In 1865 James Clerk Maxwell published A Dynamical Theory of the Electromagnetic Field. It is a long paper, still partly framed in mechanistic language (Maxwell thinks of the field as the internal stresses of an elastic medium, the “ether”), but it contains what turns out to be the most powerful act of unification in classical physics. The four equations we today associate with his name bring together, within a single coherent framework, phenomena that until shortly before had been distinct: electrostatics, magnetostatics, Faraday’s induction, and the theoretical adjustment to Ampère’s law — the displacement current — which Maxwell introduces for reasons of pure logical consistency.
The plot twist comes in the calculation of the propagation speed of field perturbations. Combining his equations in vacuum, Maxwell obtains a wave equation with speed . He substitutes the numbers — two constants measured in the laboratory with balances and coils, in experiments that had nothing to do with light — and obtains about m/s. It is the speed of light, measured by Fizeau and Foucault a few years earlier.
The inference is immediate and breathtaking: light is an electromagnetic wave. All of optics — reflection, refraction, polarisation, diffraction — must be derivable from Maxwell’s equations. In 1888 Heinrich Hertz produces in the laboratory invisible electromagnetic waves (the “radio waves”) with frequencies much lower than optical ones, and shows that they behave exactly as predicted: they travel at the same speed, they reflect, they refract, they polarise. Within twenty years physics gains a new window onto the universe (radio astronomy, X-rays, the cosmic microwave background) and a new communication technology (wireless telegraphy, radio, television).
And it is precisely within Maxwell’s equations that, a generation later, Einstein finds the spark for special relativity: if the speed emerges from the vacuum constants, and the vacuum is the same for all observers, then must be the same for everyone. The 1905 revolution is born from the question: «how can a speed be independent of the reference frame?». The answer — changing the way space and time transform — is already the story of the next chapter, the one on special relativity.
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Topics: Electromagnetic waves Concepts: Maxwell’s equations · Electromagnetic wave · Einstein’s postulates
Related exercises: Problem — EM waves without a medium · Problem — EM waves and the structure of the vacuum · Problem — Microwave oven