The Man Who Changed Everything

The influence of James Clerk Maxwell runs all through our daily lives. His electromagnetic waves bring us radio and television and provide the radar that makes safe air travel possible. Colour television works on the three-colour principle that he demonstrated. Pilots fly aircraft by control systems which derive from his work. Many of our bridges and other structures were designed using his reciprocal diagrams and photoelastic techniques.

Even more significant is his influence on the whole development of physical science. He started a revolution in the way physicists look at the world. It was he who began to think that the objects and forces that we see and feel may be merely our limited perception of an underlying reality which is inaccessible to our senses but may be described mathematically.

He was the first to use field equations to represent physical processes; they are now the standard form used by physicists to model what goes on in the vastness of space and inside atoms. He was also the first to use statistical methods to describe processes involving many particles, another technique which is now standard. He predicted, correctly, that light was a wholly electromagnetic phenomenon and that its speed was simply the ratio between the electromagnetic and electrostatic units of charge. His equations of the electromagnetic field were the chief inspiration for Einstein’s special theory of relativity and, along with his kinetic theory of gases, played a part in Planck’s discovery of the quantum of energy. His thought experiment, Maxwell’s demon, has been creatively employed in information theory and computer science.

The Cavendish Laboratory, which he designed and started up, has been the site of many discoveries, including the electron and the structure of DNA. It is sometimes said, with no more than slight overstatement, that if you trace every line of modern physical research to its starting point you come back to Maxwell. Professor C. A. Coulson put it another way: ‘There is scarcely a single topic that he touched upon which he did not change almost beyond recognition’.

The breathtaking depth and scope of his influence are all the more remarkable because his career was cut short by early death when he was in full flow. Still more remarkable is that he is so little known to the public. Everyone has heard of Newton and Einstein but Maxwell is almost unknown outside professional circles. Why this should be so is indeed a puzzle but there are a number of possible reasons.

The one most often put forward is his modesty. He never strove to promote his own work; nor was there anyone who did it for him, as T. H. Huxley did for Darwin. While true, this is at best a part explanation. During his lifetime Maxwell’s main theories had yet to be experimentally verified and he knew from the history of science that even the greatest men had sometimes been wrong. It was not so much his modesty as his philosophical caution that held him back.

Perhaps the foremost reason is that many of his ideas were ahead of their time. The point is best illustrated by his electromagnetic theory. In the 1870s there was scant support for it in Britain outside a small group at Cambridge. It was such a new type of theory that most people were simply baffled. Even some of those who could follow all the mathematics distrusted the theory because it gave no mechanical explanations. They went along with Maxwell’s earlier spinning cell model, with all its oddities, but thought that he had gone slightly mad with his dynamical theory. Among these was Maxwell’s friend, William Thomson, who was by far the most influential physicist in Britain. Someone who did take the theory seriously was Hermann Helmholtz. He was professor of physics at Berlin University and as powerful in Germany as Thomson was in Britain. In 1879 Helmholtz persuaded the Berlin Academy of Sciences to offer a prize for a conclusive experimental test of Maxwell’s theory. His star student, Heinrich Hertz, took up the challenge.

The task was formidable: to produce and detect either displacement currents or electromagnetic waves. Light waves did not serve this purpose. They were easy to detect and, according to Maxwell’s theory, electromagnetic, but had frequencies far higher than could be produced directly by any known electrical or magnetic means. Conversely, an oscillating electrical circuit—for example, one containing a rapidly repeated spark discharge —would, if the theory was right, produce waves, but the problem lay in detecting them. Maxwell and his students at the Cavendish had fought shy of such work: it was risky and the first priority for the new Laboratory was to establish a solid reputation.

For 8 years, on and off, Hertz persevered, first as a student, then as professor of physics at Karlsruhe, trying in various ways to detect the smallest signs of a displacement current in insulators. In 1887, he put a block of paraffin between the plates of a capacitor which was rapidly charged and discharged, and looked hopefully for sparks across a small gap in a detector loop. Amazingly, sparks appeared not just in his detector but all over the apparatus. Energy from his rapidly oscillating circuit was, it seemed, being transmitted through the air and reflected by the walls. Never mind the displacement current, here was strong circumstantial evidence of electromagnetic waves; could he do better and find direct proof?

Indeed he could. His brilliant experiment made use of a well-known property of all travelling waves: when reflected back directly towards the source, the forward and backward components combine to create standing waves. Since the standing waves appear simply to oscillate in the same place they are much easier to study. Another property of waves is that, for a given travelling speed, wavelength is inversely proportional to frequency; the higher the frequency the shorter the wavelength. Fortuitously, the frequency of Hertz’s spark discharge source was high enough to give waves short enough for their length to be measured in the laboratory. Using a metal sheet reflector and a spark-gap detector, Hertz found beautiful standing waves with a wavelength of about 30 centimetres.

Eight years after his death, Maxwell’s electromagnetic theory had been emphatically verified. But its significance had scarcely begun to dawn on the scientific community, let alone the public. There was surprisingly little acclaim among British scientists for their countryman’s achievement. Even in Cambridge, reaction was muted, perhaps because Hertz had outshone their own efforts.

One can hardly fault the Cavendish for failing to produce an experimenter of the calibre of Hertz but it is a fact that no-one there had made a serious and sustained attempt to confirm Maxwell’s theory. It is in no way a criticism to surmise that, had they taken the chance and succeeded, Cambridge would have become established in the public mind as the birthplace of electromagnetic waves and Maxwell as the father. They would have been called not Hertzian waves but Maxwellian.

A few years later, some people who were not established scientists began to have some success in sending and detecting electromagnetic waves. One was a young schoolmaster in Christchurch, New Zealand. When he got a scholarship to England in 1895 to take up research at the Cavendish Laboratory he brought his detector with him. Soon he was sending and detecting waves over a range of half a mile. His name was Ernest Rutherford. But Rutherford rapidly became immersed in other work and lost interest in the waves. One can see why: the Cavendish was a-buzz with exciting experiments on the conduction of electricity through gases and J. J. Thomson was on the threshold of discovering the electron. Rutherford was soon making his own discoveries in that field. Had he been differently inclined, Cambridge might have become the birthplace of radio, with a consequent further boost to Maxwell’s public reputation.

A young Italian arrived in Britain at about the same time as Rutherford. Guglielmo Marconi had come specifically to seek support for his experiments on sending and detecting waves, having failed to interest his own countrymen. Helped by an English cousin and by William Preece, chief engineer to the Post Office, he took out patents and extended the range of detection. There was still no commercial interest, so he started his own company and, in a brilliantly successful piece of publicity, equipped two ships to send reports on the 1899 America’s Cup yacht race to a shore station, from where they could be telegraphed by cable to newspapers in America and Britain. Wireless telegraphy was born. Sound radio followed, and then television and worldwide communication via satellites.

While Marconi was finding ways of putting Maxwell’s theory to everyday use, a junior official in the Swiss Patent Office was pondering the fundamental nature of space and time. Albert Einstein brooded over an apparent conflict between Maxwell’s equations of the electromagnetic field and Newton’s laws of motion. It stemmed from a famous experiment by Albert Abraham Michelson and Edward Morley which suggested that light always appears to travel at exactly the same speed, no matter how fast or in what direction the observer is moving. This seemed to contradict common sense but could be explained if distances and times appeared different to observers travelling at different velocities. A formula for converting the times and distances measured by one observer to those measured by another had been put forward by Hendrik Antoon Lorentz. The extraordinary thing was that the formula seemed to be intrinsic to Maxwell’s equations; they worked perfectly under this transformation whereas Newton’s laws did not.

Einstein resolved the conflict in his Special Theory of Relativity by turning the problem inside out. He took the constancy of the speed of light as a starting point and worked out the consequences. He arrived at Lorentz’s formula from a new direction and gave it an entirely new perspective. There were no absolute measures of space or time: all observers in uniform relative motion measured them differently and all their measurements were equally valid. A corollary of this was that Maxwell’s equations were the basic laws of the physical world. Newton’s laws were an approximation which worked well as long as the relative speeds of observers were small compared with that of light. Another corollary was the celebrated equation E = mc ²; mass was a simply an immensely concentrated form of stored energy.

Underlying all this was Einstein’s axiom that the speed of light was an absolute constant. It was the fundamental characteristic of the universe, nature’s gearing between space and time. And it was completely determined by Maxwell’s theory: its value was simply the ratio of the electromagnetic and electrostatic units of charge¹.

Even though it ran counter to common intuition, Einstein’s theory was more rapidly accepted than Maxwell’s had been. It explained perfectly the way atomic particles behaved when they travelled at speeds approaching that of light and accounted for the loss of mass when a radioactive atom decays into two smaller ones. It later provided the basis for nuclear power generation and the atomic bomb. Einstein followed up the Special Theory with his General Theory of Relativity, which explained gravity as a geometrical property of space and time. Almost nobody among the public understood it but they were captivated by the mystique of ‘curved’ space-time and Einstein became an international celebrity, everywhere acclaimed as Newton’s successor.

General Relativity was from first to last a field theory of the kind pioneered by Maxwell. Einstein was fulsome in recognition of Maxwell’s crucial contribution and our hero’s stock rose still higher with physicists. None of this, however, reached the public.

Maxwell’s electromagnetic theory is now recognised as one of the most important of all scientific discoveries. It is at the heart of physics, and shapes our everyday lives. But recognition of its importance has been gradual, cumulative and largely out of the public view. He is a giant figure who remains just out of sight.

What of Maxwell’s part in the genesis of quantum theory? The discovery in the early twentieth century that all forms of energy come in discrete packets is probably the most profound shock ever to hit the scientific world. The first rumblings came from Maxwell’s and Boltzmann’s work on gases in the 1860s and 1870s, when their theory predicted that the kinetic energy of molecules should be equally distributed over all independent modes of motion. This implied a simple formula for the ratio of the specific heats at constant pressure and constant volume, but, as we have seen, values observed in practice obstinately failed to follow the formula. Maxwell’s intuition was spot on when he concluded that ‘something essential to the complete statement of the physical theory of molecular encounters must have hitherto escaped us’. His view was reinforced when scientists began to put together the combined implications of the kinetic theory of gases, thermodynamics, and Maxwell’s electromagnetic theory in the study of so-called ‘black body’ radiation. Matters came to a head towards the end of the century, when the combined theories seemed to indicate that all the kinetic energy of molecules should long ago have been radiated away, leaving a cold, dead universe². What was missing? Nature seemed to have some hidden mechanism which curtailed radiation at the higher frequencies and so allowed a balance to be reached between the radiation that matter emitted and the radiation it absorbed. The denouement came in 1900: in what he described as ‘an act of desperation’, Max Planck produced a formula which achieved the desired balance by allowing matter to absorb radiant energy only in discrete amounts, or ‘quanta’. At first Planck mistrusted his monstrous creation and so did everyone else. It took the boldness of Albert Einstein to complete the coup in 1905 by asserting that radiation itself comes in discrete packets, now called photons.

Quantum theory has explained why the specific heats of gases do not follow the simple formula which Maxwell and Boltzmann used, why matter does not radiate away all its energy, and many things besides. There is now no doubt whatever that all forms of energy, including radiation, come in quanta. But, according to Maxwell’s electromagnetic theory, radiation consists of continuous waves, not discrete packets. Does this mean his equations are wrong? By no means: Maxwell’s theory works perfectly at any scale large enough to allow the minute graininess of energy to be averaged out and, even at smaller scales, it underpins such theories as quantum electrodynamics. It holds complete sway in its own domain but Maxwell never claimed or believed that its fields or waves represent ultimate physical reality. In his own words:

The changes of direction which light undergoes in passing from one medium to another are identical with the deviations of the path of a particle in moving through a narrow space in which intense forces act. This analogy was long believed to be the true explanation of the refraction of light; and we still find it useful in the solution of certain problems, in which we employ it without danger as an artificial method. The other analogy, between light and the vibrations of an elastic medium, extends much farther, but though its importance and fruitfulness cannot be overestimated, we must recollect that it is founded only on a resemblance in form between the laws of light and those of vibrations.

The great physicist James Jeans, writing in 1931, comments that this sounds ‘almost like an extract from a lecture on modern wave-mechanics—and a very good one too’. Maxwell’s point is equally relevant today. He is, in effect, telling us that although the things we call photons and electrons appear to us to behave sometimes like particles and sometimes like waves, we should not make the mistake of thinking that they are either. His view was exactly that later expressed by J. B. S. Haldane, who said: ‘My own suspicion is that the universe is not only queerer than we suppose, but queerer than we can suppose’.

Perhaps the most puzzling aspect of Maxwell’s relative obscurity is the poverty of official recognition in his own country. Oxford and Edinburgh gave him honorary degrees but he received only two other British awards in his lifetime: a Rumford Medal from the Royal Society of London and a Keith Medal from the Royal Society of Edinburgh. The work thus rewarded was on colour vision, and reciprocal diagrams for engineering structures. Other countries were less reticent: he received honours from New York, Boston, Philadelphia, Amsterdam, Vienna, Göttingen and Pavia.

As the years went by, other countries still seemed to be more generous with tributes than his own. When the Royal Society of London held its tricentenary celebration in 1960, the Queen attended. In her speech she praised a number of famous former Fellows—presumably listed for her by the Society. Inexplicably, Maxwell was not among them. He has been more widely commemorated elsewhere, even in countries without a strong scientific tradition: for example, the governments of Mexico, Nicaragua and San Marino are among those who have issued special postage stamps in his honour.

There are Maxwell devotees around the world. People from many countries still come to visit his burial place at Parton. His work is, even now, the subject of wide and intense study, both by students and by distinguished scientific historians such as Daniel Siegel and Peter Harman.

A small group based in Edinburgh formed the James Clerk Maxwell Foundation in 1977 and in 1993 succeeded in acquiring the house at 14 India Street where he was born. Fittingly, the house is used as a working centre for the mathematical sciences, a place for scientists, engineers and mathematicians from all countries to meet for seminars and courses. One room holds a lovingly presented display of memorabilia.

People who knew Maxwell have left us with more than his scientific achievements. We have a picture of a man who was the kind of friend everyone would love to have: generous, considerate, brave, genial, entertaining, and entirely without vanity or pretence. The friend who knew him best described his character as having ‘a grand simplicity’: he was the same all the way through and the same to everyone³.

The deep wholeness of Maxwell’s character is as plain in his scientific work as in his personal life. The little boy who never stopped asking ‘What’s the go o’ that?’ became the man who changed the way that physicists think about the world and opened the way to vast new regions of knowledge. His place in the grand scheme of things was aptly described by a scientist from the following generation. Oliver Heaviside was an acerbic and cynical man whose criticism could be withering. But when he spoke of Maxwell all world-weariness dropped away and what shone through was pure joy:

A part of us lives after us, diffused through all humanity—more or less—and through all nature. This is the immortality of the soul. There are large souls and small souls ... That of a Shakespeare or Newton is stupendously big. Such men live the best part of their lives after they are dead. Maxwell is one of these men. His soul will live and grow for long to come, and hundreds of years hence will shine as one of the bright stars of the past, whose light takes ages to reach us.