Читать книгу The Invisible Century: Einstein, Freud and the Search for Hidden Universes - Temple Grandin, Richard Panek, Temple Grandin & Richard Panek - Страница 8

Look.

And so the boy looked. His father had something to show him. It was small and round like a miniature clock, the boy saw, but instead of two hands pointing outward from the center of the face it had one iron needle. As the boy continued to look, his father rotated the object. He turned it first one way, then the other, and as he did so the most amazing thing happened. No matter how the boy’s father moved the object, the needle continued pointing in the same direction—not the same direction relative to the rest of the device, as the boy might have expected, but the same direction relative to … something else. Something out there, outside the device, that the boy couldn’t see. The needle was shaking now. It trembled with the effort. Some six decades later, when Albert Einstein recalled this scene, he couldn’t remember whether he had been four or five at the time, but the lesson he’d learned that day he could still summon and summarize crisply: “Something deeply hidden had to be behind things.”

Some things deeply hidden, actually. As the boy grew older, he learned what a few of those deeply hidden somethings were: magnetism, the subject of his father’s demonstration on that memorable day; electricity; and the relationship between the two. He learned that the existence of a relationship between magnetism and electricity was still so recent a discovery that nobody yet understood how it worked, and then he learned that within his lifetime physicists had demonstrated that this relationship manifested itself to our eyes as light. And he learned that even though nobody yet understood how light worked, what everybody did know was that it traveled along the biggest deeply hidden something of them all, one that had so far eluded the greatest minds of the age but one that was now, as a prominent physicist of the era proclaimed, “all but in our grasp.”

That something was the ether. Einstein himself sought it, in a paper he wrote in 1895, “Über die Untersuchung des Ätherzustandes im magnetischen Felde” (“On the Investigation of the State of the Ether in a Magnetic Field”). This contribution to the literature, however, wasn’t so much original scholarship as a five-finger exercise that wound up pretty much reiterating current thinking, since Einstein was only sixteen at the time and, as he cautioned prospective readers (such as the doting uncle to whom he sent the paper), “I was completely lacking in materials that would have enabled me to delve into the subject more deeply than by merely meditating on it.”

Still, it was a start. Over the following decade, Einstein would graduate from self-consciously precocious adolescent, speculating beyond his abilities, to willfully arrogant student at the Swiss Polytechnic in Zurich, to humble (if not quite humbled) clerk at the Swiss Office for Intellectual Property in Bern, where he wound up in part because his professors had refused to write letters of recommendation for someone so dismissive of their authority. As Einstein reported in a letter in May 1901, “From what I have been told, I am not in the good books of any of my former teachers.” Yet even as a patent clerk, Einstein continued to seek the ether, for the same reason that physicists everywhere were seeking the ether. When electromagnetic waves of light departed from a star that was there and hadn’t yet arrived here, they had to be traveling along something. So: What was it? Find that something, as physicists understood, and maybe electricity and magnetism and the relationship between the two wouldn’t seem so deeply hidden after all.

Among the seekers of the ether, one was without equal: the Scottish physicist William Thomson, eventually Baron Kelvin of Largs. As one of the most prominent and illustrious physicists of the century, Lord Kelvin had made the pursuit of the ether the primary focus of his scientific investigations for literally the entire length of his long career. He’d first thought he found it on November 28, 1846, during his initial term as a professor of natural history at the University of Glasgow. He was mistaken. As he wrote a friend in 1896, on the occasion of the golden jubilee of his service to the university, a three-day celebration that attracted two thousand representatives of scientific societies and academies of higher learning from around the world, “I have not had a moment’s peace or happiness in respect to electromagnetic theory since Nov. 28, 1846.”

Part of the problem with the ether was how to picture it. “I never satisfy myself unless I can make a mechanical model of a thing,” Kelvin once told a group of students. “If I can make a mechanical model, I can understand it.” In one such demonstration that was a perennial favorite of his students, he would draw geometrical shapes on a piece of india rubber, stretch the rubber across the ten-inch mouth of a long brass funnel, and, having hung the funnel upside down over a tub, direct water from a supply pipe into the thin tube at the top. As the water collected in the mouth of the funnel, the india rubber bulged, and it drooped, and it gradually assumed the shape of a globule. Soon the blob had expanded to a width nearly double the diameter of the mouth from which it appeared to be emerging, and just when the rubber seemed unable to stretch any thinner, it did anyway. All the while Kelvin continued to lecture, calmly commenting on the subject of surface tension as well as on the transformations the simple Euclidean shapes on the rubber were now undergoing. Then, at precisely the moment Kelvin calculated that neither india rubber nor the ten benches of physics students could endure any greater tension, he would raise his pointer, poke the gelatinous mass hanging before him, and, turning to the class, announce, “The trembling of the dewdrop, gentlemen!”

The trembling of the dewdrop, the angling of the gas molecule, the orbiting of a planet: the least matter in the universe to the greatest, and all operating according to the same unifying laws. Here was the whole of modern science, in one easy lesson. More than two hundred years earlier, René Descartes had expressed the philosophical hope that a full description of the material universe would require nothing but matter and motion, and several decades after that Isaac Newton had expressed the physical principles that described the motion of matter. The rest, in a way, had been a process of simply filling in the blanks—plugging measurements of matter into equations for motions, and watching the universe tumble out piecemeal yet unmistakably all of a single great mechanistic piece. The lecture hall where for half a century Kelvin demonstrated his models was a monument of sorts to this vision: the triple-spiral spring vibrator he’d hung from one end of the blackboard; the thirty-foot pendulum, consisting of a steel wire and a twelve-pound cannonball, that he’d suspended from the apex of the dome roof; two clocks, those universal symbols of the workings of the universe. Matter and motion, motion and matter, one acting upon the other; causes leading inexorably to effects that, by dint of more and more rigorous and precise examination, were equally predictable and verifiable to whatever degree of accuracy anyone might care to name: Here was a cosmos complete, almost.

The exception was the ether. When numerous experiments in the early nineteenth century began showing that light travels in waves, physicists naturally tried to describe a substance capable of carrying those waves. The consensus: an absolutely incompressible, or elastic, solid. For Cambridge physicist George Gabriel Stokes, that description suggested a combination of glue and water that would act as a conduit for rapid vibrations of waves and also allow the passage of slowly moving bodies. For British physicist Charles Wheatstone, it meant white beads, which he used in his Wheatstone wave machine of the early 1840s—a visual aid that vividly demonstrated how ether particles might move at right angles to a wave coursing through their midst and an inspiration for numerous similar teaching aids of the era.

And for Kelvin, “the nearest analogy I can give you,” as he once said during a lecture, “is this jelly which you see.” On other occasions, he might begin his demonstration with Scotch shoemakers’ wax. If he shaped the wax into a tuning fork or bell and struck it, a sound emanated. Then he would take that same sound-wave-conveying wax and suspend it in a glass jar filled with water. If he first placed corks under the substance, then laid bullets across the top of it, in time the positions of the objects would reverse themselves. The bullets would sink through the wax to the bottom while the corks would pop out the top. “The application of this to the luminiferous ether is immediate,” he concluded: a substance rigid enough to conduct waves traveling at fixed speeds in straight lines from one end of the universe to the other, if need be, yet porous enough not to block the passage of bullets, corks, or even—by the same application of scale that rendered minuscule dewdrops and giant rubber globules analogous—planets.

Not to block—but surely to impede? Surely at least to slow the passage of a planet? An elastic solid occupying all of space would have to present a degree of resistance to a (in the parlance of the day) “ponderable body” such as Earth. But to what degree precisely? In an effort to determine the exact extent of the luminiferous (or light-bearing) ether’s drag on Earth, the American physicist Albert A. Michelson devised an experiment that he first conducted in Berlin in 1881. His idea was to send two beams of light along paths at 90-degree angles to each other. Presumably the beam following one path would be fighting against the current as Earth plowed through the ether, while the beam on the other path would be swimming with the current. Michelson designed an ingenious instrument, which he called an interferometer, that he hoped would allow him to make measurements that, through a series of calculations, would determine the velocity of the Earth through the ether. The Berlin reading, however, suffered from the vibrations of the horse cabs passing outside the Physical Institute. So he moved his apparatus to the relative isolation of the Astrophysical Observatory in Potsdam, where he repeated the experiment. The reading, to his surprise, indicated nothing.

Which was impossible. An interaction between a massive planet and even the most elastic of solids surely couldn’t pass undetected or remain undetectable. “One thing we are sure of,” Kelvin told an audience in Philadelphia three years later, while on his way to lecture at Johns Hopkins University in Baltimore, “and that is the reality and substantiality of the luminiferous ether.” And if experiments of unprecedented refinement and sophistication failed to detect it, there was only one reasonable alternative course of action. As Kelvin wrote in his preface to the published volume of those Baltimore Lectures, “It is to be hoped that farther experiments will be made.”

They were. In 1887 Michelson tried again, this time with the help of the chemist Edward W. Morley. Together they constructed an interferometer far more elaborate and sensitive than the ones Michelson had used in Germany, secured it in an essentially tremor-free basement at the Case School of Applied Science in Cleveland, and set it floating on a bed of mercury for, literally, good measure. Michelson had in mind a specific number for the wavelength displacement he expected the ether would produce, and he further decided that a reading 10 percent of that number would conclusively indicate a null result. What he got was a reading of 5 percent of the displacement he thought the ether might produce—a blip attributable to observational error, if anything. Michelson found himself forced to reach the same conclusion he’d previously reported: “that the luminiferous ether is entirely unaffected by the motion of the matter which it permeates.”

“I cannot see any flaw,” said Kelvin of this experiment, in a lecture he delivered in the summer of 1900. “But a possibility of escaping from the conclusion which it seemed to prove may be found in a brilliant suggestion made independently by FitzGerald, and by Lorentz of Leiden.” Kelvin was referring to the physicists George Francis FitzGerald of Dublin, who had submitted a brief conjecture regarding the ether to the American journal Science in 1889, and Hendrik Antoon Lorentz, who in an 1892 paper and then in an 1895 book-length treatise had elaborated an entire argument along nearly identical lines: The ether compresses the molecules of the interferometer—as well as those of the Earth, for that matter—to the exact degree necessary to render a null result. In which case, the two beams of light in Cleveland actually did travel at two separate speeds, as the measurements of their multiple-mirror-deflected journeys would have shown, if only the machinery hadn’t contracted just enough to make up the difference. “Thus,” Lorentz concluded, “one would have to imagine that the motion of a solid body (such as a brass rod or the stone disc employed in the later experiments) through the resting ether exerts upon the dimensions of that body an influence which varies according to the orientation of the body with respect to the direction of motion.”

“An explanation was necessary, and was forthcoming; they always are,” the French mathematician and philosopher Henri Poincaré wrote of Lorentz in 1902 in his Science and Hypothesis; “hypotheses are what we lack the least.” Lorentz himself conceded as much. Two years later he proposed a mathematical basis for his argument while virtually sighing at the futility of the whole enterprise: “Surely this course of inventing special hypotheses for each new experimental result is somewhat artificial.”

Like other physicists at the time, Einstein thought about ways to describe the ether, as in the precocious paper he had sent to his uncle in 1895. Also like other physicists, Einstein thought about ways to detect the ether. During his second year at college, 1897–98, he proposed an experiment: “I predicted that if light from a source is reflected by a mirror,” he later recalled, “it should have different energies depending on whether it is propagated parallel or antiparallel to the direction of motion of the Earth.” In other words: the Michelson-Morley experiment, more or less—though news of that effort, a decade earlier, had reached Einstein only indirectly if at all, and then only as a passing reference in a paper he read. In any case, the particular professor he’d approached with this proposal treated it in “a stepmotherly fashion,” as Einstein reported bitterly in a letter. Then, during a brief but busy job-hunting period in 1901, after he’d left school but hadn’t yet secured a position at the patent office, Einstein proposed to a more receptive professor at the University of Zurich, “a very much simpler method of investigating the relative motion of matter against the luminiferous ether.” On this occasion it was Einstein who didn’t deliver. As he wrote to a friend, “If only relentless fate would give me the necessary time and peace!”

Like a few other physicists at the time, Einstein was even beginning to wonder just what purpose the ether served. What purpose it was supposed to serve was clear enough. Physicists had inferred the ether’s existence in order to make the discovery of light waves conform to the laws of mechanics. If the universe operated only through matter moving immediately adjacent matter in an endless succession of cause-and-effect ricochet shots—like balls on a billiard table, in the popular analogy of the day—then the ether would serve as the necessary matter facilitating the motion of waves of light across the vast and otherwise empty reaches of space. But to say that the ether is the substance along which electromagnetic waves must be moving because electromagnetic waves must be moving along something was as unsatisfactory a definition as it was circular. As Einstein concluded during this period in a letter to the fellow physics student who later became his first wife, Mileva Maric, “The introduction of the term ‘ether’ into the theories of electricity led to the notion of a medium of whose motion one can speak without being able, I believe, to associate a physical meaning with this statement.”

The problem of the ether was starting to seem more than a little familiar. It was, in a way, the same problem that had been haunting physics since the inception of the modern era three centuries earlier: space. To be precise, it was absolute space—a frame of reference against which, in theory, you could measure the motion of any matter in the universe.

For most of human history, such a concept would have been more or less meaningless, or at least superfluous. As long as Earth was standing still at the center of the universe, the center of the Earth was the rightful place toward which terrestrial objects must fall. After all, as Aristotle pointed out in establishing a comprehensive physics, that’s precisely what terrestrial objects did. An Earth in motion, however, presented another set of circumstances altogether, one that—as Galileo appreciated—required a whole other set of explanations.

Nicolaus Copernicus wasn’t the first to suggest that the Earth goes around the sun, not vice versa, but the mathematics in his 1543 treatise De revolutionibus orbium coelestium (On the Revolutions of Celstial Orbs) had the advantage of being comprehensive and even useful—for instance, in instituting the calendar reform of 1582. Still, for many natural philosophers its heliocentric thesis remained difficult, or at least politically unwise, to believe. Galileo, however, not only found it easy to believe but, in time, learned it had to be true because he had seen the evidence for himself, through a new instrument that made distant objects appear near. His evidence was not the mountains on the moon that he first observed in the autumn of 1609, though they did challenge one ancient belief, the physical perfection of heavenly bodies; nor the sight of far more stars than were visible with the naked eye, though they did hint that the two-dimensional celestial vault of old might possess a third dimension; not even his January 1610 discovery around Jupiter of “four wandering stars, known or observed by no one before us,” because all they proved was that Earth wasn’t unique as a host of moons or, therefore, as a center of rotation. Instead, what finally decided the matter for Galileo was the phases of Venus. From October to December 1610, Galileo mounted a nightly vigil to observe Venus as it mutated from “a round shape, and very small,” to “a semicircle” and much larger, to “sickle-shaped” and very large—exactly the set of appearances the planet would manifest if it were circling around, from behind the sun to in front of the sun, while also drawing nearer to Earth.

Galileo’s discovery of the phases of Venus didn’t definitively prove the existence of a sun-centered universe. It didn’t even necessarily disprove an Earth-centered universe. After all, just because Venus happens to revolve around the sun doesn’t mean that the sun itself can’t still revolve around Earth. But such a contortionistic interpretation of the cosmos—a Venus-encircled sun in turn circling Earth—had nothing to recommend it other than an undying allegiance to Earth’s central position in it. And so “Venus revolves around the Sun,” Galileo finally declared with virtual certainty, in a letter he wrote in January 1612 and published the following year, “just as do all the other planets”—a category of celestial object that, he could now state with a confidence verging on nonchalance, included the heretofore terrestrial-by-definition Earth.

An Earth spinning and speeding through space, however, required not only a rethinking of religious beliefs. It also required new interpretations of old physical data—a new physics. Galileo himself got to work on one, and in 1632 he published it: Dialogue Concerning the Two Chief World Systems. In arguing on behalf of a Copernican view of the universe, Galileo knew he was going to have to explain certain phenomena that in the Aristotelian view of the universe needed no further explanation. Actually, he was going to have to explain the absence of certain phenomena: If Earth were turning and if this turning Earth were orbiting the sun, as Copernicus contended, then wouldn’t birds be rent asunder, cannonballs be sent off course, and even simple stones, dropped from a modest height, be flung far from their points of departure, all according to the several motions of the planet?

No, Galileo said. And here’s why. He asked you, his reader, to imagine yourself on a dock, observing a ship anchored in a harbor. If someone at the top of the ship’s mast were to drop a stone, where would it land? Simple: at the base of the mast. Now imagine instead that the ship is moving in the water at a steady rate across your field of vision as you observe from the dock. If the person at the top of the ship’s mast were to drop another stone, where would it land now? At the base of the mast? Or some small distance back, behind the mast—a measurement corresponding to the distance on the water that the ship would have covered in the time between the release of the stone at the top of the mast and its arrival on the deck of the ship?

The intuitive, Aristotelian answer: some small distance back. The correct—and, Galileo argued, Copernican—answer: the base of the mast, because the movement of the ship and the movement of the stone together constitute a single motion. From the point of view of the person at the top of the mast, the motion of the stone alone might indeed seem a perpendicular drop—the kind that Aristotle argued a stone would make in seeking to return to its natural state in the universe. Fair enough. That’s what it would have to seem to someone standing on the steadily moving ship whose only knowledge of the motion of the Earth was that it stood still. That person would feel neither the motion of the Earth nor the motion of the ship and so would take into account only the motion of the stone. But for you, observing from the dock, the stone would be moving and the ship would be moving, and together those movements would make up a single system in motion. To you, the motion of the stone falling toward the ship would seem not a perpendicular drop—not at all an Aristotelian return to its natural state—but an angle. If you could trace the trajectory of the stone from the dock, it would just be geometry.

And vice versa. If, instead, you the observer standing on the dock were the one dropping a stone, then to you the motion of that stone relative to the Earth would appear perpendicular, because all you would be taking into account was the motion of the stone alone. That’s all Aristotle did—take into account only the motion of the stone. But from the point of view of the person at the top of the mast on the ship in the harbor, looking at you on the dock and taking into account the motion of the stone and the apparent motion of the dock together, the trajectory of the falling stone would describe an angle.

And there it is: a principle of relativity. Neither observer would have the right to claim to be absolutely at rest. The onboard observer would have as much right to claim that the ship was leaving the dock as that the dock was leaving the ship. Rather than standing still at the center of the cosmos, our position in the new physics was just the opposite: never at rest. After Galileo, everything in the universe was in motion relative to something else—ships to docks, moons to planets, planets to sun, sun (as astronomers would come to discover by the end of the eighteenth century) to the so-called fixed stars, those socalled fixed stars (as astronomers would come to discover by the middle of the nineteenth century) to one another, and, conceivably, our entire vast system of stars (as astronomers were trying to determine at the turn of the twentieth century) to other vast systems of stars.

Unless you counted the ether. For this reason alone, the ether was—as Einstein had first recognized as a teenager—at least somewhat objectionable. Not long after he’d written the ether paper that he’d sent to his uncle, Einstein found himself wandering the grounds at his school in Aarau, Switzerland, wondering what the presence of an absolute space would do to Galileo’s idea of relativity. If you were on board Galileo’s ship but belowdecks, in an enclosed compartment, you shouldn’t be able to detect whether you were moving or standing still, relative to the dock or anything else in the universe that wasn’t moving along with you. But if the ship were traveling at the speed of light through the ether, that’s just what you would be able to detect. You’d know you were the one traveling at the speed of light—rather than someone on the dock, for instance—because you’d see the light around you standing still.

By the early years of the twentieth century, Einstein had done only what other physicists of his era had done. He’d thought about ways to define the ether through mathematics. He’d thought about ways to detect the ether through experiments. He’d even begun to think about whether physics really needed an ether. But then, one night in May 1905, Einstein did what no other physicist of his era had done. He thought of a new way of thinking about the problem.

Einstein had been spending the evening with a longtime friend both from his student years and at the patent office, Michele Besso, the two of them talking, as they often did in their off-hours, about physics. In the preceding three years, Einstein had moved to Bern, gotten married, and fathered two children (one illegitimate, whom he and Mileva gave up for adoption). Yet all the while he’d been applying himself to the most pressing issues of contemporary physics, often in the company of his patent-office sounding board, Besso. On this particular occasion, Einstein had approached Besso for the express purpose of doing “battle” with a problem that had been plaguing him on and off for the past decade. After a lively discussion, Einstein returned home, where, all at once, he understood what he and everyone else who had been studying the situation had been overlooking all along.

“Thank you!” he greeted Besso the following day. “I have completely solved the problem.” The trouble with the current conception of the universe, he explained, wasn’t absolute space—or at least wasn’t only absolute space. It was absolute time.

“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 seven and the arrival of the train are simultaneous events.‘“ This sentence comes early in “Zur Elektrodynamik bewegter Körper” (“On the Electrodynamics of Moving Bodies”), the paper that Einstein completed and mailed to the Annalen der Physik six weeks later. In its audacious simplicity, even borderline simplemindedness, this sentence is deceptive, for with this description of one of the most mundane of human observations—one that just about any eight-year-old can make—Einstein pinpointed precisely what everyone else who had been studying the problem had missed: “time” is not universal or absolute; it is not sometimes universal and sometimes local or relative; it is only local.

The key was the speed of light. The fact that the speed of light is not infinite, as Aristotle and Descartes and so many other investigators of nature over the millennia had supposed, had been common knowledge since the late seventeenth century. So had its approximate value. In 1676, the Danish astronomer Ole Rømer used the data from years of observations at the Paris Observatory to determine that the timing of the eclipses of Jupiter’s innermost moon depended on where Jupiter was in its orbit relative to Earth. The eclipses came earlier when Earth was nearest Jupiter, later when Earth was farthest from Jupiter, suggesting that the eclipses didn’t happen at the very same moment we saw them happen. That, in fact, when we saw them depended on where they happened, nearer or farther. “This can only mean that light takes time for transmission through space,” Rømer concluded—140,000 miles per second, by the best estimates of the day.

But the combination of these two factors—that the speed of light is incomprehensibly fast; that the speed of light is inarguably finite—didn’t begin to assume a literally astronomical dimension for another hundred years. Beginning in the 1770s, William Herschel (the same observer who proved that the sun is in motion relative to the fixed stars) began systematically exploring the so-called celestial vault—the ceiling of stars that astronomers had known since Galileo’s time must have a third dimension but that they still couldn’t help conceiving as anything except a flat surface. With every improvement in his telescopes, Herschel pushed his observations of stars to greater and greater depths in the sky or distances from Earth or—since the speed of light coming from the stars is finite, since it does take time to reach our eyes—farther and farther into the past. “I have looked further into space than ever human being did before me,” Herschel marveled in 1813, in his old age. “I have observed stars of which the light, it can be proved, must take two million years to reach the earth.”

Even that distance, however, would seem nearby if the speculations of some astronomers at the turn of the twentieth century turned out to be true. If certain smudges at the farthest reaches of the mightiest telescopes turned out to be systems of stars outside our own—other “island universes” altogether equal in size and magnitude to our own Milky Way—then when we looked at the starlight reaching us from them we might be seeing not Herschel’s previously unfathomable two million years into the past but two hundred million years or even two thousand million years. And so they would go, these meditations on the meaning of light, ever and ever outward, further and further pastward, if not necessarily ad infinitum, then at least, quite possibly, ad absurdum.

Now Einstein reversed that trajectory. Instead of considering the implications of looking farther and farther across the universe and thereby deeper and deeper into the past, he thought about the meaning of looking nearer and nearer—or, by the same reasoning, closer and closer to the present. Look near enough, he realized, and you’ll be seeing very close indeed to the present. But only one place can you claim to be the present—and then only your present.

It was this insight that allowed Einstein to endow the idea of time with an unprecedented immediacy, in both the positional and the temporal senses of the word: here and now: the arrival of a train and the hands of a watch. Because the train and the hands of the watch occupy the same location, they also occupy the same time. For an observer standing immediately adjacent to the train, that time is, by definition, the present: seven o’clock. But someone in a different location observing the arrival of that same train—that is, someone at some distance away receiving the image of the train, which has traveled by means of electromagnetic waves from the surface of the locomotive to the eyes of this second observer at the speed of light, an almost unimaginably high yet nonetheless finite velocity—wouldn’t be able to consider the arrival of the train simultaneous with its arrival for the first observer. If light did propagate instantaneously—if the speed of light were in fact infinite—then the two observers would be seeing the arrival of the train simultaneously. And indeed, it might very well seem to them as if they were, especially if (using the modern value for the speed of light as 186,282 miles, or 299,792 kilometers, per second) the other observer happens to be standing on a street corner that’s about two-millionths of a light-second (the distance that light travels in two-millionths of a second, or slightly less than 2000 feet) away rather than, less ambiguously, near a star that’s two million light-years (or slightly less than 12 quintillion miles) away. And yes, if you were the observer on the street corner in the same town, gazing down a hill at a slowing locomotive pulling into the station, the arrival of the train for all practical purposes might as well be happening at the same moment as its arrival for the observer on the platform.

But what it is, is in your past.

Einstein was not in fact alone in recognizing the role that the velocity of light plays in the conception of time. Other physicists and philosophers had begun to note a paradox at the heart of the concept of simultaneity—that for two observers, the difference in distances has to translate into a difference in time. But where Einstein diverged from even the most radical of his contemporaries was in accepting as potentially decisive what the velocity of light is.

It was there in the math. In 1821, the British physicist Michael Faraday had decided to investigate reports from the Continent concerning electricity and magnetism by placing a magnet on a table in his basement workshop and sending an electrical impluse through a wire dangling over it. The wire began twirling, as if the electricity were sparking downward and the magnetism were influencing upward. This was, in effect, the first dynamo, the invention that would drive the industrial revolution for the rest of the century, and the product that Einstein’s own father and uncle would manufacture as the family business. But not until the 1860s did the Scottish physicist James Clerk Maxwell manage to capture Faraday’s accomplishment in mathematical form, a series of equations with an unforeseen implication. Electromagnetic waves travel at the same speed as light (and therefore, Maxwell predicted, are light): 186,282 miles, or 299,792 kilometers, per second in a vacuum. Meaning … what? That it would be more than 186,282 miles per second if you were moving away from the source of light, or less than 186,282 miles per second if you were moving toward the source? Yes—according to Newton’s mechanics. Yet it never seemed to vary.

On a planet that was spinning; a spinning planet that was orbiting the sun; a spinning planet orbiting a sun that itself was moving in relation to other stars that were moving in relation to one another—in this setting that, as Copernicus and Galileo and Newton and Herschel and so many other astronomers and mathematicians and physicists and philosophers had so persuasively established, was never at rest and therefore wouldn’t be at rest in relation to a source of light outside itself, always the answer to the question of what was the speed of light seemed to come up exactly the same. Just as Aristotelian philosophers considering the descent of an onboard stone would have overlooked the motion of the ship, so maybe several generations of Galilean physicists had been overlooking properties of electromagnetism. Maybe what you needed to consider was the motion of the stone, the motion of the ship, and the motion of the medium by which we perceive both, and together those three elements would constitute a single system in motion.

A few years earlier, his friend Besso had given Einstein a copy of the Austrian physicist Ernst Mach’s Die Mechanik in ihrer Entwicklung (The Science of Mechanics). This work, Einstein later recalled, “exercised a profound influence upon me” because it questioned “mechanics as the final basis of all physical thinking.” The issue for Mach wasn’t whether mechanics had worked well over the past two centuries in describing the motions of matter; clearly, it had. The issue wasn’t even whether mechanics could answer all questions about the physical universe, as the Kelvins of the world were constantly trying to prove. Rather, the issue for Mach—the root of his objection to Newtonian mechanics—was that it raised some questions it couldn’t answer.

For instance, absolute space, the existence of which is necessary to measure absolute motions: On close reading, Newton’s definition of it turned out to be every bit as circular as the reigning definition of the ether. “Absolute motion,” Newton had written, “is the translation of a body from one absolute place into another.” And what is place? “Place is a part of space which a body takes up, and is according to the space, either absolute or relative.” So what, then, is absolute space? “Absolute space, in its own nature, without relation to anything external, remains always similar and immovable.” Newton anticipated some criticism: “It is indeed a matter of great difficulty to discover, and effectually to distinguish, the true motions of particular bodies from the apparent; because the parts of that immovable space, in which those motions are performed, do by no means come under the observation of our senses. Yet the thing is not altogether desperate,” he reassured the reader, “for we have some arguments to guide us, partly from the apparent motions, which are the differences of the true motions; partly from the forces, which are the causes and effects of the true motions.” And what are these true, or absolute, motions? See above.

“We join with the eminent physicist Thomson [later Lord Kelvin] in our reverence and admiration of Newton,” Mach wrote in 1883. “But we can only comprehend with difficulty his opinion that the Newtonian doctrines still remain the best and most philosophical foundation that can be given.” Not that Mach was proposing an alternative to Newtonian mechanics; not that he was even suggesting physics was in need of an alternative. Rather, he was trying to remind his fellow physicists that just because mechanics had come “historically first” in modern science didn’t mean that it had to be historically final. This was the argument that “shook” Einstein’s “dogmatic faith” in mechanics alone as the basis of the physical world, and now, in May 1905, this was the argument that led Einstein to wonder whether mechanics and electromagnetism together could accommodate a principle of relativity—whether a synthesis of those two systems might in fact be historically next.

He tried it. First Einstein proposed that just as Newton’s mechanics don’t allow observers either on a dock or on a ship to consider themselves to be the ones absolutely at rest, neither should electrodynamics and optics. “We shall raise this conjecture (whose content will hereafter be called ‘the principle of relativity’) to the status of a postulate,” he wrote in the second paragraph of his paper. Then he accepted the constancy of the speed of light in empty space as another given—a second postulate: that the speed of light in a vacuum is always the same “independent of the state of motion of the emitting body.”

And that was all. It worked. Einstein now had two mutually reinforcing postulates, “only apparently irreconcilable”: a principle of relativity, allowing us to conduct experiments involving light either on the ship or on the dock with equal validity; and a principle of constancy, allowing the ship (or the dock, for that matter) to approach the speed of light without any light onboard (or on the dock)—including electromagnetic waves bringing images from objects to our eyes—slowing to a stop and thereby revealing whether the ship (or dock) is the one “really” in motion. In which case, as Einstein promised his readers in that same second paragraph, the “introduction of a ‘light ether’ will prove to be superfluous, inasmuch as the view to be developed here will not require a ‘space at absolute rest’ endowed with special properties.”

The rest was math—high-school-level algebra, at that. Suppose that you’re standing on a dock watching our old Galilean ship, still anchored just offshore after all these centuries. And suppose that the ship is absolutely motionless in the water. And suppose that instead of dropping a stone, someone on board is dropping a light signal—sending a beam of light from the top of the mast to the deck. If you time this simple event and get an answer of, say, one second, then you know that the distance between the top of the mast and the deck must be the distance that light travels in one second, or 186,282 miles. (It’s a big ship.)

The complications begin, just as they did in Galileo’s day, once that ship lifts anchor and sets sail. Suppose that it’s moving at a constant speed across your line of sight. If the person at the top of the mast sends a second light signal in the same manner as the first, what will you see from your vantage on the dock? The Aristotelian answer: a streak of light heading straight for the center of the Earth and therefore landing some distance behind the base of the mast—a distance corresponding to how far the ship has traveled along the water during the signal’s journey. The Galilean answer: a streak of light heading straight for the base of the mast—which is the Einsteinian answer as well. From your point of view, the base of the mast will have moved out from under the top of the mast during the descent of the beam of light, just as it did during the descent of a stone. Which means the distance the light has traveled, from your point of view, has lengthened. It’s not 186,282 miles. It’s more.

How much more you can easily find out by measuring the time of its journey—and that’s where the Einsteinian interpretation begins to depart from the Galilean. What is velocity? Nothing but distance divided by time, whether inches divided by—or, in the vernacular, per—day or kilometers per hour or miles per second. But if we accept Einstein’s second postulate, then the velocity in question isn’t just 186,282 miles per second. It’s always 186,282 miles per second. It’s constant—indeed, a constant. In the equation “velocity equals distance divided by time,” this constant is over on one side of the equals sign, off by itself, humming along at its own imperturbable rate. On the opposite side of the equals sign are the parts of the equation that can vary, that are indeed the variables—distance and time, also known as miles and seconds. They can undergo as many permutations as you can imagine, as long as they continue to divide in such a way that the result is 186,282 miles per second, or the equivalent—372,564 miles per two seconds, or 558,846 miles per three seconds, or 1,862,820 per ten seconds, and so on. Change the distance, and you have to change the time.

You have to change the time.

For more than two centuries, though, you didn’t. Now, on an evening in May 1905, you suddenly did, because on that evening Einstein, having talked the problem through with his friend Besso, realized that he needed to take into account something he’d never before adequately considered: the “inseparable connection between time and the signal velocity.” Time was a variable, a measurement that passed at different rates according to where you were. To an observer on the dock, the second light signal would had to have lasted longer than one second. To an observer on the ship, however, the second light signal would have appeared to do what the first one had done, back when the ship was anchored in the water: travel straight down to the base of the mast, 186,282 miles away. For this observer, the distance wouldn’t have differed from one signal to the next, so the time wouldn’t have, either. The shipboard observer would be measuring one second while you on the dock would have been counting two seconds or three seconds or more, depending on the speed of the ship along the water. For this reason, you would have every right to say that clocks on board the ship were moving slowly. And there it is: a new principle of relativity.

Of course, such an effect wouldn’t become noticeable unless the ship were moving at a significant fraction of the speed of light. At more modest speeds, the Galilean interpretation holds to a high degree of accuracy; as Einstein later wrote, “it supplies us with the actual motion of the heavenly bodies with a delicacy of detail little short of wonderful.” Still, according to Einstein’s math, as long as a ship is in motion at all, the distance the light travels on its angular path would have to be greater than the simple perpendicular drop you would see when the ship is at rest relative to you, and therefore the time to cover that distance would have to be greater, too. Through similar reasoning, Einstein also established that for an observer in a relative state of rest, back on the dock, the measurement of the length of a rod aboard a moving ship would have to shorten in the direction of motion, and to grow shorter the faster the ship is moving relative to the dock. And vice versa: Someone on the supposedly moving ship would have every right to consider that system to be the one at rest, and you and your so-called resting system to be the one whose dimensions would also appear to have shortened, and whose time would also appear to have slowed.

So which observer would be “right”? The observer on the ship, or you on the dock? The answer: Both—or, maybe more accurately, either, depending on who’s doing the measuring. But how much time passed really? How long is the rod really? The answer: There is no “really”—no absolute space, no ether, against which to measure the motions of all matter in the universe. There is only the relative motions of the two systems.

“For the rest of my life I want to reflect on what light is,” Einstein once said. If Einstein were correct, the universe wasn’t quite a clockwork mechanism; it didn’t function only according to the visible motions of matter. Instead it was electromagnetic, operating according to heretofore hidden principles. On a fundamental level, it was less a pocket watch than a compass.

Not that this new understanding of the universe was complete. Einstein knew that all he’d done was take into account the measurements of objects moving at uniform, or nonvarying, velocities relative to one another—a highly specialized situation. He hadn’t yet taken into account the measurements of objects moving at nonuniform, or varying, velocities relative to one another—a far more representative sampling of the universe as we know it.

Still, it was a start. In a way, Einstein’s light-centered universe was as physically distinct from the Galilean one he’d inherited as Galileo’s sun-centered universe was from the Aristotelian one he’d inherited. But like Galileo, Einstein knew his had to be true—or truer than the one it was replacing, anyway—because he had seen the evidence for himself, if only in his mind’s eye.