Einstein's Clocks and Poincare's Maps

by Peter Galison

  Barthes would have known that among those scientists imagined to float above the material world was Henri Poincaré, the extraordinary French mathematician, philosopher, and physicist who produced, quite independently of Einstein, a detailed mathematical physics incorporating the relativity principle. In elegantly worded essays, Poincaré offered these results to the wider cultured world, at the same time probing the limits and accomplishments of both modern and classical physics. Like Einstein, Poincaré presented himself as a mind unbound. In one of the most famous accounts ever written by a scientist of his own creative work, Poincaré recounted his steps toward a theory of a new set of functions that were important for several domains of mathematics:

  For fifteen days I strove to prove there could not be any functions like those I [had in mind]. I was then very ignorant; every day I seated myself at my work table, stayed an hour or two, tried a great number of combinations and reached no results. One evening, contrary to my custom, I drank black coffee and could not sleep. Ideas rose in crowds; I felt them collide until pairs interlocked, so to speak, making a stable combination. . . . I had only to write out the results which took but a few hours.14

  Not just in his account of his newly invented functions, but throughout his remarkable philosophical and popular essays, Poincaré dissected physics and philosophy by way of metaphorical worlds detached from the here and now, suspending imaginary scientists in idealized alternate universes: “Suppose a man were translated to a planet, the sky of which was constantly covered with a thick curtain of clouds, so that he could never see the other stars. On that planet he would live as if it were isolated in space. But he would notice that it revolves. . . .”15 Poincaré’s space traveler might exhibit the rotation by showing that the planet bulged around its equator, or by demonstrating that a free-swinging pendulum gradually rotates. As always, Poincaré here used an invented world to make a real philosophical-physical point.

  It certainly is possible—even productive—to read Einstein and Poincaré as if they were abstract philosophers whose goal was to enforce philosophical distinctions by fabricating hypothetical worlds rich in imaginative metaphors. Poincaré (it might be thought) had in mind such a world when he spoke of such wildly varying temperatures that objects altered their lengths dramatically as one moved up or down. Poincaré and Einstein’s attacks on Newton’s absolute simultaneity could be taken to be just such metaphorical musings, ones that employed imaginary trains, fantastical clocks, and abstract telegraphs.

  Let’s return to Einstein’s central inquiry. Invoking what may seem a quaintly metaphorical thought experiment, Einstein wanted to know what was meant by the arrival of a train in a station at 7 o’clock. I have long read this as an instance of Einstein asking a question that (as Einstein put it) was normally posed “only in early childhood,” a matter that he, peculiarly, was still asking when he was “already grown up.”16 Was this the naïveté of the isolated genius? Such riddles about time and space appear, on this reading, to be so elementary as to lie below the conscious awareness of professional scientists. But was the problem of simultaneity, in fact, below the threshold of mature thought? Was no one else in 1904–1905 in fact asking what it meant for an observer here to say that a distant observer was watching a train arrive at 7 o’clock? Was the idea of defining distant simultaneity through the exchange of electric signals a purely philosophical construct removed from the turn-of-the-century world?

  Relativity was certainly far from my mind when, not long ago, I was standing in a northern European train station, absentmindedly staring at the elegant clocks that lined the platform. They all read the same to the minute. Curious. Good clocks. Then I noticed that, as far as I could see, even the staccato motion of their second hands clicked in synchrony. These clocks are not just running well, I thought; these clocks are coordinated. Einstein must also have had coordinated clocks in view while he was grappling with his 1905 paper, trying to understand the meaning of distant simultaneity. Indeed, across the street from his Bern patent office was the old train station, sporting a spectacular display of clocks coordinated within the station, along the tracks, and on its facade.

  The origins of coordinated clocks, like much in our technological past, remains obscure. Which of the many parts of a technological system does one count as its defining feature: the use of electricity? the branching of many clocks? the continuous control of the distant clocks? However one reckons, already by the 1830s and 1840s Britain’s Charles Wheatstone and Alexander Bain, and soon thereafter Switzerland’s Mathias Hipp and a myriad of other European and American inventors, began constructing electrical distribution systems to bind numerous far-flung clocks to a single central clock, called in their respective languages the “horloge-mère” [mother clock], “Primäre Normaluhr”[primary standard clock], and the “master clock.”17 In Germany, Leipzig was the first city to install electrically distributed time systems, followed by Frankfurt in 1859; Hipp (then director of a telegraph workshop) launched the Swiss effort in the Federal Palace in Bern, where a hundred clock faces began marching together in 1890. Clock coordination quickly embraced Geneva, Basel, Neuchâtel, and Zurich, alongside their railways.18

  Figure 1.3 Bern Train Station (circa 1860—65) One of the first buildings in Bern to be provided with the new coordinated clocks. Two clocks are (barely) visible just over the oval arches on the open side of the station. SOURCE: COPYRIGHT BÜRGERBIBLIOTHEK BERN, NEG. 12572.

  Einstein, therefore, was not only surrounded by the technology of coordinated clocks, he was also in one of the great centers for the invention, production, and patenting of this burgeoning technology. Were any other major scientists whose concern was with basic physical laws of electromagnetism and the nature of philosophical time also in the midst of this vast effort to synchronize clocks? There certainly was at least one.

  Some seven years before the twenty-six-year-old patent officer redefined simultaneity in his 1905 relativity paper, Henri Poincaré had advanced strikingly similar ideas. A cultured intellectual, Poincaré was widely acclaimed as one of the greatest of nineteenth-century mathematicians for his invention of a great part of topology, his celestial mechanics, his enormous contributions to the electrodynamics of moving bodies. Engineers lauded his writings on wireless telegraphy. The wider public devoured his best-selling books on the philosophy of conventionalism, science and values, and his defense of “science for science.”

  Figure 1.4 Neuchâtel Master Clock. Beautifully decorated master clocks were objects of enormous value and civic pride. This one, in the center of the clockmaking region of Switzerland, received its time from an observatory and then launched its signals along telegraph lines. SOURCE: FAVARGER, L’ÉLECTRICITÉ (1924), P. 414.

  For our purposes, one of the most remarkable essays Poincaré published appeared in January 1898 in a philosophical journal, the Review of Metaphysics and Morals, under the title “The Measure of Time.” There Poincaré blasted the popular view, espoused by the influential French philosopher Henri Bergson, that we have an intuitive understanding of time, simultaneity, and duration. Poincaré argued instead that simultaneity was irreducibly a convention, an agreement among people, a pact chosen not because it was inevitably in truth, but because it maximized human convenience. As such, simultaneity had to be defined, which one could do by reading clocks coordinated by the exchange of electromagnetic signals (either telegraph or light flashes). Like Einstein in 1905, Poincaré in 1898 contended that in making simultaneity a procedural concept, the time of transmission would have to be taken into account in any telegraphically communicated time signal.

  Figure 1.5 Berlin Master Clock. This clock, residing at the Silesischer Bahnhof in Berlin, sent its time down the many tracks emanating from the station. SOURCE: L’ÉLECTRICITÉ (1924), P. 470.

  Had Einstein seen Poincaré’s paper of 1898 or a crucial subsequent one of 1900 before he wrote his 1905 paper? Possibly. While there is no definitive evidence one way or the other, it will, nonetheless, pr
ove worthwhile to explore the question both narrowly and more widely. For as we will see, Einstein need not have read just those lines of Poincaré. Clock coordination appeared in the pages of philosophy journals, and even occasionally in physics publications. In fact, electromagnetic clock coordination was so fascinating to the late-nineteenth-century public that the subject came in for close discussion in one of Einstein’s favorite childhood books on science.19 In 1904–05, clock-coordinating cables were thick on the ground and under the seas. Synchronized timepieces were everywhere.

  Just as commentators have grown used to interpreting Einstein’s talk of trains, signals, and simultaneity as an extended metaphor, a literary-philosophical thought experiment, there is a similarly routine metaphorical reading of Poincaré’s observations. Here too, supposedly, stands philosophical speculation, an anticipatory note to Einstein’s special theory of relativity, a brilliant move by an author lacking the intellectual courage to pursue it to its logical, revolutionary end. So familiar is this story that it has become a commonplace to treat Poincaré’s insight into coordinated time as if it were entirely isolated, a philosophical aperçu disconnected from his place in the world. But neither Poincaré nor Einstein was speaking in a vacuum about time.

  What, Poincaré asks, are the rules by which scientists judge simultaneity? What is simultaneity? His final, most forceful example turned on the determination of longitude. He began by noting that when sailors or geographers determine longitude, they must solve precisely the central problem of simultaneity that governed Poincaré’s essay: they must, without being in Paris, calculate Parisian time.

  Finding latitude is simple. If the north star is straight overhead, you are on the North Pole; if it is halfway to the horizon, you are at the latitude of Bordeaux; if it is on the horizon, you are at the latitude of Ecuador, on the equator. It does not matter at all what time you make latitude measurements—in any particular location the angle of the pole star is always the same. Finding the longitude difference between two points is famously more difficult: it requires two distant observers to make astronomical measurements at the same time. If the earth did not rotate, there would be no problem: you and I would both look up and check which stars were directly under the North Star (for example). By checking a map of the stars we could easily find our relative longitudes. But of course the earth does turn, so to fix longitude differences accurately we must be sure that we are measuring the position of the overhead stars (or sun or planets) at the same time. For example, suppose a map-making team in North America knew the time in Paris and saw that at the team’s location the sun rose exactly six hours later than it had in the City of Light. Since the earth takes 24 hours to rotate, the team would know that it was somewhere along a longitude line 6/24 (one-fourth or equivalently 90 degrees) of the way around the world to the west of Paris. But how could the explorers know what time it was back in Paris?

  As Poincaré says in his “Measure of Time,” the roving cartographer could know Paris time simply by carrying a precision timekeeping device (chronometer) on the expedition, having set it to Paris time. But transporting chronometers led to problems both in principle and in practice. The explorer and his Parisian colleagues could observe an instantaneous celestial phenomenon (such as the emergence of a moon of Jupiter from behind the planet) from their two different locations and declare that their observations were simultaneous. But this seemingly simple procedure isn’t. There were practical problems in using Jovian eclipses. Even as a matter of principle, as Poincaré noted, the time would need to be corrected because light from Jupiter travels over different paths to reach the two observation points. Or—and this is the method Poincaré pursues—the explorer could use an electric telegraph to exchange time-signals with Paris:

  It is clear first that the reception of the [telegraph] signal at Berlin, for instance, is after the sending of the same signal from Paris. This is the rule of cause and effect. . . . But how much after? In general, the duration of the transmission is neglected and the two events are regarded as simultaneous. But, to be rigorous, a little correction would still have to be made by a complicated calculation; in practice it is not made, because it would be well within the errors of observation; its theoretic necessity is none the less from our point of view, which is that of a rigorous definition.20

  Direct intuitions about time, Poincaré concluded, are incompetent to settle questions of simultaneity. To believe so is to fall into illusion. Intuitions must be supplemented by rules of measurement: “No general rule, no rigorous rule; a multitude of little rules applicable to each particular case. These rules are not imposed upon us by themselves, and we might amuse ourselves in inventing others; but they could not be cast aside without greatly complicating the laws of physics, mechanics, and astronomy. We choose these rules, therefore, not because they are true, but because they are the most convenient.”21 All these concepts—simultaneity, time order, equal durations—were defined to make the expression of natural laws as simple as humanly possible. “In other words, all these rules, all these definitions are nothing but the fruit of an unconscious opportunism.”22 Time, according to Poincaré, is a convention—not absolute truth.

  What time do the map makers make it out to be in Berlin when it is noon in Paris? What time is it down the line when the train pulls into Bern? In posing such questions, Poincaré and Einstein seem, at first glance, to be asking questions of stunning simplicity. As was their answer: two distant events are simultaneous if coordinated clocks at the two locations read the same—noon in Paris, noon in Berlin. Such judgments were inevitably conventions of procedure and rule: to ask about simultaneity was to ask how to coordinate clocks. Their proposal: Send an electromagnetic signal from one clock to the other, taking into account the time the signal takes to arrive (at approximately the speed of light). A simple idea of breathtaking consequences for concepts of space and time, for the new relativity theory, for modern physics, for the philosophy of conventionalism, for a world-covering network of electronic navigation, for our very model of secure scientific knowledge.

  This is my quarry: how, at the turn of the century, was simultaneity actually produced? How did Poincaré and Einstein both come to think that simultaneity had to be defined in terms of a conventional procedure for coordinating clocks by electromagnetic signals? Addressing these questions demands far too wide a scope to be captured by a biographical approach, though there are, to be sure, too many biographies of Einstein and not enough of Poincaré. Nor is this book a history of philosophical ideas of time, a task that could easily take us back before Aristotle. It is not a comprehensive account of the intricate development of timepieces, even electric ones. And it is not a complete history of the many broadly shared concepts of nineteenth-century electrodynamics that Poincaré and Einstein appropriated as each struggled to reformulate the electrodynamics of moving bodies.

  Instead, this is a slice through layers of physics, technology, and philosophy that cuts high and low, an exploration of synchronized clocks crisscrossing back and forth between the wiring of the oceans to marching Prussian armies. It reaches into the heartland of physics, through the philosophy of conventionalism, and back through relativistic physics. Take hold of a wire in the late-nineteenth-century telegraph system and begin to pull: it takes take you down and across the North Atlantic, up onto pebbled beaches of Newfoundland; it tracks from Europe into the Pacific and up into Haiphong Harbor; it slides along the ocean floor the length of West Africa. Follow the land-based wires and the iron and copper cables; they lead up into the Andes, through the backcountry of Senegal, and clear across North America from Massachusetts to San Francisco. Cables run along train lines, under oceans, and between the beachfront shacks of colonial explorers and the chiseled stone of great observatories.

  But wires for time did not arrive on their own. They came with national ambitions, war, industry, science, and conquest. They were a visible sign of the coordination among nations in conventions about lengths, times, and ele
ctrical measures. Coordinating clocks in the nineteenth and twentieth centuries was never just about a little procedure of signal exchange. Poincaré was an administrator of this global network of electrical time, Einstein an expert at the central Swiss clearinghouse for the new electrotechnologies. Both were also riveted by the electrodynamics of moving bodies and fascinated by philosophical reflections on space and time. Understanding this world-embracing synchronization will take us some way toward understanding what is modern about modern physics and about how Einstein and Poincaré stood at crossing points of their respective modernities.

  Surely, we learn from the astonishing contrast between Newton’s distant seventeenth- and Einstein and Poincaré’s turn-of-the-twentieth century concepts of time. Their two conceptions stand as monuments to a clash between the early modern and the modern: on the one hand, space and time as modifications of the sensorium of God; on the other, space and time as given by rulers and clocks. But the distance between 1700 and 1900 should not eclipse the near at hand. It is the near at hand that interests me—the daily world of 1900 in which it became usual, and not just for Poincaré and Einstein, to see time, conventions, engineering, and physics as of a piece. For those decades it made perfect sense to mingle machines and metaphysics. A century later that propinquity of things and thoughts seems to have vanished.

  Perhaps one reason for the difficulty we have in imagining science and technology so caught up with one another is that it has become habitual to divide history into separate scales: intellectual history for ideas that are or aim to be universal; social history for more localized classes, groups, and institutions; biography or microhistory for individuals and their immediate surround. In telling of the relation between the pure and applied, there are narratives that track abstract ideas down through laboratories to the machine-shop floor and into everyday life. There are also stories that run the other way, in which the daily workings of technology are slowly refined as they shed their materiality on the way up the ladder of abstraction until they reach theory—from the shop floor to the laboratory to the blackboard, and eventually to the arcane reaches of philosophy. Indeed, science often does function this way: from the purity of an etherial vapor, ideas may seem to condense into everyday matter; conversely, ideas seem to sublime from the solid, quotidian world into air.