Faraday, Maxwell, and the Electromagnetic Field
Page 26
…you have gone further than Maxwell and that if he had lived he would have acknowledged the superiority of your methods.18
In 1885, Hertz gained the post of professor of experimental physics at the Hochschule in Karlsruhe. Within a year, he had married the daughter of one of the other lecturers and was hard at work in the well-equipped laboratory, trying again to find the faintest sign of displacement currents in insulators. Attempt after attempt yielded no result. In the end he succeeded, but in the course of these attempts he found a far more effective way to verify Maxwell's theory.
Among the stock apparatus was a pair of so-called Knochenhauer spirals, flat coils insulated by sealing wax, that were intended to give a graphic demonstration of Faraday's principle of induction. A spark-generating circuit induced sparking across the terminals of a another circuit that was separate from the first but magnetically linked to it across a small air gap. One day, possibly while setting up a demonstration for a class, Hertz was surprised to see sparks also coming from a stray wire alongside. What was going on? At this stage, he didn't really know what he was looking for, but he followed his intuition and felt his way toward a great discovery. A year before Lodge, Hertz discovered electromagnetic waves along wires. Both had taken advantage of chance observations, but Hertz found something Lodge had missed—something to “feel” the waves with—and it was nothing more than a loop of wire with a small gap between its ends across which sparks could jump. If the detector loop was the right size and shape, it would be tuned to the frequency of the waves; they would set it resonating and generate enough electromotive force in the wire to make sparks jump across the gap. It sounds simple, but even for Hertz, the most gifted of experimenters, results came only after many hours of trial and error and were the fruit of determination as much as skill.
Waves along wires were exciting, but the ultimate test of Maxwell's theory would be to detect waves in space. Hertz's primary sparking circuit became his transmitter, and the loop of wire with the spark gap his detector.
Fig. 16.1. Schematic layout of Hertz's apparatus for producing and detecting electromagnetic waves. (Used with permission from Lee Bartrop.)
He tried many variants of both and, with the spark terminals in the detector set as close together as possible, he carried it around the room looking for sparks. Sure enough, faint sparks appeared. We now come to the historic scene that introduces this book. Using a large zinc sheet as a reflector, he moved the detector around and found some places where there was no sparking and others where the sparking was strongest. This was evidence of a standing wave that can only have been formed by a traveling wave combining with its reflection from the zinc screen. He had produced and detected electromagnetic waves in space.
For some this might have been enough, but for Hertz it was just the beginning. In a brilliant series of experiments, he examined every aspect of the new waves. He found that although the waves were reflected by any metal surface, they passed unimpeded through thick wooden doors. He also showed that the waves traveled at the speed of light; that they could be polarized, just like light; and that they could be refracted in the same way that light is through a glass lens or a prism. In a sense, his waves were light waves, but of much longer wavelength than visible light; we use them as radio waves today.
In 1888, Hertz presented his findings in a magnificent series of experimental papers—it was the second of these that Lodge had read on the train out of Liverpool. They were written in a matter-of-fact style, with no grand announcement, and at first attracted very little attention. Given Helmholtz's apparent enthusiasm for Maxwell's theory, one might have expected some excitement in Germany, but physicists there had been raised on the action-at-a-distance theories of Weber and Neumann, and even Helmholtz had interpreted Maxwell's theory in a way that held onto some of the action-at-a-distance notions and was, according to the British Maxwellians, plain wrong. It failed to explain the flow of electromagnetic energy in space, and without energy flow there could be no waves, no matter how you jiggled the mathematics. Heaviside put it bluntly, as usual:
Helmholtz's theory seems to me as if he had read Maxwell all at once, then gone to bed and had a bad dream about it, and then put it down on paper independently; his theory being Maxwell's run mad.19
Hertz, though, revered Helmholtz and didn't realize at first what a catastrophic blow he had dealt to his mentor's ideas. He knew his discoveries were significant, but he seemed to surpass even Maxwell in modesty and said he was content to let others judge their worth. Across the English Channel there was no such restraint. The British Maxwellians had made the theory their own and had no doubt of its validity. All they lacked was clear physical proof to convince skeptics, and this Hertz had handsomely supplied. He was a hero. They showered him with praise, welcomed him into their ranks with joy, and set about promoting his work with tremendous enthusiasm. Fitzgerald told the assembled company at the British Association's big meeting in Bath of the “beautiful device” by which Hertz had succeeded; Lodge made a replica of Hertz's apparatus, which he demonstrated at every opportunity; and Heaviside wrote to thank Hertz for killing off the action-at-a-distance theories:
I recognized that these theories were nowhere, in the presence of Maxwell's, and that he was a heaven-born genius. But so long as a strict experimental proof was wanting so long would these speculations continue to flourish. You have given them a death blow.20
It was later often said, with no more than slight exaggeration, that news of Hertz's discoveries reached Germany by way of England. In 1890, the Royal Society awarded Hertz its Rumford Medal, and he came to London to collect it. One free evening, Hertz, Lodge, and Fitzgerald dined together at the Langham Hotel. They must have felt the presence of a metaphorical empty chair. Heaviside, who habitually turned down invitations, would surely for once have left his room and joined them, but he was by now living two hundred miles away in Torquay. The four had become a close and mutually supportive group—four very different individuals joined in a common cause. They had brought Maxwell's theory—in truth both Maxwell and Faraday's theory—to the world.
The epoch that, in Einstein's words, began with James Clerk Maxwell was under way. The Maxwellians had opened up huge opportunities, but there were still skirmishes to be fought and shocks to be borne.
When Heinrich Hertz visited London in 1890, he had been only narrowly dissuaded from making the 400-mile round journey to Torquay to see the reclusive Heaviside. They had built up a firm friendship through letters, but neither knew this would be their only chance to meet. Hertz died from a rare bone disease in 1894 at the tragically early age of thirty-six. We can never know what else he would have achieved, but the other Maxwellians still had parts to play.
Oliver Heaviside was always in a fight with someone or other, and in the early 1890s his chief adversary was Maxwell's old friend P. G. Tait. They clashed over the new system of vector analysis, by which Maxwell's theory had been summarized in the four now-famous equations. In Tait's view, Heaviside (and, independently, Gibbs in America) had committed sacrilege by mutilating William Hamilton's beautiful quaternions. Heaviside already had widespread opposition: some from people who couldn't make heads or tails of either quaternions or the new vector notation, and some from others like William Thomson who could but preferred to stick to the old triple-equation method with its so-called Cartesian (x, y, z) coordinates. However, Tait was his fiercest opponent and both enjoyed a good scrap. When Tait described vector analysis as “a hermaphrodite monster,” Heaviside responded by calling Tait a “consummately profound metaphysicomathematician” and added:
“Quaternion” was, I think, defined by an American schoolgirl to be “an ancient religious ceremony.” This was, however, a complete mistake. The ancients—unlike Prof. Tait—knew not, and did not worship Quaternions.1
Exchanges like these appeared in the scientific journals and kept readers entertained for more than a year. As usual, Heaviside was right: today, his vectors are everywhere and quaternions are hardly
to be seen.
Meanwhile, Oliver Lodge was trying to take Hertz's experimental work further, using an ingenious new receiving device called a coherer.2 He made good progress but was once again overtaken, this time by a young Italian. Guglielmo Marconi was having similar success with similar equipment on the family estate near Bologna; he had seen very early the huge commercial potential of radio telegraphy and was set on making his fortune. Having failed to get sponsorship in his own country, he came to England and persuaded the Post Office's senior engineer, William Preece, to back him. Things went well, but the astute Marconi soon felt the bonds of state patronage tightening, cut himself free, and started his own company with help from an English cousin who had influence in the money markets of the city of London. Not only a resourceful inventor but also a persuasive salesman, Marconi was soon running well-publicized ship-to-shore trials in the Solent, a strait separating the Isle of Wight from the English mainland. He knew very little theory and worked mostly by trial and error, but now he could afford to employ the best engineers and hired Maxwell's old student, Ambrose Fleming.
With Fleming's help, Marconi planned to stage the most dramatic event possible by sending a wireless telegraph message across the Atlantic Ocean. Most physicists thought the venture was doomed because the transmitted waves wouldn't follow the curve of Earth's surface but would go straight off into space. However, Marconi's intuition said otherwise: the project went ahead, and in 1901 a signal from Poldhu in Cornwall was received by a kite-borne antenna in Newfoundland. Men had begun to harness Maxwell's electromagnetic waves for their own use, and it was as though Earth had shrunk. Wireless telegraph became standard equipment on ships, sound radio followed, then television, radar, cell phones, and worldwide transmission of signals via satellites. The miracle of near-instant communication without wires over great distances became taken for granted—a part of everyday life.3
Another aspect of the new technological epoch was the growing use of electrical energy in homes, in factories, and in transportation. It stemmed from Faraday's discoveries of the electric motor in 1821 and electromagnetic induction in 1831, but things only really got going much later in the century when, thanks to Swan's and Edison's filament light bulbs, domestic electric lighting became a commercial proposition. There was then a need to generate and distribute electricity widely and efficiently. When this was met—first by using direct-current methods and then by Nikola Tesla's brilliant multiphase alternating-current generators and distribution systems—the way was open for the development of all kinds of electrical machinery for industrial and domestic use, and for transport. Every generator, every motor, and every transformer that we use today depends on the interaction of electric and magnetic field forces. In short, not only our communications but also almost our whole way of life has come to depend on technology that exploits the electromagnetic field—a feature of the physical world that was undreamed of until it was first envisaged by Faraday, then elucidated by Maxwell.
But even more significant than the advance in technology is the way that Faraday and Maxwell's concept of the electromagnetic field transformed scientists’ view of the physical world. During the late decades of the nineteenth century a sea change was gradually taking place within the physics community as more and more people grasped the truth of Maxwell's warning: mechanical models cannot be relied on to explain physical phenomena, and to use them risks confusing representation and reality.
Faraday and Maxwell's field was intangible, and space was not just an empty geometrical container for bodies with mass but a coherent interconnected system bearing the energy of motion. It was the seat of action, rather than just an empty backdrop for Newton's point particles being propelled by straight-line forces. These were ultraradical concepts for nineteenth-century minds trained to think only of things that could be touched and measured. Properties of the field, like the electric and magnetic intensities, were abstract quantities—all they had in common with the quantities in Newton's laws of matter in motion was that they obeyed dynamical equations. Maxwell had replaced a universe in which tangible objects interacted with one another at a distance by one where abstract fields extended throughout space and interacted only locally with tangible objects.
His equations of the electromagnetic field came to take on a life of their own, divested of any mechanical association—the abstract mathematical language of the field was sufficient in itself. While Fitzgerald, Lodge, and others were searching for ingenious quasimechanical ways to interpret Maxwell's theory, Heinrich Hertz gave the simplest and best explanation. He said, “I know of no shorter or more definite answer than the following—Maxwell's theory is Maxwell's system of equations.”4
As Freeman Dyson has aptly observed, Maxwell's theory becomes elegant and clear only after one has given up the need for a mechanical model.
Here was a physical theory expressed solely by its equations, and it brought about a profound change in physicists’ concept of reality. The startlingly new idea was that reality exists on two levels. Beneath all the things that we can touch and feel (or make models of) lies a deeper reality that expresses itself in the language of mathematics. In this underlying layer are quantities, like the electric and magnetic field intensities, that are quite different from anything we can access with our senses. They must, in some sense, be real, because they give rise to all the mechanical forces that we can feel and represent in models, but the only way we can describe them is through abstract symbols in equations.
Although the idea of a two-tier reality was implicit in Maxwell's theory, he never articulated it in quite this way and it didn't fully take hold until well into the twentieth century. Nevertheless, the ground was shifting. Newton's laws of matter and motion, for two centuries the bedrock of natural philosophy, no longer provided a sufficient base for scientific thinking about all phenomena in the physical world. As Einstein put it:
Since Maxwell's time, physical reality has been thought of as represented by continuous fields and not capable of any mechanical interpretation. This change in the conception of reality is the most profound and fruitful that physics has experienced since the time of Newton.5
The theory of the electromagnetic field, encapsulated in four equations, had ushered in a new epoch and was gradually gaining general acceptance but was itself soon jolted by two discoveries made around the turn of the century. The first was the electron.
Faraday and Maxwell believed in the primacy of the field. Their electric and magnetic fields filled all space, including those parts occupied by matter. Matter interacted with the field by modifying the properties of the parts of the field with which it shared space, and one effect of this was the appearance of electric charge on the surfaces of conducting substances immersed in an electric field. In an insulating medium such as glass or air, the field took the form of an electric displacement, or polarization of the insulating particles along the lines of force; and where the lines terminated, say on two conducting metal plates, the surfaces of the plates, by virtue of their contact with the field, appeared to contain a charge, positive on one plate and negative on the other. Electric currents were similarly effects of the field. Taking these thoughts further, Heaviside had explained that current-carrying wires were merely guides for the passage of energy through the surrounding space. All this was in complete contrast to the earlier view that electricity was some kind of fluid substance that existed in conductors, and that electric and magnetic forces resulted from the charges or currents in conductors acting on one another at a distance. The field view had triumphed when Hertz found the electromagnetic waves that Maxwell had predicted, but not all theorists were content to believe that electric charge was simply an artifact of the field.
Among the doubters were the great Dutch physicist Hendrik Antoon Lorentz and Joseph Larmor, an Ulsterman who had happily settled into the life of a don at Cambridge. They began to construct versions of the field that allowed electrically charged particles to exist in their own right, and, in the end,
succeeded in modifying and extending Maxwell's theory. This wasn't all. In 1897, Lord Rayleigh's successor at the Cavendish, J. J. Thomson, discovered the electron, a material particle with an intrinsic electric charge. Here was empirical evidence of the theoretical particles that Lorentz and Larmor had postulated. They had, in a sense, completed Faraday's and Maxwell's great project by establishing the true relationship between the field and matter: electric charges reside in matter, but their effects are transmitted by the surrounding field, with which their own fields are intertwined. In his “dynamical” aether, Maxwell had retained the quasimechanical concepts of flywheel-like kinetic energy and spring-like potential energy, but Lorentz replaced it with a purely electromagnetic aether that interacted with electrons whose energy of motion was entirely due to their own electromagnetic fields. The mechanical school of thought was relinquishing its last hold: scientists had begun to see electromagnetism not merely as a companion to the traditional laws governing the motion of matter but as the new conceptual foundation for all of their studies of the physical world.
The second of the great discoveries at the turn of the century came like an earthquake. Maxwell's theory of electromagnetism predicted that so-called black bodies should radiate much more energy at high frequencies than they actually did. (A black body is a theoretical object that absorbs all the radiation that hits it.) Nature seemed to have some hidden mechanism that chopped off the high-frequency end of the radiation spectrum, but no one had any idea what it was. Then, in 1900, Max Planck, professor of theoretical physics at Berlin University, found the solution. In what he called “an act of desperation,”6 he cobbled together a formula that matched experimental results very well, but with a proviso: the energy radiated or absorbed by black bodies had to occur only in discrete amounts, or “quanta” that were proportional to the frequency of the radiation. For a while, Planck and others mistrusted his monstrous creation and went on looking for a more plausible alternative, but in 1905, a junior clerk in the Bern patent office named Albert Einstein boldly took things even further by proposing that Planck's quanta were not merely specified amounts of radiation but indivisible, discrete packets of radiation, now called photons.