by Marcus Chown
He need not have worried. For Faraday, who had been humiliated by his scientific peers, reading the letter from a Cambridge-educated physicist who took his work seriously was one of the great moments of his life. He wrote back to Maxwell, ‘I was at first almost frightened when I saw the mathematical force made to bear upon the subject, and then wondered to see that the subject stood it so well.’
Emboldened, Faraday asked Maxwell’s opinion of his speculative idea that there might be gravitational lines of force as well as magnetic ones – something he knew was so outlandish that it was likely to be laughed at by other physicists. Maxwell took the idea seriously and sent a long and thoughtful reply, to which Faraday responded, ‘Your letter is the first intercommunication on the subject with one of your mode and habit of thinking. It will do me much good, and I shall read and meditate again and again … I hang on to your words because they are to me weighty and … give me a great comfort.’
The four decades between Faraday and Maxwell precluded them from ever becoming the closest of friends, but they revered each other and shared a powerful bond: both had dared to challenge the scientific establishment, and neither could have achieved the fame he did without the other. Like Faraday, Maxwell knew what it felt like to be humiliated. His mother had died when he was only eight and he had been brought up in isolation by his father at Glenlair. On arrival for his first day at the prestigious Edinburgh Academy, the other pupils made fun of his country bumpkin accent, his social awkwardness and his homemade shoes and tunic, and christened him ‘Dafty’.
Maxwell struggled for many years to explain Faraday’s results. Although he started out with the idea that magnetic and electric fields behave like a fluid, he later devised a superior model. It addressed one of the most curious aspects of magnetism, which flew in the face of the Newtonians who believed a force of any kind between two bodies always acted along the line joining them. Magnetic force, as Ørsted had discovered, was circular. His compass needle, suspended beside a vertical current-carrying wire, pointed not at the wire but at right angles to it, and it continued to do so if the compass was moved around the wire. The magnetic force seemed to swirl around the wire like an invisible tornado. In fact, it was precisely this tornado that Faraday had exploited in his creation of the world’s first electric motor.
In his new ‘toy’ model, Maxwell imagined that all space, whether empty or occupied by matter, was packed with tiny toothed cogs that were able to spin. A cog in direct contact with a magnet rotated, which turned the cog next to it, which turned the next cog, and so on. In this way, a circular force was communicated through space from a magnet to a piece of metal in its vicinity.
But invisible cogs were only the starting point for Maxwell’s mechanical model. He also envisioned tiny beads that could move like ball bearings along the channels between the cogs and which represented electric currents. He continually tweaked his model to mimic more features of the real world. For instance, in an attempt to reproduce the fact that the magnetic strength of a material depends on the material, he made the ease with which the cogs inside matter turn depend on the type of matter they occupied. Finally, he made the cogs springy so that they could transmit internal forces across their bodies without losing energy. He made this last change at Glenlair in the summer before he and Katherine returned to London, and the moment he made it, he realised something hugely significant: the medium of cogs and beads he had concocted had exactly the properties necessary for the propagation of a wave.
In the case of a wave on a pond, a disturbance caused by a raindrop creates a temporary hummock of water. The existence of a restoring force – gravity – causes the hummock to collapse back down to the level of the pond. But because the water has mass, or inertia, it overshoots, so the hummock becomes a depression and the whole process repeats. But water is a continuous medium, so it does not simply oscillate up and down at one location. The disturbance is communicated to the next body of water, though with a delay, which in turn is communicated to the next body, with a further delay. In this way, a wave-like disturbance propagates outwards in concentric circles across the face of the pond.
Maxwell’s medium of cogs and beads exhibited both inertia and a restoring force. Consequently, if it were jiggled, a ripple-like disturbance would propagate through it just like a wave on a pond. There was one proviso: if the medium were conducting, a wave could not be sustained for any distance because the currents it generated would quickly sap the wave of energy. Instead, a wave could be supported only in a non-conducting medium in which only the most fleeting of currents could be made to flow.† Such ‘dielectric’ materials included water, air and the vacuum of empty space.
Maxwell realised that such a wave would consist of an electric field oscillating at right angles to a magnetic field, with both perpendicular to its direction of travel. As the electric field decayed in strength, the change automatically generated a magnetic field. And as the magnetic field decayed, the change automatically generated an electric field. The process would happen over and over again, and once set in motion would continue forever in a self-sustaining wave of electricity and magnetism.
According to Maxwell’s theory, the velocity of such an ‘electromagnetic wave’ depended on two parameters: the magnetic ‘permeability’ of the medium and its electrical ‘permittivity’. The first was a measure of how well a medium boosted a magnetic field – its restoring force – and the second a measure of how much it hindered an electric field – its inertia. Maxwell knew that both quantities had been measured experimentally for a vacuum, but stuck at Glenlair over the summer he did not have the reference book that contained the relevant results. The book was in the library at King’s College, which was why on this morning in October 1862 he had not waited for his cook to serve breakfast before running to catch the horse-drawn bus from Kensington High Street.
The London traffic had been terrible. It was the reason why a revolutionary underground transport system – the Metropolitan Railway – was being built between Paddington and Farringdon. Maxwell was not sure what he thought of the smoke and soot of steam trains operating below ground, but London was a city the like of which had never existed before and the underground railway was not the only massive engineering project underway in the metropolis: Joseph Bazalgette, chief engineer of London’s Metropolitan Board of Works, was building a gargantuan system of underground sewers.
Finally, the bus reached its destination and Maxwell disembarked near Waterloo Bridge. Dodging the pedestrians on the Strand, he hurried past Somerset House and arrived at King’s College. In the library, he quickly identified the reference book and found the data he needed from the experiments of Wilhelm Weber and Rudolf Kohlrausch. Plugging the numbers into his theory, he came up with a velocity for an electromagnetic wave in a vacuum. It was 193,088 miles per second.
Laboratory measurements made by the French physicist Hippolyte Fizeau in the late 1840s had given a figure for the speed of light as 193,118 miles per second; it was too close to be a coincidence. So not only was there a connection between electricity and magnetism, there was also a connection between electricity, magnetism and light! It was an extraordinary discovery that Maxwell had not foreseen when he had embarked on his work, but, incredibly, his calculations proved that light was a ripple in the electric and magnetic fields – a wave of electromagnetism.
One other person in the world had in fact guessed that there was a connection between electricity, magnetism and light: Faraday. In late September 1845, he had passed light from an oil lamp through a piece of lead borosilicate glass which he had placed between the north and south poles of a powerful electromagnet. When he turned on the power, he immediately observed a change in the light’s ‘polarisation’.‡ ‘I have succeeded’, he wrote jubilantly in his notebook, ‘in magnetising a ray of light.’
‘Faraday rotation’ was incontrovertible evidence that light responded to magnetism, which suggested that light itself was in some way magnetic. And because magn
etism was connected to electricity, it made sense that light must also be in some way electric. ‘I happen to have discovered a direct relation between magnetism and light, also electricity and light, and the field it opens is so large and I think rich,’ Faraday wrote prophetically.9
Alone in Faraday’s basement laboratory, Maxwell smiled to himself as he imagined his fellow scientist’s reaction to the news that he had proved the connection. To reach the proof he had stood on the shoulders of giants, and none towered higher than Faraday. Back on the street, he hardly noticed the crowds on Piccadilly. As he passed Green Park, he thought about the implications of his discovery. He entered Hyde Park and headed towards the Serpentine. He had promised Katherine he would be home in time to go to the stables in Bathurst Mews. They rode most afternoons, he on a hired horse, she on her bay pony Charlie, which had made the long train journey down from Glenlair. The plan was to circle Kensington Gardens and Hyde Park; it was not a patch on their favourite ride from Glenlair to Old Bridge of Urr, but it was the best they could do in smoky central London.
He owed so much to Katherine. Although he had nursed her through much ill health, she in turn had nursed him through smallpox, which had almost killed him shortly before their move to London. She was his soulmate and scientific helper. Together, they carried out experiments in the attic of their London house, the eight-foot-long, coffin-shaped light box with which they ‘painted’ with sunlight horrifying their neighbours and giving them the reputation of mad eccentrics. For the thirty-two-year-old Maxwell, the sojourn in London was proving to be the most productive episode of his career.
Maxwell hurried along the footpath beside the enormous expanse of the Serpentine, created in the 1720s by King George II as a memorial to his beloved wife, Queen Caroline. To the south of the kilometre-long lake lay the site of the 1851 Great Exhibition, one of the wonders of the century. Among the visitors to the great glass-and-iron pavilion, so enormous it had enclosed some of the park’s tallest trees, had been Charles Darwin, Charlotte Brontë, Charles Dickens and Alfred Tennyson. It had been disassembled bit by bit and reassembled at the Penge Place Estate in Sydenham, South London. To the southwest of its former site was ‘Albertopolis’, the district nicknamed in honour of the royal consort Prince Albert, who had died the previous December and whose plan it was that the Great Exhibition would leave a lasting cultural legacy in the form of museums and institutions. Maxwell had on numerous occasions visited the newly opened South Kensington Museum.10
A ferry was chugging across the Serpentine; swans, ducks and seagulls bobbed around it, but Maxwell paid them no attention. He was captivated instead by a rapidly fading rainbow in the sky. Ever since Piccadilly, a single thought had occupied him: his cog-and-bead model set no restriction on how fast or how slow the electromagnetic field might be jiggled, which could mean only that the colours of the rainbow represented a tiny range of possible frequencies. Beyond this visible ‘spectrum’, stretching away in both directions, there must exist undulations of the electromagnetic fields that were both more sluggish and more rapid than those of visible light. By convention, the rainbow contained seven colours, but in addition to these, he now realised, there must be other ‘colours’, invisible to the naked eye. Millions upon millions of them. It was an extraordinary, mind-expanding thought.
For a moment, standing on the path by the Serpentine amid squabbling seagulls, he was overwhelmed by a Faradayesque vision of reality. All about him, stretching to the very fringes of the known universe, was the electromagnetic field, like a vast invisible ocean of energy in constant upheaval, its multitudinous vibrations filling the air all around him. And he was the first person in the history of the human race to realise this.
As the English biologist Francis Crick would one day observe, ‘It is not easy to convey, unless one has experienced it, the dramatic feeling of sudden enlightenment that floods the mind when the right idea finally clicks into place. One immediately sees how many previously puzzling facts are neatly explained by the new hypothesis. One could kick oneself for not having the idea earlier, it now seems so obvious. Yet before, everything was in a fog.’11
Maxwell’s mind was racing. Might it be possible to artificially vibrate the electromagnetic fields? Was it conceivable that, by means of some yet-to-be-invented technology, invisible electromagnetic waves might be created? He could see no reason why not. But it was now late afternoon and he could not afford to daydream any longer. Quickening his pace, he hurried along the bank of the Serpentine and crossed the road into Kensington Gardens. Ahead of him, in the vestibule of 8 Palace Gardens,12 Katherine would already be dressed for her ride and waiting for him impatiently.
Karlsruhe, 12 December 1887
Heinrich Hertz knew something was leaping across the space between his transmitter and his receiver. According to Maxwell’s theory, if electromagnetic waves were spreading outwards from the stuttering spark of his transmitter like a disturbance from a stone tossed into a pond, they should induce an electric current in the conducting loop of his receiver, which in turn should cause a fresh spark to jump across the gap in the loop. He could not yet be absolutely sure that was happening, but he had an idea.
It was not quick to implement; it took almost a month and the help of his assistant, Julius Amman. But now, fastened securely to the sandstone front wall of the laboratory, between its two doors, was a large sheet of conducting zinc, four metres high and two metres wide. Hertz’s idea was to transmit a signal towards the zinc wall and attempt to pick up a reflection with his receiver.
It was an old idea. If a wave is reflected and propagates back through itself, the outgoing and incoming waves ‘interfere’ with each other. Where the peaks of one coincide with the peaks of the other, the two waves reinforce; and where the peaks of one coincide with the troughs of the other, they cancel each other out. The result is a wave that exhibits places where its amplitude is permanently large, alternating with places where it is zero. Such a ‘standing wave’ – most easily seen on a vigorously shaken washing line – appears frozen in space.
Hertz moved his receiver slowly towards the wall, which was twelve metres from his transmitter, and as he did so, he was amazed. The spark grew and disappeared, every three metres; it was the unmistakable signature of a standing wave, and exactly what he had expected. He and Amman had engineered the transmitter so that the stuttering spark in the gap caused an electric current to slosh back and forth along the three-metre conductor. The electric field associated with that current, changing fifty million times a second, radiated an electromagnetic wave with a three-metre separation between its peaks and troughs.
There was absolutely no doubt about it. Hertz had generated and detected Maxwell’s invisible electromagnetic waves. They had a wavelength of six metres – the distance over which they repeated their up-and-down motion. The world would never be the same again.
*
Maxwell never had the satisfaction of seeing his prediction confirmed. He died tragically young at forty-seven of stomach cancer, which had killed his mother at the same age, after an excruciating operation without anaesthetic. But before he died, he advanced his theory of electromagnetism by one more critical step.
Most other scientists had been utterly baffled by his intricate mechanical model with cogs and beads, though Maxwell never expected anyone to take it seriously – to him it had only ever been a model of nature, not the way nature actually was. And in 1873, he knocked away the theoretical scaffolding and expressed his theory in nothing more than mathematical equations that described the behaviour of the electric and magnetic fields.
Maxwell’s four equations of electromagnetism are so famous that today they are even emblazoned on T-shirts, often accompanied by the slogan ‘Let there be light!’ But Maxwell actually formulated a total of twenty equations to describe electricity and magnetism, and he wrote them not in terms of electric and magnetic fields but magnetic and electric ‘potentials’. It was the English electrical engineer and physicist O
liver Heaviside who, in 1885, reduced them to the condensed form that has since become synonymous with Maxwell’s name. (Though ironically, it is Maxwell’s original formulation which has proved most useful in the developments of twentieth-century physics.) It took only a simple manipulation of Maxwell’s equations to obtain a ‘wave equation’ that described an electromagnetic wave.
Even as a small boy, Maxwell had demonstrated intense curiosity. He’d incessantly ask the adults around him, ‘What’s the go o’ that?’ and, when they provided answers that did not satisfy him, ‘What’s the particular go o’ that?’ With his equations of electromagnetism, he had found the ‘go’ of electricity and magnetism.
One can only imagine what it must have felt like to have at last conquered electricity, magnetism and light. As Einstein would one day put it on conquering space, time and gravity, ‘The years of searching in the dark for the truth that one feels but cannot express, the intense desire and the alternations of confidence and misgiving until one breaks through to clarity and understanding, are only known to him who has experienced them himself.’
Maxwell’s equations are remarkable in many ways. First and foremost, they mark a seismic shift in our view of the universe. Since the time of Newton, physicists had used analogies from the everyday world to model the fundamental physical world, which is what Maxwell was seeking to do with his cogs and beads. But in throwing away this scaffolding, Maxwell had understood something profound about the universe: that reality is made of things – electric and magnetic fields – with no parallel in the everyday world of familiar objects. Their essence is captured only by mathematics, the underlying language of nature. In the twentieth century, this truth would be increasingly recognised by physicists as it dawned on them that gravity is the curvature of four-dimensional space–time, and that atoms and their constituents are describable only by abstract waves of probability. ‘One scientific epoch ended and another began with James Clerk Maxwell,’ said Einstein.
