Einstein's Clocks and Poincare's Maps

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Einstein's Clocks and Poincare's Maps Page 25

by Peter Galison


  Einstein’s fascination with machines and the conventions of the patent office spilled from his workday into the rest of his life. In incessant corresponding about machines with his friends, Conrad Habicht (of the Olympia Academy) and Conrad’s brother Paul (an apprentice machine technician), Einstein bandied about ideas for relays, vacuum pumps, electrometers, voltmeters, alternating current recorders, and circuit breakers. Paul, in particular, cooked up one scheme after another, sometimes writing Einstein every two days. On one occasion, having dropped Einstein a detailed letter about a proposed flying machine (a helicopterlike contraption), Paul directly requested advice: “Should I take out a patent immediately? Or publish without a patent or start negotiations without a patent?”61

  Einstein, too, sought patents. One of his many ideas was for a sensitive electrometer that would measure exceedingly small voltage differences. The little machine (Maschinchen) fascinated him in all its aspects, from matters of theory to the nitty-gritty of fabrication.62 He wrote to one of his collaborators about the gasoline they would need to clean ebonite (vulcanized rubber) parts, and the arrangement required to ensure that the wires would dip properly into mercury beads on the ebonite disk. “I already know from my experiments,” he added, “that the thing can be done with the mercury contacts. It is only sometimes time-consuming to put the apparatus in working order, and the mercury spurts out as soon as one turns a bit too fast.”63

  Concerns about instruments, along with experiments on real and imagined machines, held Einstein’s rapt attention. Writing to his friends he would switch, without missing a beat, from the rarified-theoretical to the practical-technological. In one letter of 1907, in the midst of telling Conrad Habicht about an article that he was writing on the relativity principle and some current work on the perihelion of mercury, Einstein in the very next sentence was back to the Maschinchen. Just about a year later, he told his friend and collaborator Jakob Laub that “In order to test [the Maschinchen] for volt[ages] under 1/10 volt, I built an electrometer and a voltage battery. You wouldn’t be able to suppress a smile if you saw the magnificent thing that I attached together myself.”64 These efforts on the Maschinchen and his later work on the gyrocompass and Einstein– de Haas effect, are but a few examples of Einstein’s particular interest in sensitive electromechanical devices that would bridge worlds of electricity and mechanics. Electromagnetic clock coordination proposals were right up his alley—they offered ways to transform small electrical currents into high-precision rotary movements.

  Time coordination patents continued to pour into the office. On 25 April 1905 at 6:15 P.M., for example, the office recorded the arrival of a patent application for an electromagnetically controlled pendulum that would take a signal and bring a distant pendulum clock into accord.65 All such inventions required documentation, including a model, specific drawings, and properly prepared descriptions and claims. Evaluating them was painstaking and often lasted for months.

  Sometime in the middle of May 1905 (and we note that Einstein moved outside Bern’s zone of unified time on May 15th), he and his closest friend, Michele Besso, had cornered the electromagnetism problem from every angle. “Then,” Einstein recalled, “suddenly I understood where the key to this problem lay.” He skipped his greetings the next day when he met Besso: “‘Thank you. I’ve completely solved the problem.’ An analysis of the concept of time was my solution. Time cannot be absolutely defined, and there is an inseparable relation between time and signal velocity.”66 Pointing up at a Bern clock tower—one of the famous Bern synchronized clocks—and then to the one and only clock tower in nearby Muri (the traditional aristocratic annex of Bern not yet linked to Bern’s Normaluhr), Einstein laid out for his friend his synchronization of clocks.67

  Within a few days Einstein sent off a letter to Conrad Habicht, imploring him to send a copy of his dissertation and promising four new papers in return. “The fourth paper is only a rough draft at this point, and is an electrodynamics of moving bodies which employs a modification of the theory of space and time; the purely kinematic part of this paper [beginning with the new definition of time synchronization] will surely interest you.”68 Ten years of thought about the physics of moving bodies, light, ether, and philosophy had culminated in this little paper.

  Figure 5.7 Bern-Muri Map. Michele Besso recalled that when Einstein excitedly told him of his realization that time had to be defined by signal exchange, he pointed to one clock tower in old Bern and to another (the only one) in the nearby town of Muri. Since it is the only vantage point from which both might have been visible, Besso and Einstein must have been standing on the hill shown to the northeast of downtown Bern. SOURCE: MODIFIED FROM SKORPION-VERLAG.

  Obviously time synchronization by the exchange of electromagnetic signals was not all of special relativity, but it was the crowning step in Einstein’s development of the theory. Coordinating clocks did not, as it had for Poincaré, enter Einstein’s reasoning as the physical interpretation of Lorentz’s fictional “local time.” Far from it. Einstein began his argument by defining the position of a point relative to rigid measuring rods (a commonplace), but now supplemented with his new definition of simultaneity: “If we want to describe the motion of a material point, we give the values of its coordinates as a function of time. However, we should keep in mind that for such a mathematical description to have physical meaning, we first have to clarify what is to be understood by ‘time’.” With no frame of ether at rest on the basis of which to pick out the one true time, the clock systems of every inertial reference frame were equivalent in the sense that the time of one frame was just as “true” as any other.

  Figure 5.8 Muri Clocktower (circa 1900). When Einstein gestured toward Muri’s only clock tower as he explained to Besso his new time-coordination scheme, this is the structure to which he pointed. SOURCE: GEMEINDESCHREIBEREI MURI BEI BERN.

  In this context, Einstein’s paper, completed by the end of June 1905, can be read in a very different fashion from our current standard interpretation. Instead of a wholly abstracted “Einstein philosopher-scientist”—lost in theory while absentmindedly merely earning his keep in the patent office—we can recognize him also as “Einstein patent officer-scientist,” refracting the underlying metaphysics of his relativity theory through some of the most symbolized mechanisms of modernity. The train arrives in the station at 7:00 P.M. as before, but now, after our long voyage through time and space, we can see it was not just Einstein who was worried about what this means in terms of distant simultaneity. No, determining train arrival times by using electromagnetically coordinated clocks was precisely the practical, technological issue that had been racking North America and Europe for the last thirty years. Patents were racing through the system, improving the electrical pendula, altering the receivers, introducing new relays, and expanding system capacity. Time coordination in the Central Europe of 1902–05 was not merely an arcane thought experiment; rather, it critically concerned the clock industry, the military, and the railroads as well as a symbol of the interconnected, sped-up world of modernity. Here was thinking through machines.

  Einstein brought into his world of principled physics the powerful and highly visible new technology embodied all around him: the conventionalized simultaneity that synchronized train lines and set time zones. A trace of that existing time-coordination system is there to see in the 1905 article itself. Reconsider the coordination scheme with which Einstein begins the paper: An observer is equipped with a clock at the center of the coordinate system. That master clock bolted to space position (0,0,0) determines simultaneity when electromagnetic signals from distant points arrive there at the same local time. But now this standard, centered system no longer appears as an abstract straw man. This branching, radial clock-coordination structure—visible in wires, generators, and clocks, displayed in patent after patent and book after book on timekeeping—was precisely that of the European system of the mother clock along with its secondary and tertiary dependents.
(See figures 5.9–5.11.) Einstein had brought to that established system the critical gaze of a physicist-patent officer: keep the idea that time had to be defined through a realizable signal-exchange, invoke the absolute speed of light, and cancel the system’s dependency on any specific, privileged spatial origin or rest frame for the ether.

  With a certain caution, we might attempt to track Einstein’s precise train of thought even further into this mid-May 1905 crossing point of the technology and physics of simultaneity. One possibility is this: sensitized to the importance of procedurally based concepts, time coordination and its precise, patent applications, and his Olympia Academy critical-philosophical discussions, Einstein could have been fully primed to take up and transform any mention of clock coordination in the context of electrodynamics of moving bodies. Perhaps at some stage Einstein had actually read Poincaré’s 1900 article in which the French savant gave his first physical interpretation of Lorentz’s (approximate) “local time” as clock coordination by signal exchange in the ether. It is certain that sometime before 17 May 1906, Einstein did read Poincaré’s 1900 paper—on that day Einstein submitted a paper of his own that explicitly used the contents of Poincaré’s article (though not local time).69 Could it be that Einstein had studied or at least seen Poincaré’s paper between December 1900 and May 1905? More specifically: had Einstein read and dismissed Poincaré’s 1900 ether-based reasoning, while, at some level of awareness, he retained the senior French scientist’s provision of a clock-synchronization account of Lorentz’s local time? Einstein did not read French easily. But he need not have read Poincaré directly; he could have encountered related ideas (in German) in Emil Cohn’s November 1904 article “Toward the Electrodynamics of Moving Systems.”70

  Figure 5.9 Favarger’s Time Network. Taking over from Hipp, Favarger led the Swiss company (after 1889, A. Peyer, A. Favarger & Cie.) to a leading position in the world of electrocoordinated clocks, not only in production but also in invention and patenting. Here Favarger depicted a prototypical network of secondary timepieces linked to a master clock. SOURCE: FAVARGER, “ELECTRIC-ITÉ ET SES APPLICATIONS” (1884–85), P. 320; REPRINTED IN FAVARGER, L’ÉLECTRICITÉ (1924), P. 394.

  Figure 5.10 Time Telegraph Network. Another paradigmatic representation of distributed electrical time. SOURCE: LADISLAUS FIEDLER, DIE ZEITTELEGRAPHEN UND DIE ELEKTRISCHEN UHREN VOM PRAKTISCHEN STANDPUNKTE (VIENNA, 1890), PP. 88–89.

  Student of a Strasbourg experimentalist renowned for his work on the speed of sound, Cohn was a successful theorist who had begun his career in the laboratory, measuring magnetism. Even as he turned decisively from bench to blackboard, Cohn relentlessly insisted on the measurable consequences of his work. By the turn of the century Cohn stood as a theorist of repute, joining fellow luminaries to deliver a paper at the December 1900 Lorentzfest. There it seems likely that he would have heard Poincaré’s lecture; at the very least he would have had good reason to see the printed version of Poincaré’s talk in the published proceedings that contained his own paper. But for our purposes, the intriguing piece of the story is this: in 1904, Cohn, like Poincaré, explicitly introduced clock coordination into his physical definition of local time, and he did so with a former experimentalist’s suspicion of purely hypothetical quantities. In this respect he was rather more like Einstein than Poincaré. Unlike Poincaré, Cohn rejected the ether, preferring “the vacuum,” and taking local time as given by light-signal coordinated clocks valid for optics if not mechanics.

  Figure 5.11 Electric Unification. Favarger wanted to wire the interior of buildings, but more ambitiously the entirety of major urban centers, as this schematic made clear. SOURCE: FAVARGER, L’ÉLECTRICITÉ (1924), PP. 427–28, PLATE 4.

  Again, the unanswerably detailed question: When did Einstein see Cohn’s procedural local time? And again, there is little certainty. Only this: sometime before 25 September 1907, Einstein had Cohn’s article in hand (that day he wrote the editor of a journal reporting just this, misspelling Cohn’s name “Kohn”). On 4 December 1907, the publisher recorded the arrival of Einstein’s review paper on relativity that contained this somewhat cryptic footnote-compliment: “The pertinent studies of E. Cohn also enter into consideration, but I did not make use of them here.”71 Again, Einstein would have had to dismiss the vast bulk of Cohn’s particular approach to electrodynamics while extracting the idea of clock coordination as relevant to the definition of simultaneity. (Yet another physicist, Max Abraham, had also begun exploring signal-exchanged simultaneity in his 1905 text on electrodynamics, though not early enough for Einstein to have seen it before submitting his article.72) The limits of reconstruction are evident, and would be even if it were written in stone that Einstein had seen one of these papers. But the larger goal must stay in view: to understand all we can of the philosophical, technical, and physics conditions that put Einstein in a position to seize clock coordination as the principled starting point of relativity. Of course, we can even sketch possibilities for the seed around which the idea condensed, while avoiding an overwrought attempt to specify exactly what the precipitating seed might have been: a half-remembered line from Poincaré or Cohn encountered in the library, a particular patent application at work, a synchronized Bernese street clock, or a philosophical text batted around the Olympia Academy. Our position is not so different from that of the meteorologists who can provide an excellent account of how a thunderstorm formed by studying the powerful updraft of an unstable column of moist air: but it is not given to know around which bits of dust the initial raindrops precipitated.

  Who saw what when? What was deleted, absorbed, provoked by each comment and paragraph? Doling out credit and priority, playing prize committee to the long-deceased is to employ an uncertain history against a futile goal. More important, more interesting is this: in the years before May 1905, simultaneity talk was growing denser among physicists as they grappled with the electrodynamics of moving bodies. Simultaneity procedures lay thicker in philosophical texts, in the cityscape of Bern, along train tracks throughout Switzerland and beyond, in undersea telegraph cables, and in the application in-pile at the Bern patent office. In the midst of this extraordinary material and literary intensification of wired simultaneity, physicists, engineers, philosophers, and patent officers debated how to make simultaneity visible. Einstein did not conjure these various flows of simultaneity out of nothing; he snapped a junction into the circuit enabling the currents to cross. Simultaneity had long been in play at many different scales, but Einstein showed how the same flashed signal of simultaneity illuminated all of them, from the microphysical across regional trains and telegraphs to overarching philosophical claims about time and the Universe.

  Back in 1900 Poincaré had launched his interpretation of time as signal exchange in the midst of his Leiden speech, attributing it, almost as an aside, to Lorentz. Einstein made signal-simultaneity central at every opportunity, from the moment in May 1905 when he stood with Besso gesturing over the hills at the clocks of Muri and Bern. In a wide-ranging review of the relativity theory at the end of 1907, Einstein reiterated the pivotal role that time must play. By his lights, Lorentz’s old theory of 1895 had shown, at least approximately, that electrodynamic phenomena would not reveal the motion of the earth with respect to an ether. Michelson and Morley’s experiment made clear that even Lorentz’s approximate equivalence was not good enough—motion through the ether could not be detected at even higher levels of accuracy. “Surprisingly,” Einstein added, “it turned out that a sufficiently sharpened conception of time was all that was needed to overcome the difficulty.” Lorentz’s 1904 (improved) “local time” was enough to address the problem. Or rather, it solved the problem if, as Einstein had done, “‘local time’ was redefined as ‘time’ in general.” Einstein’s view was that this “‘time’ in general” was precisely the time given by the signal-exchange procedure. With that understanding of time, the basic equations of Lorentz followed. So with this dramatic redefinition, Lorentz�
��s theory of 1904 could be set on the right track, with one further, not-so-small exception: “Only the conception of a luminiferous ether as the carrier of the electric and magnetic forces does not fit into the theory described here.” More precisely, Einstein dismissed the idea that electric and magnetic fields were “states of some substance,” as the ether advocates would have it. For Einstein electric and magnetic fields were “independently existing things,” as freestanding as a block of lead. Electromagnetic fields, like ordinary ponderable matter, could carry inertia. Fields did not depend on the state of an undetectable ether for which Einstein had not the slightest use.

  There were many choices open to a physicist wanting to understand this post-1905 controversy about the electrodynamics of moving bodies. Certainly Lorentz and Poincaré loomed large; Einstein’s reputation was growing. But there were dozens of ideas vying for attention: the relativity principle, the status of the ether, the absolute speed of light, the changing mass of the electron, the possibility of explaining all mass by electrodynamics. From this swirl, only around 1909 did Einstein’s articulation of time rise haltingly, contentiously, but then powerfully. (Even then there were some physicists, such as Ebenezer Cunningham in Cambridge, England, who read Einstein’s relativity very differently; he was certainly not the only physicist who while enthusiastic about the new theory did not take coordinated clocks to be the main event in the great drama of relativity.)73

 

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