by Nancy Forbes
Amazingly, Einstein produced readymade empirical evidence to support his claim: it explained the hitherto-inexplicable photoelectric effect. Experimenters had found that a beam of ultraviolet light could dislodge electrons from the surface of a metal object, causing them to be emitted. The shorter the wavelength of the light, the higher was the energy of the electrons, but, strangely, when the intensity, or “brightness,” of the beam was weakened, the energy of the electrons stayed the same, though their number decreased. Maxwell's theory on its own couldn't explain this, but Einstein's photons did so perfectly. Each photon was a separate packet containing an amount of energy that depended only on the wavelength of the light (or its frequency), so when the beam was weakened, it contained fewer photons, but each one had the same energy as before. Consequently, fewer electrons were emitted but the energy of each one was the same, identical to that of the photon that had dislodged it. The electron's energy was equal to hν, where ν was the frequency of the electromagnetic wave and h was a new quantity that came to be called Planck's constant. Its value, 6.62606957 × 10−34 joule-seconds, demonstrates the minute size of energy quanta.
So, the electromagnetic waves that Faraday had envisaged in his “Ray-vibrations” talk, that Maxwell had predicted mathematically in his “Dynamical Theory” paper, and that Hertz had produced and detected in his laboratory not only had the properties of a continuous wave but also, in an apparent paradox, also behaved like discrete packets or particles. How could the great theory of the electromagnetic field be reconciled with this apparently shattering revelation? In the course of the quantum's assimilation into mainstream physics in the early decades of the twentieth century, this wave-particle duality became a tenet of a new theory. Niels Bohr, Werner Heisenberg, Erwin Schrödinger, and Wolfgang Pauli led the way in the creation of quantum mechanics. They and others, notably Paul Dirac, also eventually adapted the “classical” field concept of electromagnetism for minute-length scales (those on the order of Planck's constant) by “quantizing” the field. Hence have come all the great field theories of modern physics, such as quantum electrodynamics and the Standard Model—the reigning model of intercoupled particles and fields by which today's physicists are carrying on Faraday's quest to unify all known forces.
There's an interesting sidelight on these great developments. The creators of quantum electrodynamics didn't just use Heaviside's compact four-equation version of Maxwell's theory. As one of them, Richard P. Feynman, explained: “In the general theory of quantum electrodynamics, one takes the vector and scalar potentials as the fundamental quantities.”7
These “fundamental quantities” are the very ones that Heaviside had eliminated when condensing Maxwell's equations, so the wisdom of Maxwell in keeping options open by retaining all the equations has been handsomely borne out.
Our story concludes with yet another great discovery—one in which the “classical” theory of the electromagnetic field played a central role—and it starts with what had been the last bastion of the old mechanical school, the aether. Even though Maxwell had abandoned his mechanical model, he was ambivalent about the aether and was never able to do away with the notion completely. In his “Dynamical Theory” paper, he still required a medium, or aether, even if it was, in effect, just a set of properties without a specified mechanism. Others persisted in constructing ever more elaborate mechanical models of the aether: Lodge's favorite model had a rack and pinion mechanism; Fitzgerald's had pulleys and bands; and William Thomson proposed one, called the vortex sponge, with a mechanism so unusual that even he couldn't find exact equations to describe it.
Since the aether occupied all space, Earth must move through it, as a ship moves through the sea. This motion was called the “aether drift,” and physicists set out to measure it. The measurement required such precision that Maxwell himself doubted whether it could be achieved in any laboratory; he proposed instead a method using observations of Jupiter's moons. Nothing came of that, but a young American, Albert Michelson, took Maxwell's doubts about earthbound methods as a challenge and developed his interferometer, an instrument that used the tiny wavelengths of light as measurement units and so made possible a degree of precision hitherto undreamed of. With his colleague Edward Morley, he devised an experiment to measure the difference in speed of the two parts of a light beam that had been split at right angles.8 Michelson and Morley carried out their experiment in Cleveland, Ohio, in 1887. Even the smallest difference in speeds would have established for all time that the aether did indeed exist, but to the experimenters’ consternation, the speed of light in both directions was identical, and repeated trials gave the same result. This was a huge disappointment, and at first the experiment was seen as no more than another failed attempt to measure the aether drift. Michelson himself rarely spoke of his result and never realized its significance.
Heaviside was, at about the same time, investigating the implications of Maxwell's theory for the behavior of moving electric charges, and in a paper published in 1889 he made the extraordinary claim that the field of a point charge moving with velocity v relative to the aether would contract in its direction of motion by the factor √(1 − v²/c²), where c was the speed of light: If the charge reached the speed of light, its field would be squashed flat. This was the first appearance of the factor √(1 − v²/c²), which has become very familiar to physicists and is sometimes called simply the relativistic factor. Heaviside's friend Fitzgerald took the idea further and proposed that all matter behaved in this way. If every object moving relative to the aether contracted by the same factor in its direction of motion, then Michelson and Morley's result was explained—their instruments would contract by exactly the amount needed to compensate for the aether drift, hence the null result. The idea seemed crazy, but Fitzgerald wasn't the only one to think along these lines—Lorentz independently made the same proposal, and the phenomenon came to be called the Lorentz-Fitzgerald contraction. This wasn't all: Lorentz went further by asserting that clocks would slow down by the same factor if they approached the speed of light—if a clock actually reached the speed of light, it would stop.
How could measuring rods shrink and clocks slow? Some began to question the existence of any absolute measures of space and time. One was the great French mathematician and occasional physicist Henri Poincaré. In a book published in 1902, he wrote:
There is no absolute uniform motion. No physical experience can therefore detect any inertial motion. There is no absolute time. Saying that two events have the same duration is conventional, just as saying they are simultaneous is purely conventional, if they occur in different places.9
Poincaré was anticipating what is now called the special theory of relativity. In an earlier paper, he had shown that the equivalent mass, m, of a quantity of electromagnetic radiation with energy E is given by an equation with a familiar ring, m = E/c², but he didn't put everything tightly together and was overtaken by another, just as Lodge had been by Hertz and Marconi.10 The scene was set for Albert Einstein, who produced his famous paper on special relativity in 1905 within a few months of the one in which he predicted the photon.
Like Heaviside, Fitzgerald, Lorentz, and Poincaré, Einstein studied Maxwell's theory and thought long and hard about its consequences, especially those for time and space. Eventually he found a devastatingly simple and direct approach that the others had missed. The laws of physics, he claimed, must be the same for all observers traveling at a uniform velocity relative to one another. Maxwell's equations were among these laws, and they gave a single value for the speed of light in a vacuum (or in air) irrespective of the observer's motion. In Einstein's view, this was enough on its own to explain Michelson and Morley's result—the speed of light was always the same for any observer traveling at a steady velocity—but what followed from this simple-sounding proposition was one of the greatest shocks ever to hit the world of science. The laws of physics were, indeed, the same for all observers in uniform relative motion. What was not th
e same were their measurements of time and space—any two observers who were moving relative to one another measured both time and space differently. To reconcile their observations required a mathematical transformation of coordinates using the factor √(1 − v²/c²); Einstein called it the Lorentz transformation. Using this transformation in conjunction with Maxwell's equations of the electromagnetic field, Einstein calculated that when a body absorbs a given amount of energy from radiation, its inertial mass increases by that amount divided by c². What then followed after a few lines of algebra was the famous equation:
E = mc²
where E is the intrinsic energy of a body, m is its mass at rest, and c is the speed of light, about 300 million kilometers per second. By Einstein's reasoning, this relationship between mass and energy was a necessary consequence of Maxwell's theory of electromagnetism. It was a finding of tremendous importance to physicists, but nobody at the time dreamed that it would be possible to make a bomb by annihilating a little mass and so liberating a vast amount of energy. As we've seen, this equation had already been published by Poincaré. All the other formulas of special relativity had also been published in one form or another, but it was Einstein who brought everything together in 1905 with a crystal-clear and utterly fresh vision.11
Another consequence of Einstein's theory was that nothing could travel faster than the speed of light. In fact, no object with mass could even reach that speed because to do so would require an infinite amount of energy. Remarkably, nature had a speed limit that was completely determined by Maxwell's theory of the electromagnetic field and depended only on the elementary properties of electricity and magnetism.
What of the aether? It needed to operate in a single universal frame of reference of absolute space and time, and Einstein had demolished those by showing that observers who were moving relative to each other measured distance and time differently. So the aether no longer had a home. Nor did it have a reason for existence. No longer was space simply the theater in which the laws of physics performed; coupled with time, it was part of the action. Space and time were entities in their own right; they obeyed the laws of special relativity and, by the same token, had exactly the properties necessary to support the electromagnetic field. As Lorentz went on to show, Maxwell's equations actually required space and time to behave as Einstein proposed. So all the efforts of the aether-model builders came to nothing in the end. Or did they? The keystone of Maxwell's theory, the displacement current, had its origin in the idea that the spinning cells in his now-discarded model could be springy. And although all the mechanical models proposed by Lodge, Fitzgerald, Thomson, and others seem bizarre today, they served in their time as stimuli for thought and so contributed to the general development of physical science. They had served as the scaffolding upon which the field theory of electromagnetism was built, to be then kicked away so that the theory could stand on its own, tall and free.
It is often said that Faraday and Maxwell provided the bridge between Newton and Einstein. While true, this statement is incomplete. Newton was known to have attributed his achievements to “standing on the shoulders of giants,” and when Einstein visited Britain it was natural for the press to ask him if he had stood on the shoulders of Newton. Einstein replied: “That statement is not quite right; I stood on Maxwell's shoulders.”12 Maxwell would have pointed out that he, in turn, had Faraday's shoulders to stand on. Their partnership made a contribution to physical science, indeed to human knowledge, comparable with those of Newton and Einstein.
Einstein said a new epoch began with James Clerk Maxwell. Maxwell himself would probably have said that it began in 1821 when Michael Faraday first imagined a circular force around a current-carrying wire. Together, they gave future generations a model for the interplay of experiment and theory, where each illuminates a path for the other. Neither man was confined to the role commonly assigned to him by casual historians. Faraday, the renowned experimenter, put forward some of the most imaginative and daring theoretical ideas; and Maxwell, the cerebral theoretician, carried out some of the most demanding experiments. Both knew that no theory counted a jot unless it stood up to the scrutiny of experiment. The dialogue between experiment and theory that they conducted was one of the most fertile ever to occur in science, and it set a priceless precedent for twentieth-century physics.
They also gave us the means to leave behind a mechanical world of rigid bodies and instantaneous straight-line forces operating at a distance, and to move to four-dimensional space-time, where time, length, and mass depend on the observer. Who could have guessed that the Newtonian outlook would turn out to be so parochial, or that there was a new world lying beneath the surface of our everyday reality? The notion of the field has been the portal to the great discoveries of modern physics, leading us to profound questions about the ultimate nature of the universe at scales of huge energy and infinitesimally small length that even far-seeing Maxwell could never have imagined.
Their paradigm-changing discoveries opened the way to today's great research in elementary particle physics, exemplified by the quest for the Higgs field, a field that endows matter with mass and gives it structure. In tacit tribute to Faraday's prescience in seeking to unify nature's forces, and growing from the seeds he sowed using his simple laboratory instruments, physicists today are still trying to unite the fundamental forces of the universe—the electromagnetic force, the weak and strong nuclear forces, and gravity—in a single, unified theory.13 Their quest requires millions of subatomic collisions to take place in massive particle accelerators in order to reach the enormous energies and minute dimensions where the four forces might be shown to be different aspects of a single, unifying force. The Higgs field has been such an alluring goal that governments have poured billions of dollars and trillions of volts of electricity into machines designed to wrest it into observable reality, and scientists at the Large Hadron Collider at the European Organization for Nuclear Research (CERN) are now celebrating success. Work goes on, and doubtless more discoveries will bring yet deeper questions.
Faraday and Maxwell remind us of what it means to be a true scientist, whose work embodies the ideal of the human intellect trying to understand nature. They were seekers of truth—inquisitive, objective, tenacious, and ethical, and without vanity or worldly ambition. Their generosity of spirit and their humility enhanced their stature as scientists. One might say that, as Victorian gentlemen, it was easier to for them to embody these ideals than it is for anybody today—the business of science was simpler then, and gentlemanliness mattered more—but the characters of Faraday and Maxwell would have shone through no matter what the age, and their greatness encompasses not only their discoveries but also their characters as scientists and as men. If there is something like heroism in science, they are heroes.
The influence of Faraday and Maxwell's work spreads far beyond their achievement in elucidating and unifying electricity and magnetism. Their concept of the field challenged a paradigm that had seemed immutable and, through their powers of thought and experiment, they began to reveal some of nature's deepest secrets. Their theory underlies all the great triumphs of twentieth-century physics, from special relativity to the Standard Model, and has made possible a vast array of new technologies that have transformed the way we live. Their brilliance still inspires our search for scientific truth, and their deep humanity still offers a shining example of how to live a scientific life. Let us hope that a true understanding of these two men and how their theory evolved will illuminate the path to further discovery in years to come.
André Marie Ampère. (Used with permission from Ken Welsh/The Bridgeman Art Library.)
Humphry Davy. (Used with permission from the Royal Institution, London, UK/The Bridgeman Art Library.)
The Royal Institution of Great Britain in the 1830s. Watercolor by Thomas Hosmer Shepherd. (Used with permission from the Royal Institution, London, UK/The Bridgeman Art Library.)
Faraday's induction ring, as it appears to
day. (Used with permission from the Royal Institution, London, UK/The Bridgeman Art Library.)
Faraday lecturing in the Royal Institution Lecture Theatre. (Used with permission from the Royal Institution, London, UK/The Bridgeman Art Library.)
Faraday in his laboratory. Engraving after a painting by Harriet Jane Moore. (Used with permission from the Royal Institution, London, UK/The Bridgeman Art Library.)
Portrait of Michael Faraday holding a bar magnet. (Used with permission from the Royal Institution, London, UK/The Bridgeman Art Library.)
Maxwell in his early thirties. (Courtesy of the Master and Fellows of Trinity College, Cambridge.)
Maxwell, aged twenty-four, holding his color top. (Courtesy of the Master and Fellows of Trinity College, Cambridge.)
James Clerk Maxwell in his mid-forties. (Engraving by G. J. Stodart from a photograph by Fergus of Greenock. From Edinburgh and Scottish Collection, Edinburgh City Libraries.)
Katherine Clerk Maxwell. (Courtesy of the Master and Fellows of Trinity College, Cambridge.)
William Thomson (Lord Kelvin). (Used with permission from Universal History Archive/UIG/The Bridgeman Art Library.)
Oliver Heaviside. (Used with permission from the Institute of Engineering and Technology, Hertfordshire, UK.)
Heinrich Hertz during his military service. (Used with permission from the Institute of Engineering and Technology, Hertfordshire, UK.)