Einstein's Clocks and Poincare's Maps

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by Peter Galison


  But here neither picture will do. Philosophical and physical reflections did not cause the deployment of coordinated train and telegraph time. The technologies were not derivative versions of an abstract set of ideas. Nor did the vast networks of electro-coordinated clocks of the late nineteenth century cause or force the philosophers and physicists to adopt the new convention of simultaneity. No, the present narrative of coordinated time fits neither of these metaphors of progressive evaporation or condensation. Another image is needed.

  Imagine an ocean covered by a confined atmosphere of water vapor. When this world is hot enough, the water evaporates; when the vapor cools, it condenses and rains down into the ocean. But if the pressure and heat are such that, as the water expands, the vapor is compressed, eventually the liquid and gas approach the same density. As that critical point nears, something quite extraordinary occurs. Water and vapor no longer remain stable; instead, all through this world, pockets of liquid and vapor begin to flash back and forth between the two phases, from vapor to liquid, from liquid to vapor—from tiny clusters of molecules to volumes nearly the size of the planet. At this critical point, light of different wavelengths begins reflecting off drops of different sizes—purple off smaller drops, red off larger ones. Soon, light is bouncing off at every possible wavelength. Every color of the visible spectrum is reflected as if from mother-of-pearl. Such wildly fluctuating phase changes reflect light with what is known as critical opalescence.

  This is the metaphor we need for coordinated time. Once in a great while a scientific-technological shift occurs that cannot be understood in the cleanly separated domains of technology, science, or philosophy. The coordination of time in the half-century following 1860 simply does not sublime in a slow, even-paced process from the technological field upward into the more rarified realms of science and philosophy. Nor did ideas of time synchronization originate in a pure realm of thought and then condense into the objects and actions of machines and factories. In its fluctuations back and forth between the abstract and the concrete, in its variegated scales, time coordination emerges in the volatile phase changes of critical opalescence.

  To dig into the records of almost any town in Europe or North America—indeed, far beyond both—reveals the struggle to coordinate time during these years of the late nineteenth century. There lie the yellowing data of railroad superintendents, navigators, and jewelers, but also of scientists, astronomers, engineers, and entrepreneurs. Time coordination was an affair for individual school buildings, wiring their classroom clocks to the principal’s office, but also an issue for cities, train lines, and nations as they soldered alignment into their public clocks and often fought tooth-and-nail over how it should be done. Step back to the archives of central governments and the cast of characters grows wider and wilder: anarchists, democrats, internationalists, generals.

  Amidst this cacophony of voices, this book aims to show how the synchronizing of clocks became a matter of coordinating not just procedures but also the languages of science and technology. The story of time coordination around 1900 is not one of a forward march of ever more precise clocks; it is a story in which physics, engineering, philosophy, colonialism, and commerce collided. At every moment, synchronizing clocks was both practical and ideal: gutta-percha insulator over ironclad copper wire and cosmic time. So variously construed was time regulation that it could serve in Germany as a stand-in for national unity, while in France at the same moment it embodied the Third Republic’s rationalist institutionalization of the Revolution.

  My aim is to pursue coordinated time through this critical opalescence, and in particular to set Henri Poincaré and Albert Einstein’s revamped simultaneity in the thick of it. Entering the sites of time production and the lanes of its distribution will bring us repeatedly to two crucial locations in the binding of clocks that joined Einstein’s and Poincaré’s transcendent metaphors of clocks and maps to altogether literal places: the Paris Bureau of Longitude and the Bern Patent Office. Standing at those two exchanges, Poincaré and Einstein were witnesses, spokesmen, competitors, and coordinators of the cross-flows of coordinated time.

  Order of Argument

  Because the fate of coordinated time cannot be tracked from a nuclear group of railroad managers, inventors, or scientists in a simple widening circle, our story will switch scales back and forth between local and global narratives. I want to introduce Poincaré in chapter 2 (“Coal, Chaos, and Convention”) in a way that may be somewhat unfamiliar. Who would guess from Science and Hypothesis, his best-selling book of 1902, that he had trained as a mining engineer and served as an inspector in the dangerous, hard-pressed coal mines of eastern France? Or that for decades he had helped run the Bureau des Longitudes in Paris, serving as its president in 1899 (and later in both 1909 and 1910)? Or that he co-edited and often published in a major journal on electrotechnology that ran abstract articles on fundamental issues of electrodynamics next to pieces about undersea cables and the electrification of cities?

  Understanding the transformation of time—its radical secularization—requires a relocation of Poincaré, whose conventionalization of simultaneity is flattened into two dimensions if he is seen purely as a mathematician-philosopher or mathematical physicist (though he was certainly both). More is needed than a simple addition of a side-interest in engineering. Poincaré figures here not as a free-floating monad who seized this or that “resource” from philosophy, mathematics, or physics to solve particular problems. Instead, throughout this book I want to situate Poincaré in the midst of powerful series of moves that, at a few critical intersections, formed roughly consistent ways of acting within physics (or philosophy or engineering). It is not that a preformed Poincaré plucked mere details of procedure from his alma mater, Ecole Polytechnique, but instead that he was also very much its product. As he put it, he and his colleagues proudly bore Polytechnique’s “factory stamp.” Chapter 2 is about that stamp, under which it was as reasonable for Poincaré to assess mining accidents as to augur the stability and fate of the Solar System or to generate abstract mathematics. It takes us close-in to Poincaré to capture this wider link between the material and the abstract. And that bond is crucial if we are to understand in subsequent chapters the multiple ways in which Poincaré insisted on examining the concept of simultaneity under the different but intersecting lights of physics, philosophy, and technology.

  But the “factory” of Poincaré’s Polytechnique education—along with the mining and mathematical years that followed—is still not yet a wide enough terrain on which to locate the secularization of time coordination. That larger territory extended even beyond France, to the colliding networks of wires and rails that the Great Powers were erecting at breakneck speed. Matching these systems at their often-contested boundaries could only be accomplished by codes and conventions that, in the 1870s and 1880s, aimed, sometimes painfully, to mesh the collision of incompatible length and time standards. So in chapter 3 we will pull back from the close-in frame of chapter 2.

  Chapter 3, “The Electric Worldmap” is after this vastly larger timescape of earth-covering networks—clashing empires of time. In those late-nineteenth-century decades, nowhere was the demand for world-covering conventions more apparent than in the drawing of global maps. Confronting a staggering increase in the volume of trade during these years, navigators were increasingly frustrated by maps with differing and often unreliable longitudinal grids. So too were colonial authorities, as they stepped up the pace of the conquest of new lands, the exploitation of resources, and the building of railroad lines. All demanded precise and consistent geodesy. These various demands came to a head in an 1884 meeting at the American State Department, when twenty-two countries fought their way toward a single prime meridian—the zero point of longitude—to be placed in Greenwich, England. Frustrated, indeed infuriated by the arrogation of that global zero-arc to the hub of the British Empire, the French delegation lobbied for a decimalized time, determined to put a French stam
p of rational enlightenment on the new world order of clocks and maps.

  Chapter 4, “Poincaré’s Maps,” picks up at an intermediate range, at the height of this French campaign of the 1890s to rationalize time—in which Poincaré played a determinative role. Charged with the evaluation of the longstanding French revolutionary proposal to decimalize time, and, with it the divisions of the circle, Poincaré and his interministerial committee encountered firsthand the competing proposals for how to conventionalize the measure of time. Indeed, it was precisely in this period that Poincaré began serving as a senior member of the French Bureau of Longitude, the agency charged with coordinating clocks around the world to produce the most accurate of maps. Here, in Europe, Africa, Asia, and the Americas, in the world of precision-synchronized times and geodesic maps, we can finally confront Poincaré’s philosophical proposal of 1898 to treat simultaneity as a convention. If simultaneity could only be specified by agreement on how to synchronize clocks, then a felicitous precedent would be to coordinate them exactly as did the telegrapher-longitude finders. This move—at once a statement of up-to-date cartography and of the metaphysics of time—is of extraordinary importance. Newton’s absolute, theological time had no place; instead there stood a procedure. Engineering common time stood where God’s absolute time had been.

  Nothing in Poincaré’s 1898 conventionalization of time directly addressed either electrodynamics or the principle of relativity. That connection came only in December 1900, as Poincaré reexamined earlier work of the Dutch physicist, Hendrik Antoon Lorentz. Back in 1895, Lorentz had advanced a theory of the electron that incorporated the following extremely clever idea. In the rest frame of the ether, where the equations governing electric and magnetic fields (Maxwell’s equations) were supposed to hold good, Lorentz spoke of “true time,” ttrue. Suppose some object, such as an iron block, were moving in this ether rest frame (traveling through the ether) and that Maxwell’s equations gave a detailed description of the electric and magnetic fields in and around the iron. How should the physics be described from a frame traveling with the iron block? It seemed as if the physics would suddenly become vastly more complicated as one tried to take account of the fact that the moving frame was racing through the ether. But Lorentz found that he could simplify the equations, making them as simple as in the ether rest frame, if he redefined the fields and the time variable. Because he had redefined the time of an event so that it depended on where the event took place, Lorentz called tlocal “local time” (Ortszeit), the same word used in everyday life to describe the (longitude-dependent) time of Leiden, Amsterdam, or Djakarta. The crucial point was this: Lorentz’s local time was purely a mathematical fiction used to simplify an equation.

  Poincaré first published a time paper in January 1898 in a philosophy journal. His goal was to show that clock coordination by means of electric telegraph exchange formed the basis for a conventional definition of simultaneity. It was technological and philosophical and had strictly nothing to do with the physics of moving bodies. By contrast, in his second move (1900), Poincaré dramatically extended Lorentz’s tlocal to the physics of altogether real (not mathematical) moving frames of reference. True, Poincaré did everything possible not to call attention to the difference between his “apparent” local time and Lorentz’s mathematical one. Nonetheless, the concept had moved: in Poincaré’s hands, local time lost its fictional status and became the time that moving-frame observers would show on their clocks as they corrected for the fact that signal exchange would beat against or run with an ether wind.

  With Poincaré’s 1900 interpretation of local time, suddenly all three series—physics, philosophy, and geodesy—intersected in the coordination of electrosynchronized clocks. Again responding to Lorentz, Poincaré made his third move with synchronized clocks in 1905–06. In 1904, Lorentz had modified his local time, tlocal, to make the equations of electrodynamics in the fictional moving frames even more similar to the “true” ether rest frame. Poincaré seized Lorentz’s result, adjusting (inter alia) the definition of local time to make the mathematical correspondence exact between fictional moving frames and the true resting one. But the crucial point for Poincaré was not that he had slightly modified Lorentz’s theory. Rather, it was this: Poincaré had demonstrated that clocks coordinated as they moved through the ether would give exactly Lorentz’s new local time and would do so for real observers moving in that frame. The relativity principle held good, even while Poincaré continued to oppose “apparent time” to “true time.” By 1906, Poincaré had placed the light-coordination of clocks front and center for three projects fundamental to modern knowledge: technology, philosophy, and physics.

  The French polymath had begun with geodesic time, shifted registers to his antimetaphysical, conventional time, and then cleared his way to the physics of local time and relativity. Throughout his physics—but also throughout his philosophy, technology, and politics—Poincaré saw his world as improvable through rational, intuitive intervention; he reveled in pushing a problem into “crisis” and then resolving it. His was the optimism of a progressive engineer willing to reassemble major struts and cables of the structures he tackled, but insisting that the built world of “our fathers” be respected, incorporated, improved.

  In chapter 5, we turn to “Einstein’s Clocks.” Not to the prophetic, world-famous, and mathematically inclined Einstein of 1933 or 1953, but to Einstein the tinkerer, souping up homebuilt instruments in his Kramgasse apartment, the Einstein riveted by the design of machines and the analysis of patents. This was neither the suddenly celebrated Einstein of post-World War I Berlin nor the abstracted, hermitlike elder Einstein of Princeton, but the thoroughly engaged 1905 youth of Bern. Though its technological infrastructure came late, when Switzerland inaugurated its rail, telegraph, and clock network, synchronized time there was a very public affair—and Bern was its center. From Bern electric time radiated outward, to the clock industry of the Jura region, to the public display of urban clocks, to the railroad, and, of course, to the patenting of synchronized clocks. Einstein was in the thick of it.

  Yet Einstein’s path to coordinated time was very different from Poincaré’s. Einstein’s vision was less ameliorist. Framing himself as a heretic and an outsider, Einstein scrutinized the physics of the fathers not to venerate and improve, but to displace. Einstein saw the coordination of time, and indeed his physics and his philosophy more generally, as part and parcel of the same critical reevaluation of the founding assumptions of the disciplines. Einstein did not move methodically from one aspect of time coordination to another. Most elements of his approach to relativity theory were already in place before he even touched the problem of time; for example, by 1901 he had already dismissed the ether that Poincaré had struggled so hard to maintain. Einstein’s engagement with critical works at the boundary of physics and philosophy were by then long-standing, and at the patent office, he and his fellow inspectors had been dissecting the machinery of time for three years. So in May 1905, when Einstein began defining simultaneity by way of electrocoordinated clocks, it was not, as it was for Poincaré, a matter of distinguishing “apparent” from “true” time alongside a quasi-fictional ether. For Einstein clock coordination was the turn of the key that would at last set in motion the theory machine that he had struggled for a decade to assemble. There was no ether; there were actual fields and particles, and there were but real times given by clocks.

  In the final chapter, “The Place of Time,” it is possible to see how the work of Einstein and of Poincaré could be both extraordinarily close yet far apart. Precisely in the uneasy relation between their competing uses of coordinated time, they stand not as progressive against reactionary approaches to nature, but as two strikingly different visions of what made modern physics modern—the consummate Polytechnician’s hopeful reforms against an outsider’s rebellion against foundations. Yet despite their differences, both were grappling with the same extraordinary insight into electrocoordinated time
, and in so doing both men stood at the crossing of two great movements. On one side lay the vast modern technological infrastructure of trains, shipping, and telegraphs that joined under the signs of clocks and maps. On the other, a new sense of the mission of knowledge was emerging, one that would define time by pragmatism and conventionality, not by eternal truths and theological sanction. Technological time, metaphysical time, and philosophical time crossed in Einstein’s and Poincaré’s electrically synchronized clocks. Time coordination stood, unequaled, at that intersection: the modern junction of knowledge and power.

  Chapter 2

  COAL, CHAOS, AND CONVENTION

  WITH THE DRAMATIC success of Poincaré’s 1902 collection of philosophical-scientific articles, Science and Hypothesis, his position in French intellectual life was unmatched. Standing at the pinnacle of mathematics, physics, philosophy, he was scientific rapporteur of a major scientific expedition and had served as president of the Bureau of Longitude. He embodied the successful Polytechnician, garnering an early reputation in mathematics and then proceeded directly to the nitty-gritty of mining engineering. Here is our central theme—intertwined abstraction and concreteness—far more closely bound for Poincaré and his contemporaries than scholars and engineers of later times ever expected. No wonder that the former students of Ecole Polytechnique asked him to use their annual address to reflect “On the Part Played by Polytechnicians in the Scientific Work of the XIXth Century.” As he prepared that 25 January 1903 lecture, Poincaré sifted through the presentations of recent honorees. “I see among my predecessors,” he told his classmates and colleagues, the “dean of our generals, numerous ministers, scientific engineers, the director of a large company, those who conquered our overseas empire and those who organized it, and those who brought from the earth, three years ago, the ephemeral splendors of the [Universal Exposition on the] Champ de Mars.” How, Poincaré asked, could a single education have produced such a combination of scientists, soldiers, and engineering entrepreneurs?1

 

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