I. That Speed

1. London. King's College.

Maxwell was calculating a number.

He was computing the speed at which electromagnetic waves would propagate through space. He was not using new experimental data—he was using electrical constants measured years earlier by Weber and Kohlrausch. Two numbers: the permittivity and permeability of free space. He plugged them into his equations and got a velocity.

310,740,000 meters per second.

The speed of light.

The speed of light had already been measured—Fizeau's experiment of 1849. The two numbers matched to within one percent.

Maxwell wrote: "We can scarcely avoid the conclusion that light consists in the transverse undulations of the same medium which is the cause of electric and magnetic phenomena."

He calculated a number. The number told him: light is an electromagnetic wave.

Electricity is light. Magnetism is light. Light is an electromagnetic wave. Three things are one thing. This was not speculation—it was what the equations said.

Faraday had touched the field with his hands. He knew electricity and magnetism were connected. But he did not know light was in there too. His hands did not reach that far.

Maxwell's equations did.

II. Childhood

June 13, 1831. Edinburgh. A lawyer's family. An only child.

His father John Clerk was a quiet man who added "Maxwell" to the family name after inheriting the Glenlair estate. His mother Frances was forty when she bore him. The family moved to the country house.

By the age of three, Maxwell was interrogating everything: "What's the go o' that?" If you gave him a general answer, he pushed back: "But what's the particular go of it?"

His mother died in 1839. Abdominal cancer. Maxwell was eight.

Forty years later, Maxwell would die of the same disease. At the same age—forty-eight.

He went to Edinburgh Academy. On his first day he wore homemade shoes and was called "Daftie" by the other boys. He did not mind. At fourteen he published his first scientific paper—on the geometry of oval curves. At sixteen he entered the University of Edinburgh. At twenty he went to Cambridge. Second Wrangler in the Mathematical Tripos (the first was a man named Routh, whom almost no one remembers).

He spent his whole life with the question he had asked at three: What's the go o' that? What's the particular go of it?

III. Translation

1. Maxwell was twenty-four. He published "On Faraday's Lines of Force."

What he did looks like translation—rendering into mathematics what Faraday had described in words and pictures. But the word translation is not enough.

Translation converts one language into another while preserving meaning. That is not what Maxwell did. When he wrote Faraday's lines of force as equations, the equations produced things Faraday had never said.

Faraday said electricity and magnetism were connected. Maxwell's equations said they were more than connected—a changing electric field generates a magnetic field; a changing magnetic field generates an electric field. They beget each other. This mutual generation propagates through space. The speed of propagation equals the speed of light. Therefore light is an electromagnetic wave.

Faraday never said anything about light. He spoke of lines of force, of the field, of the relationship between electricity and magnetism. But light grew out of his construct—not placed there by Faraday, but chiseled out by Maxwell.

This is the nature of the chisel. A chisel does not destroy. A chisel interrogates. You ask a construct "what are you, really," and if you ask deeply enough, the construct will answer with things its creator never foresaw.

Faraday built a construct: the field. Maxwell chiseled that construct: what is the mathematical structure of the field? In the chiseling, light fell out.

Translation is chiseling. Chiseling is expansion. After being chiseled, the construct grew larger—from electromagnetism to electromagnetism-and-light.

IV. Displacement Current

Maxwell's key contribution was not merely translating Faraday into mathematics. He added something of his own.

Ampère's law said that electric current produces a magnetic field. But Maxwell noticed a gap in Ampère's law—when a capacitor is charging, no current flows between the plates, yet the magnetic field persists. Ampère's law could not account for this.

Maxwell added a term: displacement current. A changing electric field is itself equivalent to a current, and also produces a magnetic field. This was not directly observed in any experiment—it was deduced from the symmetry of the equations. If a changing magnetic field can produce an electric field (Faraday's electromagnetic induction), then a changing electric field should also be able to produce a magnetic field. Symmetry demanded the term.

That term changed everything. With displacement current added, the set of equations became self-consistent. And the equations predicted something new: electromagnetic waves. A changing electric field creates a magnetic field; a changing magnetic field creates an electric field; they chase each other through space. Like ripples across the surface of a pond.

Displacement current was not something Faraday touched. Not something seen in a laboratory. It was forced out by mathematics. Forced out by chiseling.

When you chisel a construct deeply enough, the construct grows things you did not expect. Displacement current was something deep in the gap beneath the floor—Faraday's hand reached in and touched the field; Maxwell's equations reached deeper and touched light.

V. 1865

1. Maxwell published "A Dynamical Theory of the Electromagnetic Field."

The paper contained twenty equations (later simplified by Heaviside into four). These twenty equations described the behavior of electric and magnetic fields in space. They unified electricity, magnetism, and light.

Richard Feynman later said: "From a long view of the history of mankind—seen from, say, ten thousand years from now—there can be little doubt that the most significant event of the nineteenth century will be judged as Maxwell's discovery of the laws of electrodynamics. The American Civil War will pale into provincial insignificance in comparison."

Einstein called Maxwell's work "the most profound and the most fruitful that physics has experienced since the time of Newton."

Where did Einstein's special relativity begin? With Maxwell's equations. The equations said the speed of light is a constant. Einstein asked: if the speed of light is constant, what happens to time and space? The whole of twentieth-century physics grew from that question.

And that question grew from Faraday's iron filings.

Iron filings arrange themselves in arcs. Faraday sees lines of force. Maxwell writes the lines as equations. The equations produce light. The speed of light is constant. Einstein deduces relativity from the constant.

One line. From a bookbinder's hands to a new epoch in physics. Maxwell stands in the middle.

VI. Maxwell and Faraday

They met.

In 1860 Maxwell took a post at King's College, London. Faraday was still at the Royal Institution. The two places were not far apart. They became friends.

But their relationship was not the usual kind of teacher and student. Faraday was forty years older. Faraday was an experimentalist with no mathematics. Maxwell was a mathematician who rarely experimented. Their modes of thought were entirely different.

Faraday thought in images. He saw lines of force, saw curving arcs, saw space filled. Maxwell thought in equations. He saw symmetry, conservation laws, mathematical structure.

But they saw the same thing.

Maxwell respected Faraday his entire life. In all his major papers he began from Faraday. He wrote that Faraday's methods, though widely considered "indefinite and unmathematical," were in truth "of more value as an instrument of mental research" than those of trained mathematicians.

Faraday respected Maxwell in return. That 1857 letter—"I was at first almost frightened when I saw such mathematical force made to bear upon the subject"—held no jealousy. Only a confirmation: what I touched was real.

This is unlike Davy and Faraday. Davy could not fully accept being surpassed by his student. Faraday fully accepted Maxwell. Perhaps because Maxwell was not surpassing him—Maxwell was completing him. Faraday gave a painting. Maxwell gave the frame. A frame is not better than a painting. A frame lets the painting hang.

And unlike Tesla and Edison. They were opposites—one had chisel without construct, the other construct without chisel. Faraday and Maxwell were not opposites. Faraday had perception without language. Maxwell had language without perception. Together they made a complete sentence: touched it, then said it.

VII. Glenlair

1. Maxwell resigned from King's College. He returned to Scotland. To the Glenlair estate.

He lived there for six years. Writing papers. Improving the property. Living with his wife Katherine. They had no children.

In 1871 he returned to Cambridge as the first Cavendish Professor of Physics. He oversaw the construction of the Cavendish Laboratory—which would later produce over twenty Nobel laureates.

But his most important work was done at Glenlair. Far from the university, far from colleagues, alone in a Scottish country house, writing equations.

This bears some resemblance to Newton. Newton, during the plague, went home to Lincolnshire and conceived universal gravitation and calculus. Maxwell, at Glenlair, conceived the electromagnetic field theory. Both men did their greatest work in quiet places.

But there is a difference. Newton hoarded. He hid his work for years. Halley practically forced him to publish the Principia. Maxwell did not hoard. He wrote and published. He did not care about priority disputes—he cared about making things clear.

At Glenlair he wrote A Treatise on Electricity and Magnetism. Published in 1873. Two volumes. Its significance to physics is roughly comparable to Newton's Principia.

VIII. Maxwell and Newton

Maxwell achieved the second great unification in physics.

The first was Newton's. The motion of the heavens and the motion of things on earth are the same thing—gravity. An apple falling and the moon orbiting are governed by the same force. Newton unified above and below.

The second was Maxwell's. Electricity, magnetism, and light are the same thing—the electromagnetic field. Faraday's lines of force and sunlight are the same field. Maxwell unified electricity and light.

The two unifications share something: after unification, the world becomes simpler. Before, you thought there were three things (electricity, magnetism, light). After, you find there is only one.

But they differ in one respect. Newton's unification preserved an assumption: force acts at a distance, space is empty, time is absolute. Maxwell's unification broke that assumption. The field does not act at a distance. The field fills space. Electromagnetic waves take time to propagate. The speed of light is finite.

Hidden in Maxwell's equations was a bomb: the speed of light is constant in every reference frame. Newton's mechanics said velocity is relative. Maxwell's equations said the speed of light is not relative. The two were in contradiction.

The contradiction waited forty years. 1905. Einstein resolved it. He chose Maxwell, abandoned Newton. Special relativity: time and space are relative; the speed of light is absolute.

Newton laid the first floor of physics. Maxwell laid the second. Einstein discovered the two floors did not align—there was something in the gap. He pried up Newton's floor. Maxwell's is still there.

IX. Forty-Eight

November 5, 1879. Cambridge.

Maxwell died. Abdominal cancer. Forty-eight years old.

The same disease as his mother. The same age. His mother died in 1839 when he was eight. Forty years later he walked the same road.

In his final months he endured severe pain. He did not complain. He nursed his ailing wife. After his own symptoms appeared he told no one for a long time.

He asked for a quiet burial. No grand ceremony. He was buried in the churchyard at Parton, a small village near Glenlair. Not in Westminster Abbey.

On the wall of Einstein's study hung three portraits: Newton, Faraday, Maxwell.

Maxwell lived forty-eight years. What did he do in those forty-eight years? He translated Faraday's hands into equations. In the translation he chiseled out light. The speed of light is a constant. Hidden in the constant was relativity. Relativity reshaped the entire twentieth century.

He stood between Faraday and Einstein. On one side, hands. On the other, light-years. He was the one in the middle who turned hands into equations and equations into light.

One more person on the bridge. He is standing. Standing straight.

He does not crouch—Faraday crouches, hand reaching into the gap. Maxwell stands because he is writing. He needs a surface to write equations on. In his hand, a piece of chalk—not a real piece of chalk, but the posture of writing equations. He writes in the air.

What he writes is invisible. But it is there. Four equations. ∇·E, ∇·B, ∇×E, ∇×B. They hover in the air, curving like Faraday's lines of force, propagating like light.

Socrates stands on the clearing. Plato crouches drawing blueprints. Hume plays billiards. Schopenhauer looks under the bridge. Kierkegaard jumped. Turing looks at the apple in his hand. Chekhov leans against the railing. Cantor stares upward. Copernicus set down a book and walked away. Sartre paces with his pipe. Beauvoir holds a mirror. Quine said one quiet sentence. Tesla listens to the hum. Edison holds a dead lightbulb. Heisenberg's position is uncertain. Bohr holds a letter he never sent. Tolstoy holds a prescription, facing Chekhov. Shakespeare is not there. Spinoza has glass dust on his fingers. Aristotle crouches, laying floor. Faraday crouches beside him, prying up a plank, hand reaching into the gap.

Maxwell stands next to Faraday. He looks at the light Faraday pulled from the gap. He picks up the chalk. He begins to write.

As he writes, the light brightens.

Not just the light in the gap. The entire bridge surface lights up. The curved, invisible light that Faraday pulled from the gap has been released by Maxwell's equations, filling the whole of space.

In the distance. Kant is still standing there. He sees the light.^[1][2]

Notes

Han Qin (秦汉) · @hqinjarsy · Great Lives