James Clerk Maxwell

Chapter 1 · What's the Go o' That?

Galloway, a bereaved boy, and a paper at fourteen

1831 – 1850 · Edinburgh · Glenlair · Cambridge

James Clerk Maxwell was born in Edinburgh on 13 June 1831 and grew up at Glenlair, the family estate in Galloway. He was an insatiably curious child whose constant question, in the Scots of the household, was what's the go o' that — and, if the answer was insufficient, what's the particular go o' that.

His mother Frances took charge of his early education and died of abdominal cancer in 1839, when he was eight. A hired tutor proved brutal, and his father sent him to Edinburgh Academy instead.

He arrived aged ten from the country, wearing homemade shoes and a tunic his father had designed, speaking with a rural Galloway accent. The other boys called him Daftie and tore his clothes on the first day. He was, by later accounts, unbothered in a way that irritated them further, and the nickname followed him for years.

At fourteen he wrote a paper on a method for drawing oval curves using pins and thread, generalising work by Descartes. It was read to the Royal Society of Edinburgh — by a professor, because a schoolboy could not present in person.

He studied at Edinburgh University from 1847 and then Cambridge, graduating as Second Wrangler in 1854 and sharing the Smith's Prize. A contemporary said of the man who beat him that he was fortunate, since Maxwell was of a different order.

He was also, throughout, a devout Presbyterian who saw no conflict between his faith and his physics, and wrote his own prayers.

Why this matters

Maxwell's schoolboy paper on oval curves shows the pattern of his whole career: taking a geometrical or physical question and finding the general mathematical structure underneath it.

You have met the boy called Daftie. What would you ask him?

Ask Maxwell

• “What did you mean by 'what's the go o' that'?”
• “How did you cope with being bullied at school?”
• “What was your paper on oval curves about?”
• “How did losing your mother at eight affect you?”
• “Did your faith and your physics ever conflict?”

Chapter 2 · Saturn's Rings and a Tartan Ribbon

Two problems, solved in different subjects

1856 – 1861 · Aberdeen · London

At Marischal College, Aberdeen, Maxwell took on the 1857 Adams Prize question: what are Saturn's rings? A solid ring, he showed mathematically, would be torn apart by tidal forces; a fluid ring would break into blobs under wave instabilities. The only stable possibility was an enormous number of small independent particles orbiting separately. He was awarded the prize as the only entrant to produce a satisfactory answer, and was proved right more than a century later when the Voyager spacecraft photographed the rings.

He married Katherine Mary Dewar in 1858 and she worked with him in the laboratory, particularly on the viscosity of gases; the couple maintained the experimental apparatus in their own house, sometimes at uncomfortable temperatures.

When Marischal merged with another college in 1860 Maxwell was the professor made redundant, and he moved to King's College London for five extraordinarily productive years.

There, in 1861, he demonstrated the first colour photograph. His theory — that human colour vision depends on three types of receptor — implied that any colour could be reproduced from red, green and blue components. With the photographer Thomas Sutton he photographed a tartan ribbon three times through red, green and blue filters, then projected the three images together through the same filters. It worked, though partly by luck: the emulsions of the time were insensitive to red, and the red record came out largely because the red dye also reflected ultraviolet. The principle is nonetheless the basis of every colour screen and camera in use today.

He also worked out the statistical distribution of molecular speeds in a gas, introducing probability into fundamental physics for the first time.

Why this matters

Maxwell's introduction of statistics into physics — describing a gas by a distribution of speeds rather than tracking every molecule — created the method underlying statistical mechanics and much of modern physics.

You have the range of his work. What would you ask him?

Ask Maxwell

• “How did you prove Saturn's rings could not be solid?”
• “How did you make a colour photograph in 1861?”
• “Why bring probability into physics?”
• “What did Katherine Maxwell do in the laboratory?”
• “How did you take losing your professorship?”

Chapter 3 · Light Is an Electromagnetic Wave

A calculation that came out at the wrong number

1861 – 1873 · London · Glenlair

Faraday had described electric and magnetic phenomena in terms of lines of force filling space but could not express it mathematically. Maxwell set out to do exactly that.

Working through a mechanical analogy of spinning cells and idle wheels — a model he did not literally believe but used as scaffolding — he assembled the known laws and found them inconsistent. Ampère's law failed when a capacitor was charging, since no current flows through the gap. Maxwell added a term he called the displacement current: a changing electric field produces a magnetic field just as a current does.

That addition made the equations symmetrical, and it had a consequence. A changing electric field creates a magnetic field, whose change creates an electric field, and so on — a self-sustaining disturbance propagating through space. Maxwell calculated its speed from two constants measured in purely electrical experiments, with no reference to optics.

The number came out at roughly 310,000 kilometres per second — within experimental error of the measured speed of light.

He drew the conclusion that light is an electromagnetic wave, and predicted that other wavelengths must exist beyond the visible.

His 1873 *Treatise on Electricity and Magnetism* set it out in twenty equations. Oliver Heaviside and Josiah Willard Gibbs later condensed them into the four vector equations now taught as Maxwell's equations.

Heinrich Hertz generated and detected radio waves in 1887, eight years after Maxwell's death, confirming everything. Radio, radar, microwaves, television and mobile telephony all follow from that confirmation.

“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.”

— James Clerk Maxwell, 'On Physical Lines of Force', 1862

Why this matters

Maxwell's equations unified electricity, magnetism and optics into one theory and predicted the entire electromagnetic spectrum — the basis of all wireless communication.

You have the unification. What would you ask him?

Ask Maxwell

• “What is the displacement current, and why did you add it?”
• “What did you think when the speed came out as the speed of light?”
• “How did you turn Faraday's lines of force into mathematics?”
• “Did you believe in the mechanical model you used?”
• “What did you predict beyond visible light?”

Chapter 4 · Maxwell's Demon

A thought experiment that outlived its author by a century

1867 – 1879 · Glenlair · Cambridge

In a letter of 1867 Maxwell posed a puzzle about the second law of thermodynamics, which states that heat flows from hot to cold and that entropy in a closed system does not decrease.

Imagine a container of gas divided by a wall with a tiny door, operated by a being small enough to see individual molecules. It opens the door to let fast molecules pass one way and slow ones the other. Over time one side becomes hot and the other cold, with no work apparently done. The second law appears to have been violated by nothing more than knowledge.

Maxwell's own point was that the second law is statistical rather than absolute — it describes what overwhelmingly happens to enormous numbers of particles, not what must happen to each one. William Thomson named the being a demon, a label Maxwell disliked.

The puzzle refused to go away. Leó Szilárd argued in 1929 that the demon's measurement itself must have a thermodynamic cost, and in 1961 Rolf Landauer showed that erasing information necessarily dissipates heat — establishing a physical link between information and entropy. Landauer's principle underlies modern thinking about the ultimate energy limits of computation, and has been tested experimentally.

Meanwhile, Maxwell had a final institutional achievement. In 1871 he became the first Cavendish Professor at Cambridge, and designed and built the Cavendish Laboratory, which went on to produce the discovery of the electron, the neutron and the structure of DNA. He spent five years editing the unpublished papers of Henry Cavendish, discovering that Cavendish had anticipated Ohm's law and other results by decades without publishing them.

He died at Cambridge on 5 November 1879 of abdominal cancer, aged forty-eight — the same disease and the same age as his mother.

Why this matters

Maxwell's demon connects thermodynamics to information, and the resolution of the puzzle in the twentieth century established that information processing has an unavoidable physical cost.

You have the puzzle and the laboratory. What would you ask him?

Ask Maxwell

• “What was your demon actually meant to show?”
• “How was the paradox eventually resolved?”
• “Why does the second law only hold statistically?”
• “What did you design into the Cavendish Laboratory?”
• “Why spend five years editing Henry Cavendish's papers?”

Chapter 5 · The Quiet Giant

Why the most important physicist between Newton and Einstein is barely known

Maxwell is, by the assessment of most physicists, the outstanding figure of the nineteenth century in physical science, and among the general public he is far less known than Newton, Darwin or Einstein.

Part of the reason is that his achievement is mathematical rather than pictorial. Newton has an apple, Darwin has finches; Maxwell has a set of partial differential equations. Part is that he died young, before the confirmations arrived — Hertz produced radio waves eight years after his death. And part is temperament: he was modest, wrote comic verse about his own subject, avoided controversy and did not campaign for his ideas.

His influence, though, is everywhere in what followed. Einstein kept a photograph of Maxwell in his study alongside Newton and Faraday, and said that the special theory of relativity owed its origins to Maxwell's equations — because they gave a speed of light independent of the observer's motion, which was precisely the puzzle relativity resolved. Einstein described Maxwell's work as the most profound and fruitful change physics had experienced since Newton.

Quantum electrodynamics is the quantum version of Maxwell's theory. Gauge theory, the framework of all modern particle physics, generalises its structure.

And the practical consequences are difficult to overstate: every radio transmission, every wireless network, every radar installation, every microwave oven and every mobile telephone is an application of a prediction made by a Scottish physicist working from twenty equations in 1873.

Why this matters

Maxwell's equations are the direct ancestors of both relativity and quantum field theory, which makes him the hinge between classical and modern physics.

You have the quiet giant of nineteenth-century physics. What would you ask him?

Ask Maxwell

• “Why are you less famous than Newton or Einstein?”
• “How did your equations lead to relativity?”
• “What would you make of radio and mobile phones?”
• “Why did you never campaign for your own ideas?”
• “What would you have worked on with another twenty years?”

What Maxwell changed

Maxwell's equations unified electricity, magnetism and light and predicted the electromagnetic spectrum, making radio, radar and all wireless communication possible. He introduced statistical methods into physics, produced the first colour photograph, established the composition of Saturn's rings, and founded the Cavendish Laboratory.

A debate that continues

Historians of science discuss why Maxwell's public reputation lags so far behind his scientific importance, and physicists still explore the information-theoretic resolution of the demon paradox he posed.

Keep exploring — ask Maxwell

• “How do you turn a physical picture into mathematics?”
• “What convinced you that light was electromagnetic?”
• “Which of your results do you think mattered most?”

Related lives

• Michael Faraday — Discoverer of Electromagnetic Induction
• Albert Einstein — Nobel Laureate · Author of Relativity
• Nikola Tesla — Inventor of Alternating Current

Related themes

Electromagnetism and light · The electromagnetic spectrum · Thermodynamics and entropy