Einstein's Clocks and Poincare's Maps

by Peter Galison

  Figure 5.12 Einstein’s Light Clock (1913). (a) In this simplest of all explanations of the dilation of time, Einstein imagined two parallel mirrors with a pulse of light reflecting between them, each traversal constituting a “tick.” If a clock like this flew by an observer “at rest,” the observer at rest would see the pulse following a sawtooth pattern. (b) Each angled traversal would follow a longer (diagonal) path than in the straight up-and-down path of a similar clock in the rest frame. Since light travels at the same speed in every frame of reference, Einstein concluded that a tick in the mirror frame would be measured as taking longer than a tick in the rest frame. Therefore, the rest observer must conclude, time runs slow in the moving frame of reference.

  Wireless time was all the rage in those first years of the twentieth century, and France pushed the new technology hard. Poincaré played a pivotal role through his popular and technical publications on radio, but even more powerfully behind the scenes. As he had so many times before, Poincaré crossed back and forth between abstract considerations of the status of electromagnetism and the practical exigencies of putting radio technology to immediate use. That continuing engagement with the theory and practice of communication no doubt facilitated his 1902 professorial appointment at the Ecole Professionelle Supérieure des Postes et Télégraphes. When, that same year, he contributed an article on wireless telegraphy to the yearbook of the Bureau of Longitude, he began by reviewing Hertz’s famous 1888 experiments that first demonstrated the existence of radio waves. But Poincaré immediately plunged himself into practical matters, asking: How could the new “Hertzian light” supplant optical telegraphy by reaching farther and diffracting around the curvature of the earth? How could radio penetrate fog that would block visible light? Could new kinds of antennae direct and concentrate radio waves? Poincaré was as willing to attack the details of nickel-silver coatings as he was to reflect on uses of radio to avoid ship collisions in bad weather.

  Figure 5.13 Wireless Time. In 1904–05 numerous groups were experimenting with the wireless transmission of time. The American Navy was one of the first, but others were pursuing the same goal. In this figure from a widely circulated journal in France, the transmitter, receiver, and operator were all shown. SOURCE: BIGOURDAN, “DISTRIBUTION” (1904), P. 129.

  As we have seen, the French had radio worries of a geopolitical sort after the stinging demonstration of British cable monitoring and cutting capacities during the late 1890s. These were concerns that Poincaré very much shared with other members of the French administrative elite. One French diplomat warned the French Colonial Union that, as long as Britain maintained its telegraph cable monopoly, the French simply could put no faith in the confidentiality of their State messages. Using a lantern slide, he projected for his concerned listeners a dramatically colored worldmap where they could see the desperate situation for themselves. Drawn in blue were the handful of short French cables binding North Africa and France and a single long line to the United States. “Look, now, at the immense development of the red lines: they extend everywhere and encircle the entire world in a veritable spider’s web. These red lines mark the network of the English telegraphic companies.”89 Given the instabilities marked by anticolonial uprisings and conflicts threatening the peace between France and Britain, the situation was dire. In this charged atmosphere it is no surprise that for Poincaré security was a key feature of the new wireless: “Optical and Hertzian telegraphy have a common advantage over ordinary telegraphy: in times of war, the enemy cannot interrupt communication.” But while the enemy would have to be in the proper position to intercept a light signal, broadcast signals could be captured much more widely, even interfered with by the counterbroadcasting of noise. “We remember that Edison threatened his European competitors, that he would disturb their experiments if they wanted to experiment in America.” Back and forth Poincaré oscillated between the pure and the practical, like the spark in a radiotransmitter: primary and secondary circuits were his subjects, but so was the security of French diplomatic communication.90

  In a search for ever-higher sites on which to post antennae, boosters of the nascent French radio service had already begun to eye the Eiffel Tower, the fate of which remained very much undecided in 1903. Eleuthère Mascart wrote Poincaré from the Bureau of Meteorology with a plea for help in getting the Minister of War to save the tower (and therefore the station) from being dismantled. The great tower was, he argued, a military asset, not only for optical telegraphy but also for the nascent wireless experiments that had already begun. Surely Poincaré would have the ear of the Minister of War—would he try to save the tower on grounds of national defense? Meanwhile, Gustave-Auguste Ferrié, Polytechnician, engineer, and army captain, joined forces with Gustave Eiffel; in 1904 they succeeded in getting Eiffel’s tower designated a station of the French radio service. Clinching their success was the army’s much-publicized triumph with radio when, in 1907, Ferrié trundled radio equipment into battle on horse-drawn carts so that French forces fighting Moroccan rebels could communicate with their commanders in France.91

  Given his position in the Bureau of Longitude, in the scientific community, and by then more broadly within the French intellectual elite, Poincaré’s radio-time ambitions for the tower carried weight. Largely at his behest, in May 1908 the Bureau urged the establishment of a radio time signal from the Eiffel Tower that could be used to determine longitude anywhere the signal could be received. Backing from the army came easily. In the winter of 1908, the French government launched an interministerial commission to control the new radio technology, appointing Poincaré at its head. The Minister of War concurred, releasing the funds. Wireless simultaneity had become a military, as well as a civilian, priority.92

  With Poincaré presiding, the seventh meeting of the commission assembled on 8 March 1909. The director of the Paris Observatory was there; so was (the newly promoted) Major Ferrié, as well as engineers from various ministries including the Navy. Explaining the situation to the assembled, Ferrié divided time signals into two classes. A first, rough signal, accurate to about a half-second, could be used by navigators at sea. Such navigation pulses could be initiated by using signals sent by wire from the observatory. Then there were the “special” signals for high-accuracy geodesy. These would need to be crafted more carefully to achieve a precision of one-hundredth of a second.93

  If you were a radio operator in one of the colonies straining for your precise longitudinal relation to Paris, here’s what you would do once you had tuned in Paris. Eiffel Tower station would broadcast a signal once every 1.01 seconds; you would listen for the broadcast pulses beginning before midnight, Paris time. At the same time, you would set your local clock beating a short, crisp tone once every second on the second (local time). By convention you knew that the pips would begin from the Eiffel Tower at midnight Paris time, and so occur at a Paris time of 12:00:00.00, 12:00:01.01, 12:00:02.02, and so on. By counting the number of Eiffel Tower pips before the Eiffel and local beeps coincided, you could synchronize the clocks. For example, if your local whole-second tone first coincided with the Eiffel tones on the tenth Eiffel tone, then you would know that at the Eiffel tower it was midnight plus ten pips (12:00:10.10 seconds). You know the local time of the coincidental beat simply by checking your own clock. So you would subtract Eiffel Tower time (12:00:10.10 seconds) from your local time to get the longitude difference between your radio station and that great symbol of Parisian modernity. By March 1909, Poincaré’s commission had a plan for sending precision time signals by wireless.

  The next month, Poincaré traveled to Göttingen to deliver a series of lectures on pure and applied mathematics. For the first five of these presentations, Poincaré presented his technical work in German. But at the last meeting he explained to the assembled that this time, without the crutch of equations, he would return to his native tongue. The subject was the “new mechanics.” Looking around, he told those gathered that the seemingly imperishable mon
ument of Newtonian mechanics was, if not yet quite flattened, powerfully shaken. “It has been submitted to the attacks of the great destroyers: you have one among you, M. Max Abraham, another is the Dutch physicist M. Lorentz. I want to speak to you . . . of the ruins of that ancient edifice and the new building that one wants to raise in their place.” Poincaré then asked, “What role does the principle of relativity play in the new mechanics?” He continued, “We are first led to talk about apparent time, a very ingenious invention of the physicist Lorentz.” Picture, he urged his audience, “meticulous observers such as hardly exist. They demand a clock setting of an extraordinary exactitude; to be [accurate to] not one second, but a billionth of a second. How could they do it? From Paris to Berlin, A sends a telegraphic signal, with a wireless if you want, to be altogether modern. B notes the moment of reception, and that would be, for the two chronometers, the [zero] point of time. But the signal takes a certain time to go from Paris to Berlin, it can only go with the speed of light; B’s watch will therefore be slow; B is too intelligent to not have realized this; he will take care of this drawback.” Observers A and B solve the problem the way any two Bureau of Longitude telegraphers would—by crossing signals. A sends a time signal to B, and B to A.94 It is just the way the bureau has been doing business for decades—sending signals back and forth by cable between Paris and Brazil, Senegal, Algeria, America. Or, for that matter, as Poincaré would soon help make possible, by way of wireless between the “altogether modern” Eiffel Tower and Berlin.

  At 2:30 P.M. on Saturday, 26 June 1909, Poincaré and his commission gathered at the Eiffel Tower to inspect the experimental station. Ship’s Captain Colin described and explained the apparatus, summing up the latest work in radio-telegraphic inventions and pointing out and distributing a report from the American Navy on its recent radio synchronization of their ships’ clocks. Then came his summary of the ever-accelerating range of the tower itself: over the last days Colin’s troops had successfully received signals in Villejuif, 8 kilometers from the tower; in Mehun, 48 kilometers away; on up through a mid-June triumph when engineers captured a transmission 166 kilometers from the Champ de Mars. Even greater range seemed possible. Shipboard experiments had been successfully in operation since 9 June. “The commission, immediately on ending the explanations of Monsieur Colin, set the apparatus in operation.” Ammeter, wavemeter, and receiver at the ready, Poincaré’s commission elatedly witnessed a flawless (pure and stable) broadcast of time. Poincaré pressed the Chamber of Deputies for commercial radiotelephone services and for immediate funding to make the Eiffel Tower into the greatest time synchronizer in the world. Approval came on 17 July 1909.95

  Exactly one week later, on 24 July, Poincaré put the finishing touches on his opening speech for the French Association for the Advancement of Science in Lille. In early August, when he entered the town’s Grand Théâtre to deliver that address (modified from the one he had given in Göttingen) and receive the Grande Médaille d’Or, he found the city’s elite gathered to hear him speak on the new physics. Again he underlined the importance of the relativity principle, the centrality of Lorentz’s “ingenious” local time, and the necessity of telegraphic time coordination making use of the “altogether modern” wireless. Poincaré then introduced, as he had before, “another hypothesis” (that is, one beyond the hypothesis of the principle of relativity and the hypothesis of “apparent time”). This third supposition was Lorentz’s contraction: an idea “more surprising, much more difficult to accept, which disturbs greatly our current habits.” An object in motion through the ether underwent a contraction along its line of motion. As a result of its orbit around the sun, the earth’s sphere would be compressed in the direction of its motion by about 1/200,000,000 of its diameter. Nonetheless, Poincaré emphasized, that in the moving observer’s frame of reference, the slowing of “local time” and the shortening of “apparent length” so precisely compensated for each other that there would be no way for the moving observer to discover that he was, in fact, moving.96

  Poincaré’s is a description of the world that resembles Einstein’s in what the moving observer sees, yet differs in how that circumstance is explained. Here, in August 1909, Poincaré maintained his (ever-less physical) ether, whereas Einstein polemicized at every turn against what he considered an antiquated and redundant entity. Poincaré introduced the Lorentz contraction as a separate hypothesis, Einstein derived it from his definition of time. Poincaré guarded Lorentz’s venerable “local time” and “apparent lengths” though his and Lorentz’s uses of the terms were not identical: Poincaré treated apparent lengths and times as observable, Lorentz continued to treat them as fictional. For Einstein there was simply “a time for a particular frame of reference,” the time of one frame was as “true” or “real” as the time of another. No fictions. No ether. Nothing to be “explained” about the inability of an observer to detect his or her constant motion. No daylight between “true” and “apparent.” As for what could be seen: for years Poincaré had been as clear as Einstein—for any constantly moving observer all the phenomena are “well in accord with the principle of relativity.”97

  From 1908 to 1910, Poincaré’s engagement with electromagnetic simultaneity crossed and recrossed between relativity and the still-new radio technology. After recovering from a surge of Seine flood waters into their radio headquarters, the French Army’s time team at the Eiffel Tower began broadcasting simultaneity on 23 May 1910, its distinctive tones available to be plucked out of the ether (so to speak) from Canada to Senegal.98 At first the signals followed Paris time; only the next year, on 9 March 1911, did France agree to reset its (and Algeria’s) clocks by the 9 minutes and 21 seconds that riveted them to Greenwich. Charles Lallemand, who had fought alongside Poincaré in the various time and longitude campaigns (Quito, decimal time, time zones), saw the opportunity to put time unification into practice. Clocks, radios, and map making at last converged.

  Even before the Eiffel Tower station opened for business, the French longitude men had begun radio-correcting their maps, starting with Montsouris, Brest, and Bizerte, drawing up plans for use by military telegraphy and planning radio time-coordination to map French colonies. Soon they formed a collaboration with their American counterparts to exchange signals between the Eiffel Tower and the Arlington, Virginia, transmitter with sufficient precision to correct for the signal’s transoceanic time-of-flight. It was a full-dress realization of the light-signal synchronization that Poincaré had written first into his metaphysics of simultaneity and then into his physics of local time. Popular journals took notice: “Although radio signals travel through space at approximately the velocity of light, there is a slight but appreciable loss of time . . . in starting such a signal on its journey . . . and in receiving it at the other end.” When the Americans formulated experimental protocols in 1912, they discovered that the French had already solved the problem, using the coincidence method Poincaré’s commission had advanced several years earlier. “Here,” one American reporter wrote, “was a beautiful solution.”99 Wireless had made world-synchronization possible: in all directions, over vast distances, with an essentially limitless precision. Lallemand and his longitude allies hoped to coordinate Paris with other transmitters supplied with time signals by an aristocratic consortium of observatories that would “avoid all appearances of a national time.” Ministers, observatory directors, and longitude authorities agreed: the French ideal would achieve a rational, coordinated, international system with France clearly, if unautocratically, at the helm.100 Once again, the triumph would be of a convention in all its senses, building on the long series of international conferences and agreements establishing the meter, ohm, prime meridian, and the abortive attempt to create rational universality from the decimalized second.

  While French scientists wired the Eiffel Tower to align clock hands across Europe, the British kept silent, refusing to build a time transmitter of their own. According to one historian of Greenwich,
the Imperial telegraphers and astronomers saw the French and other foreign radio-time services as useful in times of peace (the British quickly installed receivers at Greenwich). In war, they reckoned, no one would broadcast time.101 Such a calculated, pragmatic stance was certainly consistent with the way the British built and controlled their international cable network. For his part, Poincaré had hardly been alone in his patriotic concerns about radio secrecy. He had emphasized the point in his very first article on radio technology in 1902, and throughout the interministerial meetings he oversaw, the delicacy of “secret correspondence” was a subject returned to often as the commission prepared for the 1912 international conferences on time and radiotelegraphy. Repeatedly the French ministerial representatives warned that German and British radio transmitters had outflanked and outclassed the French in colonial Africa.102 Powering up the Eiffel Tower as the beacon of world time (and zero point of communication with the French Empire) was therefore an effort at once practical and symbolic, military and civilian, nationalist and internationalist. Fourteenth-century villagers had mounted clocks on bell towers to reign over all who could hear them; Poincaré rang the Eiffel Tower radio-clock through the ether to echo French scientific authority across the world.

  But whether by telegraph line or by wireless, centered systems were the temporal-physical glory of Europe’s Great Powers. It was the unified German empire that von Moltke wanted, made corporal through the grand Primäre Normaluhr at the Schlesischer Bahnhof in Berlin or the baroque and elegant horloge-mère of Neuchâtel. It was Eiffel’s engineered modernity turned high-tech radio time-post; it was Britain’s cable network sliding its copper tentacles from Greenwich around its cross-continental colonies. It was the American Navy’s powerful radio transmitter directing ships on the high seas and fixing the positions of the Americas’ land stations, at the height of big-stick diplomacy.