Einstein's miracle.

In celebration of the 100th anniversary of Albert Einstein's annus mirabilis, or miracle year, 2005 has been variously declared the "World Year of Physics", "International Year of Physics" and "Einstein Year". A whirlwind of articles, books, websites, television shows, radio programmes and lectures will sweep across the general public, and plays, dances, concerts and an opera will enliven the festivities. Physics, with particular emphasis on Einstein's contributions, will for a short time become the topic du jour. The fact that he died just fifty years ago adds timeliness to the occasion. As a matter of fact, this is not the first time such an event has been organized. In 1979, the world marked Einstein's 100th birthday with a jubilee, and in 2000 he enjoyed another 15 minutes in the limelight when Time Magazine chose him as "Person of the Century".

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What is it that's so special about 1905? Since that year, science has produced countless remarkable discoveries, hundreds of worthy physicists, piles of Nobel Prize medals and a handful of truly fundamental insights rivalling Einstein's. Why the emphasis on 1905? What exactly happened back then at the dawn of the turbulent century? The answer involves not only what Einstein accomplished in 1905, when he was only 26 years old and employed as patent examiner in Bern, Switzerland, but also how he did it. The "what" determined the course of physics for the twentieth century, while the "how" gives us hope for the twenty-first.

Between March and June 1905, Einstein wrote three spectacular scientific papers on three unrelated topics, with an astonishing afterthought added to the last paper in October. Not since 1666, when Isaac Newton discovered gravity, founded the science of optics and invented calculus, had the world witnessed such a cornucopia of scientific riches pouring forth from one mind in such a rush. Perhaps it is just as well that these volcanic eruptions of creative energy occur only rarely, for each raises enough questions to keep scientists busy for centuries at a time.

The second of Einstein's three papers was the most conventional and easily understood, but it turned out to be the most stupendous in its consequences. As is often the case in science, the subject itself was as insignificant as its implications were revolutionary. The problem was a strange little conundrum known as Brownian motion, after the English physician Robert Brown, who had noticed in 1828 that microscopic grains of pollen floating on the surface of water perform a restless, random dance. The phenomenon was rendered incomprehensible by the fact that this motion persists long after the water has had a chance to calm down and come to rest. In some experiments, Brownian motion was found to continue in a stationary sealed container for over a year. What could cause this perplexing behaviour? What kept it going?

For decades, physicists had trotted out all sorts of hypotheses to make sense of the matter. Invisible vortices, sound in the surrounding atmosphere, bubbles in the water, light radiation, electric charges and other effects were examined and discarded. Einstein came across the enigma earlier in his miracle year while preparing his PhD [Doctor of Philosophy] dissertation on the properties of molecules. In his customary visual way of thinking, he imagined a grain of pollen as a bowling ball pummelled from all directions by water molecules the size of marbles. If the molecules were even tinier, say, as small as grape seeds, and incredibly numerous, their puny pushes from all directions would cancel out and leave the bowling ball stationary. On the other hand, if they had more heft and were as big as baseballs (and correspondingly less numerous), they could occasionally knock the bowling ball around. It all depended on the weight of a molecule, which in 1905 was not yet well established. By making an educated guess, Einstein was able to predict the average distance between kinks in the zigzag path of a typical grain of pollen. Thus, he managed to explain Brownian motion as a consequence of collisions with invisible water molecules in perpetual motion.

The novelty of Einstein's theory was the assumption that atoms are real. Today, when we can see and manipulate individual atoms, it is difficult to imagine that as recently as 1905 their existence was still far from established. The idea of atoms had originated in Greek antiquity and over the millennia had gathered impressive credentials as a unifying and simplifying theme in physics and chemistry. However, all that time, atoms could be thought of as convenient fictions with no claim to reality. For many physicists, they resembled the 100 cents that make up a dollar without implying that they are material components of a dollar bill. Until 1905, atoms could be safely dismissed as scientific bookkeeping devices. Einstein's molecules were different. If he was right, the punch they pack would propel them out of the realm of theory into the everyday world of real, material fact.

A mere three years later, French physicist Jean Perrin succeeded in measuring the step size of Brownian motion and found that Einstein's prediction was right. For this elegant feat of experimental physics, Perrin later received a Nobel Prize. After 2,000 years in intellectual limbo, atoms became as real as marbles. Every aspect of physics and chemistry would be transformed. Even biology, which would soon enter the age of molecular genetics, builds its theoretical structures on the rock-solid foundation of the underlying atomic reality. It is not an exaggeration to say that the understanding of the world in terms of real, discrete atoms is the most fundamental doctrine of modern science. As the late American physicist Richard Feynman put it, of all scientific pronouncements, the potent atomic doctrine contains "... the most information in the fewest words ...". From bits of pollen in a dish, Einstein extracted the lesson that launched science on its proper course for the new century.

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In contrast to the Brownian motion article, which established an ancient hypothesis as fact, the first of Einstein's three papers reached back only five years. Its subject--also a minor puzzle that defied explanation--was the photoelectric effect, the liberation of electrons from a shiny metal surface by a beam of light. The process converts light energy into an electrical signal and is applied in devices like electronic cameras. Experiments had revealed a strange inconsistency. When the intensity of the applied light, and hence the total incoming energy, was raised, the speed of the emerging electrons did not increase. The electrons behaved like soccer balls that upon being kicked harder did not fly higher or farther. But the whole thing seemed to be more of an annoyance than a crisis. Most physicists ignored it. But not Einstein, who parlayed the photoelectric effect into a scientific revolution. He reasoned that the energy of a beam of light might be carried by a large number of discrete bundles--"particles" of light later called photons. If each photon carries a small, fixed amount of energy, it can impart only a feeble kick to an electron it encounters in the shiny metal. Increasing the energy of the impinging light would only increase the number of photons, and hence of electrons, while leaving the speed of each electron unaffected. Thus the photoelectric paradox could be resolved.

The notion that light consists of discrete bundles was not entirely original. It had been advanced tentatively by German physicist Max Planck in 1900. But he was emphatic in regarding these bundles as mere bookkeeping devices. He was a classical physicist trained in the wave theory of light, and the notion of particles of light was utterly repugnant to him. Only a young iconoclast like Einstein could muster the courage to take the idea literally. Even Einstein though called his photon hypothesis "heuristic", which means "leading toward further inquiry", or "advanced for the purpose of raising new questions". A heuristic hypothesis is provisional rather than dogmatic. With it, Einstein deduced a very simple equation relating the energy of incoming light to the speed of emerging electrons. It took American physicist Robert Millikan a decade to check this relationship, but when he did, Einstein was found to be right again. His heuristic approach paid off beyond expectations.

The photon hypothesis turned out to be the key that unlocked the secret of the structure of the atom. The creation of quantum theory--the strange language of the atom--began with the crucial realization that the emission of light by an atom is not a smooth continuous flow like the emission of sound by a violin, but a sudden, discrete event, a little burst of energy. It is sometimes said that later in life Einstein did not believe in the quantum theory. That's an exaggeration. After all, he had personally kicked off the quantum revolution in 1905--how could he disavow his own grandchild? Unlike his younger colleagues, though, Einstein never accepted the quantum theory as the final word. Science, he thought, is better served by heuristics than by dogma.

The last of Einstein's three celebrated papers introduced the special theory of relativity and eventually brought him universal fame. Its title, "On the Electrodynamics of Moving Bodies", hints at the humble origin of the theory, but reveals nothing of its true nature. It was well known that if you insert a magnet into a loop of wire connected to a light bulb, the bulb will light up. Alternatively, if you hold the magnet steady and slip the loop--bulb and all--over it, the same thing happens. Nineteenth century physicists had succeeded in describing both effects in mathematical detail but in completely different terms. It did not bother them unduly that two similar effects--the lighting up of the bulb--had two very dissimilar explanations.

Einstein, on the other hand, was convinced that the two experiments must have a common cause. Stubbornly, he complained that the proliferation of causes was unbearable (unertraglich) to him. He said it was this theoretical blemish that forced him into positing the "principle of relativity": only the relative motion of two objects may enter into a physical theory, never the absolute motion of a single object. Accordingly, the physical explanation of the magnet-and-wire experiment cannot depend on whether the magnet is moving or stationary. There can only be one explanation for both ways of lighting up the bulb! Without realizing it, we experience the principle of relativity in our everyday lives. In a transatlantic jet flying steadily at high speed, there is no experiment one can perform to detect or measure the speed of the jet without communicating with the outside world. In 1905, the absolute speed of the jet became a phantom concept without scientific meaning.

The principle of relativity and its apparent inconsistency with the known fact that light, contrary to a jet, does have an absolute speed forced Einstein into a radical revision of the notions about space and time, which had been accepted since the time of the great Newton. Characteristically, he used bits and pieces of mathematical machinery developed by others, but interpreted them in novel ways. From his formulas he predicted that a moving clock slows down, a moving meter stick shrinks in length, and no material object can reach the speed of light. At the low speeds of cars and airplanes, these effects are almost undetectably minute. None of them had therefore been observed directly and some had to wait decades for corroboration, but Einstein's theoretical arguments were sufficiently compelling for serious physicists to accept them well before experimental physics caught up with the theory.

At the end of the miracle year, as an afterthought, came the October surprise: E = [mc.sup.2]. In a short paper, almost a footnote, Einstein reported the formula relating energy to mass and the speed of light--surely the most famous equation in all of science. It was a straightforward consequence of the theory of relativity; had he noticed it earlier, he would certainly have included it in the third paper. It states that in all matter, regardless of whether it happens to be coal or chocolate pudding, a vast amount of energy lies buried. Einstein had no idea in the winter of 1905 how this energy could be released or used, but hinted that nature might have ways of converting mass into energy and vice versa. The identification of such processes, including those that power stars as well as nuclear reactors and atomic bombs, lay half a century in the future. Einstein did not participate in these developments, but they established E = [mc.sup.2] as an essential clue to understanding matter and energy.

Today, we know for a fact that nature is atomistic, quantum mechanical and relativistic. Twentieth century physics has provided us with a cogent world view that ranges from subatomic particles to the limits of the observable universe. Inasmuch as we are all parts of and participants in this material world, we are in debt to Einstein for pointing the way toward a comprehensive grasp of the stage upon which our lives are played out. Furthermore, our entire technology of lasers, computers, communication devices and nuclear power traces its roots directly to Einstein's annus mirabilis.

But for all their historic implications, the most astonishing aspect of Einstein's accomplishments is not what he did but how he did it. He had none of the trappings of conventional scientific inquiry--no laboratory, no collaborators, no staff and no research grant. He was just a man at a desk, with paper and pencil; his only tool was pure thought. The true miracle is that this tool, applied to a thorough knowledge of what had been learned before, is sufficiently powerful to penetrate the secrets of nature. Einstein himself did not use the word miracle very often and would certainly not have applied it to his own contributions. But in 1936, in an article entitled Physics and Reality, he wrote: "The eternal mystery of the world is its comprehensibility.... The fact that it is comprehensible is a miracle."

There is the real lesson for our generation. Somehow, miraculously, we humans have been granted the ability to understand the world, if only we apply ourselves diligently. Einstein gives us hope that if he could accomplish what he did in 1905, there is a chance that we, too, can come to understand and solve the problems that confront us at every turn. Predicting tsunamis, avoiding global warming, preventing AIDS, harnessing renewable energy, charting the brain, curing cancer--these are among the difficult challenges we face in the twenty-first century, but they do not have to overwhelm us. Einstein assures us that the world is comprehensible.

The comprehensibility of the world is a miracle we all, believers and unbelievers alike, would do well to celebrate this year.

Hans Christian von Baeyer is Professor of Physics at the College of William and Mary, in Williamsburg, Virginia, United States, where he has taught for 37 years. His professional specialty is in high energy theory, but for the last 25 years he has been writing about science. His latest book, entitled "Information--The New Language of Science", was published by Harvard University and translated into German.

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