting from idealized “atoms” of charge? This was the burden of Lorentz’s electron theory. Starting with his 1892 paper, Lorentz and his followers used the electron theory to explain one property of matter after another—conduction of electricity and of heat, dielectric behavior, reflection and refraction of light, and more. Thus, they laid the groundwork for the subjects we now call electronics and materials science. And in 1897 Joseph John Thomson showed experimentally that electrons really do exist. (One could say that the electron was conceived in 1892 and delivered in 1897.)

Much of Lorentz’s 1892 paper deals with the seductive, though not unproblematic, idea that the mass of electrons could be a consequence of their electric charge. Moving charge generates both electrical and magnetic fields, which resist change and back-react on the electron’s motion. Might that back-reaction account for the electron’s inertia—hence its mass? Such ideas have an ancient history: Aristotle wanted to account for the inertia of matter through the back-reaction of air. Lorentz’s vision of electromagnetic mass was immensely influential. It inspired hard technical work, notably by Lorentz himself and by Henri Poincaré, that anticipated major parts of Einstein’s special theory of relativity.

Quantum mechanics changed the rules of the game, and the idea that electromagnetic back-reaction alone is responsible for the mass of the electron no longer appears viable. Remarkably, however, my colleagues and I have successfully explained the mass of protons, neutrons and other strongly interacting particles using a closely related idea. The inertia of those particles arises from back-reaction of the gluon fields of electromagnetism’s big brother, quantum chromodynamics. Although the Higgs particle is sometimes credited with giving matter mass, its contribution to the mass of ordinary matter is actually quite small. Lorentz’s beautiful idea, in modern form, accounts for most of it.

Lorentz’s electron theory, though eventually superseded in detail, was pivotal. By recognizing the right answers and posing the right questions, he readied the path to relativity, quantum theory and the physics of today. Near the end of his own life, Albert Einstein penned Lorentz a memorable tribute: “For me personally he meant more than all the others I have met on my life’s journey.”

*This article was published in print as "Happy Birthday, Electron."*