Next time you turn on your TV, think of James Clerk Maxwell. In one of the greatest feats of human thought he predicted the electromagnetic waves that bring the signal from the transmitter to your set. He also provided the means of producing the coloured image on your screen by showing that any colour can be made by combining red, green, and blue light in the appropriate proportions.
He was born in 1831 into a distinguished Scottish family and went to a top school in Edinburgh before studying at both Edinburgh and Cambridge Universities. In an astonishing and short career (he died aged 48), Maxwell made groundbreaking discoveries in every branch of physics that he turned his hand to. But in the International Year of Light 2015 it is fitting that we celebrate in particular his discoveries about light: not only his electromagnetic theory, first published 150 years ago, but also his demonstration of the way we see colours.
Both topics pressed on his mind once he had completed his degree at Cambridge, but it was the colour problem that he tackled first. At the time, nobody knew how we see colours. In the early 1800s the English physiologist and physicist Thomas Young had put forward the interesting idea that the human eye has three types of receptor, each sensitive to a particular colour, and that the brain manufactures a single perceived colour according to the relative strengths of the signals along each of the three channels. But Young couldn’t supply supporting evidence and his theory had been largely neglected for the best part of half a century. Then Maxwell’s mentor James Forbes had thought of taking a disc with differently coloured sectors, like a pie chart, and spinning it fast so that one sees not the individual colours but a blurred-out mix. Painters traditionally mixed red, yellow and blue to get other colours, so Forbes did the same, but the results were puzzling. For example, when mixing yellow and blue, he didn’t get green, as painters did, but a dull sort of pink. And he couldn’t get white, no matter how he mixed the colours.
Maxwell soon discovered the source of his mentor’s confusion. Forbes had failed to distinguish between mixing colours in the light that reaches the eye, as when spinning a disc, and mixing pigments, as a painter does. Pigments extract colour from light – what you see is whatever light is left over after the pigments have done their extraction. So perhaps Forbes’ choice of the painter’s primary colours, red, yellow and blue, was wrong. Maxwell tried, instead, mixing red, green and blue and the results were spectacular. Not only did he get white, by using equal proportions of the three colours, it seemed that he could get any colour he wanted, simply by varying the proportions of red, green and blue.
To put things on a proper footing he ordered sheets of coloured paper in many colours from an Edinburgh printer and had a special disc made, with percentage markings round the rim, a handle, and a shank for winding a pull-string: he called it his colour top. He cut out paper discs of red, green and blue and slit them so they could be overlapped on the colour top with any desired amount of each colour showing. This way, he was able to measure what percentages of red, green and blue on the spinning disc matched the colour of whatever paper was held alongside. Using this homely device he devised Maxwell’s colour triangle, a diagram which showed the proportions of red, green and blue needed to make any colour. It differs only in detail from the standard chromaticity diagram used today. For more precise experiments, he invented an ingenious “colour box” which used prisms and narrow slits to extract pure spectrum colours from sunlight and combine them in any desired proportions.
A few years later, in 1861, Maxwell accepted an invitation from Michael Faraday to speak at the Royal Institution in London, and chose to talk about colour vision. It was the perfect opportunity to demonstrate the three colour principle but his spinning disc was too small for people at the back to see clearly and his colour box could only be used by one person at a time. He decided instead to attempt something that had never been done before – to produce a colour photograph. He took three ordinary black and white photographs of the same object, one through a red filter, one through a green filter, and one through a blue; then projected them through the same filters on to a screen, superimposing the three beams of light to form a single image. The audience sat spellbound as the image of a tartan ribbon appeared on the screen in glorious colour. Maxwell had taken the world’s first colour photograph.
Nobody managed to repeat Maxwell’s feat and it was many years before the next colour photograph appeared. The mystery was solved 100 years later by a team from Kodak Research Laboratories. The experiment should never have worked because the plates Maxwell used were completely insensitive to red light. By a bizarre chain of favourable coincidences, ultraviolet light had acted as a surrogate for red. Lucky Maxwell! But perhaps he made his own luck: it was a rule with him never to discourage a man from trying an experiment, no matter how dim the prospects of success. After all, he said, “if he doesn’t find what he is looking for, he may find something else”.
Maxwell may have been lucky with the photograph but his way of producing a full-colour picture by mixing red, green and blue has stood the test of time. To see it demonstrated, just turn on a TV.
The task of producing a complete theory of electromagnetism was much harder but in three awe-inspiring stages, spread over nine years, he succeeded. Maxwell began by reading all he could about the work already done by others, and found he had to make a choice. On the one hand, there was the highly mathematical approach of men like André Marie Ampère, by which forces were assumed to result from electric charges or magnetic poles acting on one another at a distance, with the space between them playing only a passive role. On the other hand, there was the experimental work of Michael Faraday, who proposed that space itself was infused with electric and magnetic “lines of force”. Current opinion strongly favoured action-at-a-distance because it gave precise formulae whereas Faraday, who knew no mathematics, gave none. But, to Maxwell, Faraday’s ideas rang true and he set out to try to represent them in mathematical language.
Maxwell was a master at spotting analogies in different branches of the natural world, and he began by using the steady flow of an imaginary incompressible fluid as an analogy for both electric and magnetic lines of force. This way, he showed that all the known formulae for electric and magnetic forces in static conditions could be derived equally well from the conventional action-at-a-distance theories or from Faraday’s lines of force. A stupendous achievement but, for the present, Maxwell couldn’t think how to deal with changing lines of force. As was his way, he got on with other work while ideas brewed at the back of his mind.
Six years later he came up with a new model. He filled all space with imaginary tiny spherical cells that could rotate and were interspaced with even smaller particles that acted like ball-bearings. By giving the cells a small but finite mass and a degree of elasticity, Maxwell constructed a mechanical analogy for magnetic and electric lines of force, and showed that any change in one induced a change in the other. This extraordinary model yielded not only all the known formulae of electricity and magnetism, it predicted electromagnetic waves that travelled at a speed determined solely by the basic properties of electricity and magnetism, This speed turned out to be within 1½ percent of that at which light had been measured by experiment – compelling evidence that light itself was electromagnetic. An astounding result, but the response of fellow-scientists was muted. The goal in any branch of physics, they believed, was to identify nature’s true mechanism, and they regarded Maxwell’s model as an ingenious but flawed attempt to do this for electromagnetism and light. Everyone expected that Maxwell’s next step would be to refine the model but, instead, he put the model on one side and set out to build the whole theory from scratch, using only the laws of dynamics.
The result, two years later, was the magnificent paper whose 150th anniversary we are now celebrating: “A Dynamical Theory of the Electromagnetic Field”. Here, the spinning cells were replaced by an all-pervading medium that had inertia and elasticity but no specified mechanism. In what seemed like a conjuring trick, he used a method devised by the French mathematician Joseph Louis Lagrange that treated a dynamic system like a “black box”: by specifying the system’s general characteristics one could derive the outputs from the inputs without knowing the detailed mechanism. This way, he produced what he called the equations of the electromagnetic field; there were twenty of them. When he presented the paper to the Royal Society the audience simply didn’t know what to make of it. A theory based on a bizarre model was bad enough, but one based on no model at all was incomprehensible.
Up to the time Maxwell died, in 1879, and for several years afterwards, no one else really understood his theory. It sat like an exhibit in a glass case, admired by some but out of reach. Maxwell could easily have condensed the theory but remarked that “to eliminate a quantity which expresses a useful idea would be a loss rather than a gain at this stage of our enquiry”. Not everyone thought this way: in 1885 a self-taught former telegraph operator called Oliver Heaviside succeeded in making the theory accessible by summarising it in the four now famous “Maxwell’s equations”. It is right that they are called Maxwell’s equations but they are, in part, Heaviside’s creation too.
The first two of these four equations described how static electric and magnetic fields behave. The third and fourth equations defined the relationship between electricity and magnetism. They showed that any spatial variation in the electric field caused the magnetic field to vary in time, and vice versa, and predicted that every time an electric current changed, or a magnet jiggled, waves of electromagnetic energy would spread out into space at a fixed speed determined solely by the elementary properties of electricity and magnetism. This speed was that of light but, according to the theory, light waves were only a small part of a vast spectrum of possible waves, with wavelengths varying from nanometres to kilometres. Even with Heaviside’s simplification, all this remained a theory with more sceptics than adherents until, in 1888, Heinrich Hertz emphatically verified it by producing and detecting Maxwell’s waves in his laboratory. Inventors like Guglielmo Marconi latched on to Hertz’s discovery, and their radio telegraphy was followed by sound radio, television, radar, satellite navigation and mobile phones.
There is more. Though Maxwell never pursued the point, his equations imply that the measured speed of light is always the same regardless of whether the observer is travelling towards the light source or away from it. This fact necessarily leads to Einstein’s special theory of relativity which, among other things, tells us that mass is a form of energy and that nothing can go faster than light: nature has a speed limit, and it depends entirely on the elementary properties of electricity and magnetism.
By bringing the power of mathematics to Faraday’s hitherto derided idea of lines of force in space, Maxwell has transformed both the world and the way scientists think about it. As Oliver Heaviside used to say, “Good old Maxwell!”
Basil Mahon has had careers as an officer in the Royal Electrical and Mechanical Engineers and as a Statistician in the British Civil Service, where he ran the 1991 census in England and Wales. He has since followed up a lifetime interest in science and its history by writing. He is the co-author, with Nancy Forbes, of Faraday, Maxwell, and the Electromagnetic Field: How Two Men Revolutionized Physics (Prometheus Books, 2014); and the sole author of The Man Who Changed Everything: the Life of James Clerk Maxwell (Wiley, 2003) and Oliver Heaviside: Maverick Mastermind of Electricity (IET 2009).