Einstein's Clocks and Poincare's Maps
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I returned the Helmholtz volume and am now rereading Hertz’s propagation of electric force with great care because I didn’t understand Helmholtz’s treatise on the principle of least action in electrodynamics. I’m convinced more and more that the electrodynamics of moving bodies as it is presented today doesn’t correspond to reality, and that it will be possible to present it in a simpler way. The introduction of the name “ether” into theories of electricity has led to the conception of a medium whose motion can be described, without, I believe, being able to ascribe physical meaning to it.18
Electricity, magnetism, and currents, Einstein concluded, should be definable not as alterations of a material ether but as the motion of “true” electrical masses with physical reality through empty space. A motionless, nonmaterial conception of the ether might work better than a material one, and (following Lorentz’s widely hailed theory) many leading physicists had just such a conception in mind.
Faced with the inability of experimentalists to either drag the ether or detect motion through it, Einstein sometime around 1901 disposed even of this static insubstantiality. Ether, that centerpiece of nineteenth-century physical theories, was gone. For Einstein it was neither the ultimate constituent of electrical particles nor the all-pervasive medium necessary for light to propagate. Even before Einstein had set foot through the patent office door, crucial pieces of the puzzle were in place; he may well have already begun invoking the relativity principle.19 Certainly he was reconsidering the meaning of Maxwell’s equations while latching onto a realistic picture of moving electrical charges. He had dismissed the ether. Still, none of these considerations directly bore on time.
From 1900 through 1902, Einstein struggled at the margins of institutionalized science. Despite having received his mathematics-teaching diploma from ETH in July 1900, he found himself unable to secure a university job. He took up tutoring and began pushing, outside university walls, into two domains of theoretical physics. On the one hand, he explored the nature of thermodynamics (the science of heat) along with its foundation and extension through statistical mechanics (the theory that heat was nothing but the motion of particles). On the other hand, he strove, not yet in print, to grasp the nature of light and its interaction with matter. Above all else, he wanted to know how electrodynamics would look for moving bodies.
Einstein’s relentless optimism and self-confidence, combined with a biting disregard for complacent scientific authority, shows in a myriad of letters. In May 1901, he confided to Mileva that “Unfortunately, no one here at the Technikum [the ETH] is up to date in modern physics & I have already tapped all of them without success. Would I too become so lazy intellectually if I were ever doing well? I don’t think so, but the danger seems to be great indeed.”20 Or the next month, having written up a custom-made critique of Paul Drude (a leading figure in the theory of electrical conduction), Einstein told Mileva: “What do you think is lying on the table in front of me? A long letter addressed to Drude with two objections to his electron theory. He will hardly have anything sensible to refute me with, because the things are very simple. I am terribly curious whether and what he is going to reply. Of course, I also let him know that I don’t have a job, that goes without saying.” If Einstein wouldn’t budge an inch on physics, he had no more intention of altering his personal life to suit the disapproving glances of his nearest and dearest. When friends apparently criticized his personal comportment, he rejected their judgment out of hand: “imagine the Wintelers railed against me . . . & said that I have been leading a life of debauchery in Zurich.”21
From early in his time at Polytechnique, Poincaré had formed lifelong bonds with his teachers. He admired his elders, filially naming many of his own mathematical creations after them. Einstein, by contrast, appears to have been absolutely undeterred by the head-shaking of his old teachers, his incessant job rejections, or, for that matter, his mother’s stinging disapproval of Mileva Mari. So when Drude dismissed Einstein’s objections in July 1901, the younger scientist simply relegated him to the throng of clay-footed authority:
There is no exaggeration in what you said about the German professors. I have got to know another sad specimen of this kind—one of the foremost physicists of Germany. To two pertinent objections which I raised against one of his theories and which demonstrate a direct defect in his conclusions, he responds by pointing out that another (infallible) colleague of his shares his opinion. I’ll soon make it hot for the man with a masterly publication. Authority gone to one’s head is the greatest enemy of truth.22
Einstein might “make it hot”; but these authorities were not about to respond to his thermo-pressure with a shower of job offers. One after another, rejections arrived, including one for the position of senior teacher, Mechanical Technical Department in the Cantonal Technikum at Burgdorf.23 When his friend the mathematician Marcel Grossmann landed a position at the Cantonal School in Frauen-feld, Einstein congratulated him heartily, adding that the security and good work it afforded would certainly be welcome. Einstein, too, had tried applying. “I did it only so that I wouldn’t have to tell myself that I was too faint-hearted to apply: for I was strongly convinced that I have no prospects of getting this or another similar post.”24
Then came a genuine prospect of employment. The Swiss Patent Office in Bern had placed an advertisement for an opening. Einstein wrote directly: “I, the undersigned, take the liberty of applying for the position of Engineer Class II at the Federal Office for Intellectual Property, which was advertised in the Bundesblatt [Federal Gazette] of 11 December 1901.”25 Assuring the patent office that he had studied physics and electrical engineering at the School for Specialist Teachers of Mathematics and Physics at ETH, he promised that all the documents were ready and waiting. On 19 December 1901, he rejoiced to Mileva: “But now listen & let me kiss you and hug you with joy! [Friedrich] Haller [head of the patent office] has written me a friendly letter in his own hand, in which he requested that I apply for a newly created position in the patent office! Now there is no longer any doubt about it. [Former ETH classmate, Marcel] Grossmann has already congratulated me. I am dedicating my doctoral thesis to him, to somehow express my gratitude.”26 Job in hand, or almost so, he and Mileva could marry.
Even his attitude toward his old thesis evaluator, Kleiner, brightened. On 17 December he had told Mileva that he’d “descend upon . . . that bore Kleiner.” Einstein wanted permission to work during Christmas vacation. “To think of all the obstacles that these old philistines put in the way of a person who is not of their ilk, it’s really ghastly! This sort instinctively considers every intelligent young person as a danger to his frail dignity, this is how it seems to me by now. But if he has the gall to reject my doctoral thesis, then I’ll publish his rejection in cold print together with the thesis & he will have made a fool of himself. But if he accepts it, then we’ll see what a position the fine Mr. Drude will take . . . a fine bunch, all of them. If Diogenes were to live today, he would look with his lantern for an honest person in vain.”27
Two days later, Diogenes’s little lantern cast humanity in a warmer light: “Today I spent the whole afternoon with Kleiner in Zurich and otherwise talked with him about all kinds of physical problems. He is not quite as stupid as I thought, and moreover, he is a good guy.” True, Kleiner had not yet read his thesis, but Einstein was not worried. His attention had already shifted elsewhere: “[Kleiner] advised me to publish my ideas about the electromagnetic theory of light in moving bodies together with the experimental method. He thought that the experimental method proposed by me is the simplest and most appropriate one conceivable.”28
Encouraged, no doubt, by this unexpected support, Einstein dug deeper into the theories of the ether and motion within it. He resolved to study Lorentz and Drude on the electrodynamics of moving bodies (it is perhaps a measure of his disconnection from the mainstream that he had not already done so) and borrowed a physics volume from his friend Michele Besso. Poincaré endlessl
y stressed in his lectures of 1899 how valuable older physics approaches were. Maxwell, Hertz, Lorentz, and many others were all worth studying in detail because even when parts misfired, each captured “true relations” among physical quantities. That form of patience was not for Einstein. One ether-theory text impressed him only by its obsolescence, as he told Mileva late in 1901: “Michele gave me a book on the theory of the ether, written in 1885. One would think it came from antiquity, its views are so obsolete. It makes one see how fast knowledge develops nowadays.”29 Not long before, he had told her that he and Besso had been pondering together “the definition of absolute rest.”30
In the early weeks of 1902, Einstein moved his modest collection of household items from Schaffhausen (where he had a temporary post in a private school) to Bern, and began once again to search for tutorial students on 5 February 1902:
Private lessons in
MATHEMATICS AND PHYSICS
for students and pupils
given most thoroughly by
ALBERT EINSTEIN, holder of the fed.
Polyt. Teacher’s diploma
GERECHTIGKEITSGASSE 32, 1ST FLOOR
Trial lessons free.31
A few days later his prospects looked good. The young tutor’s notice netted two students, Einstein was planning on writing to the great expert on statistical mechanics, Ludwig Boltzmann, and his studies outside of a narrow band of physics were proceeding apace: “I have almost finished reading [Ernst] Mach’s book with tremendous interest, and will this evening.”32
Maurice Solovine, who had come from Romania to study at the University of Bern, was one new student, along with another friend of Einstein’s, Conrad Habicht, who was pursuing his doctorate in mathematics. Together the three founded their “Akademie Olympia,” an informal club for discussing philosophy or whatever else aroused their curiosity. Solovine: “We would read a page or a half a page—sometimes only a sentence—and the discussion would continue for several days when the problem was important. I often met Einstein at noon as he left his desk and renewed the discussion of the previous evening: ‘You said . . . , but don’t you think . . . ?’ Or: ‘I’d like to add to what I said yesterday. . . .’”33
Mach was on the agenda. Mach the philosopher-physicist-psychologist stood for a relentlessly critical attitude toward that which could not be made accessible to the senses. Though Einstein never subscribed entirely to what he considered Mach’s overemphasis on the sensory, Einstein did pull from Mach’s writings a critical club to be wielded against idle metaphysical chatter such as the notions of “absolute time” and “absolute space.”34 In Einstein’s favorite work of Mach’s (The Science of Mechanics, 1883) he would have found a polemic against Newton’s absolute time and space that began by citing the master: “Absolute, true, and mathematical time, of itself, and by its own nature, flows uniformly on, without regard to anything external. . . . Relative, apparent, and common time is some sensible and external measure of absolute time.” Such thoughts disclosed, according to Mach, not the Newton of hard-boiled facts, but the Newton of medieval philosophy. For Mach, time was not something primitive against which phenomena were measured. Quite the opposite: time itself derived from the motion of things—the earth as it spins, the pendulum as it swings. To attempt to get behind the phenomena to the absolute was futile. Mach’s condemnation was clear: “This absolute time can be measured by comparison with no motion; it has therefore neither a practical nor a scientific value; and no one is justified in saying that he knows aught about it. It is an idle metaphysical conception.”35
Over the following years, Einstein often emphasized how important this time analysis of Mach was for him. For example, in a 1916 article memorializing Mach, Einstein insisted: “These quotations [from The Science of Mechanics] show that Mach clearly recognized the weak points of classical mechanics, and thus came close to demanding a general theory of relativity—and this almost half a century ago! It is not improbable that Mach would have hit on relativity theory if in his time . . . physicists had been stirred by the question of the meaning of the constancy of the speed of light. In the absence of this stimulation, which flows from Maxwell-Lorentzian electrodynamics, even Mach’s critical urge did not suffice to raise a feeling for the need of a definition of simultaneity for spatially distant events.” As it had for Poincaré, simultaneity for Einstein crossed electrodynamics with philosophy.36
Up for discussion by the Olympia Academy was also Karl Pearson, the Victorian mathematician-physicist known for his contributions to statistics, philosophy, and biology. But intriguingly Pearson, drawing on Mach as well as the German philosophical tradition, also put the naive reading of “absolute time” under the critical microscope. Einstein and his academicians would have found in Pearson’s 1892 Grammar of Science another sharply critical assessment of the relation of all observable clocks to Newton’s absolute time: “[T]he hours on the Greenwich astronomical clock, and ultimately on all ordinary watches and clocks regulated by it, will correspond to the earth turning through equal angles on its axis.” So all clock time is ultimately astronomical time. But many factors could alter the great earth-clock in its rotation—tides, for example. “Absolute, true, mathematical time,” as Newton called it, is something we use to describe our sense impressions (a “frame,” as Pearson put it). “But in the world of sense-impression itself [absolute intervals of time] have no existence.” Watching stars cross the spider lines of our transit instruments from one midnight to the next on two different occasions, we notice that the average person registers roughly the same sequence of sense impressions. Fine, says Pearson. Assign those two midnight-to-midnight intervals the designation “equal.” But we should not fool ourselves; this has nothing to do with absolute time: “The blank divisions at the top of and bottom of our conceptual time-log are no justification for rhapsodies on the past or future eternities of time, for rhapsodies which, confusing conception and perception, claim for these eternities a real meaning in the world of phenomena, in the field of sense impression.”37
Along with Mach and Pearson, Richard Avenarius’s Critique of Pure Experience found its way to the Olympians’ reading list; it, too, took a skeptical attitude toward that which lay outside the grasp of experience. Other works on the discussion roster included John Stuart Mill’s Logic, which cautioned against “the prevailing hypothesis of a luminiferous ether”; Dedekind’s sharp analysis of the number concept; and David Hume’s dismantling of induction in the Treatise on Human Nature.38 But of all these works that framed the basic notions of science against a critical background of that to which the human mind had access, Solovine singled out one book for special commentary, a volume that had just appeared in German in 1904: “. . . Poincaré’s Science and Hypothesis, which engrossed us and held us spellbound for weeks.”39 From it Einstein and his Olympians could find strong backing for Mach’s and Pearson’s views. Poincaré also alludes to his crucial article, “The Measure of Time.”
It may be that Einstein and his academy raced off to find “The Measure of Time” in its original form (published in a French philosophy journal). That seems unlikely. But there’s an intriguing twist. Unlike the English or French versions, the German publishers of Science and Hypothesis translated and included a good-sized excerpt from the conclusion to “Measure of Time” as a footnote. So in 1904, in plain German, the Olympia Academy would have had before them Poincaré’s explicit denial of any “direct intuition” about simultaneity, his insistence that rules defining simultaneity were chosen for convenience not truth, and his final pronouncement: “All these rules and definitions are only the fruit of an unconscious opportunism.” In fact, the French-to-German translators went further, providing references to the long line of philosophers, physicists, and mathematicians who had blasted absolute time in favor of relative time, with Locke and d’Alembert leading the way and with one of the creators of non-Euclidean geometry, Loba-schewski, there to report that time was just “motion designed to measure other motions.”
Pendulum clock, spring clock, spinning earth: Poincaré’s German translators insisted that we had our choice of which motion to use as the unit of time that would define the time “t” of physics. But that choice had nothing whatsoever to do with absolute time. Instead, the choice underscored yet again Poincaré’s argument for “opportunism” in the physical definition of simultaneity and duration.40
While it would be a mistake to assume that the finer details of any single philosopher’s thought leapt whole into Einstein’s work, there is no doubt at all that he emerged from these early Bern years with a powerful sense of the distinction between that which was accessible to our experience and that which was, so to speak, inaccessibly hidden behind the curtain of the perceptible. Such an emphasis on the knowable, especially as knowable through that which can be grasped of the natural world through the senses, was key to the doctrine of positivism laid out by Auguste Comte and pursued by his many followers. As Einstein told philosopher Moritz Schlick in 1917: “Your representations that the theory of rel[ativity] suggests itself in positivism, yet without requiring it, are . . . very right. In this also you saw correctly that this line of thought had a great influence on my efforts, and more specifically, E. Mach, and even more so Hume, whose Treatise of Human Nature I had studied avidly and with admiration shortly before discovering the theory of relativity. It is very possible that without these philosophical studies I would not have arrived at the solution.”41
Philosophy mattered. Far from ungrounded in a cultural Zeitgeist, Einstein’s advocacy for a procedural notion of simultaneity and against metaphysical, absolute time fit directly into this series of moves to shore up the basis of physical knowledge by Mach, Pearson, Mill, and Poincaré. One by one Einstein and his little circle sought out their books for discussion.