Einstein's Clocks and Poincare's Maps

by Peter Galison

  Continuing his éloge to the Nobel committee, Poincaré acknowledged that people often judge theories such as Lorentz’s as fragile. The sight of the ruins of past theorizing may make anyone into a skeptic, he allowed. But if Lorentz’s theories were to join others in the vast cemetery of defeated accounts of the world, no one could justifiably claim that Lorentz had randomly predicted true facts (faits vrais). “No, it is not by chance, it is because [Lorentz’s theory] revealed to us relations unknown until then between facts that apparently were strangers one to the other, and that these relations are real; and that they would be so even if electrons didn’t exist. It is that sort of truth that one can hope to find in a theory, and these truths will survive beyond the theory. It is because we believe that the work of Lorentz contains many such truths that we propose that he be rewarded for them.”66

  A Triple Conjunction

  By the end of 1902, Poincaré had spent a full decade facing the problem of time coordination from three very different perspectives. As one of the exalted Bureau of Longitude’s Academy members since January 1893, Poincaré had helped lead the institution in its quest to cover the world with synchronized time. When the issue of conventionally restructuring time into a decimal system arose in earnest during the mid-1890s, it was Poincaré who had directed the effort to evaluate the alternatives, culminating in the 1897 report. Then back to philosophy: in 1898 he proclaimed to a primarily philosophical audience that simultaneity was nothing other than a convention, a convention that would define simultaneity precisely as his Bureau had done with their telegraphic coordination of clocks. From the Revue de Metaphysique et de Morale, it was but a few months before Poincaré was back, deeper than ever, in expeditionary longitudinism. From 1899 forward he had been the liaison between the Academy and the complex and dangerous longitude mission to Quito while the mission struggled to bind time and geography through telegraphically flashed simultaneity. That summer of 1900 he issued his strongest-yet philosophical statement of the conventionality of simultaneity, a statement that appeared in one of the most widely cited sections of Science and Hypothesis. Then a return to physics. In December 1900, Poincaré “reviewed” Lorentz’s theory, turning Lorentz’s mathematical fiction “local time” into a telegrapher’s procedure, where observers moving through the ether synchronized clocks by exchanging signals.

  This was not merely a matter of “generalizing” from the physics to the philosophy or “applying” abstract notions from mathematics or philosophy to physics. Instead, Poincaré was working out a new concept of time, showing how it fit into the rules of three different games: geodesy, philosophy, and physics. Just because the statement of synchronization and simultaneity functioned within all three of Poincaré’s worlds, it took on a singular importance.

  All through Poincaré’s work lay a Third Republic progressivism, a sense that all aspects of the world could be improved through an engaged reason, a rational, machinic modernism. His faith carried the optimism of an abstract engineering, an undying belief that it was within the reach of reason to get at any aspect of the map, whether of the geographical world or that of science. All things being equal, Poincaré would just as soon resolve a problem the way he handled the decimalization dispute—by setting the various positions against one another and cooly picking out the simplest (most convenient) relations among terms. Relations were what was real to Poincaré (the relations captured by Newton or Lorentz or by mathematics), not the particular objects of our senses. “It may be said . . . that the ether is no less real than any external body; to say this body exists is to say there is between the color of this body, its taste, its smell, an intimate bond, solid and persistent; to say the ether exists is to say there is a natural kinship between all the optical phenomena, and neither of the two propositions has less value than the other.”67 Objective reality was nothing other than the commonly held relationships among the phenomena of the world. There was no otherworldly plane of existence for Poincaré. The importance of scientific knowledge lay in the persistence of particular true relations, not in a back-of-the-curtain reality of Platonic forms or ungraspable noumena.

  Poincaré generally shied away from overt political reference or moral absolutes. Still, once or twice, a different tenor breaks the neutral, moderated tone of his commentaries. We know, he told the General Association of Students in May 1903 in a Parisian restaurant, that there are twin fields on which action has to be taken: toward scientific truth and toward moral truth. “It seems that there is an antinomy between our two dearest aspirations, we want to be sincere and serve the truth; we want to be strong and capable of acting. . . . From here the violence of the passions raised by a recent affair. On both sides, most were driven by noble intentions.” Alluding to the Dreyfus Affair then wracking the country, Poincaré’s anodyne summary muted his own torn responses—his powerful devotion to the French army and his equally urgent allegiance to standards of demonstration. On 4 September 1899, in the midst of Alfred Dreyfus’s second trial, Poincaré had intervened by proxy. His letter slammed the scientific basis of the charge that it was Dreyfus who had written an incriminating torn sheet of paper (the famous bordereau) promising French state secrets to a German military attaché: “It is impossible,” Poincaré concluded, that anyone “with a solid scientific education” could give credence to the nonsensical use of statistics presented by the prosecution. Despite that stark judgment, the court reconvicted Dreyfus, though the President of the Republic issued a pardon.68 (Poincaré defended Dreyfus again a few years later on technical grounds, though stronger ones.) Return now to Poincaré’s 1903 address to the assembled students. Action had to join thought, he insisted.

  The day when France has no more soldiers, but only thinkers, Wilhelm II will be the master of Europe. Do you think then that Wilhelm II would have the same aspirations as you? Do you count on him using his power to defend your ideal? Or do you put your confidence in the people, and hope that they will commune in the same ideal? That’s what one hoped in 1869. Do not imagine that what the Germans call right or liberty is the same thing that we call by the same names. . . . To forget our country is to betray the ideal and the truth. Without the soldiers of Year II, what would have remained of the Revolution?69

  Poincaré added that every generation wonders about the fate of its work, none more than his. “Cruelly hit at the moment they arrived at manhood, my contemporaries set to work to repair the disaster [of the Franco-Prussian War]. . . . Years passed and deliverance did not come. And so we ask ourselves, have you inherited this dream, without which all our sacrifices would be in vain? Maybe . . . that which for us appeared as an intolerable injustice, . . . a bleeding wound is, for you, just a bad historical memory, like the distant disasters of Agincourt or Pavia.”70

  Crises and recuperation were always in view for Poincaré: in politics, but also in philosophy and in science. If his generation’s political ideal was to “repair the disaster” of 1871, there were nearer opportunities where the scientific machine could re-arrange, repair, improve. In April 1904 he had a second opportunity to repair the damage caused by the Dreyfus crisis. Asked by the court to address the status of the famous bordereau, Poincaré, with two scientist-colleagues at the Observatory, scrutinized the evidence. They remeasured the handwriting by using precision astronomical instruments and recalculated every last bit of the prosecution’s probabilistic reasoning designed to show the statistical near-certainty that the bordereau was Dreyfus’s. Poincaré’s conclusion: the handwriting analysis was nothing but the illegitimate application of badly reasoned probability on an incorrectly reconstituted document.71 Backed by Poincaré’s 100-page report of 2 August 1904, the intervention succeeded. Poincaré crushed, for example, the prosecution’s claim that Dreyfus had written the word “intérêt” on the bordereau. Alphonse Bertillon, the prosecution’s star handwriting expert, had contended that the word could only have been written using the grid of a military map—a scale that famously set the diameter of a “sou” equal t
o a kilometer. Along with his mathematician colleagues, Poincaré created an enormous enlargement of that single word, mapping it, as it were. Their conclusion: Bertillon’s claims about the curvature, length, axis, and height of the letters were as arbitrary (changing for each letter) as his spurious microcaligraphic analysis of the circumflex accent. There was no “geometrical particularity” to this word. Nothing at all implied it was written by someone working at a staff officer’s desk using military cartography.72 Impressed, the court exculpated Dreyfus. Once again, Poincaré had mapped a technical fix to a profound crisis. This time it had taken more than a chart of coefficients (Poincaré’s ploy to resolve the crisis of decimalization). But in a sense, the spirit was the same: reasoning through machines and calculations, he helped defuse a crisis.

  Crises arose elsewhere. In September 1904, just a few weeks later, the International Congress of Arts and Science gathered at St. Louis, Missouri, for an international exposition to celebrate progress. Delivered in the midst of a World’s Fair built to model the world (here Paris, there London, Turin, New York), Poincaré’s speech on the future of physics appropriately aimed to encapsulate the whole field and to identify its weak points. Time coordination featured prominently, set within a larger frame of progressive continuity: “[Y]es, there are indications of a serious crisis [in physics],” Poincaré conceded early on in his talk, but “let us not be too disturbed. We are assured that the patient will not die of this sickness and we can even hope that the crisis will be beneficial, for past history seems to guarantee it.”73

  By Poincaré’s lights, mathematical physics had received its first ideal form in Newton’s law of gravity. Every body in the Universe, every grain of sand, every star was attracted to every other body by a force inversely proportional to the square of their separation. This simple law, varied and applied to different kinds of forces, formed the first phase of the history of physics. Out of that peaceable kingdom a crisis emerged when Newton’s picture proved inadequate to the complex industrial processes physicists confronted in the nineteenth century. New principles were needed, principles that could characterize the whole of a process without specifying, as Newton might have had it, every last detail of the machine. Such new principles included the stipulation that the mass of a system always stayed the same or that the energy of a system remained constant over time. One great triumph was Maxwell’s theory, which embraced all of optics and electricity, describing the whole as states of a great, world-pervading ether.

  Did this nineteenth-century, second phase of physics far exceed Newton’s dreams? Of course. Did it show the futility of the first phase? Poincaré advised his World’s Fair audience, “Not in the least. Do you think that this second phase could have existed without the first?” Newton’s idea of central forces had led to the principles of the second period (Poincaré’s own). “It is the mathematical physics of our fathers that familiarized us little by little with these various principles, which has habituated us to recognize them under the different clothing with which they disguise themselves.”74 Our forebears compared the principles with experience, learned how to modify their expression to adapt them to the givens of experience, enlarged the principles, and consolidated them. Eventually we came to see these principles, including the conservation of energy, as experimental truths. Bit by bit the older conception of central force came to seem superfluous, even hypothetical. The frame of Newtonian physics shook.

  Poincaré’s staging of this new “crisis” was, characteristically for him, a preamble to recuperation. Echoing the meliorist position he had taken for fifteen years, he insisted that shedding past beliefs did not demand rupture: “The frames are not broken, because they are elastic; but they have been enlarged; our fathers, who established them, have not worked in vain; and we recognize in the science of today the general traits of the sketch that they traced.”75 For Poincaré, physics in 1904 nonetheless stood at the threshold of a new phase in its epochal history. Radium, “that great revolutionary,” had destabilized accepted truths of physics, precipitating crisis. Every principle of nineteenth century physics tottered.

  One hope had been that meaning could be given to the ether by measuring how fast the earth was sailing through it. Poincaré lamented that all such attempts, even Michelson’s most accurate ones, had ended in failure, driving theorists to the limit of their ingenuity. “[I]f Lorentz has managed to succeed, it is only by accumulating hypotheses.” Of all those Lorentzian “hypotheses,” one stood out for Poincaré above all others:

  [Lorentz’s] most ingenious idea was that of local time. Let us imagine two observers who want to set their watches by optical signals; they exchange their signals, but as they know that the transmission is not instantaneous, they take care to cross them. When the station B receives the signal of station A, its clock must not mark the same time as station A at the moment of the emission of the signal, but rather that time augmented by a constant representing the duration of the signal.

  At first, Poincaré considered the two clock-minders at A and B to be at rest—their two observing stations were fixed with respect to the ether. But then, as he had since 1900, Poincaré proceeded to ask what happened when the observers are in a frame of reference moving through the ether. In that case “the duration of the transmission will not be the same in the two directions, because station A, for example, moves towards any optical perturbation sent by B, while the station B retreats from a perturbation by A. Their watches set in this manner will not mark therefore true time, they will mark what one can call local time, in such a way that one of them will be offset with respect to the other. That is of little importance, because we don’t have any way to perceive it.” True and local time differ. But nothing, Poincaré insisted, would allow A to realize that his clock will be set back relative to B’s, because B’s will be offset by precisely the same amount. “All the phenomena that will be produced at A for example, will be set back in time, but they will all be set back by the same amount, and the observer will not be able to perceive it because his watch will be set back; thus, as the principle of relativity would have it, there is no means of knowing if he is at rest or in absolute movement.”76

  Yet coordinated clocks were not enough by themselves to rescue all of classical, principle-based physics. According to Poincaré, the challenges of radioactivity hovered like storm clouds over the discipline. Energy conservation: challenged by the spontaneous emission of energetic radioactive particles. Mass conservation: in trouble because fast charged particles acted as if their mass depended on their velocity. Action-reaction: threatened because, according to the Lorentz theory, a lamp projecting a beam of light recoiled before the light beam arrived somewhere else where it caused the absorber to recoil. Even the relativity principle appeared threatened, for which the physicist-physicians had called in the antidotes of “local time” and length contraction. What to do? Surely, trust the experimenters. Yet for Poincaré the chain of responsibility ended with the theorists: theorists had produced this mess; they should resolve it. And any theoretical rescue of principled physics could not take place by abandoning the “physics of our fathers.” Instead, progress demanded reworking the past: “let us take the theory of Lorentz, turn it in every direction; modify it little by little, and perhaps everything will work out.” Poincaré hoped that the organism of physics would reveal its constant identity even as it changed, like an animal shedding its shell for a new one. To abandon a principle such as the principle of relativity would be, he insisted, to sacrifice “a precious arm” in the battle at hand.77

  Poincaré and Lorentz did “turn the theory in every direction,” altering it as best they could. In May 1904, Lorentz modified his old assumption about length contraction and his fictional “local time” in such a way that, when the shortened length and local time were inserted into the equations of physics, the equations were no longer approximately the same in any frame of reference moving inertially through the ether, but instead identical.78 That striking vindicat
ion of Poincaré’s understanding of the relativity principle—as he called it—was enough to set the French polymath to work. On 5 June 1905, he summarized his results to the French Academy of Sciences. For the first time, he had a theory adequate to account for both optical experiments and the new fast electron experiments, both, as he had long hoped, inside the “elastic frame” of Lorentz’s physics. Published fully in 1906 as “On the Dynamics of the Electron,” the paper finished Poincaré’s longstanding project by pushing the clock synchronization scheme one last step: The synchronization of clocks led to Lorentz’s improved local time, from which it followed that the equations of physics took on the same form in all frames of reference.

  Just a few months later, in the winter semester of 1906–07, Poincaré spelled out for his students precisely how Lorentz’s improved “local” time fit with the Lorentz contraction to make it fully impossible to detect motion of the earth with respect to the ether.79 Again in 1908 he insisted that the apparent time of transmission is proportional to the apparent distance: “it is impossible to escape the impression that the principle of relativity is a general law of Nature, that one could never by any imaginable means, have evidence of anything but the relative speeds of objects”—motion with respect to the ether would never be found.80 Here was a monument to Poincaré’s decades-long attempt to improve the machinery of physics while keeping the “elastic frame” of the old—a “new mechanics” that guarded the ether while challenging old ideas of space, time, simultaneity. It was the modernism of an abstract machine.

  However beautiful the theory in its embodiment of the relativity principle, Poincaré had long made it clear that principles rose from experiment, acknowledging that those roots meant that experiments could spell trouble for principles. The relativity principle was no exception. Indeed, at the very beginning of his “On the Dynamics of the Electron,” Poincaré warned that the entire theory could be endangered by new data.81 Lorentz too smelled trouble from the laboratory. In a letter to Poincaré of 8 March 1906, Lorentz took pleasure in the coincidence of their results. But that concordance meant that both of them faced a similar peril: “Unfortunately, my hypothesis of the flattening of electrons is in contradiction with the results of new experiments by Mr. [Walter] Kaufmann and I believe I am obliged to abandon it; I am therefore at the end of my Latin and it seems to me impossible to establish a theory that demands a complete absence of the influence of translation on electromagnetic and optical phenomena.”82