A Cataclysm of Thought

In 1905 Albert Einstein, a twenty-six-year-old clerk, published five epochal papers. One was later awarded a Nobel Prize. Reading them today, our reviewer is thrilled by their genius
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EINSTEIN'S MIRACULOUS YEAR:
Five Papers That Changed the Face of Physics




I'VE often been struck by the fact that philosophy students read Kant's Critique of Pure Reason, political-science majors read the U.S. Constitution, and literature classes read Shakespeare, but students of science rarely read the works of Mendeleev or Lavoisier or Einstein. The widely used college textbook from which I learned mechanics, the area of physics whose foundations were laid largely by Isaac Newton, contains a beautiful exposition of classical mechanics but only a handful of mentions of Newton, no excerpts from his Principia, and no pages at all on the history of the subject. From this one observation an intelligent creature from outer space could determine that there exists a profound difference between the disciplines we call natural science and those we call humanities or art or social science. Modern textbooks on science give no sense that scientific ideas come out of the minds of human beings. Instead science is portrayed as a set of current laws and results, inscribed like the Ten Commandments by some immediate but disembodied authority.
This absence of history is not entirely a bad thing. Science prides itself, with much justification, on its claim that the final equation or experimental result is far more important than the path taken to achieve that result or the views of the scientist in arriving there. The "objective" nature of scientific results, free from the fingerprints of their discoverers, helps great scientific ideas to attain their universality and staying power. Every day electrical engineers can successfully apply Ohm's law without knowing who Ohm was or that he struggled with messy piles of metallic disks and moist cardboard to reach his discovery. Moreover, new mathematical methods are brought to bear, and ideas and results are revised or recast as the subject advances. It would be a decided burden on students to relive much of the outmoded history. Over time science has proved itself to be a vertical subject, and most science students and their teachers want the latest, right off the top. The record of trial and error and the dusty original papers can always be attended to by historians.

So, twenty-five years after my days and nights as a physics major, I have on my desk a small book containing five papers published by Albert Einstein in 1905 -- on the sizes of atoms, relativity, and quantum theory. And I find myself thrilled by these papers. Why? Because through the original choice of words and arguments, through the simple but profound ideas and thought processes, even through the errors (yes, Einstein sometimes published errors), I have been able to gaze into the mind of this great scientist in a way that no distillation or restatement or commentary would allow. In these papers one can see an enormously gifted human being grappling with the nature of the world. The physics and mathematics are too technical for all but professional physicists, and the level of genius is practically incomprehensible. But in the discussion of ideas and in the deep questioning and hesitations one recognizes a fellow thinker at work.

draws its material from the second volume of The Collected Papers of Albert Einstein, a mammoth collaboration of the Einstein Papers Project at Boston University, Princeton University Press, and the Hebrew University of Jerusalem. The plan is to publish all of Einstein's scientific papers and political writings and much of his available correspondence -- more than twenty-five volumes' worth -- both in original form and in English translation. The papers here first appeared in the prestigious German physics journal Annalen der Physik, all within a single year.

In 1905 Einstein was a poor twenty-six-year-old clerk in a patent office in Bern, Switzerland. He and his wife, Mileva Maric, had in 1903 given away a daughter named Lierserl, who was born before their marriage; they now lived with their infant son, Hans Albert, in a two-room rented apartment on 49 Kramgasse that could be reached only by a steep staircase. At this time the brilliant young physicist felt estranged from the world. He had renounced his German citizenship at the age of sixteen, out of contempt for the authoritarian German military and his impending draft. In addition he suffered under his parents' disdain for his wife, who was Serbian and was four years older than Albert. (His mother once said to him, "She is a book like you -- but you ought to have a wife.... When you'll be 30, she'll be an old witch.") And since graduating from the Federal Institute of Technology, in Zurich, in 1900, he had repeatedly been refused jobs in Europe's academic establishment, many of whose eminences he considered self-satisfied men far below him in scientific ability. The young Einstein was an embattled loner. Yet although he was unemployed much of the time in the years immediately following his graduation, he managed to publish several scientific papers. Then, in 1905, still working in obscurity, he produced five articles that changed physics for all time. Any of these papers would have brought him lasting recognition. One earned him the Nobel Prize. Two provided definitive new evidence for the existence and sizes of atoms and molecules; two proposed a radical new conception of time and space (the special theory of relativity) and tossed out as a by-product the famous formula E=mc2; and the fifth gave the first theoretical evidence that light flows in discrete packets of energy, like water droplets, rather than in a continuous stream. Surprising to me, it was only this last paper that Einstein himself referred to as "revolutionary."

AT the end of the nineteenth century, physics basked in the glow of extraordinary achievement. Newton's laws of mechanics, which described how particles respond to forces, together with his law of gravity had been successfully applied to a huge range of terrestrial and cosmic phenomena, from the bouncing of balls to the orbits of planets. The theory of heat, called thermodynamics, had reached its climax with the melancholy but deep second law of thermodynamics: any isolated system moves inexorably and irreversibly to a state of greater disorder. Or, alternatively, every machine inevitably runs down. All electrical and magnetic phenomena had been unified by a single set of equations, called Maxwell's equations after James Clerk Maxwell, the nineteenth-century Scottish physicist who completed them. Among other things, the equations demonstrated that light, that fundamental natural phenomenon, is a wave of electromagnetic energy, traveling through space at 186,000 miles per second. The new areas of physics known as statistical physics and kinetic theory had shown that the behavior of gases and fluids can be understood on the basis of collisions between large numbers of tiny objects, assumed to be the long-hypothesized but invisible atoms and molecules.

This detailed knowledge enjoyed by late-nineteenth-century physicists was accompanied by a world view, much of which was so obvious as to be left to the unconscious. First and most important, the physical cosmos was subject to rational laws, and those laws could be discovered by humankind. (Volumes could be written on this.) Next, all substance was composed of energy and matter. Energy, like light, came in a continuous form; it could be subdivided indefinitely into smaller and smaller amounts. Matter, however, such as rocks, came in particulate form and consisted of a limited number of indivisible objects -- atoms. A piece of matter could be subdivided only until individual atoms were reached and no further.

It was also believed that a gossamer substance, called the "ether," filled all of space and was the medium by which light traveled. (It was thought that light waves could not propagate through a vacuum any more than sound waves could; thus the postulation of the ether.) Although this belief may seem highly particular, it implicitly required the profound notion that there exists a condition of absolute rest. According to wave theory, one can always measure one's motion relative to the medium that propagates a wave, and one knows in particular when one is at rest in that medium. For example, water waves appear to travel more slowly if one moves along after them rather than remaining still in the pond. Physicists reasoned that if an ether pervaded all of space, as it must for our eyes to perceive the twinkling of distant stars, then experiments with light should always reveal how the earth was moving through the ether; the all-pervasive ether would thus constitute a condition of rest against which all motion could be measured. Both Aristotle and Newton subscribed to the belief in absolute rest. For Aristotle, it was the earth, lying at rest at the center of the cosmos, that provided the fixture against which motion could be measured. For Newton, the pervasive substance at rest was the Being of God, who "by existing always and everywhere ... constitutes duration and space." For nineteenth-century physicists, it was the ether that was at rest.

Finally, physicists and everyone else believed in the absolute nature of time: a second for me is a second for you. Time flows at an equal and absolute rate always and everywhere. This belief was so eminently reasonable, so ingrained in human experience and perception of the world, as to be beyond question.

In sum, as the nineteenth century entered its last decade, physics surveyed its vast kingdom and was pleased. Some cracks, however, were appearing in the marble façade. Huge and unexplained quantities of energy had recently been observed emanating from certain elements -- the phenomenon called radioactivity. Other emissions of radiation, the so-called atomic spectra, exhibited surprising regularities, but no one had arrived at a theoretical understanding of them. And in 1897 physicists identified a new building block of matter, tiny in size: the electron, which was evidently ejected from the innards of atoms. Was the sacred and indivisible atom divisible after all? Henry Adams shrieked over this possibility in his Education.

On another front all attempts to probe the hypothetical ether had failed. Yet wasn't an ether necessary for the propagation of light? Experimental physicists had also observed that a unique kind of light emerged from all hot, blackened cavities held at a constant temperature. The detailed nature of this light, called black-body radiation, was completely independent of the size, shape, or composition of the cavity -- as surprising as if human beings all over the world were to utter the same sentence upon being asked a certain question. Clearly, black-body radiation held some secret about the fundamental nature of matter and energy, but physicists had little clue. Another puzzle with disturbing implications appeared under a microscope: tiny particles suspended in a fluid seem to dance to and fro endlessly -- a phenomenon first documented by the botanist Robert Brown and called Brownian motion. No one had given a satisfactory explanation for the phenomenon. Furthermore, because the second law of thermodynamics states that all such motion eventually grinds to a halt, some physicists proposed a failure of that law for microscopic dimensions.

Amid many successes these basic questions about the nature of atoms, matter, and energy deeply troubled such prominent physicists as Ludwig Boltzmann, Max Planck, and Hendrik Antoon Lorentz. Onto this stage of certainties and uncertainties stepped the young Einstein in 1905. By the end of the year little was left standing.

THE five papers have an uneven geography, being spare and mathematically dense for long stretches and then opening out into essayistic prose on matters of principle. One can almost see the journal editors wincing at some of the verbiage. Here and there Einstein summed up prior experimental and theoretical results in general terms, but he made surprisingly few references to the existing physics literature. One might be tempted to attribute this omission to his isolation from the academic establishment in 1905 if the feature was not apparent throughout his later work. A more plausible explanation is that Einstein was not especially influenced by this or that particular result but instead was guided by the big picture as he saw it.

What delighted me about Einstein's two papers on atoms and molecules was his unflinching confrontation with experiment. Here was a great theoretician authoritatively deriving equations for the way in which small spheres budge the fluid flow around them, yet when he arrived at a final result with xs and ys, he did not simply tuck away his pencil and paper, as many theorists do, but inserted actual laboratory numbers to make definite predictions. For example, at the end of his paper on Brownian motion, titled "On the Motion of Small Particles Suspended in Liquids at Rest Required by the Molecular-Kinetic Theory of Heat," he derived an equation for the distance a suspended particle should travel in time t after bouncing back and forth owing to random collisions with individual molecules of the surrounding liquid. The equation shows that the tinier the surrounding molecules (and thus the more of them), the smaller the expected jitter of the suspended particle in a given time. If matter were infinitely divisible, and atoms infinitely small, a suspended particle would not jitter at all. Thus the mere observation of Brownian motion testifies to the existence of atoms and molecules. But then Einstein went a step further. He substituted specific experimental values for suspended particles in water (particle diameter of one thousandth of a millimeter, water coefficient of viscosity of .0135, water temperature of 17 degrees Centigrade, and an assumed value of 6 x 1023 for the number of molecules in a standard weight, equivalent to an assumed molecular diameter of one millionth of a millimeter). The result was that the suspended particle should cover a distance of about six thousandths of a millimeter in one minute.

This final prediction was a concrete number, not an equation, and it was readily verifiable with technology then current. This was a "go-no go" prediction. If an experimenter arrived at a number close to this one, the underlying theories of thermodynamics and kinetics would be supported and the hypothesized approximate size of molecules confirmed. If a very different number was found, then Einstein's understanding and theoretical calculations were wrong. He ended his paper with the statement "Let us hope that a researcher will soon succeed in solving the problem presented here, which is so important for the theory of heat."

LIKE the great Danish theorist Niels Bohr, Einstein loved to provoke his imagination with contradictions and paradoxes. He began his first paper on relativity theory with a beautifully simple statement of two paradoxes in the understanding of electromagnetic phenomena. The first was that all experimental results showed that only relative motion was measurable. For example, a magnet moving upward through a coil of wire produced exactly the same electrical current as that produced when the coil of wire moved downward around the magnet at the same speed. One could not say from experiment that either the magnet or the coil was at rest while the other moved -- only that the two were in motion relative to each other. Yet Maxwell's equations for electromagnetism gave different results depending on whether one considered the magnet at rest or the coil at rest. (As Einstein later showed, the problem was not with Maxwell's equations but with the understanding of time and space used to transform a frame of reference in which the magnet was at rest into one in which the coil was at rest.) The second paradox was that the wave theory of light seemed to require an ether, yet all experimental attempts to measure motion through the ether had failed.

After summarizing these problems, Einstein postulated that a condition of absolute rest did not exist. The ether was then "superfluous," in his language -- it had not been measured because it did not exist. Only relative motion was measurable in physics; hence the origin of "relativity." We have all experienced relativity in mechanics. If you sit on a train that is either at rest or moving at constant speed and look at another passing train without looking at the landscape, you cannot tell which train is moving and which train is at rest; you can only say that each train moves past the other at a certain relative speed.

Einstein then made the additional, seemingly outrageous postulate that the speed of light is always the same, independent of the motion of whatever body emits the light. I will explain why this second postulate seems outrageous, especially following the first. At the turn of the century two mechanical models for motion were known: wave motion and particle motion. In wave motion the speed of the wave is fixed relative to the medium that carries it. Any motion of the medium is then added to or subtracted from the motion of the wave. For example, a canoeist (the wave) who paddles at three miles per hour in still water (the medium) will pass the shore at eight miles per hour when paddling with a current of five miles per hour. In particle motion the traveling particle requires no medium, and its speed is fixed relative to its emitter. Take a pitcher who throws a ball at ninety miles per hour. If before making his throw our pitcher steps onto a conveyor belt that is racing toward the batter at ten miles per hour, the ball will zing across the plate at very nearly a hundred miles per hour.

Now to the extravagant violation of common sense. Einstein's first postulate, eliminating the ether, would seem to require that the propagation of light follow the particle-motion model, in which the speed of a light ray would be fixed relative to its emitter. If the emitter moves, the net speed of light changes. Yet Einstein's second postulate said no. Einstein proposed that if our pitcher decides to shine a flashlight at the batter instead of throwing a ball, the light rays will cross the plate at 186,000 miles per second whether the pitcher shines from the mound or from a conveyor belt moving toward the batter. In short, Einstein had conjectured that something very peculiar happens at high speeds.

Speeds involve distance and time. If relative speeds approaching the velocity of light do not add and subtract according to common sense, then intervals of distance and time do not either. The young Einstein's esoteric postulates were in effect questioning common notions of time and space. Einstein was well aware of the philosophical import of his ideas, because as a student he had read Kant, Hegel, and other philosophers. Kant argued that certain fundamental concepts, such as the nature of time and space, had to be fixed in the human mind prior to experience as necessary conditions for human beings to perceive the external world. Einstein, however, regarded all concepts as subject to revision based on experiment. There were no sacred cows -- everything was open to question. A few pages into his paper he began questioning the meaning of time with the profound innocence of a child.

If we want to describe the motion of a particle, we give the values of its coordinates [position] as functions of time. However, we must keep in mind that a mathematical description of this kind only has physical meaning if we are already clear as to what we understand here by "time." We have to bear in mind that all our judgments involving time are always judgments about simultaneous events. If, for example, I say that "the train arrives here at 7 o'clock," that means, more or less, "the pointing of the small hand of my watch to 7 and the arrival of the train are simultaneous events." It might seem that all difficulties involved in the definition of "time" could be overcome by my substituting "position of the small hand of my watch" for "time." Such a definition is indeed sufficient if a time is to be defined exclusively for the place at which the watch is located; but the definition is no longer satisfactory when series of events occurring at different locations have to be linked temporally.

Sentences like these hide ideas of staggering significance. Part of Einstein's great genius was to dig deep into our unconscious assumptions about such primal concepts as time and space and to raise these concepts to the level of consciousness. Once there, these concepts could be articulated, questioned, and probed.

After the above passage Einstein went on to propose a working definition of time for events in different locations (essentially, a method for synchronizing clocks). Then he derived what his two postulates required for the temporal and spatial measurements of observers in motion relative to each other. The result, which has been long since confirmed in quantitative detail, is that time is not absolute. A second for me is not necessarily a second for you. The duration between two events depends on the motion of the observer relative to the events. For example, the elapse of one second by a watch you are wearing will take about 1.1547 seconds by my watch if I am rushing toward you at half the speed of light. These discrepancies become tiny at the low speeds of everyday life, and Einstein realized that all of our (faulty) intuition about time is based on such everyday speeds. Einstein was a physicist, not a mathematician, and he was keenly aware of the importance of experiments in the assessment of theories. Yet he also appreciated the limitations of experiments and of human sensory perception. One sees this fine balance throughout his work.

EINSTEIN'S caution about interpreting experience is seen again in his paper on quantum physics. He began by pointing out physicists' views of the "profound formal difference" between matter and energy -- the former granular, composed of a finite number of indivisible atoms, and the latter continuous and infinitely divisible. Indeed, Einstein wrote, Maxwell's wave theory, in which light is considered continuous, "has proved itself superbly in describing purely optical phenomena." But then he wrote, "One should keep in mind, however, that optical observations refer to time averages rather than instantaneous values." Here he was hinting that if light were composed of large numbers of tiny units, like atoms, most experiments would not detect that fact. Analogously, a meteorologist who measures daily rainfall by the rise of water in a cup would not know that rain arrives in individual drops. In the rhetoric of this first section of the quantum paper Einstein revealed his strong preference for unity. He would have liked a world in which everything was composed of "atoms" or else everything was continuous, just as he preferred that a condition of absolute rest not exist for electromagnetics if it did not exist for mechanics. At the age of twenty-six he was already guided by his philosophical leanings as well as by his keen intuition.

Next Einstein used an unexpected thermodynamic calculation to show that the detailed appearance of black-body radiation was exactly what one would expect if light consisted of a gas of "atoms," or quanta, each with an energy proportional to the frequency of light. Here and elsewhere in these papers I was extremely impressed by Einstein's mastery of thermodynamics and kinetic theory, at a level well beyond the training received by graduate students in physics today. With Einstein's proposal of light quanta, the energy of light spreading out from a light bulb is "not distributed continuously over ever-increasing volumes of space, but consists of a finite number of energy quanta localized at points of space that move without dividing, and can be absorbed or generated only as complete units." Einstein further showed that his quantum theory of light could explain details of the recently observed photoelectric effect, in which electrical currents were created in metals by irradiating them with ultraviolet light. It was for this explanation that he received the Nobel Prize sixteen years later. Physicists today believe that everything is quantum.

In a letter to his friend Conrad Habicht, in late May of 1905, Einstein wrote that his granular theory of light was "very revolutionary." In fact, he did not consider his quantum proposal to be on solid ground, derived from first principles. His hesitation is revealed in the title of the paper: "On a Heuristic Point of View Concerning the Production and Transformation of Light." Even after a full theory of quantum physics was developed by Werner Heisenberg and Erwin Schrödinger in the 1920s, Einstein never completely accepted the theory and its probabilistic view of reality.

ALTHOUGH the many radical ideas in his 1905 papers were only slowly accepted, Einstein soon began to receive appreciative letters from such leading scientific figures as the experimentalist Philipp Lenard and the theorist Max Planck, each the most distinguished in his field in the German- speaking world. Some of these letters were addressed to "Esteemed Colleague," even though Einstein had barely completed his doctoral dissertation, and their senders were soon startled to discover that "A. Einstein" was a twenty-six-year-old patent-office clerk. By May of 1909 Einstein had been appointed "extraordinary professor of theoretical physics" at Zurich University, and two months later he received the first of his many honorary degrees, from the University of Geneva.

Einstein never had another year in which he showed the same ferocity of intellectual upheaval. Most theoretical physicists do their best work early, by the age of thirty-five, and perhaps Einstein needed a young person's agility of mind for the efforts of 1905. Perhaps the cataclysm of thought in the Swiss patent office was facilitated by his isolation from the academic establishment and his general sense of alienation from the world. Or perhaps, until his great work on gravity a decade later, he felt that he had exhausted most of the accessible topics of fundamental importance. In another letter to his friend Habicht, in September of 1905, Einstein wrote, "There is not always a ripe theme for musing over. At least not one that excites me."

At the age of sixty-seven, long after he had become perhaps the most celebrated scientist of all time, Einstein reflected back on these early years and his motivations to pursue science.

Even when I was a fairly precocious young man, the nothingness of the hopes and strivings which chases most men restlessly through life came to my consciousness with considerable vitality.... Out yonder there was this huge world, which exists independently of us human beings and which stands before us like a great, eternal riddle.... The contemplation of this world beckoned like a liberation, and I soon noticed that many a man whom I had learned to esteem and to admire had found inner freedom and security in devoted occupation with it.

Alan Lightman is the John E. Burchard Professor of Science and Writing and a senior lecturer in physics at the Massachusetts Institute of Technology. His books include the novel (1993) and a collection of short stories, (1996).


Illustration by Hanoch Piven

The Atlantic Monthly; January 1999; A Cataclysm of Thought; Volume 283, No. 1; pages 88-96.



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