James Clerk Maxwell


James Clerk Maxwell

“One scientific epoch ended and another began with James Clerk Maxwell.”

Don’t believe me? Well, I wasn’t the first person to say it – Albert Einstein said it first.

When Einstein was asked if he had stood on the shoulders of Newton, he replied: “No, I stand on Maxwell’s shoulders.”

And Richard Feynman, another of the 20th century’s greatest physicists said:

“…the great transformations of ideas come very infrequently… we might think of Newton’s discovery of the laws of mechanics and gravitation, Maxwell’s theory of electricity and magnetism, Einstein’s theory of relativity, and… the theory of quantum mechanics.”

James Clerk Maxwell is one of the giants of physics. Unfortunately, his work is less famous than that of the other greats – possibly because his crowning glory – Maxwell’s Equations – are so hard to understand.

In producing these equations, he was the first scientist ever to unify any of nature’s fundamental forces. He discovered that electricity and magnetism are actually, at the deepest level, the same force – the electromagnetic force. In doing so, Maxwell proved that light is an electromagnetic wave, and so made a link between electricity, magnetism and optics.

As if this achievement were not enough, his kinetic theory of gases accurately explained the origin of temperature.

He introduced statistics and probability into the physics of the very small, laying the foundation for quantum theory.

He was the first person ever to produce a color photograph; and he used mathematics to explain Saturn’s rings over 100 years before the Voyager spacecraft confirmed that he was absolutely right.

In addition to his great discoveries, in his personal life, he was known for his capacity for hard work, his friendliness, personal kindness and generosity.

Maxwell’s School Life

James Clerk Maxwell was born into a wealthy family in Edinburgh, Scotland on June 13, 1831. His father was a lawyer, and his mother died when he was only eight years old.

He attended high school in Edinburgh – Edinburgh Academy – where he published his first academic paper, ‘Oval Curves’ at the age of just 14. By this age, he had also completely memorized the Bible. Maxwell was an evangelical protestant, who believed his religion was a private affair. Like Isaac Newton, he saw no disagreements between his science and his religion.

Unable to properly understand the genius in their class, some of the boys at school gave Maxwell the name ‘Dafty.’ Maxwell was usually completely unconcerned by this, and made firm friends with Lewis Campbell, who went on to became a professor of Greek at the University of St Andrews and Peter Guthrie Tait, who became a professor of physics at Edinburgh University.

Maxwell’s school classes had as many 60 children in them. One of his classmates, W. Macfarlane later said of him:

Clerk Maxwell, when he entered the Academy, was somewhat rustic and somewhat eccentric. Boys called him ‘Dafty,’ and used to try to make fun of him. On one occasion I remember he turned with tremendous vigour, with a kind of demonic force, on his tormentors. I think he was let alone after that, and gradually won the respect even of the most thoughtless of his schoolfellows.

Maxwell at University – A Student, then Professor

Aged 16, Maxwell entered Edinburgh University for three years, taking courses in physics (it was then called natural philosophy), mathematics, and philosophy. He found the courses rather easy, leaving plenty of free time for his own private scientific research. Maxwell continued to publish serious scientific papers while studying for his degree.

Aged 19, he moved to Cambridge University, studying mathematics, becoming a Fellow of Trinity College when he was 24, sharing the Smith’s Prize for theoretical physics and mathematics with Edward Routh.

In 1856, aged 25, he was awarded Edinburgh’s highest prize in mathematics, the Straiton Gold Medal, and in the same year, he was appointed to the Chair of Natural Philosophy at Aberdeen University, where he stayed for four years.

During this time he formulated and published his brilliant analysis of how Saturn’s rings could be stable for a long time. Britain’s top astronomer of the time, the Astronomer Royal, Sir George Biddell Airy said of the work:

It is one of the most remarkable applications of mathematics to physics that I have ever seen.

Saturn and its rings.

Saturn, with its large number of narrow rings shown in detail. In 1859, Maxwell predicted that Saturn’s rings would be made of a huge number of independently orbiting particles which, if they were to be stable long-term, would to have be arranged in a series of narrow rings. In 1980, his prediction was confirmed by images sent back by Voyager 2. Images by NASA.

While at Aberdeen, he gave a weekly, free lecture at a working men’s college. He also married Katherine Mary Dewar, the daughter of the University’s principal. Maxwell lost his job at Aberdeen when a merger of University colleges left him redundant.

In 1860, aged 29, he took a professorship at King’s College, London.

In this year, he established that each molecule of air at room temperature and pressure collides 8 billion times a second with other molecules on average.

Maxwell stayed in London until 1865, carrying out much of his most notable work.

He then returned to his family home in Scotland for six years, which he devoted to experiments, calculations and writing away from the duties his professorship had involved. In 1866 he wrote:

I have now my time fully occupied with experiments and speculations of a physical kind, which I could not undertake as long as I had public duties.

During this time he wrote much of the groundbreaking ‘Treatise on Electricity and Magnetism’, which was published in 1873.

In 1871, he became Cavendish Professor at Cambridge University, where he remained until his death in 1879, aged just 48.

Color in the Human Eye and Photography

Maxwell at the Royal Society of Edinburgh

A 24 year old James Clerk Maxwell, photographed with one of his color wheels in 1855 when he presented his work Experiments on Colour to the Royal Society of Edinburgh.

Experimenting with spinning color wheels, Maxwell deduced that the light receptors in the human eye are capable of seeing just three colors of light.

Later he reasoned that he could make use of his deduction to make a colored photograph – of tartan. He had photographs taken of tartan, first through a red light filter, then a green filter, then a blue filter.

The result of projecting the three images simultaneously on to a screen was a color image of the tartan cloth – the world’s first color photo, in 1861.

Maxwell's first color image

Part of the first color image ever produced by photography. A smaller black and white version is shown for comparison.

Electromagnetism – The First Unification of Nature’s Forces

Maxwell’s work in electromagnetism was inspired by his analysis of experimental results and observations coming from people like Ampere, Oersted, and, especially, Michael Faraday.

Maxwell used mathematics to investigate the fundamental causes of electrical and magnetic behavior, producing what are, to professional physicists, some of the most beautiful equations they use – Maxwell’s Equations. These equations are difficult to understand, and usually aren’t taught until later years in university physics or applied mathematics courses.

Maxwell proved that there must be electromagnetic waves, whose speed he was able to calculate. Maxwell’s calculated speed turned out to be identical to the speed of light, which people already knew from experiments. Maxwell then knew that light must be an electromagnetic wave.

He also pointed out that radiant heat and possibly other, as yet undiscovered electromagnetic rays, would travel at the speed of light. We now know that indeed there are other rays, such as radio waves, microwaves, UV rays and x-rays, and they all do travel at the speed of light.

Hard to Understand, they are the Key to our Modern World

Although we now recognize the genius, and indeed beauty of Maxwell’s work, it was controversial when he first published it in 1864. Not many people realized that Maxwell’s Equations accurately and completely described electromagnetism.

Maxwell's Equations

Maxwell’s Equations presented using vector calculus

In 1887, eight years after Maxwell’s death, Heinrich Hertz finally demonstrated by experiment that there truly are electromagnetic waves, which behave in exactly the way Maxwell had predicted.

By 1901 Guglielmo Marconi was transmitting radio waves – the lowest energy form of electromagnetic waves – across the Atlantic Ocean, from Britain to Canada. The era of modern, wireless telecommunications had begun.

The Kinetic Theory of Gases and Statistical Physics – the end of Newton’s Physics

In his kinetic theory of gases, Maxwell was able to establish that the temperature of a gas was entirely dependent on the speed of the individual atoms or molecules that made up the gas.

He realized that the gas particles would not all move at the same speed, because collisions between them would speed some of them up and slow some of them down. Maxwell showed that particles in a gas would have a distribution of different speeds and what the distribution would be.

maxwell boltzmann distribution

Maxwell-Boltzmann distributions of gas speeds at three different temperatures. At higher temperatures, gas particles move with higher average velocities

From this work, Maxwell demonstrated that the Second Law of Thermodynamics – the law that heat always flows from higher temperature objects to lower temperature objects – is a statistical law, based on the behavior of huge numbers of particles. Although some individual particles might disobey the law, the majority obey the law. It is even possible that the law could be broken on a larger scale, but the likelihood of this happening is incredibly small.

A Drop in the Ocean
Maxwell likened the chances of one of these statistical laws being broken on a large scale to the chances of pouring a glass of water into the ocean, then later dipping the glass into the ocean and finding that it filled up with exactly the same molecules you had poured in earlier.

Using the average properties of gas molecules, and the distribution of behaviors of gas molecules, Maxwell developed statistical physics. His methods were the keystones of the following century’s quantum physics, where no longer could we be absolutely sure about the behavior of small particles – we could only look at the chances of their behaving in particular ways.

Maxwell helped move physics away from the classical, mechanical world view of Newton towards the quantum, probabilistic view that we rely on today – a view that Albert Einstein was never happy with, saying famously that ‘God does not play dice with the Universe.’

An Early Demise

Sadly, James Clerk Maxwell was not to enjoy a long life. He died of abdominal cancer in 1879 at the age of just 48. Strangely, his mother had died at the same age, from the same disease. With Maxwell’s passing, the world had lost one of its greatest minds.

Talking About Maxwell – Quotes

Richard Feynman“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 19th century will be judged as Maxwell’s discovery of the laws of electrodynamics.”

Richard Feynman
Theoretical Physicist
Stephen Hawking“Maxwell is the physicist’s physicist.”

Stephen Hawking
Theoretical Physicist
Jane Cay“It was humiliating, to be asked so many questions one couldn’t answer by a child.”

Jane Cay
Maxwell’s aunt, who helped educate him
Heinrich Hertz“From the outset Maxwell’s theory excelled all others in elegance and in the abundance of the relations between the various phenomena which it included.”

Heinrich Hertz
Albert Einstein“The special theory of relativity owes its origins to Maxwell’s equations of the electromagnetic field.”

Albert Einstein
Theoretical Physicist
Max Planck“He achieved greatness unequaled.”

Max Planck
Theoretical Physicist
Carl Sagan“The equations were to represent Nature, and Nature is, Maxwell believed, beautiful and elegant… This essentially aesthetic judgement by a nerdish physicist, entirely unknown except to a few other academic scientists, has done more to shape our civilization than any ten recent presidents and prime ministers.”

Carl Sagan
Astrophysicist, Planetary Scientist
JJ Thomson“The discovery of electrical waves… has had a profound influence on civilization; it has been instrumental in providing the methods which may bring all inhabitants of the world within hearing distance of each other and has potentialities social, educational and political which we are only beginning to realize.”

J.J. Thomson
James Jeans“When he crossed the bridge from Astronomy to Physics he left behind him for ever the prospect of becoming a great astronomer – but only to become the greatest mathematical physicist the world has seen since Newton.”

James Jeans
Astronomer, Physicist, Mathematician

Author of this page: The Doc
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