Einstein’s diagnosis: “insufficient consideration” had been paid to the most fundamental concepts of physics. He claimed that if these basic concepts were properly understood, the apparent contradiction between the relativity and the light principles would vanish. Einstein proposed, therefore, to begin at the very beginning of physical reasoning, asking, What is length? What is time? And especially: What is simultaneity? Everyone knew that the physics of electromagnetism and optics depended on making measurements of time, length, and simultaneity, but as far as Einstein was concerned, physicists had not paid enough critical attention to the basic procedures by which these fundamental quantities were determined. How could rulers and clocks yield unambiguous space and time coordinates for the phenomena of the world? In Einstein’s judgment, the predominant view that physicists should concern themselves first with the complex forces that held matter together had it backward. Instead, kinematics had to come first, that is, how clocks and rulers behaved in constant, force-free motion. Only then could the problem of dynamics (for example, how electrons behaved in the presence of electrical and magnetic forces) be usefully addressed.
Einstein believed that physicists would only find consistency by sorting out the measurements of space and time. To make spatial measurements, a coordinate system is needed—by Einstein’s lights, a system of ordinary rigid measuring rods. For example: this point is two feet along the x-axis, three along the y, and fourteen up the z-axis. So far, so good. Then came the surprising part, the reanalysis of time that contemporaries like the mathematician and mathematical physicist Hermann Minkowski saw as the crux of Einstein’s argument.4 As Einstein put it: “We have to take into account that all our judgments in which time plays a role are always judgments of simultaneous events. If, for instance, I say, ‘That train arrives here at 7 o’clock,’ I mean something like this: ‘The pointing of the small hand of my watch to 7 and the arrival of the train are simultaneous events’.”5 For simultaneity at one point, there is no problem: if an event located in the immediate vicinity of my watch (say, the train engine pulling up beside me) occurs just when the small hand of the watch reaches the seven, then those two events are obviously simultaneous. The difficulty, Einstein insisted, comes when we have to link events separated in space. What does it mean to say two distant events are simultaneous? How do I compare the reading of my watch here to a train’s arrival at another station there at 7 o’clock?
For Newton the question of time held an absolute component; time was not and could not be merely a question of “common” clocks. From the instant Einstein demanded a procedure in order to give meaning to the term “simultaneous,” he split from the doctrine of absolute time. In an apparently philosophical register, Einstein established this defining procedure through a thought experiment that has long seemed far from the play of laboratories and industry. How, Einstein asked, should we synchronize our distant clocks? “We could in principle content ourselves to time events by using a clock-bearing observer located at the origin of the coordinate system, who coordinates the arrival of the light signal originating from the event to be timed . . . with the hands of his clock.”6 Alas, Einstein noted, because light travels at a finite speed, this procedure is not independent of the place of the central clock. Suppose I stand next to A and far from B; you stand exactly halfway between A and B:
A——me———you—————B
Both A and B flash light signals to me, and both arrive in front of my nose at the same moment. Can I conclude that they were sent at the same time? Of course not. It is obvious that B’s signal had a much longer way to travel to me than A’s signal, and yet they arrived at the same time. So B’s signal must have been launched before A’s.
Suppose I stubbornly insist that A and B must have launched their signals simultaneously; after all, I got the two signals at the same moment. Immediately I run into trouble, as you can bear witness: if you were standing exactly halfway between A and B, then you would have received B’s light before A’s. To avoid ambiguity, Einstein did not want to make the simultaneity of the two events “A sends light” and “B sends light” depend on where the receiver happens to be standing. As a procedure for defining simultaneity, “simultaneous receipt of signals by me” is a disaster, an epistemic straw man who cannot tell a consistent story.
Figure 1.1 Central Clock Coordination. In his 1905 paper on special relativity, Einstein introduced—and rejected—a scheme of clock coordination in which the central clock sent a signal to all other clocks; these secondary clocks set their times when the signal arrived. For example, if the central clock sent its time signal at 3:00 P.M., each secondary clock synchronized its hands to that same 3:00 P.M. when the pulse arrived. Einstein’s objection: the secondary clocks were at different distances from the center so close clocks would be set by the arriving signal before distant ones. This made the simultaneity of two clocks depend (unacceptably to Einstein) on the arbitrary circumstance of where the time-setting “central” clock happened to be.
Figure 1.2 Einstein’s Clock Coordination. Einstein argued that a better and nonarbitrary solution to the simultaneity question was this: set clocks not to the time that the signal was launched, but to the time of the initial clock plus the time it took for the signal to travel the distance from the initial clock to the clock being synchronized. Specifically, he advocated sending a round-trip signal from the initial clock to the distant clock and then setting the distant clock to the initial clock’s time plus half the round-trip time. In this way the location of the “central” clock made no difference–one could start the procedure at any point and unambiguously fix simultaneity.
Having knocked the straw out of this straw man, young Einstein proposed a better system: let one observer at the origin A send a light signal when his clock says 12:00 to B at a distance d from A; the light signal reflects off B and returns to A. Einstein has B set her clock to noon plus half the round-trip time. A two-second round-trip? Then Einstein has B set her clock to noon plus one second when she gets the signal. Assuming that light travels just as fast in one direction as the other, Einstein’s scheme amounts to having B set her clock to noon plus the distance between the two clocks divided by the speed of light. The speed of light is 300,000 kilometers per second. So if B is 600,000 kilometers from A when B receives the light signal, she sets her clock to 12:00:02, noon plus two seconds. If B were 900,000 kilometers away from A, B would set her clock to 12:00:03 when she gets the signal. Continuing in this way, A, B, and anyone else participating in this coordination exercise can all agree that their clocks are synchronized. If we now move the origin, it makes no difference: every clock is already set to take into account the time it takes for a light signal to arrive at the clock’s location. Einstein liked this: no privileged “master clock,” and an unambiguous definition of simultaneity.
With the clock coordination protocol in hand, Einstein had cracked his problem. By relentlessly applying the simple procedure of coordination and his two starting principles, he could show that two events that were simultaneous in one frame of reference were not simultaneous in another. Consider: the length measurement of a moving object always depends on making simultaneous position measurements of two points (if you want the length of a moving bus, it behooves you to measure the position of the front and back at the same time). Because the determination of length requires the simultaneous measurements of front and back, the relativity of simultaneity led to a relativity of lengths—my frame of reference will measure a meter stick moving by me as less than a meter long.
Astonishing in and of itself, this relativity of times and lengths led to many other consequences, some more immediate than others. Because speed is defined as distance covered in a certain time, combining the motion of objects had to be reconsidered in Einstein’s theory. A person running in a train at a speed of 1/2 the speed of light (with respect to the train) while the train barreled along at 3/4 the speed of light would, in Newtonian physics, be moving relative to the ground at
1 1/4 times the speed of light. But by rigorously following the definition of time and simultaneity, Einstein showed that the actual combined speed would be less than that—indeed always less than the speed of light no matter what the speed of the train or the runner in the train. Nor was that all: Einstein could explain previously puzzling optical experiments and make new predictions about the motion of electrons. Finally, Einstein’s starting assumptions about light speed and relativity, coupled with his clock coordination scheme, helped show that there weren’t really two different explanations of the coil, magnet, and lamp but just one: a magnetic field in one frame was an electric field in another. The difference was one of perspective—the view from different frames of reference. And all without a whiff of ether. A short time later, Einstein was to use relativity to produce that most famous of all scientific equations, E = mc2. With consequences that at first seemed restricted to the most sensitive of barely possible experiments to the utter transformation of the military-political domain forty years later, Einstein had found mass and energy to be interchangeable.
Much lies behind Einstein’s relativity besides the coordination of clocks. Without exaggeration, one could say that the collective mastery of electricity and magnetism was the great accomplishment of nineteenth-century physical science. Theoretically, Cambridge physicist James Clerk Maxwell had produced a theory that showed light to be nothing other than electric waves and so unified electrodynamics and optics. Practically, dynamos had brought electric lighting to cities, electric trams had altered cityscapes, and telegraphs had transformed markets, news, and warfare. By the century’s end physicists were making precision measurements of light—staggeringly accurate attempts to detect the elusive ether; they were refining work in electricity and magnetism to dissect the behavior of the newly accepted electron. All this led many of the leading physicists (not just Einstein and Poincaré) to consider the problem of an electrodynamics of moving bodies to be one of the most difficult, fundamental, and acute problems on the scientific agenda.7
By Einstein’s own account, the recognition that synchronizing clocks was necessary to define simultaneity was the final conceptual step that let him conclude his long hunt, and that—time coordination—is the subject of this book. Indeed, Einstein judged the alteration of time in relativity theory to be that theory’s most striking feature. But his assessment did not immediately carry the day, even among those who counted themselves as Einstein’s backers. Some embraced relativity after experiments on the deflection of electrons seemed to lend it support. There were those who used the theory only when physicists and mathematicians had reworked it into more familiar terms that did not put so much stress on the relativity of time. Through tense meetings, exchanges of letters, articles and responses, by 1910 a growing number of Einstein’s colleagues were pointing to the revision of the time concept as the salient feature. In the years that followed, it became canonical for both philosophers and physicists to hail clock synchronization as a triumph in both disciplines, a beacon of modern thought.
Younger physicists, including Werner Heisenberg, began in the 1920s to pattern the new quantum physics on what they took to be Einstein’s tough stance against concepts (like absolute time) that referred to nothing observable. In particular, Heisenberg admired Einstein’s insistence that simultaneity refer exclusively to clocks coordinated by a definite and observable procedure. Heisenberg and his colleagues pressed their insistence on observability hard: if you want to speak about the position of an electron, show the procedure by which that position can be observed. If you want to say something about its momentum, then display the experiment that will measure it. Most dramatically, if even in principle you could not measure both position and momentum simultaneously, then position and momentum simply did not both exist at the same time. Einstein famously bridled at that conclusion, even as his quantum colleagues pleaded with him to acknowledge that they had only extended to atoms Einstein’s own acute criticism of time, and simultaneity. It was far too late for Einstein to call his relativistic genie back into the bottle, but he worried the new physics carried too far the spirit of his insistence on observable procedures—and so underestimated the formative role of theories in fixing what could be seen. As Einstein wryly observed, “A good joke should not be repeated too often.”8
The good joke spread. Psychologist Jean Piaget made the investigation of the “intuitive” time concept in the child into an important research area. Einstein’s time coordination began serving as a model—and soon the model—for a new era of scientific philosophy. Gathering in the Austrian capital to found a new antimetaphysical philosophy, the physicists, sociologists, and philosophers of the Vienna Circle hailed synchronized clock simultaneity as the paradigm of a proper, verifiable scientific concept. Elsewhere in Europe and in the United States, other self-consciously modern philosophers (as well as physicists) joined in hailing signal exchange simultaneity as an example of properly grounded knowledge that would stand proof against idle metaphysical speculation.9 To Willard Van Orman Quine, one of the most influential American philosophers of the twentieth century, all knowledge was ultimately revisable (he even held that logic might eventually need alteration). Yet as Quine surveyed the whole of scientific understanding, he chose as most durable Einstein’s definition of simultaneity through clocks and light signals, judging that it was Einstein’s time concept that we “should be most inclined to preserve when called upon to make future revisions of . . . science.”10 For a philosophical century marked by vast changes in knowledge, in a climate hostile to eternal, unbending truths, there was no higher praise.
Of course not everyone admired the relativity of time. Some lampooned it, others tried to rescue physics from it. But very broadly by the 1920s, both physicists and philosophers recognized that Einstein’s question, What is time? set a standard for scientific concepts that demanded something more finite, more humanly accessible than Newton’s metaphysical, absolute time. Einstein himself suggested that he had drawn an effective philosophical sword against absolute time from the eighteenth-century critical work of David Hume, who had forcefully argued that the statement “A causes B” meant nothing more than the regular sequence, A then B. Key for Einstein, too, was the Viennese physicist-philosopher-psychologist Ernst Mach’s work lambasting concepts disconnected from perception. Among Mach’s (sometimes excessive) roundup of idle abstractions, none figured as a greater offender than Newton’s “medieval” notions of absolute space and absolute time. Einstein also studied time through the microscope of other scientists’ inquiries, among them those of Hendrik A. Lorentz and Poincaré. Each of these lines of philosophical reasoning—and others that we will encounter—form part of our story of time and timepieces. Yet a purely intellectual history leaves Einstein hovering in a cloud of abstractions: the philosopher-scientist brandishing thought experiments against the dusty Newtonian dogma of absolute time. Einstein confounding a contemporary scientific-technical cadre too sophisticated to ask basic questions about time and simultaneity. But is this cerebral account sufficient?
A Critical Opalescence
Certainly Einstein and Poincaré often looked back on their work as if it originated entirely outside the material world. In this respect, it is useful to reflect on a speech Einstein delivered in early October 1933 to a massive rally organized to aid refugees and displaced scholars. Scientists, politicians, and the public jammed London’s Royal Albert Hall. Hostile demonstrators threatened to stir things up; a thousand students came to serve as protective “stewards.” Einstein warned of the imminence of war, of the hatred and violence looming over Europe. He urged the world to resist the drive toward slavery and oppression, and pleaded with governments to halt the impending economic collapse. Then, suddenly, the political thread of Einstein’s speech snapped. There was a sudden pulling back from worldly crisis, as if the calamity of current events had stretched him beyond his limits. In a different register he began to reflect on solitude, creativity, and quiet, on moments he h
ad spent lost in abstract thought surrounded only by the productive monotony of the countryside. “There are certain occupations, even in modern society, which entail living in isolation and do not require great physical or intellectual effort. Such occupations as the service of lighthouses and lightships come to mind.”11
Solitude was perfect for a young scientist engaged with philosophical and mathematical problems, Einstein insisted. His own youth, we are tempted to speculate, might be thought of this way: we might read the Bern patent office where he had earned a living as no more than such a distant oceanic lightship. Consistent with Einstein’s garden of otherworldly contemplation, we have enshrined Einstein as the philosopher-scientist who ignored the clutter of the patent office and the chatter of the hallway to rethink the foundations of his discipline, to topple the Newtonian absolutes of space and time. Newton to Einstein: it is easy enough to represent this transformation of physics as a confrontation of theories floating above the world of machines, inventions, and patents. Einstein himself contributed to this image, emphasizing in many places the role of pure thought in the production of relativity: “[T]he essential in the being of a man of my type lies precisely in what he thinks and how he thinks, not in what he does or suffers.”12
The picture we so often see is of an Einstein otherworldly, oracular, communing with the spirits of physics; Einstein pronouncing on the freedom of God in the creation of the Universe; Einstein shucking off patent applications as so much busywork between him and the philosophy of nature; Einstein summoning a world of pure thought experiments featuring imaginary clocks and fantastical trains. Roland Barthes explored this imagined persona in his “Brain of Einstein,” where the scientist appears as nothing but his cerebrum, an icon of thought itself, at once magician and machine without body, psychology, or social existence.13
Einstein's Clocks and Poincare's Maps Page 2