Einstein's Clocks and Poincare's Maps

by Peter Galison

  The widening gyre of technological, symbolic, and abstract physics spiraled outward. Telegraphers, geodesists, and astronomers understood the Poincaré-Einstein clock coordination by means of quite literal, everyday wired (and wireless) clock coordination. At the Ecole Supérieure des Postes et Télégraphes, where Poincaré had taught since 1902, the telegraphic and wireless networks were never only metaphorical. They were the company business. On 19 November 1921, physicist Léon Bloch explained the meaning of time in a major lecture on relativity theory, using a technology that his audience of students and faculty knew like the backs of their hands:

  Figure 5.14 Eiffel Station Schematic. Military radio saved the Eiffel Tower, although Poincaré’s efforts to use it as a vast antenna in a time-transmission system eventually produced a facility available to both civilians and the armed forces. This figure depicts the master clock (in the Paris Observatory) and its links to the Tower’s radio transmitter. SOURCE: L. LEROY, “L’HEURE” (N.D.), PP. 14–15.

  What do we call time on the surface of the earth? Take a clock that gives astronomical time—the mother pendulum of the Observatory of Paris—and transmit that time by wireless to distant sites. In what does this transmission consist? It consists of noting at the two stations that need synchronization, the passage of a common luminous or hertzian signal.103

  Figure 5.15 Eiffel Radio Time (circa 1908). The Eiffel Tower radio station was located in these unprepossessing shacks at the foot of the structure. SOURCE: BOULANGER AND FERRIÉ, LA TÉLÉGRAPHIE SANS FIL ET LES ONDES ELECTRIQUES (1909), P. 429.

  By the time of Bloch’s lecture, clock coordination by exchange of electromagnetic waves was a practical routine. For a full decade Post and Telegraphs, the Bureau of Longitude, and the French Army had been routinely correcting for signal time in their myriad of long-distance synchronizations.104 Einstein and Poincaré’s time coordination was born in a world of machines and it clearly was received that way, not just in France. In Germany it was the experimenter-turned-theorist Cohn who had seized light-signal synchronization shortly after Poincaré and lost little time after Einstein’s 1905 paper in using pictures of clocks and models to publicize the new simultaneity. In Cambridge, England, it was the experimenters (not the more mathematical theorists) who first seized on the procedures of clock coordination. For American theoretical physicist John Wheeler, the identification of theory with mechanisms and devices tracked across the whole of his career, from early radio and explosives through his apprenticeship to engineers and engineering physicists during World War II. When he and Edwin Taylor wrote their widely used text Spacetime Physics in 1963, they too invoked a universal machine and displayed it at the beginning of their book (see figure 5.16).

  Machines tied clocks and maps ever closer together. At the beginning of World War II, MIT scientists used improvements in timing to develop the Long Range Aid to Navigation (LORAN) system that guided Allied ships across the Pacific. Postwar projects by the American Navy and Air Force tumbled out one after the other under such names as “Transit” and “Project 621B.” As the Cold War intensified, the American military demanded ever more precise locating systems to aim intercontinental ballistic missiles from shifting platforms and to guide soldiers through the unmarked jungles of southeast Asia.

  During the 1960s, American defense planners turned satellites into radio stations that would beam timed signals to earth. More accurate and stable timepieces drove these orbiting transmitters, pinging time at first from quartz crystals and later from the cesium oscillations of space-based atomic clocks. By the time the $10 billion Global Positioning Satellite (GPS) system was up and functioning in the 1990s, its twenty-four satellite-based clocks ticked with a precision about which Poincaré only fantasized in his Göttingen or Lille lectures of 1909: 50 billionths of a second per day providing a resolution on the earth’s surface of fifty feet. In a certain sense, the system resembled Eiffel Tower time: GPS also used a kind of coincidence method to synchronize clocks. But now the satellites broadcast a string of pseudo-random numbers (that is to say random enough for these purposes)—six thousand billion digits. The receiver then matched this string against its own, identical, internally stored set. By determining the offset between the two series, the logic circuits of the receiver could determine the time difference, and knowing the speed of light, the receiver’s distance to the satellite. If the receiver was already synchronized, only three satellites would be needed to fix the receiver’s position in three-dimensional space, but since the mobile ground receiver would normally not have the correct time, a fourth satellite (to set the time) was required.

  Figure 5.16 Lattice of Space and Time. Lost in many discussions of relativity are the machinelike procedures by which time and space coordinates were to be mapped. These are eminently visible in this fanciful machine depicted in the relativity textbook by Edwin Taylor and John Wheeler. SOURCE: TAYLOR AND WHEELER, SPACETIME PHYSICS (1966), P. 18.

  In a trading zone of engineering-philosophy-physics, relativity had become a technology, one that swiftly displaced traditional surveying tools. In fact, by processing the data after the fact and using GPS measurements of a known position to pinpoint transient errors in the system, early twenty-first-century surveyors could use the GPS to determine a second, unknown location within millimeters. So accurate had the system become that even “fixed” parts of the earth’s landmass revealed themselves to be in motion, an unending shuffle of continents drifting over the surface of the planet on backs of tectonic plates. In place of “absolute continents,” earth scientists demanded a new universal coordinate system, one unattached to any particular surface feature but instead rotating, in the imaginative eye of science, in silent coordination with the interior of the planet. GPS was soon landing airplanes, guiding missiles, tracking elephants, and advising drivers in family cars.

  Figure 5.17 Global Positioning System. Not unlike Poincaré’s time-transmitting Eiffel Tower, the late-twentieth-century GPS satellites provided precision timing (and therefore positioning) for both civilian and military users. Built into this orbiting machine were software and hardware adjustments required by Einstein’s theories of relativity. The result is a planet-encompassing, $10 billion theory-machine. SOURCE: RAND CORPORATION, RAND MR614-A.2.

  For all these purposes relativistic time coordination was deep in the machine. According to relativity, satellites that were orbiting the earth at 12,500 miles per hour ran their clocks slow (relative to the earth) by 7 millionths of a second per day. Even general relativity (Einstein’s theory of gravity) had to be programmed into the system. Eleven thousand miles in space, where the satellites orbited, general relativity predicted that the weaker gravitational field would leave the satellite clocks running fast (relative to the earth’s surface) by 45 millionths of a second per day.105 Together, these two corrections add up to a staggering correction of 38 millionths (that is, 38,000 billionths) of a second per day in a GPS system that had to be accurate to within 50 billionths of a second each day. Before the first cesium atomic clock launch in June 1977, some GPS engineers were sufficiently dubious about these enormous relativistic effects to insist that the satellite’s atomic clock broadcast its time “raw.” Its relativity-correction mechanism idled onboard. Down came the signal, running fast over the first twenty-four hours almost precisely by the predicted 38,000 billionths of a second. After twenty days of such gains, ground control commanded the frequency synthesizer to activate, correcting the broadcast time signal.106 Without that relativistic correction, it would have taken less than two minutes for the GPS system to exceed its allowable error. After a single day, satellites would have been raining erroneous positions, skewed by some six miles, onto the earth. Cars, bombs, planes, and ships would have veered wildly off course. Relativity—or rather relativities (special and general)—had joined an apparatus laying an invisible grid over the planet. Theory had become machine.

  Imitating historic precedents, symbolic and physical protests against globalized, ins
trumentalized time were not far behind. In this case one group of protesters explicitly wanted to object concretely to the use of GPS in precision weapons, counterinsurgency warfare, police actions, and nuclear war planning. In the predawn hours of 10 May 1992, two activists from Santa Cruz, California, disguised themselves as Rockwell International workers and broke into the clean room at Seal Beach, California, where the company was readying NAVSTAR GPS satellites for the air force. Slamming an axe into one completed satellite sixty times, they caused nearly $3 million worth of damage. As they approached a second satellite, Rockwell security personnel seized them at gunpoint and turned them over to the police. Dubbing themselves the Harriet Tubman–Sarah Connor Brigade (linking the heroine of the underground railroad to the heroine of “Terminator 2: Judgment Day”), the two militants pleaded guilty and served about two years in jail.107 In 1996, the FBI reported that the Unabomber, known for his eighteen-year bombing campaign against scientific figures, modeled himself on another temporal anarchist in Joseph Conrad’s Secret Agent, which he had read a dozen times.108 Around the axis of global time, fictional, scientific, and high-tech time machines (and their opponents) crossed and recrossed.

  Beating overhead in church spires, observatories, and satellites, synchronized clocks have never stood far from the political order—not in the 1890s, not in the 1990s. Poincaré’s and Einstein’s universal time machines linked technology, philosophy, politics, and physics. Or perhaps we should put it differently: these synchronizing time machines never functioned entirely in the arcane abstract or in the mutely material. The coordination of time is inevitably abstract-concrete.

  TURN-OF-THE-CENTURY Europe and North America were crisscrossed with lines of coordination: webs of train tracks, telegraph lines, meteorological networks, and longitude surveys all under the watchful, increasingly universal clock system. In this context, the clock coordination system introduced by Poincaré and Einstein was a world machine: a vast, at first only imagined, network of synchronized clocks that by the turn of the next century had metamorphosed from networks of submarine cables hauled by schooners to a microwave grid broadcast from satellites. There is a sense in which Einstein’s special theory of relativity has always been a machine, an imaginative one to be sure, but one suspended in a constantly evolving real skein of wires and pulses that synchronized time by the exchange of electromagnetic signals.

  Such a technological reading of this most theoretical development suggests one final observation. It has long struck scholars that the style of Einstein’s “On the Electrodynamics of Moving Bodies” does not even look like an ordinary physics paper. There are essentially no footnotes to other authors, very few equations, no mention of new experimental results, and a lot of banter about simple physical processes that seem far removed from the frontiers of science.109 By contrast, pick up a typical issue of the Annalen der Physik and a very different form appears in nearly every article, characterized by the standard point of departure: an experimental problem or a calculational correction. Typical physics articles were and are filled with references to other papers; Einstein’s article does not fit this mold. It could be that Einstein’s youthful arrogance had simply taken over, perhaps he had dispensed with the niceties of footnotes, altered the form of the usual introduction, and redesigned the typical conclusion as an idiosyncratic matter of individual taste. Certainly self-confidence is what Albert Einstein lacked least.

  But read Einstein’s contribution through the eyes of the patent world and suddenly the paper looks far less idiosyncratic, at least in style. Patents are precisely characterized by their refusal to lodge themselves among other patents by means of footnotes. If you aim to demonstrate the utter originality of your new machine (and upon originality hinges the patent), you can hardly do worse than shower the inspector with a storm of footnotes to prior work. In the fifty or so Swiss electric clock patents granted in the years around 1905, for example (they are typical), there is not a single footnote either to another patent or to a scientific or technical article.110 This comparison does not prove, of course, why Einstein did not cite others in that first paper. But it may help make sense of why a young patent officer in a hurry may not have felt impelled to situate his work in the matrix of papers by a Lorentz, a Poincaré, an Abraham, or a Cohn. After three years of evaluating hundreds of patents under Haller’s rigorous demands for analysis and presentation, the specificities of patent work had become, for Einstein, a way of life, a form of work, and (as he suggested to Zangger) a precise and austere style of writing.111

  Along the same lines, Einstein’s relatively accessible framing of the problem of space and time would have come as second nature to a patent examiner. According to Swiss patent law (and not only Swiss law), the description of the invention was to be “representable through a model, the unity of the invention defended, the consequences of the patent must be unambiguously laid out and lucidly ordered, so the whole is easily understood by properly certified technicians as well as by specialists.”112 In all his theoretical papers written around 1905, Einstein ended with a series of assertions about what the experimental consequences would be. In the case of the relativity paper, he concluded with the sharp, numbered paragraphs occasionally used in physics papers but standard in the “claims” section required by Swiss statute to appear at the end of every patent.113 Strikingly, from 1905 Einstein began describing (and occasionally drawing) devices, not only for his little electrostatic Maschinchen but also as key components of his theoretical arguments.

  Would General Field Marshal von Moltke have appreciated the irony? Sixteen-year-old Einstein, a young man who had abandoned his German citizenship chafing at the “herd mentality” of the militarist Prussian state, had at age twenty-six, completed the aged officer’s project in a certain sense.114 Time had ever more completely become identified with timekeeping, and Einheitszeit a means to the technopolitical establishment of procedural, distant simultaneity across the globe. Einstein’s clock synchronization system, like its more mundane predecessors, reduced time to procedural synchronicity, tying clocks together by electromagnetic signals. Indeed, Einstein’s scheme for clock unity went much farther, extending beyond city, country, empire, continent, indeed beyond the world, to the infinite, now pseudo-Cartesian universe as a whole.

  Here the irony inverts. For while Einstein’s clock coordination procedure built on decades of intense efforts toward electromagnetic time unification, he had removed the crucial element of von Moltke’s vision. There was, in Einstein’s infinite, imagined clock machine, no national or regional Primäre Normaluhr, no horloge-mère, no master clock. His was a coordinated system of infinite spatiotemporal extent, and its infinity was without center—no Schlesischer Bahnhof linked upward through the Berlin Observatory to the heavens and down along the rails to the edges of empire. By infinitely extending a time unity that had originally been conceived according to the imperatives of German national unity, Einstein had both completed and subverted the project. He had opened the “zone of unification,” but in the process not only removed Berlin as the Zeitzentrum but also designed a machine that upended the very category of metaphysical centrality.

  Absolute time was dead. With time coordination now defined only by the exchange of electromagnetic signals, Einstein could finish his description of the electromagnetic theory of moving bodies without spatial or temporal reference to any specially picked-out rest frame, whether in the ether or on earth. No center remained, not even the vestigial centrality of the special ether rest frame that Poincaré had retained. Einstein had constructed his abstract relativity machine out of a material world of synchronized clocks.

  Chapter 6

  THE PLACE OF TIME

  Without Mechanics

  By December 1907, Patent Officer Einstein was no longer an obscure bureaucrat. Minkowski wrote to request a relativity reprint, congratulating the young scientist on his success. Wilhelm Wien debated him on the possibility of faster-than-light signaling. Max Planck and Max Laue j
oined the young physicist in conversation; one of the best experimentalists in Germany, Johannes Stark, commissioned an article from him on the relativity principle. No longer could Einstein breezily omit the work of his contemporaries; his engagement in the circle of physicists was now active, and his footnotes reflected it. Theorists Emil Cohn and H. A. Lorentz joined Einstein’s reference list in his 1907 review of relativity, as did experimentalists Alfred Bucherer, Walter Kaufmann, Albert Michelson, and Edward Williams Morley.1 Einstein even addressed Lorentz’s “local time” directly, as he had not in 1905. But Poincaré’s name was nowhere among the thirty-two footnotes. Einstein continued to pass over the older scientist in utter and unbroken silence.2

  Einstein began by assuming that there was no measurable difference between physical processes observed when they were at rest and those same physical processes were they conducted in a constantly moving boxcar. He took as his starting point what Poincaré, Lorentz, and other leading physicists had, earlier in the game, been working painstakingly to prove. Poincaré and others had asked how electrons flattened as they moved through an all-pervasive ether, how the electron could remain stable despite its distortion, how the ether reacted as electrified bodies and light passed through it. But in Einstein’s paper, all that the French polymath had done vanished. Not just the bits on the ether and electron structure: absent as well was any reference to Poincaré’s simplification and correction of the transformations in Lorentz’s theory, Poincaré’s powerful mathematical advances (including the introduction of the four-dimensional spacetime), Poincaré’s articulation of a principled physics, and perhaps most dramatically, Poincaré’s interpretation of Lorentz’s “local time” as a convention of clock coordination executed by the exchange of light signals. Not a trace.