Einstein's Clocks and Poincare's Maps

by Peter Galison

  For Poincaré, the trunk of the tree of knowledge was precisely this engaged mechanics, an intuitively grounded mathematical understanding of nature that, at myriad points, shot branches into experiment and technology. Searching in a thousand ways, Poincaré aimed for an understanding of the world that could on the one hand speak to students trying to comprehend their place in an injured France and on the other hand to scientists, cartographers, and politicians struggling to wire together an empire that would bind Paris to Dakar, Haiphong, and Montreal. He wanted a mechanics of forces and energy, but one sufficient to undergird analysis of celestial mechanics, the shape of the earth, or the behavior of telegraph wires. As he reminded his fellow anciens polytechniciens in 1903, the required mixture was one of theory and action. In Poincaré’s case that meant at one time responding to British telegraphic hegemony by fostering French radio signaling, at another by dismantling the unscientific indictment against Dreyfus with astronomical instruments and the calculus of probabilities.

  His was a world where truth and the ultimate reality of things meant far less than the establishment of communicable, stable, durable relations—the kind of reliable relations that made action possible. As Poincaré put it, “science is only a classification and . . . a classification can not be true, merely convenient. But it is true that it is convenient, it is true that it is so not only for me, but for all men; it is true that it will remain convenient for our descendants; it is true finally that this can not be by chance. In sum, the sole objective reality consists in the relations of things.”15 A world of scientific rationality without metaphysical profundity: objective relations, not metaphysical objects.

  For Poincaré, joining the abstract and concrete in this flat world of relations meant being able to negotiate hard-fought conventions in the human world. Sorting and negotiating the needs and demands of railroad magnates, astronomers, physicists, and navigators lay front and center in the decimalization of time. And as a leading figure at the Bureau of Longitude, Poincaré grasped time through the detailed, material procedures of engineering protocols: organizing, analyzing, reporting on the expeditions of the military-scientific colleagues he so admired as they hammered together observatory shacks in the high Andes or on the coastal stations of Senegal. Time, for Poincaré, resided in our world, our convenience, our exchange of optical and electrical telegraph signals. The metaphysical world behind appearances was nothing. As he wrote in “The Measure of Time,” “We . . . choose these rules [of simultaneity] not because they are true but because they are the most convenient.”

  For Poincaré the choice of how to measure simultaneity made time richer, not poorer. It meant he could work the time concept back and forth among the protocols of longitude or decimalization, the abstractions of a science-inflected philosophy, and the principles of a new physics. “Let us watch [scientists (savants)] at work and look for the rules by which they investigate simultaneity,” Poincaré urged.16 This is precisely what Poincaré did as he struggled to synthesize the work of his circle of philosophers, physicists, and cartographers. Time-as-procedure stood in all three series:

  Simultaneity is a convention, nothing more than the coordination of clocks by a crossed exchange of electromagnetic signals taking into account the transit time of the signal.

  This move has provided the central drama of this book, charging its historical moment with a critical opalescence. What was it? In one sense it was a conventional, regulated procedure, a practical, ever-more-precise method for the day-to-day establishment of simultaneity for the sake of fixing longitude, a theory machine. As a technical convention, it occurred again and again in the pages of the Annals of the Bureau of Longitude. At the same time, for Poincaré it was a philosophical exploration of questions of time and simultaneity, a statement that he could present as his prime example of a conventional stance toward scientific laws and principles. Simultaneity was no more than electromagnetic coordination grounded in principled agreement. In this philosophical register, the utterance appeared appropriately and dramatically in the Review of Metaphysics and Morals, fitting perfectly into the longer conversation Poincaré had been conducting with a circle of French philosophers, many of whom had emerged from Polytechnique. Finally, beginning in 1900, Poincaré presented this simple simultaneity statement to an audience of physicists as an interpretation of Lorentz’s “local time” as if Lorentz had implicitly and all along held such a view. When Poincaré turned to theorizing about the electron, the simultaneity procedure could grace the published proceedings of a physics conference dedicated to Lorentz or the Proceedings of the Academy of Sciences.

  Is clock coordination “really” a technological, a metaphysical, or a physical intervention? All three. We may as well ask if the Place de l’Etoile is truly in the Avenue des Champs Elysées, the Avenue Kleber, or the Avenue Foch. In fact, as in a great metropolitan intersection, the enormous interest of the simultaneity question lies precisely in its position at the center of a vibrant crossing of great intellectual avenues.

  Repeated ceaselessly from East Africa to the Far East, the procedure of electromagnetic clock coordination was at once thoroughly technological and altogether theoretical. It was brass tubes with fragile, suspended mirrors, and it was global control of “universal time.” It was vast lengths of copper cable protected by heavy gutta-percha insulation, lying a mile under the ocean and served by brass telegraph keys inside crude observatory shacks; it was also the phantasmagorical reach of empire. Surveyors and astronomers pored over personal equations, calculating and correcting measurements through simultaneity on their way to the map, the final, prized product of their longitude work. But clock coordination was also the assembly of synchronized clocks strung together like beads along a continent-spanning chain through Europe, Russia, and North America. This fusion of technology and science drew together (though often in all-out struggle) Swiss horlogiers, American train schedulers, British astronomers, and members of the German General Staff. At one extreme, time synchronization represents technology conditioning humdrum daily procedure at every two-bit whistle-stop. As such it is a substantial part of the thick social history of the New England or Brandenburg countryside. At the other extreme, it stands for the symbolic reach of modernity that had mayors, physicists, and philosophers, pronouncing on the conventionality of time while poets payed homage to the annihilation of space by speed. In this register, clock coordination was rarified history, pursued at the pinnacle of European philosophy and mathematical physics.

  For Poincaré, the modern technology of time was not external to his scientific life—not a “context” that from some mythical “outside” shaped, influenced, or distorted thought. Poincaré was in and of this compound world, a product of and professor in the Ecole Polytechnique where the material and the abstract shaped one another at every moment. He proudly bore the “factory stamp.” Poincaré’s work on time was of a historical era and of a place; one aspect is not an accidental influence on another. To externalize Ecole Polytechnique or the Bureau of Longitude as entities outside Poincaré’s true self is to break linkages among technical and cultural actions that he and his late-nineteenth-century contemporaries saw as joined. Not only had Poincaré held the presidency of the Bureau on three separate occasions, but he also served as one of its elite Academy members for twenty years, published regularly in its journal, and played leading roles in its most active committees on the measurement of time. Nor is it “external” to Einstein’s physics that he trained at ETH, an institution committed by its very charter to joining theory and praxis, or that he capped that instruction with a seven-year apprenticeship at the Bern patent office, as a quality control officer in the production-machine of modern electrotechnology. No, these are not influences moving Einstein and Poincaré from the outside. They were rather fields of action that conveyed the high value of machines grasped through reason—production sites for technology (through science) and science (through technology).

  Circa 1900, to speak of the t
ransmission-corrected synchronization of clocks was both central and ordinary. Transmission correction of time was a working tool for the longitude finder and routine for city engineers in Paris and Vienna, who knew about time delay all too well through their frustrating attempts to pump exact time through pneumatic tubes under their cities. By 1898, the transmission delay of a time pulse was a standard problem for the squadrons of engineers, cartographers, physicists, and astronomers who were creating simultaneity every day of the week.

  So in January 1898, when Poincaré published his argument for time-as-convention, he was speaking the technology of clocks as well as the language of philosophy. The same utterances now could be heard in different registers. “Simultaneity is a convention,” or “synchronizing clocks demands transmission-corrected electrical coordination”—Are these philosophical observations or do they “really” belong to brass and copper technology? Is the Place de l’Etoile really in the Avenue Kleber or the Avenue Foch?

  In December 1900, Poincaré cleared a third avenue through the Place de la Simultanéité, when he began using clock synchronization—first approximately and later, exactly—to assign meaning to Lorentz’s local time. At that point three fields were fully engaged: telegraphic longitude, philosophical conventionalism, electrodynamic relativity. It is our loss that we have dessicated this remarkable moment, split it into fragments, and scattered them over the disconnected academic departments of philosophy, physics, and metrology. Poincaré struggled to hold that modern and modernizing world together—to fix it, uphold it, defend it.

  Young Einstein also stood in the midst of this trading zone of philosophy, technology, and physics. But he was never out to repair and uphold any empire—neither the French, nor the Prussian, nor the Newtonian. Delightedly mocking senior physicists, teachers, parents, elders, and authority figures of all kinds, happily calling himself a “heretic,” proud of his dissenting approach to physics, Einstein shed the nineteenth century’s ether with an outsider’s iconoclastic pleasure. Not for him was the increasingly desperate hunt for a stable basis of the Solar System, or for a bedrock foundationalism that would ground all of physics in mechanics or electrodynamics. Instead, Einstein was content—more than content—to find theory-devices that worked. Heuristics, temporary but effective means of going forward with the theory, were machines. So was his light clock, or the myriad of machinelike thought experiments that he proposed for thinking through the inertia of energy, E = mc2. And so, most importantly for our purposes, was his time machine, that infinite array of clocks connected and coordinated by the well-regulated exchange of light signals.

  As important as time coordination was for Poincaré as a pragmatic, conventional aid to the building of a new mechanics, it was more crucial for Einstein. For Einstein it was procedurally defined time that served as the starting point from which the Lorentz contraction would be derived. Like a classical arch, for Einstein time synchronization held the principled column of relativity in stable union with the principled column of the absolute speed of light.

  Did Einstein really discover relativity? Did Poincaré already have it? These old questions have grown as tedious as they are fruitless. No doubt originally propelled by the offensive and widespread Nazi-era assaults on Einstein’s place in physics, the struggle over “who discovered relativity” continued for decades: Who found the theory? What is its essence? Is the core of relativity really the dismissal of the ether, or is it the mathematical formula for transforming space and time? Is it an unshakeable commitment to the relativity principle or is it the applicability of the principle to all physical interactions or is the theory rightly identified with the derivation of time and space transformations from the synchronization of clocks? Or is relativity really no more than correct predictions of what can be observed in experiments? Above all, relativity—and the relativity of time in particular—became synonymous with modern physics and modernity more generally. From our perspective, assigning a graded checklist to Einstein and Poincaré counts as the least interesting part of the story of time and simultaneity.

  Far more important is to situate Poincaré and Einstein at the two nodal points of turn-of-the-century time coordination, grasping the characteristic ways in which each navigated the flows of technology, physics, and philosophy, and understanding how each struggled to rip simultaneity from the metaphysical firmament and bring it to earth as a procedurally defined quantity. Time standardization was the order of the day, for each scientist a natural extension of the standardization of length. It announced itself on the faces of public clocks, railroad schedules, and inside regulated schoolrooms and factory floors. In the Paris Observatory of the 1890s, Wolf was winding electromagnets to keep astronomical clocks in step and supervising the distribution of dozens more throughout the streets of Paris. Cornu was adjusting the giant pendulum on his regulator clock, joining mechanics and electromagnetism to formulate a rigorous analysis of electrosynchronization. Teams of itinerant observers worked incessant time-exchanges with Senegal, Quito, Boston, Berlin, and Greenwich. Anglo-Saxon astronomers hawked time to railroads, while French stargazers hoped the glorious precision of the observatory would be imitated through the whole of the country—reflections of a mother clock cast from mirror to mirror until the light of temporal rationality spilled through every street in the republic.

  Creating this standardized, procedural time was a monumental project that utilized creosote-soaked poles and undersea cables. It required a technology of metal and rubber, but also reams of paper, bearing, contesting, and sanctifying local ordinances, national laws, and international conventions. As a result, conventional, turn-of-the-century time synchronization never inhabited a place isolated from industrial policy, scientific lobbying, or political advocacy. It would ease matters if we could attribute the late-nineteenth-century push toward standards to a single drive-wheel: if we could say that it all came down ultimately to railroad magnates or decisively to scientists or exclusively to philosophers. But the restructuring of time was not that simple.

  Time was complex because, long before the nineteenth century, clocks and simultaneity were already more than gears, pendula, and pointers. In the eighteenth century, for example, the precision chronometers of the long-suffering British clockmaker John Harrison appeared in a larger print world about the longitude problem as well as in diaries and satires about timekeeping and mapping. From the start, Harrison’s precision clocks assumed a “planetary” significance.17 Forging back earlier than the eighteenth century still does not shake timepieces loose from the cultures in which they were built. Sand clocks and church clocks carried much besides the assignment of time; they conveyed different, overlapping authorities of God, of the feudal lord, of the memory of mortality. There simply is no getting behind the cultural to some primordial moment in which time was nothing but sand, shadow, or a mechanical pointer.

  What emerged in the late nineteenth century was not merely the issue of a particular invention—coordinated clocks certainly existed before then. Instead, Europe and North America experienced a dramatic, global alteration in the place and density of electrodistributed time. Linked clocks of the late nineteenth century covered the world. Circles of such wide-spanning technologies pulled each other along. Trains dragged telegraph lines, telegraphs made maps, maps guided rail-laying. All three (trains, telegraphs, maps) contributed to a growing sense that long-distance simultaneity made the question, What time is it now somewhere else? at once practical and evocative. When we read Einstein’s and Poincaré’s many discussions of the new ideas of time and space cast in the lexicon of automobiles, telegraphs, trains, and cannons, we are seeing the conditions under which these questions became commonplace.

  We can think of simultaneity as the intersection of arcs, where each arc stands for a long sequence of “moves” within a field. Take the physics we have followed. Clearly there is no single, unchanged meaning of simultaneity from the early 1890s through 1905. Local time (Ortszeit) began in a geographical sense,
became Lorentz’s fictionally offset local time, turned into Poincaré’s light-signal observable offset local time, shifted to Poincaré’s offset and dilated “apparent” time, only to take a new form in Einstein’s relativistic time. These shifts in the meanings of time did not take place all at once and did not play out purely in the domain of physics. Instead, they are better understood as a series of moves in an evolving game. Consistent with the use of “move” in the everyday sense of a game, a “move” in this more technical sense was sometimes a statement (or convention), sometimes a physical procedure. Remarkably, there was enough sense of continuity for Poincaré and Lorentz to see their work as building step by step, even though the aims of the game they were playing were also evolving. (If in 1894 Lorentz’s goal was to solve an equation by making a moving object in an electric and magnetic field look as if it were at rest in the ether, his goal [and Poincaré’s] in 1904–05 was to produce laws of physics that led to the same measurable results in any constantly moving frame of reference.)