Insight Editions · No. 237
Einstein’s Clocks, Poincaré’s Maps
Empires of Time
Peter Galison
How the synchronisation of clocks by signal, a matter of railways, telegraphs and maps, became at once technology, philosophy and physics in the work of Poincaré and Einstein.
A study guide to Einstein’s Clocks, Poincaré’s Maps by Peter Galison. Shared free for personal reading; not for sale and not endorsed by the authors or publishers. Please read and buy the original.
Defining simultaneity by exchanging signals and correcting for transit time was not a pure thought experiment: it was the daily work of telegraph longitude-finders, railways and clock networks, and Poincaré and Einstein stood at its two institutional hubs.
History of physics, technology and philosophy, 1860–1912: the meter, pneumatic and electric clocks, time zones, the 1884 Prime Meridian Conference, decimal time, cable longitude, Lorentz's local time, the Bern patent office, Eiffel radio time, GPS.
1883 North American zones; 1884 Greenwich wins; 1898 "The Measure of Time"; 1900 local time as clock time; May 1905 Einstein's clocks; 1911 Paris adopts Greenwich; 38 μs/day GPS relativity correction.
Readers who want to see how infrastructure, philosophy and theory co-produce a concept, and why Poincaré's and Einstein's relativities were two different modernisms.
The Book on One Page
Peter Galison asks how, around 1900, simultaneity came to be defined by a procedure: send an electromagnetic signal from one clock to another and correct for its travel time. The usual story treats Einstein's 1905 trains and clocks as metaphors from a mind above the world. Galison's thesis is that clock coordination was simultaneously technology, philosophy and physics, a moment of "critical opalescence" in which ideas and machines flickered between abstract and concrete at every scale, and that Poincaré at the Paris Bureau des Longitudes and Einstein at the Bern patent office stood at its two great exchanges.
- The world of conventions. The 1875 Convention of the Meter and the 1889 burial of prototype M showed France winning standards of space; time resisted. Paris's pneumatic and electric clock networks failed while observatories in Boston sold time, railways voted in North American zones (1883), and Britain and America beat France for the prime meridian at Washington (1884).
- The electric worldmap. Telegraph longitude ("the American method"), the 1866 Atlantic cable and a world polygon of cabled simultaneity closing to 150 yards made distant simultaneity a routine engineering problem; surveyors corrected for signal transit by halving the difference of the two directions.
- Poincaré's three moves. Shaped by Polytechnique's "factory stamp," mining, chaos and conventionalism, he ran the 1897 decimal-time commission, joined the Bureau (1893), and declared simultaneity a convention (1898); in 1900 he showed Lorentz's fictional local time is what signal-synchronized clocks in a moving frame actually read; by 1905–06 he had exact relativity while keeping the ether and a "true" time.
- Einstein's clocks. ETH's hands-on training, Mach, Pearson, Hume and Poincaré read in the Olympia Academy, Haller's critical discipline and a Swiss boom in electric-time patents formed the man who in May 1905 made clock synchronization the capstone of a principle theory with no ether and no master clock.
- Afterlife. Minkowski's spacetime, Eiffel Tower radio time (1910), the 1911 French switch to Greenwich and, eventually, GPS, where relativity is programmed into orbiting clocks.
- Two modernisms. Poincaré's constructive, reforming modernism of convenient "true relations" versus Einstein's critical, austere modernism of principles mirroring nature; neither reducible to things-shape-thoughts or thoughts-shape-things.
| Ch | Title | One-line payload |
|---|---|---|
| 1 | Synchrony | Simultaneity needs signal-synchronized clocks; the idea lived in trains and wires, not just thought experiments |
| 2 | Coal, Chaos, and Convention | Poincaré's "factory stamp": mine inspector, discoverer of chaos, conventionalist about geometry |
| 3 | The Electric Worldmap | Meter, failed Paris clocks, US time zones, cable longitude, and Greenwich's 1884 victory |
| 4 | Poincaré's Maps | Decimal time, Senegal and Quito, the surveyors' rule, and local time made real (1898–1906) |
| 5 | Einstein's Clocks | ETH, Olympia, patents and Bern's clocks behind May 1905; Minkowski, Eiffel radio, GPS |
| 6 | The Place of Time | Solvay 1911, two modernisms, and history that looks up and down at once |
Synchrony
Galison opens with the idea at the centre of special relativity: to speak of distant simultaneity you must synchronize clocks by exchanging signals and correcting for transit time. The standard story treats this as pure philosophy, a young genius asking a child's question. Galison's claim is that clock coordination around 1900 was simultaneously physics, philosophy and heavy industry, and that Einstein and Poincaré both stood at the institutional crossroads where these met.
Newton's river and Einstein's "times"
For Newton, true time could never be read off a clock. Clocks gave only pale copies of an absolute time belonging to the "sensorium of God", a single river flowing uniformly behind tides, planets and moons. Einstein's world had no room for a "universally audible tick-tock". Time meant nothing except by reference to a definite system of linked clocks, and clock systems in relative motion disagree: two events simultaneous for one observer are not simultaneous for another. "Times" replace "time." Late in life Einstein addressed his predecessor directly in his autobiographical notes: "Newton, forgive me", you found the only way possible in your age for a man of the highest thought.
The idea Galison tracks is easy to state. To talk about simultaneity at a distance you must synchronize your clocks: start with one, flash a signal to the other, and adjust for the time the flash takes to arrive. With that procedural definition the last piece of the relativity puzzle fell into place. The book is about that procedure, which Galison treats as both lofty abstraction and industrial concreteness: a world where the mayor of New York discoursed on the conventionality of time and the Emperor of Brazil waited by the ocean for the telegraphic arrival of European time.
The 1905 paper as usually told
"On the Electrodynamics of Moving Bodies" (1905) became the best-known physics paper of the twentieth century, and its dismantling of absolute time is the crown. It has come to stand for a clean break with all earlier framings of space and time.
The magnet-and-coil asymmetry
Einstein opened with an asymmetry in the theory that was absent from the phenomena. Almost every physicist in 1905 believed light waves must be waves in something, the all-pervasive ether, and hoped a mature ether theory would unify heat, light, electricity and magnetism. The ether produced the asymmetry Einstein rejected.
- Coil moves, magnet at rest in the ether. The charges in the coil cross a magnetic field and feel a force that drives current round the coil and lights the lamp.
- Magnet moves, coil at rest. The magnetic field near the coil grows; by Maxwell's equations the changing field generates an electric field that drives the current.
- Einstein's objection. The ether is unobservable, so there is one phenomenon (coil and magnet approach, lamp lights) and it deserves one explanation. The two frames are just two perspectives.
Two postulates
Galileo had pictured a closed cabin below deck on a smoothly sailing ship: fish swim in their bowl and drops fall straight, so no mechanical experiment reveals the ship's motion. Einstein raised this to a principle covering electricity, magnetism and light as well as mechanics.
- Relativity postulate. Physical processes are independent of the uniformly moving frame in which they occur; no experiment picks out the frame "truly" at rest.
- Light postulate. Light always passes an observer at 300,000 km/s, whatever the speed of its source. A conductor's mailbag thrown from a train adds the train's speed; a lantern on a train moving at 150,000 km/s still sends light past the platform at 300,000 km/s.
Each postulate looked reasonable alone. Relativity had been familiar in mechanics since Galileo, and Poincaré among others had analysed its prospects in electrodynamics. If light was a wave in a rigid ether, light speed should be independent of the source, just as sound speed is independent of the speed of the car that honks. Together they seemed contradictory: an observer moving through the ether should see light run faster or slower, revealing absolute motion. Yet precise optical experiments detected no ether motion at all.
Einstein's diagnosis was "insufficient consideration" of the basic concepts. Before dynamics (how electrons behave under forces) came kinematics: how rulers and clocks behave in force-free motion. Only by asking what length, time and above all simultaneity mean, operationally, could the contradiction dissolve.
"That train arrives here at 7 o'clock"
Einstein wrote that all judgments involving time are judgments of simultaneous events: "the pointing of the small hand of my watch to 7 and the arrival of the train are simultaneous events." For events next to the watch there is no problem. The difficulty is linking events separated in space. Hermann Minkowski saw this reanalysis of time as the crux of the paper. From the moment Einstein demanded a procedure to give "simultaneous" meaning, he split from absolute time.
Einstein first considered a single clock-bearing observer at the origin who times every event by when its light arrives. Galison's line diagram makes the flaw plain: put me next to A and far from B, with you exactly halfway between.
- Signals arrive together at me. B's signal had farther to travel, so it must have left earlier; simultaneous receipt does not mean simultaneous emission.
- Insist they were simultaneous anyway. Then you, at the midpoint, receive B's light before A's, and the verdict depends on where the receiver stands. "Simultaneous receipt by me" is an epistemic straw man.
Einstein's synchronization rule (1905)
- Send. Observer A sends a light signal at 12:00 to B at distance d.
- Reflect. The signal bounces off B and returns to A.
- Set. B sets her clock to noon plus half the round-trip time. With equal speeds both ways this equals 12:00 + d/c.
- Example. At 600,000 km, B sets 12:00:02; at 900,000 km, 12:00:03.
- Result. No privileged master clock: move the origin and nothing changes, because every clock already allows for signal travel time.
Consequences
Applied relentlessly, the rule plus the two postulates showed that events simultaneous in one frame are not simultaneous in another.
- Length. Measuring a moving bus needs simultaneous readings of front and back, so relativity of simultaneity yields relativity of length: a meter stick passing me measures less than a meter.
- Velocity addition. A runner at ½c in a train moving at ¾c would, in Newton's physics, move at 1¼c; Einstein's combined speed is always less than c.
- Coil and magnet unified. A magnetic field in one frame is an electric field in another; one phenomenon, two perspectives, "without a whiff of ether."
- Mass-energy. Shortly afterwards relativity gave E = mc², whose consequences ran from barely possible experiments to the transformation of military politics forty years on.
Behind all this stood the century's collective mastery of electromagnetism: Maxwell's unification of light and electricity; dynamos, electric light, trams and telegraphs transforming cities, markets, news and warfare; precision optical searches for the ether; the newly accepted electron. Many leading physicists, not only Einstein and Poincaré, rated the electrodynamics of moving bodies among the hardest open problems in science.
How clock synchronization became a model of knowledge
By Einstein's own account, synchronizing clocks was the final conceptual step of a long hunt, and he judged the alteration of time the theory's most striking feature. Contemporaries did not immediately agree: some accepted relativity because of electron-deflection experiments, others only after mathematicians recast it in terms that played down time. By 1910 a growing number pointed to the new time concept as the heart of the matter, and it then became canonical in physics and philosophy alike.
- Heisenberg and quantum mechanics. In the 1920s Werner Heisenberg modelled quantum theory on what he took to be Einstein's stance: if position and momentum cannot be measured together even in principle, they do not both exist. Einstein bridled, worrying that the new physics underrated the role of theory in fixing what can be seen: "A good joke should not be repeated too often."
- Piaget. Jean Piaget made the child's intuitive concept of time a research programme.
- Vienna Circle. The logical empiricists hailed signal-synchronized simultaneity as the paradigm of a verifiable scientific concept.
- Quine. W. V. O. Quine, who held even logic revisable, singled out Einstein's definition of simultaneity as what we "should be most inclined to preserve" in future revisions of science.
Einstein credited philosophical weapons too: David Hume's analysis of causation as regular sequence, and Ernst Mach's attack on concepts cut off from perception, with Newton's "medieval" absolute space and time as chief offenders. He also studied Lorentz and Poincaré. Galison's complaint is that a purely intellectual history leaves Einstein "hovering in a cloud of abstractions".
- Isaac Newton: absolute time as divine sensorium; the target of the whole story.
- Albert Einstein: Bern patent examiner, author of the 1905 relativity paper and its clock-synchronization definition.
- Henri Poincaré: mathematician, philosopher, engineer; Bureau des Longitudes; conventional simultaneity in 1898.
- Hendrik A. Lorentz: Dutch electron theorist whose "local time" both men reworked.
- Ernst Mach and David Hume: philosophical critics of unobservable absolutes Einstein drew on.
- Hermann Minkowski: saw the time analysis as the crux of relativity.
- Charles Wheatstone, Alexander Bain, Mathias Hipp: builders of electrical clock-distribution systems.
The myth of the otherworldly genius
Both protagonists cultivated an image of pure mind. In October 1933, at a refugee-aid rally in London's Royal Albert Hall guarded by a thousand student stewards, Einstein broke off his warnings about war to praise solitary occupations, "the service of lighthouses and lightships", as ideal for a young scientist. It is tempting to read the Bern patent office as such a lightship. Einstein fed the image: what matters about "a man of my type" is "what he thinks and how he thinks, not in what he does or suffers." Roland Barthes's essay "The Brain of Einstein" captured the icon: a cerebrum, magician and machine with no body or social existence.
Poincaré presented himself the same way. His famous account of discovering the Fuchsian functions: fifteen days of fruitless effort, then one evening of black coffee and sleeplessness in which "ideas rose in crowds" and interlocked. His essays populate imaginary worlds: a man on a permanently cloud-covered planet who could still prove its rotation by the equatorial bulge or a Foucault pendulum; a world with temperature gradients that change the lengths of objects. Read this way, both men's trains, clocks and telegraphs are metaphors.
| Standard reading | Galison's reading | |
|---|---|---|
| Einstein's train at 7 o'clock | A child's question asked by a grown-up genius | A live engineering question in Bern, 1904–05 |
| Poincaré's telegraph example | Philosophical aperçu, timid anticipation of Einstein | Daily practice of the Bureau des Longitudes |
| Patent office | Lightship of solitude | Clearinghouse for electrotechnology |
| Clocks | Imaginary props | Real networks under streets and seas |
Coordinated clocks were everywhere
Galison's own epiphany came on a northern European platform: the clocks agreed to the minute, and even their second hands clicked in synchrony. These clocks were coordinated, and across the street from Einstein's patent office stood the old Bern train station with clocks coordinated inside the station, along the tracks and on its facade.
- 1830s–1840s Charles Wheatstone and Alexander Bain in Britain build electrical systems tying distant clocks to one central clock.
- 1850s Mathias Hipp in Switzerland follows; Leipzig is the first German city with electrically distributed time.
- 1859 Frankfurt installs a distributed time system.
- 1890 Hipp, director of a telegraph workshop, sets 100 clock faces marching together in Bern's Federal Palace.
- 1890s Coordination spreads to Geneva, Basel, Neuchâtel and Zurich and their railways.
The central clock had a name in every language: horloge-mère (mother clock), Primäre Normaluhr (primary standard clock), master clock. Decorated master clocks, such as Neuchâtel's, which took its time from the observatory and sent it along telegraph lines, or the one at Berlin's Silesischer Bahnhof dispatching time down every track, were objects of civic pride. Einstein was not just surrounded by this technology; he sat in a great centre of its invention, production and patenting. Clock coordination even featured in one of Einstein's favourite childhood science books. "In 1904–05, clock-coordinating cables were thick on the ground and under the seas."
Poincaré, 1898: "The Measure of Time"
Seven years before Einstein, Poincaré advanced strikingly similar ideas. He was famous for creating much of topology, for celestial mechanics and for electrodynamics; engineers praised his writing on wireless telegraphy; the public bought his best-sellers on conventionalism and "science for science".
In January 1898, in the Revue de métaphysique et de morale, "The Measure of Time" attacked the view, associated with Henri Bergson, that we have an intuition of time, simultaneity and duration. Poincaré argued that simultaneity is a convention, chosen not because it is true but because it is most convenient, and that it must be defined by reading clocks coordinated by electromagnetic signals, allowing for transmission time.
Longitude as the decisive example
Poincaré's strongest example was longitude. Latitude is easy: the pole star's altitude gives it at any hour (overhead at the North Pole, halfway at Bordeaux's latitude, on the horizon at the equator). Longitude differences need two distant observers measuring at the same time, because the earth turns. If a North American team knew Paris time and saw the sun rise six hours later than in Paris, it was 6/24 of the way round, 90° west. The problem is knowing Paris time.
- Carry a chronometer set to Paris time; troublesome in practice and principle.
- Observe an instantaneous celestial event, such as a moon of Jupiter emerging from the planet's shadow; impractical, and in principle the light paths to the two observers differ.
- Exchange telegraph signals with Paris. Reception in Berlin follows sending in Paris "by the rule of cause and effect"; transmission time is normally neglected, but rigorous definition requires a correction.
We choose these rules, therefore, not because they are true, but because they are the most convenient.Henri Poincaré, "The Measure of Time", 1898
Intuition is "incompetent" to settle simultaneity. Instead there is "a multitude of little rules applicable to each particular case", definitions adopted to make the laws of physics, mechanics and astronomy as simple as possible, "the fruit of an unconscious opportunism." Time is a convention, not absolute truth.
Did Einstein read Poincaré? Galison leaves it open: there is no definitive evidence that Einstein saw the 1898 essay or Poincaré's 1900 paper before 1905. Einstein did read Science and Hypothesis with his Bern friends, but that book does not contain the clock-synchronization passage. Galison's larger point is that Einstein did not need to: the procedure was in philosophy journals, occasional physics papers, popular books and the streets. Critics note that "available in the environment" is weaker than "used", a tension that runs through the whole book.
Critical opalescence
Galison refuses both standard metaphors for science and technology. In one, ideas condense downward from blackboard to laboratory to shop floor; in the other, practice sublimes upward from shop floor to theory to philosophy. Neither fits. Philosophy did not cause the deployment of coordinated railway and telegraph time, and the networks did not force physicists to adopt conventional simultaneity.
An ocean at its critical point. Picture a sealed world of ocean and water vapour. Heat it so the liquid expands while the vapour is compressed until their densities nearly match. Near that critical point, pockets everywhere flash between liquid and gas, at every scale from a few molecules to the size of the planet. Drops of every size scatter every wavelength, purple off small ones and red off large, and the whole world shimmers like mother-of-pearl: critical opalescence. Galison's punchline: time coordination from about 1860 to 1910 was such a state, with ideas and machines flickering back and forth between abstract and concrete at every scale, so it cannot be told as a one-way flow in either direction.
The archives bear this out. Time coordination involved school buildings wiring classroom clocks to the principal's office, cities and railways soldering alignment into public clocks and fighting "tooth-and-nail" over how, and governments whose cast included anarchists, democrats, internationalists and generals. It was a story of physics, engineering, philosophy, colonialism and commerce colliding, "gutta-percha insulator over ironclad copper wire and cosmic time". In Germany time regulation stood for national unity; in France it embodied the Third Republic's rationalist institutionalization of the Revolution. Two exchanges matter most: the Paris Bureau des Longitudes and the Bern Patent Office.
Order of the argument
Galison's plan switches scale between local and global. Wires for time "did not arrive on their own": they came with national ambitions, war, industry, science and conquest.
| Ch | Scale | What it does |
|---|---|---|
| 2 | Close-in | Poincaré as mining engineer and Polytechnicien with the school's "factory stamp"; Bureau des Longitudes president in 1899, 1909, 1910; co-editor of an electrotechnical journal |
| 3 | Global | Cables, empires, and the 1884 Prime Meridian Conference: 22 countries, zero longitude at Greenwich, French fury and the push for decimal time |
| 4 | Intermediate | Poincaré's 1890s decimalization commission, Bureau longitude work, and three moves on time: 1898 convention, 1900 local time as real clock time, 1905–06 exact Lorentz local time |
| 5 | Local | Einstein the tinkerer in Bern: patent office, Swiss clock industry, coordinated urban time, the May 1905 breakthrough |
| 6 | Comparative | Two modernities: the Polytechnicien's reform against the outsider's rebellion |
The preview also sets up the contrast to come. Lorentz (1895) had defined local time (Ortszeit, the same word used for the longitude-dependent time of Leiden or Djakarta) as a mathematical fiction that made the equations in a moving frame look like those in the ether rest frame. In December 1900 Poincaré made local time the reading of real clocks synchronized by signals that beat against or run with the ether wind. In 1905–06 he adjusted Lorentz's 1904 version so clocks moving through the ether give exactly the new local time, while still contrasting "apparent" and "true" time. Einstein, by contrast, had dismissed the ether by 1901, had dissected the machinery of time at the patent office for three years, and in May 1905 treated clock coordination as "the turn of the key" that set his theory machine running: no ether, only fields, particles and real times given by clocks.
The book's claim in one line: technological time, metaphysical time and philosophical time crossed in electrically synchronized clocks, and time coordination stood at "the modern junction of knowledge and power". Poincaré and Einstein are not progressive versus reactionary; they are two different visions of what made modern physics modern.
Coal, Chaos, and Convention
Galison relocates Henri Poincaré: not a free-floating mathematician-philosopher but the product of École Polytechnique's "factory stamp", where abstract theory and engineering action were bound together. Three early episodes show the pattern: a coal-mine explosion he investigated as a mining engineer, the three-body problem where he found chaos, and his doctrine that geometric axioms are conventions. Across all three runs one method: choose the most convenient representation freely, then hold fast to the invariants that survive every choice.
The Polytechnique "factory stamp"
By 1902, with Science and Hypothesis a best-seller, Poincaré stood at the summit of French mathematics, physics and philosophy, had been scientific rapporteur of a major expedition and president of the Bureau des Longitudes. On 25 January 1903 the school's alumni asked him to speak "On the Part Played by Polytechnicians in the Scientific Work of the XIXth Century." His predecessors as speakers included the dean of generals, ministers, engineers, a company director, "those who conquered our overseas empire and those who organized it," and the organizers of the 1900 Universal Exposition. How could one education produce all that?
His answer: competitive exams, the school's military "nobility", and above all a shared culture of mechanics. Even the purest Polytechnique mathematician, such as Augustin-Louis Cauchy, drew on mechanics. His teacher Alfred Cornu liked to say that mechanics was the cement of the Polytechnician's soul. "There it is, that factory stamp I was looking for; our physicists, our mathematicians are all a bit mechanicians." University scientists fretted about the unity of science; Polytechnicians worried about joining thought with action, which Poincaré thought inoculated them against fin-de-siècle melancholy about the "failure of science." The school could evolve, but "the alliance of theory with practice must not be broken."
A school without parallel
Founded in 1794, Polytechnique trained an elite corps of engineers in mathematics-based science to modernize the military and then staff the highest levels of the State and, later, the empire. Comparisons fail: more scientific than the classically schooled British elite, more mathematical than American engineers, less inclined to precision laboratory work than German physics students. Students entered by the concours and wore uniform.
- Monge's founding programme. Gaspard Monge used projective geometry to bind engineering to advanced mathematics: geometry trained minds, revealed truth and shaped stone, wood and fortifications.
- Drift to abstraction. In the early nineteenth century, pushed by the conservative Cauchy, mathematics shed its worldly ambition; specialised engineering schools drew off applications.
- After 1871. Germany's crushing victory (Alsace-Lorraine lost, Germany unified and building institutes) triggered French soul-searching over railways, military preparation and technical schools. Pasteur blamed a failure of French science. Polytechnique, whose students were already in uniform, was in the dock.
- Cornu's balance. Alfred Cornu, the model Third Republic Polytechnician, moved between pure and applied: optics for physicists, astronomers, meteorologists and clockmakers; a massive-pendulum astronomical clock at Nice that he visited yearly; and a detailed mathematical theory of coordinating clocks by electric signals. Poincaré noticed both habits.
Cornu's course used stylised demonstrations: students learned deep respect for experiment without hands-on skill, saw mathematical structures as the endpoint of science, and put little faith in the literal truth of atoms or fields. When Polytechnique hired a chemist, the faculty aimed to balance believers in atoms against non-believers.
Poincaré as a student
Poincaré entered in November 1873. He tracked rivals' grades like a hawk, earned 19–20 out of 20 in mechanics, found simpler proofs than his professor, and was fascinated by the workers' dexterity and Siemens ovens at a crystal factory. To his mother he described the school less fondly: an "immense machine" whose movement you follow or get passed, using only memory and elocution, doing what 20 generations of X did and "2n + 1 generations of conscripts" will do. Poincaré's career then tracked Cornu's: star at Polytechnique, then the École des Mines, back to teach at Polytechnique, State engineering service, and both on the board of the Bureau des Longitudes and the editorial team of an electrotechnical journal.
The relation of pure science to technology is "a vast and slowly undulating sea." For a brief moment after 1871, Cornu and his allies flattened it around Polytechnique into roughly equal claims. Inside that "immense machine", where technology and mathematical physics circulated with equal force, Poincaré became Poincaré.
Coal: the Magny explosion, 1879
Graduating in 1875, Poincaré moved with the other two top students of his class (Bonnefoy and Petitdidier) to the École des Mines. His mentor Ossian Bonnet asked for a lighter load so he could do mathematics; the school refused, so he wrote his thesis (submitted 1878) while learning ventilation shafts, with geological fieldwork in Austria and Hungary (1877).
Philosophical company
His sister Aline introduced him to the philosopher Émile Boutroux, whom she later married. Boutroux, trained in Heidelberg, brought a Kantian conviction that much of science is "more of the mind than out there"; through him Poincaré met Jules Tannery, an ardent secular Republican mathematician. The circle sought a middle way between science as observation and science as mental creation. Around 1877 Poincaré wrote to Aline that induction deserves "reserve": observation shows only "the sensations that it produces in us," never substance; what lies beyond "will remain to us forever but a dead letter."
Fellow Polytechnician Auguste Calinon published a treatise on mechanics and geometry in 1885 and sent Poincaré his Critical Study of Mechanics after they met in August 1886. Calinon rejected absolute motion as metaphysical, unverifiable even in principle, and said two events are simultaneous only if seen "at the same time," even allowing for the brain's registration time: "the very idea of time is... Inherent to the mode by which our brain functions." Poincaré's lost reply apparently addressed "at the same time" first, agreeing that "it is by our sensations alone that we judge simultaneity." This is a psychophysiological Kantianism, distinct from the German version.
The inspection and the disaster
Poincaré became "ordinary engineer" in March 1879 and began inspections at Vesoul on 4 April: Saint-Charles nearly exhausted ("veins both poor and irregular," 4 June), aeration and gas at Sainte-Pauline (25 September), smelting at Saint-Joseph (27 October).
Magny, 31 August 1879. At 6:00 p.m. 22 men went down; at about 3:45 a.m. an explosion blew out every lamp. Four survivors reached the surface. Master miner Juif led a party back in and smothered smouldering clothes before they ignited timber, coal or a second gas blast. Sixteen-year-old Eugène Jeanroy was found alive and died next day; every other man found was dead, many badly burned. Poincaré entered the mine almost immediately, mid-rescue, despite the risk of a secondary explosion.
His job was to find the first spark. He turned to the Davy safety lamps (Humphry Davy, 1815: a flame enclosed in fine wire mesh that admits air and light but stops flame escaping). Lamps 414 and 417 (Félix and Doucey) were never found; lamp 18 was crushed by a cave-in. Lamp 476 had no glass and two tears: one long and wide from inside pressure, one rectangular from outside, matching, all the miners agreed, a standard-issue pickaxe. It was signed out to Auguste Pautot, 33, yet it hung from a timber a few inches off the ground beside the body of Émile Perroz, whose own lamp was found intact elsewhere.
Poincaré's inference, step by step
- Two rival hypotheses. Upstream victims usually burn, downstream ones suffocate; all Magny's dead were burned, suggesting an explosion in the "half-moon" beyond the last man (Doucey). Rival: an explosion at the top of the lift, at Perroz's workspace by lamp 476. Both "equally well" fit the facts.
- The pick. Perroz was a coal loader with no pick, so Pautot must have punctured the lamp and the two men inadvertently swapped.
- Eliminating gas sources. Some veins lay outside the air flow; others were too old to degas.
- The low lamp. Gas from a distant source would rise to the roof, not reach a lamp hanging near the floor.
- The standing corpse. Slow venting would have asphyxiated Perroz, who died standing; so gas burst in suddenly, probably from a vent a single step away.
- Conclusion. The punctured lamp ignited the methane; incompletely burned gas then set off a secondary explosion where it met the main air current.
The report mixed analysis with feeling: it recommended Juif for compensation, hoped the men died instantly, and listed the 9 widows and 35 young children left behind: "Even the generous efforts of the company will perhaps be insufficient to relieve so much misery." He returned on 29 November to measure air flow and pressures, submitted the report at Vesoul on 1 December 1879, and the same day learned of a junior lectureship at Caen. He never left the Corps des Mines: chief engineer 1893, inspector general 16 June 1910. Just before his death in 1912 he wrote "Les Mines", headed by a small picture of a Davy lamp: "One spark is enough to ignite... I refuse to describe the horrors that follow."
Galison calls the Magny pits "still-smoldering" in Poincaré's mind "thirty-five years earlier" when he wrote "Les Mines"; from 1879 to 1912 is 33 years. A trivial slip, but the larger claim also deserves a check: the Magny report shows Poincaré's habit of rival hypotheses tested against evidence, yet Galison does not show that mining practice shaped his later physics, only that both lived in the same person.
Chaos: the three-body problem and the prize
The problem
One body moves in a straight line; two bodies under Newtonian gravity have exact solutions; planets attracted only by the sun can be computed. Three mutually attracting bodies (sun, earth, moon) need 18 interrelated equations: positions x, y, z for each body (9) plus momenta (9), reducible to 12 with clever coordinates.
Poincaré cared neither for the pure mathematician's rigor nor for better numerical schemes. He showed that the usual approximation methods for ephemerides (the tables of celestial positions navigators relied on) gave dramatically wrong long-run predictions. He needed a new approach: the qualitative theory of differential equations.
The stream, not the droplet. Do not follow one droplet downstream to compute its speed so many centimetres on. Ask instead about the pattern of the whole flow: how many vortices form, six, two or none? Where do streams collect or escape? For the solar system: under what conditions does an asteroid fly off into space or plunge into the sun? Poincaré wanted the physiognomy of the equation first; formulas, numbers and rigor could come later.
This was a return, with far more sophistication, to the visual-geometric Polytechnique of Monge, against Lagrange, who boasted his Analytical Mechanics contained not one diagram. In 1881 Poincaré asked whether a body will "always remain in a certain region of the heavens" or drift away forever, "a thousand questions" answerable once trajectories could be constructed qualitatively. In 1885 he noted his mathematics resembled "the great astronomical problem of the stability of the solar system." Mechanics was always near: the factory stamp.
King Oscar's prize
- Mid-1885 Nature announces a competition for the 60th birthday of King Oscar II of Sweden; Gösta Mittag-Leffler, editor of Acta Mathematica, recruits judges Charles Hermite and Karl Weierstrass.
- 31 January 1887 Poincaré, aged 32, elected to the Academy of Sciences, opening a stream of administrative posts (Bureau des Longitudes, interministerial commissions); almost all of his ~100 non-technical writings come after this.
- 1 June 1888 Entries due; the first question is the three-body problem. Poincaré's motto: "For the stars do not cross their prescribed limits."
- 1889 Poincaré wins "hands down," proving (he thought) the stability of the solar system and introducing many new methods.
- July 1889 Edvard Phragmén, 26, an Acta editor, finds problems; on 16 July Mittag-Leffler says all but one "could disappear almost immediately."
- 1 December 1889 Poincaré confesses "the distress this discovery has caused me."
- 4–5 December 1889 The issue has already gone out; Mittag-Leffler telegraphs Berlin and Paris to recall every copy.
- 1890 Revised memoir published, containing chaos.
Between the announcement and the deadline Poincaré also wrote on intuition in mathematics. Contemporary mathematicians mocked the vague concepts and "frail structures" of "our fathers" and paraded new continuous functions with no definable slope, a "teratological museum" of monsters that seemed to be the majority. Poincaré refused to teach beginners from that museum. Intuition is how "the mathematical world remains in contact with the real world"; for every pure geometer there are a hundred practitioners; logic criticizes but intuition invents. "A mathematician without intuition is like a writer locked in a cell with nothing but grammar."
Poincaré maps
The model was a small asteroid circling within the Sun–Jupiter system. Poincaré's simplifying idea: forget the full trajectory and look stroboscopically, each time the asteroid comes round.
Vocabulary of the Poincaré map
- Section. A vast sheet perpendicular to the orbit; each return punches a hole (strictly, a point in position-momentum space).
- Fixed point F. A periodic orbit punches the same hole forever.
- Stable axis S. A curve through F along which successive punctures converge to F.
- Unstable axis U. A curve along which punctures run away from F (or approach it in the infinite past).
- Saddle. A marble rolled along a saddle's spine settles in the middle (stable); one rolled sideways falls off (unstable).
- Homoclinic point H. A point where S and U cross somewhere other than F.
The prize memoir claimed that punctures fleeing one fixed point would settle onto another: a bounded, ordered world matching the motto. The error lay in the homoclinic case.
- H lies on both axes. As a point of S, its successive punctures H1, H2, H3 march along S toward F.
- U must pass through them all. As a point of U, every consequent of H must also lie on U, so the extended unstable curve has to swing out and back to hit H1, H2, H3 and so on.
- Nearby points do the same. A point C near H on U first approaches F, then retreats along U, crossing S again (at C6) and creating new homoclinic points X, each of which forces further folds.
- Result. An endlessly folding lattice; asteroids near U wander over the whole map.
These intersections form a type of trellis, tissue, or grid with infinitely fine mesh... I shall not even try to draw it.Poincaré, New Methods of Celestial Mechanics
The scandal handled
Mittag-Leffler wrote that the memoir would still be "a work of genius," suggested Poincaré write a letter saying stability was not proven in all cases, and added that a good word for Phragmén would help, since a chair was open. Copies had reached only Hermite and Camille Jordan in Paris and Weierstrass in Berlin; a servant was sent to collect Jordan's. Mittag-Leffler was relieved that Leopold Kronecker, Weierstrass's enemy, had none. Weierstrass was icy: in Germany prize essays were printed as judged, and stability was not peripheral but central. What remained of the positive programme?
Poincaré did not proclaim a revolution. He showed that though chaotic orbits were infinite in number, they were improbable: "the [unstable orbits] were the exception and the [stable ones] the rule." Absolute stability gave way to probabilistic stability. The real aim of celestial mechanics, he said, was not ephemerides but "to ascertain whether Newton's law is sufficient to explain all the phenomena," and implicit qualitative relations serve that as well as formulas.
The cost of the error. Galison tells the recall but not the bill: historians of the episode (notably June Barrow-Green) found that Poincaré paid for the reprinting, about 3,585 kronor, more than the 2,500 kronor prize itself. Galison also notes that a century later chaos was hailed as "postmodern physics"; Poincaré himself framed it conservatively, a crack in stability to be contained probabilistically, not a new science.
Modern long-term integrations of the solar system (Jacques Laskar and colleagues) confirm Poincaré's discovery: planetary orbits are chaotic, with a Lyapunov time of about 5 million years, so positions cannot be predicted beyond roughly 60 million years. Yet Poincaré's probabilistic stability largely holds: in large ensembles only about 1% of runs destabilize Mercury's orbit before the Sun leaves the main sequence some 5 billion years hence.
Convention: geometry as a choice of language
Poincaré's attention to structures rather than things shaped his view of non-Euclidean geometry. For centuries Euclid defined proper reasoning, and readers of Kant (or misreaders) had built Euclidean space into the mind. Some greeted non-Euclidean geometry as liberating modernity, others feared lost certainty. Poincaré took a pragmatic line (1891):
- Not a priori. If the axioms were known before experience, we could not so easily imagine alternatives.
- Not experimental. If they were empirical, we would constantly revise them: no body is perfectly rigid, so we would "discover" triangles whose angles do not sum to exactly 180°.
- Therefore chosen. Experience guides the choice of geometry, but the choice is free, governed by simplicity.
Geometry as a group
For Poincaré a geometry is a group: a set with an operation that is (i) reversible (adding a whole number is undone by subtracting it), (ii) contains an identity (adding 0), and (iii) is closed (adding 5 then 8 equals adding 13). Experience tells us which groups are useful; the idea of a group is innate. We pick Euclidean geometry because its group matches the group of rigid-body motions, solid objects being what we handle. Other geometries are no more false than polar coordinates are false relative to Cartesian ones.
Ants on a saddle. Intelligent ants live on a saddle surface and call the shortest path between two points "straight." Ant Mathematician: "The angles of a triangle sum to less than two right angles." Human Mathematician, describing the same figure in Euclidean terms: a curvilinear triangle whose sides are arcs of circles meeting the fundamental plane orthogonally has angles summing to less than two right angles. Same facts, two idioms, like French and German. So the ants' geometry is as consistent as ours, and having a concrete interpretation it "may be applied."
One geometry cannot be more true than another; it can only be more convenient.Poincaré, 1891
The famous 1891 line: the axioms of geometry "are conventions." Asking whether Euclidean geometry is true is like asking whether the metric system is true and the old weights and measures false. Euclidean geometry "is, and will remain, the most convenient." The new element was the analogy with meters and kilograms versus feet and pounds, which, Galison stresses, carries the trace of a whole world of real-life conventions.
Variants and invariants
| Free choice (variant) | Fixed points (invariant) |
|---|---|
| Coordinate system | Length of a line under rotation |
| Approximation scheme | Vortices, knots, saddle points, spirals of a flow |
| Euclidean or non-Euclidean geometry | Relations among experimental results |
| Rival physical theories (atoms or not) | Experimental "fixed points" |
Manipulate the flexible aspects of knowledge as tools and choose the form that makes the problem simple; then seize the relations that stand fast whatever the choice, because those are the knowledge that endures.
Where did conventionalism come from?
Galison lists the candidate "roots" and calls the result rhizomatic, not single-rooted.
- Mathematics. Felix Klein's programme of many geometries; Sophus Lie, whom Poincaré cited, on the "two-fold arbitrariness" of representing x and y by a point or a line and in this or that coordinate system, chosen for "advantage and convenience"; Hermann Helmholtz on rigid bodies and definitions; Bernhard Riemann; Hermite.
- Pedagogy. Polytechnique's agnostic teaching, in which rival theories each had their day; Poincaré's own lectures on electricity and optics in 1888, 1890 and 1899 did the same.
- Philosophy. The Boutroux circle: neither raw empiricism nor pure idealism, an active mind, suspicion of metaphysics; Calinon's work led Poincaré "straight toward the problem of simultaneity."
- Metrology. The worldwide system of weights, measures and time conventions, which Galison insists was not an external "influence" like a magnet under iron filings but a practice Poincaré was inside.
By 1892 Poincaré had a unified stance spanning non-Euclidean geometry, qualitative dynamics and philosophy: conventions above, invariants below. To see how this became a theory of simultaneity, Galison pulls the camera back from the man to the wires, treaties and clocks of 1870–1910, where conventions of space and time "scintillated with a critical opalescence."
The Electric Worldmap
Galison pulls back to the planet: between 1875 and 1912 the Great Powers wired the world, and every collision of networks (rail, telegraph, cable, map) demanded conventions of length, longitude and time. France won the meter and lost the meridian; Britain's cables and America's railways set the pace in time. Coordinated time was not a scientist's abstraction but a contested, commercial, imperial infrastructure, and "simultaneity" was the daily working problem of longitude-finders sending signals down wires and under oceans.
Standards of space: the Convention of the Meter
Paris, 20 May 1875, 2:00 p.m.: 17 plenipotentiaries sign the Convention of the Meter, creating an International Bureau of Weights and Measures to certify new prototypes of meter and kilogram, supplant competing national measures and link them to the standards used to map the earth.
- Diplomacy meets science. Foreign minister Duke Louis Decazes invited politicians and scientists such as Wilhelm Förster (director of the German Bureau of Weights and Measures and the Berlin Observatory) in 1869. By March 1875 he set aside science, where delegates had only "relative competence", for "questions of a political and conventional order" where they had "absolute competence": binding international law. A telegraph convention of 1865 was a precedent.
- Dumas's case. Organic chemist Jean-Baptiste Dumas, perpetual secretary of the Academy since 1868, argued that the 1851 London exhibition exposed "chaos" among national systems. The meter's geodesic origin (one ten-millionth of a quarter meridian, adopted 1799) was "absolutely without interest for commerce, for industry and even for science". What mattered was decimals. The centre should be "neutral, decimal, international", and, it went without saying, in Paris.
- Making the bars. For 14 years French engineers and British metallurgists developed a tough platinum-iridium alloy; a British firm forged bars with an X cross-section; the French built a universal comparator reproducing a length to 0.0002 mm. Preparing 30 standard bars took 13,000 diamond-point inscriptions; any slip meant repolishing. Armand Fizeau (ether drag by moving water) and Albert Michelson (the interferometer) contributed.
Burial of the meter, Breteuil, 28 September 1889. 18 delegates vote unanimously: the prototype "will from now forward represent, at the temperature of melting ice, the metric unit of length." Each delegate draws a ticket from an urn assigning his country a meter bar. Then the script stalls: one of the three vault keys belongs to the absent director of the French Archives. When the president proposes asking France's commerce minister, Swiss astronomer Adolph Hirsch objects that the conference is international, not French, and will deal only with the foreign minister. Diplomacy produces the key. At 1:30 p.m. prototype M, in a velvet-lined brass cylinder, and kilogram K under triple bell jars go into the vault with their metal "witnesses," behind doors needing three separately held keys.
M was "manifestly in France and yet not in France, religiously redolent and yet stridently rational, absolutely material and yet completely abstract." In an age when "family, country, church" became "family, country, science", M and K were emblems of the Third Republic: buried in specificity, risen in universality. French papers noted with "patriotic satisfaction" that after the "disaster of 1870" foreigners conceded French precision.
Conventions multiplied because systems collided: at expositions, at colonial borders, at railway junctions where trains smashed into each other. They were "patches at the ragged fronts" where telegraph, electric and railway networks met. When a challenger disputed the new bars' fidelity to the old Archives meter, Förster ruled that the base of the metric system could not depend on "uncertain and incessant corrections": M now ruled alone.
Convention: one word, three resonances
- The Convention of Year II: the revolutionary assembly that introduced decimal space and time.
- A convention: an international treaty, the diplomatic tool France pushed hardest in the later nineteenth century, partly against British imperial power.
- Convention in general: a quantity or relation fixed by broad agreement.
- In sum: "a convention, fixed by convention, in the tradition of the Convention."
Time resists: the failures of Parisian clocks
Time would not lie in a vault. A French review of the early 1880s complained that every clock had its own "personality." Paris and Vienna in the late 1870s built pneumatic clock networks: steam plants pumped compressed air through underground pipes and pulses set clocks across the city; customers bought dials in showrooms.
- The 15-second delay. The pressure pulse took about 15 seconds to reach the network's far ends. By 1881 that discrepancy was visible to astronomers, bridge engineers and then the public.
- The fix. Engineers first shrugged (minute hands jump in whole steps), then offset the central clock by 15 seconds and fitted retarding counterweights to each clock according to its distance from the centre. Transmission delay corrected by distance: a pneumatic rehearsal of the signal-delay correction Poincaré would later theorize.
Two things stand out: time-awareness had become acute (before the nineteenth century, clocks often had no minute hand), and even sound-speed transmission time was seen as a defect to correct.
Le Verrier's electric plan
Urbain Le Verrier, director of the Paris Observatory and co-discoverer of Neptune, proposed in 1875 to unify Parisian time electrically, extending the Observatory's internal order to the city and boosting French clockmaking. Cornu and Fizeau backed it: "a perfect Polytechnique project." The commission included Gustave Tresca (who supervised the meter bars), physicist Edmond Becquerel (father of Henri), architect Eugène Viollet-le-Duc (church clocks posed structural problems) and Observatory astronomer Charles Wolf, designer of its electric time system.
- The design (reported January 1879, after Le Verrier's death). A dozen secondary clocks linked by cable to the Observatory's mother clock, each set to run 15 seconds per day fast; an electromagnetic pulse slowed each pendulum into step; each secondary then reset others, giving 40 public clocks right to the minute.
- The exclusion. Railway clocks were left out for fear of liability in accidents; the commission trusted the companies would "spontaneously" follow, so that "the unification of time in Paris will be the unification of time in all of France." Galison calls this a "temporal hall of mirrors."
- The failure. Ice in the sewers cut the wires; clocks ran free, "hawking their own peculiar times." The commission and chief engineer traded accusations over patents. By spring 1883 not one secondary-linked public clock received current. In 1889 the Observatory director asked that any mention of "observatory time" be erased from the city's clocks and worried about foreigners seeing the mess at the 1900 Exposition.
Galison's contrast is sharp: France triumphed with the meter but conceded, as French authors admitted, that London, "home of the twelve-inch foot," led in standardizing time. His Parisian evidence is rich, but the comparison with London and Berlin relies more on French self-criticism than on parallel archival depth; the contrast may be overdrawn.
Times, trains and telegraphs
The General Review of Railroads (1888) began its discussion of time with the meter, "one of the most glorious creations of French genius," and complained that rail and telegraph had created "normal or national hours" with a new confusion like the old one of weights and measures.
- Three times in a French station. Local city time; Paris mean time on courtyard and waiting-room clocks; platform clocks running 3–5 minutes slow to give passengers a margin.
- Brest and Nice. Railway time ran 27 minutes ahead of Brest and 20 minutes behind Nice.
- Elsewhere. Russia unified time in January 1888; Sweden set clocks one hour from Greenwich; Germany "staggered" under multiple Land times.
- North America. On the railways' April 1883 decision, zones from "Intercolonial time" in the east to "Pacific time" in the west, based on Greenwich; the Revue admired even the beauty of American colour time maps.
The Revue's moral: in America it was railroaders who told the October 1884 Washington scientists that further change was "useless and inopportune," and only when railways and telegraphs adopt time reform will other administrations follow. Time reform should not be left to geographers, geodesists and astronomers. When Poincaré joined the Bureau des Longitudes in 1893, clocks in Paris ran with stunning precision in the Observatory and appalling inaccuracy in the streets; the French were proud of their principled, mathematical approach and keen to extend the meter's rationality to time.
America had no Le Verrier. Its synchronization was "always critically opalescent": town councils, railway superintendents, telegraphers, societies, diplomats and observatories competing, so that "astronomers sold time like businessmen and railroaders spoke to the universal order of nature." The American science the French most admired was the Coast and Geodetic Survey, mapping a fast-growing country, and mapping meant longitude, which meant time.
Longitude by clock, and its failure
Local time comes from the sky: the moment a star crosses the north-south line. Compare it with the time at a reference point (Washington, Paris, Greenwich); three hours earlier than Washington means one-eighth of the globe to the west. So the map-maker's question was always distant simultaneity: what time is it now at the reference point?
- Chronometers. Carry clocks set to home time. Temperature, damp and motion made this one of the hardest machine problems ever, consuming the life of John Harrison in the eighteenth century and still unsolved in the nineteenth.
- Lunar distances. Use the moon against the stars as a sky clock; its position was hard to compute and hard to measure except at rare occultations.
The chronometer expeditions, 1849–51. To fix the longitude gap between America and Europe, the Coast Survey ran 7 voyages each way from August 1849, each with 12 chronometers; in 1851 37 chronometers rode five sailings from Liverpool and two from Cambridge, Massachusetts. After 93 chronometers crossed, astronomers claimed the transatlantic time difference to 1/20 second. But the westward and eastward results disagreed, impossibly. Cold mid-ocean temperatures probably slowed the clocks, pushing Cambridge too far west on British maps and Liverpool too far west on American ones. More tenders and better compensators only produced more conflicting data.
The "American method"
The telegraph cracked the problem. In summer 1848, Harvard Observatory and Coast Survey astronomers tested it. Sears Walker wondered whether they could transmit a star transit directly; William Cranch Bond proposed making a clock escapement act as a telegraph key, so its ticks would sound all along the line, and recording them on a smoothly turning cylinder far away. Comparing marks from the local clock with marks from the distant clock gives the time difference by measuring distances on paper, not by stopping a clock as a star crosses a spider-thread reticle.
By the end of 1851 lines ran Cambridge to Bangor, Maine, with a relay to Halifax, Nova Scotia. Bond was gratified that England called it the "American method" and that the Astronomer Royal had laid wires at Greenwich to adopt it.
Railways adopt telegraphic time
- 5 November 1849. New England railways agree to run on "true time at Boston as given by William Bond & Son, No. 26 Congress Street."
- 12 August 1853. Two Providence and Worcester trains collide at a blind curve; 14 die; newspapers blame a conductor with a slow watch. Another bad-watch crash days earlier adds pressure, and telegraphic time becomes standard railway technology.
- 1852. The Astronomer Royal sends electric signals over telegraph lines to public clocks and railways in Britain.
- Late 1853. Harvard's director boasts the "beats of our clock" can be made audible at any telegraph station "within several hundred miles."
Through the 1860s and 1870s synchronized time spread into stations, neighbourhoods and churches like gas, water or electric power, "a circulating fluid of modern urban life," with one difference: it depended directly on scientists.
Marketing time: Harvard's time business
Harvard Observatory soon leased a telegraph line to send star-determined time to Boston. By 1871 it charged for the service; in 1875 it netted $2,400; by 1877 over $8,000 had gone into instruments, clocks and lines, and graduate student Leonard Waldo was put in charge.
- The product. A Frodsham master clock corrected daily at 10:00 a.m. to a fraction of a second; pulses every 2 seconds all day, skipping each minute's 58th second and, every fifth minute, seconds 34–60, for identification; backup from clockmakers William Bond & Sons; a remotely dropped copper time ball atop a Boston building for citizens and navigators.
- The marketing. With Western Union's encouragement, a pamphlet to 100 New England towns; target customers were railways, jewelers, clockmakers, manufacturers and private watch owners.
- The demand. A Rhode Island cardboard manufacturer wrote on behalf of Providence citizens "having fine watches": was the signal Cambridge time or Boston time, corrected for the longitude difference? Cardboard needs no split-second timing; precision had become a value in itself.
- The clock room (completed 2 March 1877). A sealed basement room about 10 ft × 4 ft 2 in × 9 ft 10 in with double walls, a felt-sealed safe door, three clocks on marble slabs on brick piers, read through thick glass because human presence disturbed accuracy.
Waldo reported that the community had been "unconsciously educated" to uniform time: subscribers detected and commented on errors of a fraction of a second. Trains and fire bells never needed 0.2 rather than 0.4 seconds; a modernist sensibility of precision outran every practical need, and Waldo both pushed and was pushed by it.
Hartford and the borders of time dominions
Losing Hartford, 1878–80. In July 1878 Hartford worthy Charles Teske sought Harvard time, having won over the fire department (whose noon bell set public time) and the mayor. But "we have here in Hartford all sorts of time and everybody claims that his time is correct"; rousing interest was "like awakening the dead." Waldo saw the real constraint: "the Rail Road regulates the time of towns along its line," and the New York–Hartford line put Hartford in New York's time radius, while New London, Providence and Springfield fell in Cambridge's. Cambridge lost: the fire department bought a marine chronometer, "good enough by those who are ignorant of the minuteness of your Time Signal," Teske wrote bitterly. Two years later Connecticut legally adopted New York meridian time from Yale Observatory, and railways were obliged to forward electric time, mount coordinated station clocks and pass time to intersecting lines.
A New York & New England Railroad manager fumed that a "ridiculous law" forced his Boston-time trains onto New York time at the state line. Cultures of precision varied: by the end of 1877 Chicago's Dearborn Observatory fed half a dozen jewelers, four railways and the Board of Trade, keeping its signal "within half a second" and calling a second "close enough for all practical purposes." Harvard's mania came from longitude work, where surveyors wanted tenths or thousandths of a second, and from Boston's high-end watch culture: "The culture of precision ticked sooner and louder in Boston than in Chicago."
| Anglo-American | French | |
|---|---|---|
| Who drives time unification | Railways, telegraph firms, observatories selling time | State astronomers, Polytechnicians |
| Observatory and railway | Wires pulled straight into stations | Railways deliberately excluded (1879) |
| Justification | Commerce, safety, convenience | Completing the Age of Reason |
| Result by 1883 | Working zones and city time | Failed Paris network; rail on Paris time |
The American Metrological Society and the reformers
Frederick A. P. Barnard, president of Columbia University, founded the American Metrological Society; on 30 December 1873 it adopted a constitution to bring weights, measures and moneys into "simple commensurability." Its targets included the zero of longitude, units of force, pressure, temperature and electricity. It was French rationalism "through a commercial lens," aimed at Congress, states, schools and railway yards.
- Cleveland Abbe, meteorologist with the U.S. Signal Service, joined after his 1874 amateur aurora observers could not agree on a common time; he was promptly made chair of the time committee and lobbied Congress (1882) and congresses in Venice (1881) and Rome (1883).
- The 1879 programme. Local astronomical time had already given way to a mishmash of railway times. Step one: collapse 75 railway meridians into 3 zones (4, 5, 6 hours west of Greenwich). Better still: one national "Railroad and Telegraph Time" six hours west of Greenwich, displayed in every public building, prison, mint, lighthouse, post office and postal car, legal for all purposes "on and after July 4th, 1880." Here Americans modelled civil time on train time, the exact reverse of Le Verrier's hope that trains would copy astronomers.
- William F. Allen, 33, secretary of the General Time Convention of railway officials and editor of the Travelers' Official Railway Guide, "the time shuffler of all time shufflers," hesitated in June 1879 between scientists' continental vision and passengers' local habits. Abbe: "Abolish old times is the watchword."
- Charles Dowd, a schoolteacher, petitioned Allen unsuccessfully with his own zone plan.
Sandford Fleming's cosmopolitan time
Sandford Fleming, Canadian railway engineer (maritime lines, the Pacific railway plan, Toronto's Palace of Industry, the beaver on Canada's first stamp, later the transpacific cable), thought at imperial scale. From 1876 he mocked chronometry "inherited from a remote antiquity": a traveller from London to India passes through Paris, Rome, Brindisi and Alexandria times and new times daily at sea, and in Bombay local time splits from railway time pinned to Madras.
Fleming's terrestrial time (1876, 1879)
- 24 lettered meridians. The prime meridian, then A at 15°, B at 30°, through X at 345°.
- The earth as a clock. An imaginary clock at the earth's centre with its hour hand fixed toward the sun; when meridian C crosses the line to the sun it is C o'clock everywhere.
- Simultaneous everywhere. If Big Ben reads C:30:27, so do clocks in Times Square and Tokyo, with the telegraph "affording the means of securing perfect synchronism."
- Local comfort. Watches with rotatable faces putting local noon at the top, or twin dials for local and terrestrial time.
- Scale. About 400,000 miles of telegraph and 95,000 miles of rail in Europe and Asia, with a million miles of rail expected.
Nations, Fleming wrote, were measuring the day in two sets of twelve "as if they had recently emerged from barbarism." His 1879 version pressed for a prime meridian at Greenwich, after reviewing failed rivals: Cape Verde; Mercator's Corvo in the Azores (where the compass pointed true north); Cadiz (Spain); Pulkovo (Russia); Naples (Italy); Cape Lizard (Britain); Rio (Brazil); and Charles Piazzi Smyth's Great Pyramid. Greenwich won on shipping: nearly three-quarters of world shipping set its course by it, and its antimeridian ran through the Bering Strait, almost all water. Abbe enlisted telegraph and railway companies (March 1880); Barnard displayed Fleming's watches.
Opposition from three directions
| Opponent | Position | Argument |
|---|---|---|
| Piazzi Smyth, Scottish Astronomer Royal | Mystical anti-metric | The inch and cubit link to the Great Pyramid's sacred metrology; metric reform is "fatal to national interests" |
| George Airy, Astronomer Royal (July 1881) | Practical localism | Ask "what the mass of people want"; cosmopolitan time is for sailors "and there its utility ends"; Greenwich too far east even for England; "I do not imagine that it will ever be received" |
| Rear Admiral John Rodgers, U.S. Naval Observatory (June 1881) | Scientific nationalism | "The Sun is the national clock"; why should 50 million Americans take the time of 30 million English? Scientists "sometimes overestimate their functions" |
Barnard soothed Fleming by calling Airy "opinionated" (recalling his blunder in the Neptune priority dispute), won over Colonel Clarke of the Ordnance Survey, and lost the chair of the Law of Nations time committee to William Thomson (Lord Kelvin), who had not even been told he was on it and needed to be "educated." Barnard also had to rein in Fleming's scattershot polemics: "I esteem it bad policy to evince uncertainty on the eve of battle."
1883: the railways vote time into being
Reformers worked at clashing scales: terrestrial time (Barnard, Fleming), national observatory time (France, Britain, U.S. Naval Observatory), with railways and cities as wild cards. In late 1882 Allen endorsed one-hour zones. Congress resolved to ask the president to call an international conference with three U.S. Delegates; the Post Office adopted a common time; Barnard lobbied President Chester A. Arthur and Secretary of State Frederick T. Frelinghuysen; the civil engineers and the AAAS backed reform. A brief southern rebellion with its own system was crushed.
At the General Time Convention in St. Louis, 11 April 1883, Allen denounced the "Hard Scrabble" system of 50 interlacing standards as "an abomination and a nuisance," and showed two maps: a clean three-colour zone map and a quilt of current chaos (too complicated to mass-print, so it cost twice as much). The zero could be anywhere; claiming Washington or the "Hub of the Universe" (Boston) was local vanity, since "the villages of Gum Tree and of Hard Scrabble are on the same meridian." "For all ordinary business transactions one standard is as good as another, so long as all agree to use it."
Railroad trains are the great educators and monitors of the people in teaching and maintaining exact time.William F. Allen, 1883
Allen's experiment. Cut a city off from rail and telegraph for a month, and on the first night secretly set every clock and watch half an hour fast or slow. Allen bet that not one person in a thousand would notice. The punchline: for most people, time was no longer read from the sun but received from the network; without trains and wires, the temporal order of the world would drift from its moorings.
Allen closed with a parable: a small sect resolved, first, "That the saints should govern the earth"; second, "That we are the saints." The opposition was not a defence of "God's true time," which almost nobody invoked. Everyone accepted railway-telegraph simultaneity; by September 1883 a guide listed 47 lines on New York time, 36 on Chicago's, 33 on Philadelphia's. Critics attacked observatories fattening on time sales ("the meat upon which these star-gazers feed"), almanac publishers worried about sunrise tables, and most disputed only where the lines should run.
- 70,000 miles of road lined up behind reform a week before the 11 October 1883 convention in Chicago's Grand Hotel; Boston's telegram ("the city, the railroads, and the observatory only await affirmative vote") drew applause.
- Votes by mile of track: 27,781 member miles plus 51,260 non-member miles = 79,041 miles for Greenwich-based zones; 1,714 against.
- Switch date: noon, 18 November 1883, "the day of two noons."
- New York: Mayor Franklin Edson approved on 19 October 1883; city time became that of the 75th meridian, a few minutes west of City Hall. The Naval Observatory dropped its national-time ambitions.
New York's mayor and aldermen now talked like philosophers: local time "suits the convenience of the people... Because all agree to use it"; time is "conventional and arbitrary" and should follow the people's interests. By 1883 the conventionality of simultaneity was common talk in New York as in Paris, hammered into rails and wires before any physicist made it a principle. Barnard to Fleming, 22 October 1883: "This settles the question forever, for this hemisphere... Paris will probably never consent to use Greenwich time."
Time into space: mapping the world by cable
Paris observatory time in 1884 was not about trains. The Observatory was no business, and French astronomy never sanctified empire with natural theology as some British counterparts did. For Polytechnicians, decimalization, unification and rationalization were Enlightenment ideals tied to national recovery after 1870 and to the secular, progressive rationality of the Third Republic. Their home was the Bureau des Longitudes, by 1884 chiefly engaged in mapping the world electrically.
When Poincaré wrote in 1898 that simultaneity is a convention, he had been a member of the Bureau since 4 January 1893 (until his death in 1912); he was elected president in September 1899, and again in 1909 and 1910, issuing reports, leading commissions and overseeing longitude operations. The Bureau's vast "theory machine" for turning signal exchange into longitude is the key to his reconception of time.
Why the old methods failed
In 1866 the Bureau sent six parties to the Americas, Africa, China, Japan and the Pacific and Indian Ocean islands to fix secondary reference points by lunar culminations. The moon crosses the star field about once in 30 days while the stars wheel round once a day, so any error in placing the moon is multiplied about thirty-fold in time, and errors at sea killed sailors. Eclipses (Columbus used one; an American steamer went to Labrador on 18 July 1860 to compare with Spain) and occultations (four Pleiades stars; Venus on 24 April 1860, watched at Fredericton and Liverpool) each produced a new number.
- Mapping as war. In the Civil War the Coast Survey worked with Union admirals in North Carolina and on the Mississippi; George Dean reduced telegraphic data for positions of southern military sites; topographers plotted rebel works round Charleston and Savannah and marched with Sherman. After the war the survey had telegraphic positions of almost every major town from Calais, Maine to New Orleans; Benjamin Gould led its telegraphic longitude work.
- The transatlantic impasse. Old results disagreed by more than 4 seconds, the newest and best among the most discordant; chronometric and astronomical methods differed by an irreducible 3.5 seconds, though the law required the best possible transatlantic longitude.
The Atlantic cable and Gould's longitude, 1866
- August 1857 First attempts to lay a North Atlantic cable; repeated breaks.
- June 1858 Fleet leaves Plymouth; a nine-day gale three days out; one sailor driven mad.
- 6 August 1858 First signals pass, then the cable fails; cabling halts during the Civil War.
- July 1865 The Great Eastern, five times larger than any other ship, sails from Valentia Island; after 1,200 miles the cable is lost.
- 27 July 1866 A new cable from Heart's Content, Newfoundland to Valentia works; survey time signals begin at once.
- 14 October 1866 First star transits at Valentia, 3:00 a.m.
- 24 October 1866 Gould's first transatlantic time signal; four more exchanges follow.
- 11 December 1866 A sharp frost insulates the faulty land line into Calais, Maine; the pulse finally runs through.
- End of 1866 Dean's team reaches Boston with the Harvard–Greenwich longitude difference.
Observatory at cable's end. Gould sailed 12 September 1866, carted his crates 42 miles across Ireland on a spring-cushioned cart, and was refused a land-line connection by the British cable company (fear of lightning). So he built an 11 × 23 ft shack bolted to six buried stones beside the telegraph house at Foilhommerum Bay, "remote from any other dwelling-house except the unattractive cabins of the peasantry." In seven weeks under a "peculiarly unastronomical sky" there were four days without rain and one clear night; Dean in Newfoundland saw nothing at all. The battery was a percussion cap with a morsel of zinc and a drop of acidulated water. Valentia cabled "GOULD," Newfoundland answered "DEAN," then half-second pulses with five-second gaps. The signal was too weak for the drum, so they used William Thomson's mirror galvanometer: a tiny magnet on a suspended mirror, twisted by the cable current, sliding a spot of kerosene lamplight across damp paper.
The worldwide polygon of simultaneity
The French then laid a line from Brest via St. Pierre to Duxbury, Massachusetts, and Dean planned a joint check with the French navy. Closed loops became the test of accuracy: (Brest–Paris) + (Paris–Greenwich) + (Greenwich–Brest) = 0, and it did.
- Francis Green, U.S. Navy (1873–84). From spring 1873, in the side-wheeler Gettysburg, Green fixed Panama, Cuba, Jamaica, Puerto Rico and more; from 1877 he used the London–Lisbon–Recife cable to map South America's east coast from Pará to Buenos Aires, settling disputes such as a 30-second (eight-mile) discrepancy at Fort Villegagnon in Rio's bay. The signal ran Greenwich, Land's End, 828 miles of cable to Carcavellos, Lisbon Observatory, across the Atlantic and over the Brazilian Naval Arsenal's walls to a Thomson galvanometer. St. Vincent at Porto Grande was "merely a heap of cinders."
- Pedro II's clock (July 1878). Emperor Pedro II of Brazil, fresh from a world tour (the U.S. In 1876, Troy with Schliemann, the Holy Sepulchre, the Paris Academy, Victor Hugo, lunch with Queen Victoria), came to Green's ramshackle observatory to watch European time arrive by wire.
- The portable observatory. A scraped north line, a brick pier, a carried marble slab, a brass transit instrument; an 8 × 8 ft wooden hut assembled by two sailors in an hour, canvas roof, crammed with clocks, keys and a drum or galvanometer.
- West coast, 1883–84. Galveston, yellow-fever Vera Cruz, Salina Cruz–Valparaíso cable; quarantines; Peru under Chilean military occupation; the U.S. Minister S. L. Phelps secured the occupying admiral's help; rain in Paita for the first time in seven years turned it to "fetid mud." They sailed home 5 April 1884.
Octave de Bernardières, a new kind of naval officer trained by the astronomers at Montsouris (and co-author of a 336-page report on the Berlin–Paris longitude), raced the Americans. From 18 January 1883 he seized three good nights linking Valparaíso to Panama and Paris; just after, the Panama cable snapped. Result: the flagpole over Valparaíso's stock exchange stood 4 h 55 min 54.11 s earlier than the Montsouris time room. On 7 April 1884, via astronomer Hervé Faye, he urged the Academy to build "an immense geodesic network that would encompass the entire globe." Cables now crossed the Andes at 12,000 feet; with the new Lima–Panama line and routes via Buenos Aires and Cape Verde, the circuit totalled some 20,000 miles of copper.
- 8 vertices: Paris, Greenwich, Washington, Panama, Valparaíso, Buenos Aires, Rio de Janeiro, Lisbon; reckoned both ways, the polygon closed to within 150 yards.
- Spokes: Americans mapping India; the French in a bamboo hut at Haiphong.
- Bordeaux Observatory (Annales, 1890) existed to set ships' chronometers; on 19 November 1881 it fixed itself 11 min 26.444 s west of Paris, ± 0.008 s.
- By 1880: 90,000 miles of mostly British submarine cable, a £90 million machine binding every inhabited continent.
"For through copper circuits flowed time, and through time the partition of the worldmap in an age of empires." A universal first meridian would put one nation's capital at the centre of every map.
Washington, October 1884: the battle over neutrality
In August 1882 President Arthur and Congress resolved to call a conference. In October 1883 the International Geodetic Conference in Rome heard Adolphe Hirsch argue that nature picks out a prime latitude (the equator, set by the earth's spin) but no prime meridian; even the wandering magnetic pole cannot. The choice is "purely practical and conventional." Postal and telegraph unions, the meter, electrical standards, intellectual-property and wartime conventions all pointed the same way. Rome recommended Greenwich, with the date change at the antimeridian. The Washington conference opened 1 October 1884 at the State Department under Frelinghuysen, who renounced any U.S. Claim. Poincaré read the proceedings and later quoted them verbatim.
| France | Britain and United States |
|---|---|
| Lefaivre: politicians should be "philosophers and cosmopolitans," not mere Rome "experts" | Rutherfurd: meridian through Greenwich's transit instrument |
| Janssen: Paris is as well wired as Greenwich; Richelieu's Ferro was statutorily 20° west of Paris, "Paris disguised" | Evans: it must bisect a great observatory (Paris, Berlin, Greenwich, Washington), not a mountain or strait |
| A meridian should be "geographical and impersonal," not chosen by "the largest number of clients" | Sampson: 70% of shipping uses Greenwich; scientifically any meridian will do |
| Neutral options: Bering Strait (divides Old and New Worlds) or the Azores (cables nearby) | Rutherfurd: Paris Observatory sits in a tremor-shaken city and should move |
| "Let us place the crown on the brow of science" | Adams: "call things by their right names"; sentiment and amour propre will stall everything |
- Janssen's pedigree. During the 1870 siege of Paris he escaped by balloon in violent winds to observe an eclipse in Algeria. He invoked French hydrography, the Connaissance des Temps, and the meter's victory over the pied de Roi: rational science should trump royal trade. France would sacrifice if others did; any agreement "cannot protect only one contracting party." Anyplace neutral; anyplace but Greenwich.
- Old grudges. John Couch Adams had clashed with the French over Neptune and over Laplace's lunar theory; Janssen reached back to Newton versus Leibniz on the calculus: "The love of glory is one of the noblest motives of men... We must also be careful not to permit it to produce bad fruits."
- "Longitude is longitude." General Strachey rejected separate geographical and astronomical longitudes; Janssen: a chemist's weighing differs from a merchant's, "yet it is still a weight."
- What is neutral? Cleveland Abbe: a "neutral" longitude is "a myth, a fancy, a piece of poetry"; if Russia retook Alaska or America bought half of Siberia, the Bering Strait would not be cosmopolitan; only the stars are neutral.
- Tonnage. Fleming: Greenwich guided 72% of shipping tonnage, Paris 8%; he offered a meridian 180° from Greenwich in the "uninhabited" Pacific, a proxy fooling no one, least of all the inventors of Ferro.
Science appears here only as the humble vassal of the powers of the day to consecrate and crown their success.Albert Lefaivre, Washington, 1884
The neutral meridian motion won only France, Brazil and San Domingo; 21 nations voted no. Lefaivre: Greenwich's only merit was the interests grouped round it, "material superiorities, commercial preponderances"; "all empires have fallen" and this one would too, and Britain and America would not even reciprocate by taking the meter. William Thomson agreed with Janssen in all but his disdain: it was a "business arrangement." Greenwich passed with 21 for, San Domingo against, France and Brazil abstaining.
Counting the votes. The conference record lists 25 nations, and the Greenwich resolution passed 22–1–2 (San Domingo against; France and Brazil abstaining). Galison gives 21 in favour here and "twenty-two countries" in his introduction. More substantively, Galison's framing of the conference as French reason versus Anglo-American commerce follows the French delegates' own rhetoric; British and American participants also argued from scientific practice (telegraphic connectivity, existing charts), and France itself kept Paris Mean Time legally until 1911.
The day, the clock, and decimal time
- Allen's asymptote. Fresh from his railway victory, W. F. Allen told the delegates electricity might let "the pendulum of a single centrally located clock, beating seconds," regulate every city on earth.
- When does the day begin? Some wanted the Rome antimeridian (for Gregorian dates); astronomers wanted noon so nights would not split across dates; the Ottoman delegate kept both heure à la franque (midnight) and heure à la turque (from sunrise) for "reasons of a national and religious character."
- Decimal time. Defeated everywhere, the French made a last stand. In Year II the Convention had decreed 10-day décades, 10-hour days and the right angle in 100 parts; Laplace used it in Celestial Mechanics; public resistance was massive and Napoleon killed it in his deal with the Church. Janssen argued the Revolution failed because it "did violence to the habits of daily life"; this time decimal time would apply only where useful, in science.
In France, from meter to longitude to time, conventions were bound to the legacy of the Convention. Reading Washington as a step on an inevitable march toward rational standards misses the "fluctuating, contingent, opalescent" character of synchronization, and its constant crossing between the pragmatic and the philosophical.
Poincaré's Maps
Galison sets Poincaré inside the Bureau des Longitudes in the years 1893–1906: chairing the commission to decimalize time, reading reports from longitude expeditions in Senegal and Ecuador, and wrestling with a Paris–Greenwich discrepancy. The telegraphic surveyors' routine rule, transmission time = half the difference of the two apparent longitudes, is exactly the rule Poincaré made philosophical in "The Measure of Time" (1898) and physical in his 1900 reinterpretation of Lorentz's local time. Poincaré's conventional simultaneity was not a metaphor: it was the Bureau's daily practice, raised to philosophy and then to physics, while he kept the ether and a "true" time behind the apparent one.
After Washington: Greenwich, Germany and a bomb
On 9 March 1885 Janssen told the Academy that the Americans had packed the meeting with small allied states, and that France's neutral meridian remained "the impartial, scientific, and definitive solution." Others joined the dissent: in 1889–90 the Abbé Tondini de Quarenghi, for the Bologna Academy, campaigned to move the prime meridian to Jerusalem, centre of three continents and sanctuary of three religions.
Moltke: unified time for mobilization
Germany had no quarrel with Greenwich; its problem was internal disunity. Field Marshal Helmuth von Moltke had preached railways since 1843 ("a few million on the completion of our railways is far more profitably employed than on our new fortresses"); by autumn 1867 he claimed he could mass 360,000 men in three weeks and 430,000 in four. After 1870–71 both sides agreed that his precision-synchronized trains had destroyed the Second Empire. The General Staff rehearsed moving 3 million soldiers in 100,000 rail cars. In 1889 the military asked the Reichstag for standard time; the politicians refused.
The Reichstag, 16 March 1891. Moltke, a hero before whom men stood silent (he died about a month later), spoke in his scratchy voice. Germany had five times: Berlin (north Germany and Saxony), Munich (Bavaria), Stuttgart (Württemberg), Karlsruhe (Baden) and Ludwigshafen (Rhine Palatinate), "a ruin which has remained standing out of the once splintered condition of Germany." For travellers an inconvenience; for railways and troop mobilization a grave practical difficulty. He proposed a standard on the 15th meridian (about 50 miles east of the Brandenburg Gate), with all local time "swept away"; science wanted even more, "a world time, based upon the meridian of Greenwich." Factories and farms could shift opening hours (open the gates at 6:29 in March if you like). "Sehr wahr," came the cry. Germany adopted Central European Time in 1893, and much of Europe followed.
Greenwich Park, 15 February 1894
French anarchist Martial Bourdin took a ticket from Westminster Bridge to Greenwich. Two observatory assistants heard a sharp explosion ("That is dynamite! Spot the time") and logged it at 4:51. Bourdin was found dying below the observatory, his hand blown off. Anarchists suspected a police setup; others linked it to the bombing of the Chamber of Deputies (December 1893) and a Paris café three days earlier. Joseph Conrad's The Secret Agent (1907) fixed the image: an attack on "learning, science," with "the shocking senselessness of gratuitous blasphemy," because "the blowing up of the first meridian is bound to raise a howl of execration."
Lallemand's case for Greenwich
Even in France some backed Greenwich. Charles Lallemand, Bureau member and Poincaré's ally, rejected a single universal time (no Japanese would live by Greenwich's hour) but praised the Americans' "admirable practical sense of Business' men" for inventing time zones, a compromise uniting universal and local time.
- Speed of victory (1897). In just 10 years zones had conquered nearly the whole civilized world; in Europe only France, Spain and Portugal held out.
- The cost to France. A mere 9 minutes 21 seconds of delay would bring France into line.
- Date purgatory. Between the antimeridians of Paris and Greenwich lay a 250-mile equatorial strip where the date was ambiguous: 31 December 1899 or 1 January 1900, depending on your map.
- Neutrality answered. The 24-hour zone system was itself neutral, and nine-tenths of sailors already used Greenwich; Paris had long counted from Ferro; and even the "neutral" meter quickly became a copy of a Paris bar. French maps need not be scrapped; overprint new lines in another colour. "All men of progress" should back time reform.
Decimalizing time: Poincaré's commission
The Washington conference had "expressed the hope" that astronomical and nautical days would both begin at midnight (astronomers began theirs at noon so as not to split a night of observing). In 1894, prompted by the Canadian Institute and the Astronomical Society of Toronto, the minister asked the Bureau's opinion. Poincaré weighed inconveniences. Changing dates mid-observation inconveniences the astronomer, but the sailor already faces worse with a million distractions and shoals ahead; let astronomers write "night of 11–12." The serious objection: changing would break comparability of the Nautical Almanac, Connaissance des Temps and Berliner Jahrbuch. Only an international accord would do; until then France should wait.
In February 1897 the Bureau's president set up a commission, with Poincaré as secretary, to ask why the Convention of 1793 failed to decimalize time and the circle, and whether the objections still held.
- Bouquet de la Grye, hydrographer: the meter succeeded because it ended real incoherence among local measures; decimal time failed because everyone already shared the same time units, so reform "sinned precisely by their lack of unity."
- Maurice Loewy, Bureau president: the Revolution lacked foreign partners; dreamed of full decimalization but accepted a compromise.
- General de la Noë: the army geographical service (and Belgium's) already used decimal angles.
- Alfred Cornu: the French had lost the duodecimal habit; the British engineers, raised on inches and feet, could not see decimals' advantages.
- Noblemaire, Paris-Lyon-Méditerranée railway: changing the 24-hour day is doomed, but decimal hours simplify journey arithmetic.
- Commander Guyou, navy: divide the circle into 400; let science use decimals and the public keep its habits.
- Henri Becquerel, Physical Society president: hands off the second.
The railwayman's example: leave at 8:45 a.m., arrive 3:24 p.m.; in decimal hours 15.40 − 8.75 = 6.65 h, with no a.m./p.m. Confusion. The Naval School commandant thought physicists, who had adapted to centimetres, grams and seconds, would adjust easily.
The physicists revolt
Becquerel was not amused (April 1897). The CGS system had been adopted internationally only in 1881 and decreed for all State business in April 1896; its cornerstone was the sexagesimal second (1/3,600 hour). A decimal second (1/10,000 hour) would change every mechanical and electrical unit, and with them the practical ampere, volt, ohm and watt, and every instrument: "What a huge expenditure without any profit, neither for science, nor for industry!"
Poincaré's table
On 7 April 1897 Poincaré answered not with argument but with a table of conversion factors (ignoring powers of ten), choosing the system whose arithmetic is least inconvenient.
| Circle divided into | Factor for angles above a full circle | Factor to convert arc to time (hours) | Factor to convert to 360° |
|---|---|---|---|
| 100 | 1 | 24 | 36 |
| 200 | 2 | 12 | 18 |
| 400 | 4 | 6 | 9 |
| 240 | 24 | 1 | 15 |
| 360 | 36 | 15 | 1 |
Only the 400-part circle avoids every two-digit multiplication: "objectively" the least inconvenient. Tabula rasa, he said, the best system would be 400 parts (100 grads per quadrant, 100 km per grad), but "we cannot break completely with the past," given public repugnance and scientists' own traditions. Final compromise: keep the 24-hour day, divide the hour into 100 minutes and the minute into 100 seconds, and adopt the grad (1/400 circle). It passed by voice vote and later 12 to 3.
| Camp | Position |
|---|---|
| Poincaré, Loewy, majority | 24 h day; decimal hour; circle in 400 grads; any decimal system beats 8h25m40s |
| De la Grye | Circle in 240, so each hour = 10 units of rotation |
| Physicists, sea captains, telegraphers | Keep 360° with decimal subdivisions; keep the second |
| Faye | Circle in 100 |
| Hydrographic service | Reprinting 3,000 charts and scrapping every sextant and chronometer is ruinous |
| Cornu | Decimalize the day, not the artificial hour |
Cornu versus Poincaré in print
In their journal L'Éclairage Électrique (late 1897), Cornu attacked his protégé's compromise as the work of "an unstable and divided majority." The meter had met a triple test: clear benefit to a majority, no great harm to others, and public enthusiasm. Time met none; it was already unified across countries. The natural unit was the day: 1/100 day is about a quarter hour, and 1/100,000 day = 0.864 s, close to a heartbeat. Decimal fractions of an hour are unnatural: 36 s, 3.6 s, 0.36 s, too long or too short for any pendulum. The body (pulse about 1 s, reaction about 0.1 s), the clocks and the sun all favoured the second. "Interests trump logic."
Poincaré answered as a reforming engineer. The point was to abolish monstrosities like 8h25m40s or 25°17′14″; any decimal system would do. Industrial measurement only compares one thing with another; the shopkeeper measuring cloth never recalls that the meter is a forty-millionth of the meridian. Only the absolute units suffer.
Poincaré's limit case. Suppose decimal time spreads so completely that not one clock reading old seconds survives anywhere. Then the rare physicist determining the absolute ohm must multiply by 36. "And for them to avoid this operation we are daily to impose tedious calculations on thousands of mariners along with millions of schoolchildren?" Count how often we fix a position at sea or add two times, against how often we measure absolute resistance. The punchline is pure Poincaré: convenience, measured by use, decides the convention; let the English worry about "the natural theology of absolutes."
July 1900: facing foreign hostility, the Foreign Ministry declined to back the reform, and "after a hundred years, the revolutionary struggle to rationalize time expired." The zone fight went on: on 25 April 1899 the polemicist Sarrauton attacked the Boudenoot bill (delay Paris time 9 min 21 s: "France towed by England" and the collapse of the metric system) and backed the Gouzy–Delaune bill: 100-minute hours, 100-second minutes, 24 zones, longitude from the Bering Strait from 1 January 1900. It never passed. France adopted the Greenwich meridian on 9 March 1911.
Just before "The Measure of Time" appeared in January 1898, the words that define Poincaré's philosophy (convention, convenience, continuity with the past, simplicity) were being fought over by navigators, electricians, astronomers and railwaymen in a commission he ran. Physical, conventional and coordinated time "converged in whirling reformist debate that was thoroughly abstract and yet altogether concrete."
Of time and maps: Senegal
In 1885 the Navy asked the Bureau to fix Dakar and Saint-Louis in "our colony" of Senegal; the report appeared in 1897, reaching Poincaré just before he wrote "The Measure of Time." Governor Louis Faidherbe had violently annexed Wolof and Cayor lands by 1865; a Saint-Louis–Dakar railway was under construction by 1885; resistance continued to the eve of the First World War. Exact coordinates at Dakar were to anchor a French cable down West Africa to the Cape. Longitude, track, telegraph and time reinforced each other.
- 1 hour a night: the astronomers' rented slot on the British Cadiz–Tenerife cable.
- 2.5 million francs a year: what France paid British companies for just the Tenerife–Senegal, West African, Saigon–Haiphong and Obock–Perim cables.
- Blocked French cables: Réunion–Madagascar–Djibouti–Tunis (1886), French West Indies–New York (1887), Brest–Haiti (1892–93).
- 260 km of wire from Dakar to Saint-Louis across Cayor, often cut; dew so heavy that where 5 insulators sufficed in France, 70 failed.
- 41 min 12.207 s: final San Fernando–Saint-Louis longitude difference.
- 0.326 s: difference between the two apparent directions, "double the time taken for the transmission of the electrical wave plus other errors."
The 1895 expedition. Relayed by astronomer Cecilio Pujazón at San Fernando, the team sailed on the Orénoque and reached Dakar on 15 March 1895. Governor Seignac-Lesseps put troops at their disposal; they ate in the mess, the chief astronomer complaining of no decent hotel. The pendulum went into the concrete blockhouse of the fort guarding the coal park; the meridian telescope stood outside, the collimator on the gun-battery parapet. At Saint-Louis, "the political centre of our colony," a governor's edict barred movement during observations (footsteps disturbed the pendulum); the few locals allowed by went barefoot, without carts. Observations ran 26 March–11 April; signals to Dakar 29 April, San Fernando 2 May. Problems: a north-south river blocked the meridian sight; "marauders" stole the collimating spike almost daily; Spanish land lines were jammed by election traffic. Then came corrections for temperature, observers' personal equations, and the galvanometer mirror's sluggishness.
Cables were weapons. British companies employed no foreigners and evidently read French traffic to Dakar and Saigon before the French did. At the 1885 Cable Convention Britain insisted on belligerents' right to cut enemy lines, convenient for the owner of 24 of the world's 30 cable ships. In the 1898 Fashoda crisis, as Captain Marchand staked a claim on the Nile, British troops stayed in touch with London while the French cable "inexplicably went silent"; it came back to life only when the governor at Dakar loaded the cannon.
Where is Paris? The Paris–Greenwich longitude
- July 1825 Rival observers synchronize clocks by rockets fired over the Channel.
- 1854 Le Verrier and Airy by telegraph: 9 min 20.51 s.
- 1872 U.S. Coast Survey campaign: 9 min 20.97 s, almost half a second more.
- 1888 Joint campaign (Astronomer Royal, General Perrier, Admiral Mouchez): paired English and French observers side by side, shared line, shared battery-powered lamp, piers 20 ft apart at Montsouris. English result 9 min 20.85 s; French 9 min 21.06 s.
- 1892 Repeated: still a fifth of a second apart; again the French find Paris farther from London.
- 1897–98 Under Loewy and then Cornu, the Paris Observatory and the International Geodetic Conference demand a definitive exchange.
The two great observatories that claimed to map the world could not agree on their own separation to a fifth of a second. Conventions were not confined to geometry or philosophy; they were everywhere the Bureau looked.
"The Measure of Time" read literally
When Poincaré proposed in 1898 that simultaneity is a convention, calculating Paris time from London, Berlin or Dakar was not an abstract problem; it was the most pressing issue of the Bureau's map-making mission. He knew astronomical events (transits of Venus, lunar occultations, eclipses of Jupiter's moons) had long been overtaken by the telegraph as the best standard of simultaneity. He had taught the theory of telegraphic transmission from at least 1892–93, reviewed measurements of signal speed in iron and copper wire, and in 1904 lectured at the École Supérieure de Télégraphie on the telegrapher's equation and undersea cables.
The surveyors' rule
Surveyors had always corrected for observer reaction time and instrument inertia (the galvanometer mirror's swing), the "personal error in noting." They also measured transit time across the ocean: on the 1866 Atlantic cable, 0.314 s (25 October), 0.280 s (5 November), 0.248 s (6 November).
Transmission-time correction (worked with an exaggerated 5-minute delay)
- Setup. West station is truly 1 hour west of East.
- East → West. East sends at its noon; West receives at 11:05 its time and, uncorrected, reads a difference of −55 min: apparent = real + transit.
- West → East. West sends at its noon (13:00 East); East receives at 13:05, reading −65 min: apparent = real − transit.
- Longitude. Real difference = ½ (E→W + W→E): the transit times cancel.
- Transit time. τ = ½ (E→W apparent − W→E apparent).
- Hidden convention. It assumes the signal speed is the same in both directions, exactly the assumption Einstein later built into his definition.
The rule was "part of the procedural mantra of every long-distance surveying team in the world." The Paris–Berlin report (de Bernardières, Captain Le Clerc, Loewy, 1882) listed among its errors the "non-instantaneity of the transmission of the electric flux," assumed equal speeds both ways, scripted even the greetings between stations, and carried a section headed "Conventions Relative to the Exchange of Signals." The 1890 Bordeaux report lists "the delay S of the electrical transmission." For Poincaré not to have known this, Galison says, he would have had to ignore every Bureau report for years: "This begs credulity."
- ~1/50 s: light's travel time over 6,000 km.
- ~1/10 s: an electrical pulse over the same length of undersea copper cable, several times slower than light.
- 0.001 s: the precision to which longitudes were claimed.
- ~0.5 km: east-west error at the equator per second of time error.
Calinon's circle
In 1897, exactly as Poincaré was immersed in decimal time, Auguste Calinon published a 30-page Study of the Various Quantities of Mathematics. Does a vessel of water take equally long to empty each time? Answering presupposes an independent time measure, which raises the same question: what calibrates the calibrator? Poincaré quoted him: to suppose the earth's rotation is constant "is to suppose that one knows how to measure time." Calinon added that time divisions were historically chosen for utility, and scientists pick the clock motion that makes planetary laws as simple as possible: duration is "a variable, chosen... Because it lends itself particularly well to the expression of simple laws."
What the 1898 essay was, and was not
- It was the crossing point: the measurement of time is a convention tied to real procedure; only Poincaré stood both in the Montsouris clock room and in the Revue de métaphysique et de morale, turning a routine correction into a philosophical redefinition.
- It was not physics. Not one word on reference frames, electrodynamics or Lorentz's electron theory. Like his geodesists, Poincaré treated the delay as one correction among others, wedged "between the inertial hesitation of an oscillating mirror and the psychophysiology of the observers."
- Its conservatism. The "multitude of little rules" were meant to preserve the simplicity of Newton's laws, for which no simpler alternative could be imagined; conventions are "the fruit of an unconscious opportunism."
- Anonymity. No one claimed authorship of the surveyors' rule; it lay "below the threshold of signed patents or authored scientific papers," part of the sea of anonymous technical knowledge.
How strong is the inference? Galison shows that delay corrections were routine in Bureau reports, and that Poincaré invoked telegraphic longitude in 1898. He does not produce a document in which Poincaré cites a specific longitude report as his source; the case rests on institutional proximity ("this begs credulity"). Most historians accept the link for Poincaré, whose essay explicitly asks us to "watch [the longitude savants] at work." Galison also dates Poincaré's membership of the Bureau to 4 January 1893 in one place and calls 1892 the year of his election in another.
Mission to Quito, 1899–1907
The next great Bureau project was Ecuador, with Poincaré as scientific secretary. At the 1889 Exposition an American geodesist had asked for a new measurement of a meridian arc near the equator: if the earth bulges at the equator (as Newton predicted), a 5° arc there is shorter than one near the poles; the task was now to fix the oblateness with modern precision. Ecuador's president agreed, but General Eloy Alfaro's Liberal Revolution (from 5 June 1895) delayed it. At Stuttgart on 7 October 1898 the Americans pressed again and the British demanded France say what it would do. If the U.S. Coast Survey took the job, Poincaré said, "the honor of our country would be ravished."
- Reconnaissance. The education minister offered 20,000 francs; an avant-garde left Bordeaux 26 May 1899 and covered 3,500 km of mountains in four months, returning on the last day of the century. Meanwhile Britain censored cables during the Boer War (17 November 1899), and on 15 December 1899 the French cabinet approved an imperial cable network of 100 million francs.
- Poincaré's appeal (23 July 1900). France should not abandon a position where "our fathers hoisted... The intellectual flag of France," the arc first measured by Godin, Bouguer and La Condamine from April 1735. The fieldwork needed men who could endure exhaustion and "obtain obedience" from "half-civilized servants": officers of the army's geographical service. The Academy would control the science by examining notebooks.
- The design (25 July 1900). Three bases measured with the instruments used for the French meridian; astronomer François Gonnessiat of Lyon at Quito making simultaneous observations; funding from an anonymous donor, later revealed as Prince Roland Bonaparte. Telegraph lines Quito–Guayaquil (with relay) and Quito–north station; if relays added error, Poincaré would boost battery power and cut them out. Guayaquil linked by undersea cable through North America to the world net.
Life on the arc. Captains Maurain and Lallemand left on 9 December 1900, the day before Poincaré lectured at Leiden. By April 1902: 120 mules, 40 Indian porters, 6 Ecuadorian officers; the bimetallic measuring bar carried on a man's back; dew-swollen micrometer threads made sighting nearly impossible from 6 to 9 a.m.; dust storms at 11. In 1903: Lieutenant Perrier spent three months in cloud at Mirador, 12,000 ft, managing one of twenty-one measurements in fifteen days; snow squalls tore roofs off at Tacunga; Lallemand fell into a crevasse on Cotopaxi; the weather was blamed on the Martinique eruption. Locals, believing the markers signalled buried gold, dug them up: in 1904 stations were destroyed 18 times, forcing remeasurement of 360 pairs of points. Informants' "visibility" reports proved "not exact" (they had never climbed so high, and "visibility" meant enough to walk). Lallemand caught yellow fever. After eight years the expedition returned in 1907.
The colonial texture of these expeditions (barefoot locals, "marauders," "half-civilized servants," treasure-hunting "natives") comes straight from the French reports; Galison quotes it without much comment on the people whose land was being gridded.
Philosophy, 1900: the four conventions
Days after the Quito report, on 2 August 1900, Poincaré addressed the International Congress of Philosophy: are the principles of mechanics alterable? The French treated mechanics as deductive; the British as experimental. Which parts are experimental, which mathematical, which conventional?
Poincaré's four theses on mechanics (1900)
- No absolute space. We conceive only relative motion, yet state mechanics as if absolute space existed.
- No absolute time. That two durations are equal "has no meaning, and can only acquire a meaning by a convention."
- No intuition of distant simultaneity. We lack direct intuition even of two events in different places being simultaneous ("I have explained this in... 'Mesure du Temps'").
- Geometry as language. Is Euclidean geometry "only a kind of convention of language"?
Absolutes existed before mechanics no more than "the French language can be logically said to have existed before the truths which are expressed in French." Are the laws of acceleration and composition of forces arbitrary? "Conventions, yes; arbitrary, no": they rest on the experiments that led the founders to adopt them. Experiments are raw materials; theory aims "to increase the output of the scientific machine." Experiment cannot simply refute a principle; at worst it shows the principle approximate, "and we know that already." The section became one of the most cited passages of Science and Hypothesis (1902).
At the International Congress of Mathematicians (Paris, August 1900) he again sided with intuition: Felix Klein, studying whether a Riemann surface admits a function with given singularities, replaced it by a metal surface of varying conductivity connected to a battery: "the current must pass." Not rigorous, but "a kind of moral certainty"; a logician "would have rejected with horror such a conception." Machine-thinking in pure mathematics.
Lorentz's ether theory and "local time"
H. A. Lorentz had helped define the new profession of theoretical physicist and made Maxwell usable outside Britain. Against British reductions of everything to ether vortices and strains, his world had two kinds of thing: fields (states of a motionless ether) and charged particles moving through it.
The ether problem and Lorentz's devices
- Dragged ether? If matter dragged the ether, earth's motion would be undetectable; but Fizeau's light-through-flowing-water experiment showed at most partial drag.
- Fixed ether? Then earth's motion through it should show. Michelson's interferometer (1881) split a beam into perpendicular arms; an ether wind should shift the fringes on rotation. They did not budge.
- Contraction (1892). Lorentz posited that bodies moving through the ether contract along their motion by just the factor needed to hide the wind.
- Local time (1895). For a body moving at speed v, define t_local = t_true − vx/c²; in terms of it, the equations for the moving body look like those for a body at rest. A mathematical fiction, used only because it made the formal result work.
In his 1899 Sorbonne course Poincaré did not link local time to signal synchronization; the correction for the earth's motion was only about three-billionths of a second per kilometre, so he proposed to ignore it. Meanwhile, as Bureau president in 1899, he was immersed in clock coordination: on 23 June 1899 he asked Astronomer Royal William Christie to restart the Paris–Greenwich comparison; Christie (3 August) asked for time, suggested a plumb-line versus spirit-level levelling error, rejected French Army hints that British clocks were at fault, and proposed repeating the procedure between two piers within each observatory to isolate errors from the Channel cable; Poincaré (9 August) asked for full reduction methods and promised to open the French books.
Leiden, 10 December 1900: local time becomes clock time
At the Lorentz Festschrift in Leiden, Poincaré criticized the theory's violation of action and reaction: a cannon recoils at once, but in Lorentz's theory an atom acts on the ether and the receiving matter reacts only later, while the ether seems too insubstantial to carry momentum. Yet "good theories are flexible... If a theory reveals to us certain true relations, it can dress itself in a thousand diverse forms." Then, without citing his 1898 essay, he made the decisive move.
The local time t′ is the time indicated by watches set in this manner.Poincaré, Leiden, 1900
Observers set their watches by optical signals, correct for transmission time, but, ignoring their own motion, assume the signals travel at the same speed both ways and cross them A→B and B→A.
Poincaré's derivation (1900), in words
- Frame. Clocks A and B ride a platform moving at v through the ether.
- Headwind and tailwind. A→B light moves at c − v relative to the platform; B→A at c + v.
- Naive coordination fails. The observers, ignorant of their motion, assume equal speeds and apply the surveyors' crossing rule.
- Result. Their clocks end up offset by −vx/c² relative to true ether time: exactly Lorentz's local time.
- Meaning. Local time is no fiction; it is what real clocks synchronized by the telegraphers' procedure in a moving frame actually show.
At Leiden the same procedure that Poincaré knew as longitude-finder and as philosopher entered physics: a triple intersection of geodesy, philosophy and electrodynamics in one act of clock synchronization.
Lorentz's reply of 20 January 1901 conceded the action-reaction problem (forces on a rigid, immovable ether are "mathematical fictions"; an infinitely massive ether "seems to me pretty artificial") but said nothing about the reinterpretation of local time. In January 1902 Poincaré nominated Lorentz for the Nobel Prize, praising his "ingenious invention of 'reduced time'": events in different places can seem simultaneous when they are not, as if one clock lagged, and no experiment could reveal it. Theories may die, but Lorentz's revealed "relations... That would be so even if electrons didn't exist," truths that "will survive beyond the theory." Lorentz won in 1902 (with Zeeman).
A triple conjunction
By the end of 1902 Poincaré had faced time coordination for a decade from three sides.
This was neither "generalizing" from physics to philosophy nor "applying" philosophy to physics: a new concept of time was shown to fit the rules of three different games, and its working in all three gave it singular weight.
Relations are what is real
Poincaré's outlook was Third Republic progressivism: an engaged, "machinic" reason could improve any map, geographical or scientific, ideally by setting positions against each other and picking the simplest relations. Relations (Newton's, Lorentz's, mathematics') were real, not objects of sense or Platonic forms. "To say the ether exists is to say there is a natural kinship between all the optical phenomena," no less real than saying a body exists because its colour, taste and smell hang together.
Dreyfus: another technical fix
The bordereau. On 4 September 1899, during Alfred Dreyfus's second trial, Poincaré wrote (read by proxy) that no one "with a solid scientific education" could credit the prosecution's statistics; Dreyfus was reconvicted, then pardoned. In May 1903 he told students there was an antinomy between serving truth and being strong enough to act ("On both sides, most were driven by noble intentions"), and warned that "the day when France has no more soldiers, but only thinkers, Wilhelm II will be the master of Europe... Without the soldiers of Year II, what would have remained of the Revolution?" In April 1904, asked by the court, he and two Observatory colleagues remeasured the handwriting with astronomical instruments and redid every probability. Their 100-page report of 2 August 1904 demolished Alphonse Bertillon's claim that the word "intérêt" was traced on a military-map grid: the supposed regularities were arbitrary, changing letter by letter. The court exonerated Dreyfus (1906). Galison's point: reasoning through machines and calculation, Poincaré defused a crisis, as with his decimal table.
St. Louis, 1904: crisis without rupture
At the International Congress of Arts and Science at the St. Louis World's Fair (September 1904) Poincaré diagnosed "a serious crisis" in physics, adding that "the patient will not die."
Poincaré's three phases of physics
- Phase 1: central forces. Newton's inverse-square attraction between every grain of sand and every star, varied for other forces.
- Phase 2: principles. When industrial-scale processes defeated detailed mechanisms, physics rose to principles describing whole processes: conservation of mass, of energy, least action, action and reaction, relativity; Maxwell's ether-based electromagnetism was its triumph. It grew from phase 1: "the mathematical physics of our fathers" taught us to recognize the principles "under the different clothing with which they disguise themselves."
- Phase 3: crisis. Radium, "that great revolutionary," threatens every principle: energy (spontaneous radioactive emission), mass (velocity-dependent mass of fast electrons), action-reaction (Lorentz's lamp recoils before the absorber), relativity (rescued only by local time and contraction).
- Remedy. "The frames are not broken, because they are elastic." "Let us take the theory of Lorentz, turn it in every direction; modify it little by little, and perhaps everything will work out." Giving up relativity would sacrifice "a precious arm."
Of Lorentz's many hypotheses, "his most ingenious idea was that of local time." Observers who cross their signals in a moving frame get transmission times that differ in the two directions, so their watches mark local, not true, time; but "that is of little importance, because we don't have any way to perceive it": every phenomenon at A is delayed by the same amount as A's watch, so "there is no means of knowing if he is at rest or in absolute movement."
1904–06: the dynamics of the electron
- May 1904. Lorentz modified contraction and local time so that the equations of electrodynamics became exactly, not approximately, the same in every inertial frame moving through the ether.
- 5 June 1905. Poincaré summarized his results to the Academy: a theory covering optical experiments and the new fast-electron experiments inside Lorentz's "elastic frame."
- 1906. "On the Dynamics of the Electron" published in full: clock synchronization yields Lorentz's improved local time, and the equations of physics take the same form in all frames.
- 1906–07 and 1908. Poincaré taught how improved local time and contraction make the earth's motion through the ether undetectable; apparent transmission time is proportional to apparent distance; "it is impossible to escape the impression that the principle of relativity is a general law of Nature."
Poincaré's "new mechanics" kept the ether as the intuitive frame and kept the split between true time (ether rest frame) and apparent or local time, while matching the relativity principle exactly. It was "the modernism of an abstract machine": improve the machinery of physics, but within the elastic frame built by the fathers.
Both men feared the laboratory. Poincaré warned at the start of the 1906 paper that new data could endanger the theory; on 8 March 1906 Lorentz wrote that Walter Kaufmann's electron-deflection results contradicted his flattening electron, "I am therefore at the end of my Latin." In the end the greatest threat came not from Kaufmann's magnets but from "an unknown twenty-six-year-old physicist at the Bern patent office," who threw aside electron structure, the ether and the true/apparent distinction and put the coordinated clock in as "the capstone of the relativistic arch."
Priority and its limits. Poincaré by 1905–06 had the Lorentz transformations (his name for them), proved they form a group, stated the relativity principle as a universal law, noticed the invariant x² + y² + z² − c²t², and sketched a Lorentz-invariant gravity. Some authors (most famously Edmund Whittaker in 1953) therefore credited relativity to Poincaré and Lorentz. Galison sides with the mainstream view: the mathematics largely coincided, but Poincaré kept the ether and a privileged true time, and never claimed Einstein's theory as his own (he did not cite Einstein, nor Einstein him). Galison also does not mention that Kaufmann's data were soon shown unreliable (Bucherer, 1908, and later analyses favoured the Lorentz–Einstein formula), so the experimental crisis that worried Lorentz was illusory.
Einstein's Clocks
Galison turns to Bern, 1902–1905: an unknown patent examiner, trained at the hands-on ETH, steeped in Mach, Pearson, Hume and Poincaré's Science and Hypothesis, schooled by Friedrich Haller to distrust every inventor, and surrounded by a Swiss boom in electrically coordinated clocks and their patents. In May 1905 a conversation with Michele Besso led him to time, and within weeks the clock-synchronization definition became the key that made his principled theory work. Einstein's clocks were at once philosophical, physical and technological: the procedure of a theory machine built by someone who spent his days taking real machines apart.
Switzerland's electric time
In June 1905 the contrast was stark. Poincaré, 51, Academician, professor, chair of commissions, author of 200+ technical papers and a best-selling philosophy (which Einstein had read). Einstein, 26, an unknown patent clerk in a walk-up flat in Bern. Switzerland was no colonial power, had no great longitudinal spread and came late to telegraph and rail; but once rails and wires arrived, clock synchronization took off in a nation for which precision timepieces were national pride and economic lifeline.
- Matthäus Hipp. Blacklisted in Württemberg for republican activity around 1848, Hipp built electrically maintained pendulums (a heavy free pendulum given an electromagnetic boost only when needed) far more regular than mechanical ones, and recording chronoscopes that transformed experimental psychology, measuring the speed of nerves, telegraphs and light with astronomer Adolphe Hirsch. More artisan-entrepreneur than savant, he founded telegraph and apparatus works in Bern, Neuchâtel and Zurich and built the first public electric clock network in Geneva (1861).
- Favarger. In 1889 the firm became A. De Peyer and A. Favarger et Cie; to 1908 it pushed mother clocks beyond observatories and railways to steeples and hotel wake-up clocks. Branching ever more clocks needed relays and amplifiers, and a flood of patents followed.
- Bern. On 1 August 1890 Bern's coordinated clocks started together; the press hailed a "Revolution in Clocks." Wilhelm Förster of Berlin sniffed that any city clock not right to the minute was "downright contemptuous of people."
Favarger's war on "time anarchy" (Paris, 1900)
At the International Congress on Chronometry at the 1900 Exposition, Albert Favarger, Hipp's successor, asked why electric time distribution lagged telegraphy and telephony.
Favarger's diagnosis and programme
- No "ami complaisant." Remote clocks lack the constant human attendant that steam engines, dynamos and telegraphs enjoy.
- Technician gap. The best engineers staff power and communications, not time.
- No public funding. Strange for a public that has made its own the adage "Time is money."
- Need. Exactitude and universality to the second; only electricity, not mechanical, hydraulic or pneumatic systems.
- Trains. At 100–200 km/h (55 m/s) every tick counts; "the nonautomatic system... Is the direct cause of the time anarchy that we must escape."
- Trust. "If even just one [clock] is lying one suspects the sincerity of them all"; security only when every clock shows "unanimity at the same time at the same instant."
- The last frontier. The International Bureau of Weights and Measures had conquered length and mass; time remained, to be won by an ever-widening electric network from an observatory-linked mother clock.
"Time anarchy" carried a charge: Peter Kropotkin's Memoirs of a Revolutionist (1898–99) told how a week with the Jura watchmakers, with their egalitarian relations and independence of thought, made him an anarchist. Favarger's concern was broader disintegration of personal and social regularity. Synchronization was "all at once political, profitable, and pragmatic."
Theory-machines: Einstein before the patent office
The chasing-light puzzle and ETH
At 16 (summer 1895) Einstein wrote on how the ether would deform under a magnetic field, and later recalled imagining riding alongside a light wave: he would see an electromagnetic field undulating in space but frozen in time, which no one had ever observed. Something was wrong; he did not know what.
He entered the ETH (founded 1855) after a failed first application. Galison contrasts the two schools:
| École Polytechnique (Poincaré, 1873) | ETH Zurich (Einstein, 1896) | |
|---|---|---|
| Ideal | Elite trained in high mathematics, applied later | Immediate link of theory and practice for industry |
| Mechanics | The mathematician's "factory stamp" | Set up by a mining engineer in 1855 |
| Experiment | Watched as demonstrations | Done by hand in a well-equipped lab |
| Theory of devices | Cornu writes an elegant theory of synchronized clocks | H. F. Weber lectures on heat conduction in granite and glass |
| Atoms | Proud agnosticism; balance believers and sceptics | Matter-of-fact: heat is molecular motion; compute the molecules |
By summer 1899 Einstein told Mileva Marić that material ether theories must go; ETH did not teach much Maxwell, so he taught himself from Heinrich Hertz, who had pared Maxwell to bare equations, demonstrated radio waves, and doubted that the "names" electricity and magnetism referred to anything substantial. Einstein: "The introduction of the name 'ether' into theories of electricity has led to the conception of a medium whose motion can be described, without... Being able to ascribe physical meaning to it." Electrodynamics should describe real charges moving through empty space. By about 1901 he had dropped even Lorentz's static, insubstantial ether and may already have been using the relativity principle. None of this yet touched time.
Outsider years, 1900–1902
- No job. Diploma in July 1900, then rejections, including a technical teaching post at Burgdorf; tutoring; work in thermodynamics and statistical mechanics and on light and matter.
- Defiance. "No one here at the Technikum is up to date in modern physics" (May 1901). He sent Paul Drude two objections to his electron theory; when Drude replied by citing an "(infallible)" colleague, Einstein wrote: "Authority gone to one's head is the greatest enemy of truth." The Wintelers accused him of "debauchery"; he shrugged.
- Contrast. Poincaré honoured his teachers, naming mathematical objects after them; Einstein was undeterred by teachers, rejections, or his mother's opposition to Mileva.
- The job. He applied on the 11 December 1901 advertisement for Engineer Class II at the Federal Office for Intellectual Property; on 19 December he exulted that director Friedrich Haller had personally invited him to apply. Supervisor Alfred Kleiner, "that bore," turned out "not quite as stupid as I thought" and urged him to publish his ideas on light in moving bodies with his proposed experiment.
- Impatience with the old. A 1885 ether book from Michele Besso "one would think... Came from antiquity." He and Besso pondered "the definition of absolute rest." Poincaré, by contrast, taught that old theories capture "true relations."
The Olympia Academy and the philosophers
From 5 February 1902 Einstein advertised private lessons in mathematics and physics at Gerechtigkeitsgasse 32, "trial lessons free." Students Maurice Solovine (from Romania) and Conrad Habicht became, with him, the Akademie Olympia: a page, half a page, sometimes one sentence could fuel days of argument.
The Olympia reading list and what it gave Einstein
- Ernst Mach, The Science of Mechanics (1883): Newton's "absolute, true, and mathematical time" is "an idle metaphysical conception"; time derives from motions of things (earth, pendulum).
- Karl Pearson, The Grammar of Science (1892): all clock time is ultimately earth-rotation time; "equal" intervals are a conceptual frame; absolute intervals "have no existence" in sense impression.
- Richard Avenarius, Critique of Pure Experience: scepticism toward what lies beyond experience.
- John Stuart Mill, Logic: caution against "the prevailing hypothesis of a luminiferous ether."
- Richard Dedekind on number; David Hume's Treatise, dismantling induction and causation.
- Poincaré, Science and Hypothesis (German edition 1904), which "engrossed us and held us spellbound for weeks" (Solovine).
The German footnote. Unlike the French and English editions, the German translation of Science and Hypothesis (by Ferdinand and Lisbeth Lindemann) printed a long excerpt from the conclusion of "The Measure of Time" as a footnote: no "direct intuition" of simultaneity, rules chosen for convenience, "all these rules and definitions are only the fruit of an unconscious opportunism." The translators added a genealogy of relative time (Locke, d'Alembert, Lobachevsky's "motion designed to measure other motions"). So the Olympians likely had Poincaré's conventional simultaneity in plain German in 1904.
Einstein later credited this reading. In his 1916 obituary of Mach he said Mach "came close to demanding a general theory of relativity," but lacking the stimulus of the constancy of light speed from Maxwell–Lorentz electrodynamics, "even Mach's critical urge did not suffice to raise a feeling for the need of a definition of simultaneity." To Moritz Schlick (1917): Mach, "and even more so Hume," whose Treatise he studied "shortly before discovering the theory of relativity"; "very possible that without these philosophical studies I would not have arrived at the solution."
Principles, not conventions
His first papers (1902–04) were on thermodynamics and statistical mechanics, whose two great principles (energy conserved, entropy never decreases) became his ideal of a principle theory. Poincaré's book praised physics of principles too, but the words did not travel intact.
- Lost in translation. French convention carried treaty, scientific agreement and the Convention of Year II; the German translators split it into Übereinkommen (accord) and konventionelle Festsetzung (conventional stipulation).
- Not mere definitions. Einstein never held, as Poincaré did, that principles survive purely by convenience; for him they supported physics: "the burning desire to grasp principles has caused me to spend most of my time on fruitless endeavors."
- Machines. He saw the patent office as a pleasure, not a burden: a colleague found it boring, "certain people find everything boring"; patent work "enforced many-sided thinking and also provided important stimuli to physical thought."
| Poincaré, Lorentz, Abraham | Einstein (1905) |
|---|---|
| Start from dynamics: forces that hold, flatten and contract electrons | Start from kinematics: principles plus clocks and rods |
| Constructive theory of matter in the ether | Principle theory, modelled on thermodynamics |
| Contraction caused by molecular forces | Contraction a consequence of redefined time |
| Ether kept as intuitive frame; true vs apparent time | No ether; only times read on synchronized clocks |
Before May 1905 Einstein acknowledged only the basics of Lorentz's 1895 theory and none of Poincaré's electrodynamics, and before entering the patent office he left "not the slightest clue" of interest in clocks, time or simultaneity.
Patent truths
Einstein started at the Bern patent office in June 1902: a job, and "a rigorous school for thinking machines." Director Friedrich Haller ordered: "When you pick up an application, think that anything the inventor says is wrong"; resist falling into "the inventor's way of thinking... You have to remain critically vigilant." For a young man already contemptuous of lazy authority, the order must have been gratifying.
- Learning to see drawings. Haller: "As a physicist you understand nothing about drawings." Einstein was made permanent in September 1903, but Haller held back promotion until he "fully mastered machine technology."
- Backing. When a patent agent cited a German patent-office ruling against Einstein's finding, Haller "took my side on all points."
- Promotion. In April 1906 he became technical expert, second class, "among the most esteemed experts at the office," as applications for electric time patents swelled.
- The walk. Every day from his flat on the Kramgasse to the office he passed the coordinated clock towers and electric street clocks branched to the central telegraph office, and walked beneath one of Bern's most famous clocks; the work, he told a friend, was "uncommonly diversified and there is much thinking to be done."
A cascade of coordinated-time patents
- 3–4 a year: Swiss electric-time patents 1890–1900 (2 in 1890, 6 in 1891).
- 8 in 1901, 10 in 1902, 6 in 1903, 14 in 1904, the peak year between 1889 and 1910; many more surely died under the examiners' gaze.
- ~12: technical experts at their wooden podiums alongside Einstein, who as technical expert third class handled chiefly electromagnetic and electromechanical patents.
- June 1902–October 1909: Einstein's patent years.
- Colonel David Perret: a receiver driven by a DC chronometric signal (patent 30351, 12 March 1904); "An Electric Installation for the Transmission of Time" (patent 27555, filed 5:30 p.m. 7 November 1902).
- Favarger: a receiver turning the mother clock's alternating current into one-way motion of a toothed wheel (filed 25 November 1902, issued 2 May 1905, later widely used).
- L. Agostinelli (Terni): a central clock "indicating the time simultaneously in several places separated from one another" (patent 29073, 1904).
- Siemens: "Motherclock Relay" (29980, 1904). Magneta (29325, filed 11 November 1903), maker of the remotely set clocks in the Federal Parliament. A Bulgarian mother-clock patent (1904).
- Other themes: remote alarms, electromagnetic regulation of pendulums, time over telephone and wireless, railway departure monitors, multi-zone displays, lightning protection, silent receivers. On 25 April 1905 at 6:15 p.m. an application arrived for an electromagnetically controlled pendulum bringing a distant clock into accord.
Machines at home and in the family
- Family business. Father Hermann and uncle Jakob Einstein built their firm on Jakob's patents for sensitive, clocklike electricity meters; one featured at the 1891 Frankfurt Electrotechnical Exhibition, a few pages from a backup mother-clock mechanism. A Jakob Einstein–Sebastian Kornprobst patent explicitly claimed use in clockwork.
- Surviving opinions. Most were routinely destroyed; two survive because of litigation. In 1907 he dismissed an AEG dynamo claim as "incorrectly, imprecisely, and unclearly prepared." In the Anschütz-Kaempfe v. Sperry gyrocompass case he showed an 1885 gyroscope could not move freely in three dimensions and so could not work in a ship's pitch and roll; Anschütz won. In 1926 Einstein contributed to an Anschütz patent and drew royalties until 1938; in 1915 the gyrocompass modelled his theory of the magnetic atom and the Einstein–de Haas experiment.
- Patent habits of mind. To Heinrich Zangger (July 1917) he complained that abstract passages were not worded "clearly and pointedly enough," blaming "the conventions at the Patent Office" for his exacting standards.
- The Maschinchen. With Conrad and Paul Habicht he traded ideas on relays, vacuum pumps, electrometers and circuit breakers (Paul asked whether to patent a helicopter-like flying machine). Einstein designed a sensitive electrometer for tiny voltages, fussing over gasoline for cleaning ebonite and mercury contacts that "spurt out as soon as one turns a bit too fast"; in 1907 he switched in one letter from relativity and Mercury's perihelion to the machine, and in 1908 built a test battery and electrometer at which Laub "wouldn't be able to suppress a smile."
Coordinated-clock patents were "right up his alley": devices that turn small electrical currents into high-precision rotary movement, bridging electricity and mechanics, exactly the kind of sensitive electromechanical system Einstein tinkered with all his life.
May 1905: "I've completely solved the problem"
Sometime in mid-May 1905 (on 15 May Einstein moved outside Bern's zone of unified time), he and Michele Besso had attacked the electrodynamics problem from every angle. "Then suddenly I understood where the key to this problem lay." Next day, skipping greetings: "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." By Besso's recollection Einstein pointed to one of Bern's synchronized clock towers and then to the single clock tower of Muri, the aristocratic suburb not yet tied to Bern's Normaluhr.
Days later he promised Conrad Habicht four papers; the fourth, "only a rough draft," was "an electrodynamics of moving bodies which employs a modification of the theory of space and time; the purely kinematic part of this paper will surely interest you." The paper was done by the end of June 1905: ten years of thought on light, ether and philosophy compressed into one short article.
- 1895 Aged 16: chasing a light wave; ether essay.
- 1896–1900 ETH; teaches himself Hertz and Maxwell.
- c. 1901 Drops the ether entirely; relativity principle likely in play.
- June 1902 Enters the Bern patent office.
- 1902–04 Olympia Academy reads Mach, Pearson, Hume, Poincaré (German edition 1904).
- 1904 Peak year of Swiss electric-time patents (14).
- Mid-May 1905 The Besso conversation: time is the key.
- End of June 1905 "On the Electrodynamics of Moving Bodies" completed.
- April 1906 Promoted to technical expert, second class.
Clocks as the capstone
Synchronization was not all of special relativity, but it was the crowning step. It did not enter, as for Poincaré, as the physical interpretation of Lorentz's fictional local time. Einstein began with rigid rods and added: "for such a mathematical description to have physical meaning, we first have to clarify what is to be understood by 'time'." With no ether rest frame to pick out a true time, every inertial frame's clock system is equally true.
Read this way, the 1905 paper shows not "Einstein philosopher-scientist" but "Einstein patent officer-scientist," refracting the metaphysics of relativity through some of the most symbolic mechanisms of modernity. Determining a train's 7 o'clock arrival with electromagnetically coordinated clocks was the practical problem that had racked Europe and North America for thirty years.
The straw man was a mother clock
Einstein's rejected scheme, a single clock at the origin with distant clocks timed by when signals reach it, is no abstract straw man. That branching, radial structure was the mother clock with secondary and tertiary dependents shown in wires, generators and clocks, "in patent after patent and book after book on timekeeping." Einstein kept the idea that time is defined by a realizable signal exchange, invoked the absolute speed of light, and cancelled the dependence on any privileged origin or ether rest frame.
| The technical system | Einstein's 1905 critique |
|---|---|
| A mother clock at a privileged centre | No privileged clock or origin |
| Secondaries set when the signal arrives | Correct for signal travel (half the round trip) |
| Correction for wire delay as a practical fix | Light speed c absolute and equal both ways by definition |
| One system at rest | Every inertial frame has its own equally valid clock system |
Who else had signal-defined local time?
- Poincaré (1900). Certainly read by Einstein before 17 May 1906, when he submitted a paper using its contents (though not local time). Whether he saw it before May 1905 is unknown; Einstein did not read French easily.
- Emil Cohn (November 1904), "Toward the Electrodynamics of Moving Systems," in German. A former experimentalist (student of a Strasbourg acoustics specialist) who spoke at the 1900 Lorentz Festschrift and probably heard Poincaré, Cohn defined local time by light-signal-coordinated clocks, rejected the ether for "the vacuum," and distrusted hypothetical quantities, rather like Einstein. Einstein had Cohn's article by 25 September 1907 (misspelling him "Kohn") and footnoted in December 1907: "The pertinent studies of E. Cohn also enter into consideration, but I did not make use of them here."
- Max Abraham (1905) explored signal-exchange simultaneity in his textbook, too late for Einstein's paper.
The thunderstorm and the dust. A meteorologist can explain how a storm formed from a rising column of unstable moist air, yet cannot say around which specks of dust the first raindrops condensed. Galison's seeds for Einstein's idea: a half-remembered line of Poincaré or Cohn, a patent application, a synchronized Bern street clock, a text argued over at the Olympia Academy. The punchline: playing prize committee to the dead is futile; what matters is that simultaneity talk thickened everywhere before 1905, and "Einstein snapped a junction into the circuit enabling the currents to cross."
How much did the patent office matter? This is Galison's most contested claim. Einstein's examiner files from 1902–1907 were destroyed, so there is no document showing he examined a clock-synchronization patent, and he never mentioned clock patents as a source. Einstein himself credited Hume, Mach and the Besso conversation. Critics (among them historians of relativity such as John Norton) argue that Einstein's path ran through electrodynamics and the light postulate, and that clocks were the obvious operational language for any physicist; Galison's evidence is environmental (patent statistics, clock towers, family business). Galison anticipates the objection by refusing to name a single cause, but the book's rhetoric ("Here was thinking through machines") sometimes runs ahead of its documents.
Einstein's own retrospective (1907)
In his 1907 review, Einstein said Lorentz's 1895 theory had shown only approximately that the earth's ether motion was undetectable; Michelson–Morley demanded more. "Surprisingly, it turned out that a sufficiently sharpened conception of time was all that was needed." Lorentz's 1904 local time solved the problem once "'local time' was redefined as 'time' in general," the time given by signal exchange. Only "the conception of a luminiferous ether... Does not fit." Fields are not "states of some substance" but "independently existing things," as freestanding as a block of lead, able to carry inertia.
After 1905 many ideas competed: the relativity principle, ether, light speed, velocity-dependent electron mass, electromagnetic mass. Einstein's articulation of time rose "haltingly, contentiously, but then powerfully" only around 1909; Ebenezer Cunningham in Cambridge, an enthusiast for the theory, did not see clocks as the main event.
Clocks first: Minkowski and spacetime
Hermann Minkowski of Göttingen (whose ETH lectures the young Einstein had ignored) had made his name applying geometry to number theory. He singled out Einstein's attack on time as the key, which with his own four-dimensional spacetime opened a new physics; in private drafts it was "mightily revolutionary." Time "as a concept unequivocally determined by phenomena, was deposed from its high seat"; there are only "times," plural.
The map nailed to a board. Mark an observatory on a map, nail the map through your house, and rotate it 45°. The horizontal separation A and vertical separation B both change (align house and observatory vertically and A vanishes), yet the true distance C does not. Minkowski showed that the Lorentz transformations are such a rotation in four dimensions, preserving a new distance: (spacetime interval)² = (time difference)² − (space difference)², in units where c = 1. Poincaré had found this invariant in 1906; Minkowski made it the foundation.
Henceforth space by itself and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve independence.Hermann Minkowski, Cologne, 21 September 1908
The Cologne lecture evoked Plato's cave: physicists who spoke of space and time separately watched only shadows; reality lay in the four-dimensional "absolute world," revealed by mathematicians. Einstein first resisted the formalism as needless complication, then found spacetime indispensable for gravitation; physicists flocked to Minkowski's idiom as an easier road into relativity. Poincaré had already (early 1907) dismissed the project: translation into four-dimensional geometry would be "great pains for little profit" and "always have the air of a translation." As so often, he "pointed out new lands, identified the passes to them, and then chose to make his own stand on terra cognita." Minkowski died suddenly in 1909.
"What is a clock?" (1910)
By a clock we understand any thing characterized by a phenomenon passing periodically through identical phases.Einstein, 1910
By the principle of sufficient reason, what happens in one period is identical with what happens in any other. Hands sweeping a dial or the oscillations of an atom will do: a clock need not be macroscopic. Written for physicists, this read at once as philosophy, and the Vienna Circle (Schlick, Carnap) and Hans Reichenbach in Berlin took it so.
Zurich, 16 January 1911
Before the Naturforschende Gesellschaft Einstein showed "the thing at its funniest": a clock, better a living organism, sent on a near-light-speed round trip returns scarcely aged while those at home have aged through generations. He now praised Minkowski's "highly interesting mathematical elaboration" and began representing physics as geometry in four dimensions.
Alfred Kleiner, his old examiner, praised the time concept as the uniquely Einsteinian innovation: we used to imagine "somewhere in the world there exists a clock that categorizes time," but time "depends on the states of motion." The relativity principle itself was only a "clarification." Kleiner mourned the ether: without it, "propagation in a medium which is not a medium," formulas without a "mental image." Einstein replied that the ether had real intuitive value in Maxwell's day, but once no one pictured it mechanically it became "nothing but a burdensome fiction."
Principles: probable pillars, not disguised definitions
Zurich exchanges. Rudolf Lämmel asked whether the relativity world picture was inevitable or merely expedient. Einstein: the principle "narrows the possibilities; it is not a model, just as the second law of thermodynamics is not a model"; it is "logically not necessary," only "made probable by experience." Ernst Meissner (ETH Privatdozent) urged that, after time, every physical concept must be revised for invariance; Einstein replied that exact experiments matter more than "brooding." Meissner: "You did not carry out any physical investigations in the laboratory, you were brooding instead." Einstein: yes, and see "the fine predicament in which that brooding about time has put us."
| Poincaré | Einstein | |
|---|---|---|
| Status of principles | "Conventions and definitions in disguise" | Pillars supporting knowledge |
| Source | Suggested by experience; kept for convenience | Made probable, never certain, by experience |
| If experience resists | Keep at great inconvenience, or amend | Test with the most exact experiments |
Recognition
- Max von Laue (1911): Einstein's "groundbreaking work," one radical critique of time, solved the riddle of Lorentz's real but undetectable ether.
- Max Planck (Columbia, 1909): the new time concept "surpasses in boldness everything achieved so far... non-Euclidean geometry is child's play in comparison."
- Einstein: the relativity of simultaneity is "the most important, and also the most controversial theorem" of the theory.
- Emil Cohn (1913), The Physical Aspect of Space and Time, illustrated the "Lorentz-Einstein Relativity Principle" (no Poincaré) with photographs of a wire-and-wood clock model: Strasbourg sends light at time 0 to Kehl; it returns at time 2; Kehl is correctly set if it read 1 on arrival. Einstein praised it in print.
Einstein's light clock (1913). Two parallel mirrors; a light pulse bouncing between them; each crossing is one tick. Seen from the ground, a light clock moving to the right traces a sawtooth: each diagonal path D is longer than the clock's own height h. A basketball player's dribble also traces a sawtooth, but spectators see the ball move faster along the diagonal. Light cannot: by postulate it moves at c in every frame. So each tick of the moving clock takes longer by the ratio D/h. The punchline: everything in a moving frame runs slow for the stationary observer, and nothing but clocks, mirrors and the light postulate was needed to show it.
Radio Eiffel: time through the ether
While Einstein worked at the patent office, time took to the air. The U.S. Navy tested low-power radio time signals from New Jersey in September 1903 and ordered broadcasts from Cape Cod and Norfolk in August 1904; Switzerland and France were busy in 1904. The director of La Nature reported Paris Observatory trials synchronizing distant clocks to 2–3 hundredths of a second and dreamed of time broadcast to ships and "the ordinary household." Radio-time patents began arriving in Einstein's office.
Poincaré, radio and French security
Poincaré became professor at the École Professionnelle Supérieure des Postes et Télégraphes in 1902 and wrote that year on wireless for the Bureau's yearbook, moving from Hertz's 1888 experiments to practical questions: reaching beyond the earth's curvature, penetrating fog, directional antennas, nickel-silver coatings, collision avoidance. Security loomed. A diplomat showed the French Colonial Union a lantern-slide map: a few short blue French cables against the red "spider's web" of British lines encircling the globe. Poincaré: optical and Hertzian telegraphy share an advantage, "in times of war, the enemy cannot interrupt communication," though broadcasts can be intercepted or jammed (he recalled Edison threatening to disturb competitors' experiments).
- 1903 Éleuthère Mascart asks Poincaré to help save the Eiffel Tower from demolition as a military asset.
- 1904 Captain Gustave-Auguste Ferrié and Gustave Eiffel get the tower designated a station of the French radio service.
- 1907 Ferrié's horse-drawn radio carts link French forces fighting in Morocco with commanders in France.
- May 1908 At Poincaré's behest the Bureau urges an Eiffel Tower time signal for longitude anywhere.
- Winter 1908 An interministerial radio commission is created with Poincaré as chair.
- 8 March 1909 Seventh meeting: Ferrié proposes rough signals (±0.5 s) for navigators and "special" signals (±0.01 s) for geodesy.
- 26 June 1909 The commission inspects the tower station: reception at Villejuif (8 km), Mehun (48 km), then 166 km; shipboard tests since 9 June; a flawless broadcast.
- 17 July 1909 Funding approved.
- 23 May 1910 After the Seine floods, regular time signals begin, heard from Canada to Senegal.
- 9 March 1911 France and Algeria shift clocks 9 min 21 s to Greenwich time.
The coincidence method for radio longitude
- Eiffel pips. The tower beats once every 1.01 s, starting at midnight Paris time: 12:00:00.00, 12:00:01.01, 12:00:02.02...
- Local beats. Your clock beats every whole second of local time.
- Count. Find the Eiffel pip that coincides with a local beat; if it is the 10th, Paris time is 12:00:10.10.
- Subtract. Local time of that beat minus Paris time gives the longitude difference, a vernier in time.
- Later refinement. Eiffel–Arlington exchanges corrected for the signal's transatlantic time of flight; in 1912 the Americans found the French "had already solved the problem": "Here was a beautiful solution."
Göttingen and Lille, 1909
In April 1909 at Göttingen, after five lectures in German, Poincaré switched to French for the "new mechanics." Newton's monument was shaken by "great destroyers": Max Abraham in the audience, and Lorentz. Relativity led to "apparent time, a very ingenious invention of the physicist Lorentz." Picture observers wanting clocks set to "a billionth of a second": A in Paris signals B in Berlin, "with a wireless if you want, to be altogether modern"; B, "too intelligent" to ignore the transit time, crosses signals. In Lille in August 1909 (receiving the Grande Médaille d'Or of the French Association for the Advancement of Science) he added a third hypothesis, Lorentz contraction, "much more difficult to accept": the earth flattened along its orbit by about 1/200,000,000 of its diameter, compensated exactly by local time so no observer can detect motion.
| Poincaré (1909) | Einstein |
|---|---|
| Keeps an ever less physical ether | Ether "superfluous," antiquated |
| Contraction a separate hypothesis | Contraction derived from the definition of time |
| "Local" and "apparent" vs "true" time and length | Each frame has its own time, all equally real |
| Must explain why motion cannot be detected | Nothing to explain |
| Observable predictions agree with relativity | Same predictions |
Centred systems and their opposite
Britain built no time transmitter: it installed receivers at Greenwich and reckoned no one would broadcast time in war. French ministers warned before the 1912 time and radio conferences that German and British transmitters outclassed France's in colonial Africa, and the commission returned again and again to "secret correspondence." Fourteenth-century villagers mounted clocks on bell towers to rule all who heard them; Poincaré rang the Eiffel Tower radio-clock through the ether to echo French scientific authority across the world. Lallemand hoped for an observatory consortium that would "avoid all appearances of a national time," with France unautocratically at the helm. On 19 November 1921 physicist Léon Bloch explained relativistic time to the Postes et Télégraphes school by the mother pendulum of the Paris Observatory and "the passage of a common luminous or hertzian signal."
From Eiffel to GPS: relativity as machine
Clock coordination was received as machinery: Cohn in Germany, experimenters rather than mathematicians in Cambridge, and John Wheeler, whose career ran from radio and explosives to wartime engineering, put a "universal machine" at the start of Spacetime Physics with Edwin Taylor.
- LORAN (MIT, Second World War) guided Allied ships across the Pacific by timing.
- Transit, Project 621B and Cold War successors served missile aiming from moving platforms and jungle navigation.
- GPS (1990s, $10 billion): 24 satellites with quartz, then cesium clocks, stable to about 50 ns per day, giving about 50 ft resolution. Each satellite broadcasts a pseudo-random code (some six thousand billion digits); the receiver matches it against its own copy; the offset gives time difference and, via c, distance. Four satellites are needed because the receiver's clock is not synchronized: three for position, one for time. Post-processed surveys reach millimetres, revealing continental drift and demanding coordinates tied to the planet's interior rather than "absolute continents."
- ~12,500 mph: orbital speed; special relativity slows satellite clocks by ~7 μs/day.
- ~11,000 miles up: weaker gravity speeds them by ~45 μs/day (general relativity).
- 38 μs/day net gain, against a budget of 50 ns/day.
- < 2 minutes: time to exceed the error budget without correction; ~6 miles of position error after one day.
- June 1977: the first cesium clock in orbit broadcast "raw" at sceptical engineers' insistence; it ran fast by almost exactly the predicted 38,000 ns per day; after 20 days the correcting synthesizer was switched on.
Time standards in 2026. GPS now flies about 31 operational satellites, with GPS III spacecraft replacing older blocks and adding civil signals such as L5; Europe's Galileo, China's BeiDou and Russia's GLONASS offer independent constellations with the same relativistic corrections built in. The leap second is being retired: the 27th CGPM (November 2022) resolved to let UT1 and UTC diverge by a larger tolerance by or before 2035, and WRC-23 endorsed this; no leap second has been inserted since end-2016, and a faster-spinning Earth even raised the prospect of a first negative one. Optical clocks (strontium, ytterbium, aluminium-ion) now reach uncertainties near 10⁻¹⁸, a hundred times better than cesium, so metrologists have a roadmap to redefine the SI second; the 2026 CGPM was the earliest possible decision point, and a redefinition around 2030 is widely seen as realistic. At this precision clocks become height sensors: chronometric (relativistic) geodesy measures gravitational potential differences equal to about 1 cm of height, and laboratory clocks have resolved time dilation across a millimetre. Einstein's synchronized clocks have become Poincaré's maps again.
Protest and the abstract-concrete
On 10 May 1992 two Santa Cruz activists disguised as Rockwell workers broke into the Seal Beach clean room and struck a NAVSTAR GPS satellite some 60 times with an axe, causing nearly $3 million damage; the "Harriet Tubman–Sarah Connor Brigade" pleaded guilty and served about two years. In 1996 the FBI reported that the Unabomber modelled himself on a character in Conrad's The Secret Agent, which he had read a dozen times. Synchronized clocks "have never stood far from the political order"; time coordination "is inevitably abstract-concrete."
The 1905 paper as a patent
Scholars have long noted how odd "On the Electrodynamics of Moving Bodies" looks: essentially no citations, few equations, no new experiments, much talk of simple processes. Annalen papers typically opened with an experimental problem or a calculation and bristled with references.
Patent conventions visible in the 1905 paper
- No citations. Patents prove originality by not situating themselves among prior work; in the ~50 Swiss electric-clock patents granted around 1905 there is not one footnote to another patent or paper.
- Representable by a model. Swiss law required the invention be "representable through a model," its unity defended, consequences "unambiguously laid out and lucidly ordered," understandable to technicians and specialists alike.
- Claims at the end. Einstein's 1905 papers end with experimental consequences; the relativity paper closes with sharp numbered statements like a patent's claims.
- Devices in arguments. From 1905 he described and sometimes drew devices as parts of theoretical arguments.
The patent-style reading is suggestive, not proven, as Galison concedes ("does not prove... Why Einstein did not cite others"). Other explanations fit: Einstein's isolation from the literature (he admitted knowing little of Lorentz's later work or Poincaré's), youthful confidence, and the short-paper conventions of the Annalen, which did publish some reference-light theoretical notes. The numbered "claims" also resemble standard summaries of results.
Moltke completed and subverted
At 16 Einstein had renounced German citizenship, chafing at Prussian "herd mentality"; at 26 he finished, in a sense, the old field marshal's project of Einheitszeit: time identified with timekeeping, distant simultaneity set by procedure, now extended beyond city, nation, empire and planet to an infinite universe. But he removed the element Moltke cared about most.
Einstein completed and subverted the master-clock project: by extending a unity of time conceived for German national unity to infinity, he removed Berlin as Zeitzentrum and "designed a machine that upended the very category of metaphysical centrality." Not even the vestigial centre of Poincaré's ether rest frame remained. "Einstein had constructed his abstract relativity machine out of a material world of synchronized clocks."
The Place of Time
Galison closes by setting the two men side by side: close in mathematics and in their light-signal clocks, far apart in what they thought physics was for. Poincaré's was a constructive, reforming modernism of convenient, true relations, keeping the ether and "apparent" time to repair an elastic frame; Einstein's a critical, austere modernism that tore out idle gears and wanted theory to mirror nature's symmetries. Simultaneity as signal exchange stood at a "triple intersection" of technology, philosophy and physics, and only a history that refuses to separate things from thoughts can see why.
Mutual silence
By December 1907 Einstein was no longer obscure: Minkowski asked for a reprint, Wilhelm Wien argued with him about faster-than-light signals, Planck and Laue corresponded, and Johannes Stark commissioned his review of relativity. That review cited Cohn, Lorentz, Bucherer, Kaufmann, Michelson and Morley and discussed local time; among 32 footnotes, Poincaré was absent. Missing too: Poincaré's corrected Lorentz transformations, his four-dimensional spacetime, his principled physics and his clock-synchronization reading of local time. "Not a trace."
Poincaré answered with silence for seven years, though Einstein was on every tongue. Each probably saw the other as beside the point: to Einstein, Poincaré was another senior physicist who could not grasp the end of the ether; to Poincaré, Einstein offered heuristic derivations of the Lorentz transformations while ignoring the real questions, ether and electron structure.
Yet Poincaré was no reactionary. He hailed a "new mechanics" at Göttingen and St. Louis. At Lille (1909) he added a wistful note: Newtonian mechanics seemed solid, "but scientific theories are like empires, and if Bossuet was here, he would no doubt find eloquent accents in which to denounce their fragility." Bossuet's 1681 Discourse on Universal History, written for the Dauphin, which Poincaré excerpted in a 1912 volume: Assyrians, Medes, Persians, Greeks and Romans fall one on another, "nothing solid among men." Poincaré now saw both his empires, the Newtonian and the French, as fragile.
Solvay, 1911: "No mechanics"
Brussels, late 1911. Einstein (32) and Poincaré (57) met for the first and only time at the first Solvay Conference. Maurice de Broglie recalled Poincaré asking, "What mechanics are you using in your reasoning?" Einstein: "No mechanics." For Poincaré, for whom physics was mechanics, old or new, and mechanics was the Polytechnician's "factory stamp," the answer was impossible. Einstein lectured on light quanta, calling quantum theory not "a theory in the ordinary sense" but a useful tool (in 1905 he had called light quanta "heuristic"). Poincaré's summary: the new research threatened not only mechanics but "the very concept of a natural law. Could we still express these laws in the form of differential equations?" And the same theory leaned on old mechanics and on hypotheses that negate it: with "two contradictory premises" anything can be proved. Einstein to a friend: Lorentz "a living work of art"; "Poincaré was simply negative in general... He showed little grasp of the situation."
| Shared ground | |
|---|---|
| Problem | Fascination since youth with the electrodynamics of moving bodies |
| Method | Theories built at the crossroads of technology, philosophy and physics |
| Mathematics | Lorentz's work; the group structure of the transformations |
| Principle | Relativity principle as a constitutive foundation |
| Time | Time in moving frames read from light-signal-synchronized clocks |
| But | Poincaré: world repair, adjustment, rewriting Lorentz. Einstein: tearing down was "a bracing pleasure" |
The recommendation and the last papers
One of the most original minds I have known.Poincaré on Einstein, November 1911
Back in Paris, Poincaré wrote to Pierre Weiss supporting Einstein for an ETH chair: Einstein adapts to new conceptions, is not attached to classical principles, and turns problems into predictions; most of his paths will be "dead ends," but one may be right, "and that suffices. It is just so that one must proceed. The role of mathematical physics is to pose questions properly, it is only experiment that can resolve them." The university that secures "this young master" will be "assured of drawing from it great honor."
- Last geometry (11 December 1911). Ill (he had had prostate surgery a few years before) and stuck on the three-body problem for two years, Poincaré asked the editor of the Palermo Circolo matematico to publish an incomplete paper full of figures, "particular solutions" rather than a general rule. It helped found topology; George D. Birkhoff soon proved its central conjecture (Poincaré's "last geometric theorem").
- "Space and Time," London, 4 May 1912. "The properties of time are therefore merely those of our clocks." The ether, long thinning, went unmentioned; the "principle of relativity according to Lorentz" replaced the old mechanical one; events simultaneous in one frame are not in another. Yet his conclusion was conventionalist: "Today some physicists want to adopt a new convention... They consider this new convention more convenient; that is all. And those who are not of this opinion can legitimately retain the old one... I believe, just between us, that this is what they shall do for a long time to come."
- Moral education (26 June 1912). As president of the French League of Moral Education, amid clerical battles and conflict with Germany in North Africa, he called discipline the only defence against "an abyss of sufferings": "Mankind is... Like an army at war." Build new structures "using the old bricks."
- Death. Surgery on 9 July 1912; death after an embolism on 17 July 1912. Galison's fitting monument: the Eiffel Tower's precision time signals, spreading "an expanding sphere of Hertzian light" across Africa and the Atlantic by techniques Poincaré had brought into geodesy, epistemology and physics.
Small inconsistencies. Galison says the Eiffel Tower "began radiating its precision time signal" later in 1912, but his own chapter 5 dates regular broadcasts to 23 May 1910; the 1912 date fits the refined scientific signals and the October 1912 International Time Conference in Paris, which created the Bureau International de l'Heure. He also calls Franz Ferdinand's assassin "Gavrilo Principe" (it is Princip). On the larger question, Galison's "no meeting of minds" story fits the record, though late in life (1955) Einstein conceded that Poincaré had gone further than Lorentz toward the new view.
Two modernisms
Against de Broglie's verdict
In 1954 Louis de Broglie lamented that Poincaré, "impossible to be closer to the thought of Einstein," failed to take "the decisive step" and so lost France the glory, because his mathematician's spirit was "a little too critical," treating theories as convenient choices among equivalents rather than following a physicist's intuition. Galison rejects this. Poincaré did reach "the end of his thought": a Third Republic Polytechnician's hopeful vision of a calculable, improvable world. If anything he attended too much to the real world: in 1898–99 he judged relativistic corrections real but negligible because he was weighing them against actual longitude-timing errors. Calling him "conservative" misses that his sight-line ran to the Enlightenment, institutionalized by century's end as French empire. Cracks call not for melancholy or mysticism but for repair by reasoned action, whether of a coal mine, a planetary theory, the world map or Lorentz's electrons.
The sole objective reality consists in the relations of things.Henri Poincaré
The Place de l'Étoile
Poincaré's central sentence, in Galison's formulation: simultaneity is a convention, nothing more than the coordination of clocks by a crossed exchange of electromagnetic signals taking into account the transit time. It appeared in the Annales du Bureau des Longitudes as technical procedure, in the Revue de métaphysique et de morale as philosophy, and from 1900 in Lorentz Festschrift proceedings and Comptes rendus as physics. Is it "really" technological, metaphysical or physical? "We may as well ask if the Place de l'Étoile is truly in the Avenue des Champs Élysées, the Avenue Kléber, or the Avenue Foch."
The procedure was at once brass tubes with suspended mirrors and global control of universal time; copper and gutta-percha a mile under the sea, and "the phantasmagorical reach of empire"; humdrum practice at "every two-bit whistle-stop" of New England or Brandenburg, and mayors, physicists and philosophers pronouncing on the conventionality of time. For Poincaré, Polytechnique and the Bureau were not "context" or "influence" from outside; nor were ETH and seven years at the patent office "external" to Einstein. They were fields of action valuing machines grasped through reason.
Moves along arcs
Galison models the history as arcs, each a sequence of "moves" (statements, conventions or procedures) in an evolving game, crossing at simultaneity. The meaning of local time shifted step by step:
The aims of the game shifted too: in 1894 Lorentz wanted to make a moving object's equations look like one at rest in the ether; by 1904–05 he and Poincaré wanted laws giving the same measurable results in every inertial frame. The physics arc crossed a technology arc (American telegraphic longitude from the Civil War; by 1899 the Bureau a global node for defining simultaneity; Eiffel radio; the Paris–London dispute) and a philosophy arc (the Boutroux circle; Polytechnicians Calinon and Jules Andrade dissecting time). The intersection did not necessitate Poincaré's revision, but it explains why he, there and then, seized the measure of time. After his death his nephew Pierre Boutroux told Mittag-Leffler that Poincaré's lifelong drive was "to fill the white spaces on the map of the world": the Magny lamp, the Poincaré map, Dakar and Quito, the ether and the electron.
Contrasting the two modernisms
| Dimension | Poincaré | Einstein |
|---|---|---|
| Stance to the past | Reform, repair the "elastic frame" of the fathers | Outsider's iconoclasm, "heretic" |
| Machines | Abstract engineering; runs a team cabling Quito | Hands-on; spins an ebonite wheel in a homemade device |
| Ether | Tool for intuition; kept as thinking aid | "Idle gear from an obsolete mechanism" |
| Time | Local/apparent vs true | Each frame's time equally true |
| Contraction | Separate hypothesis | Derived from synchronization |
| Theory and world | Convenient true relations, surface not depth | Theory must match the phenomena's symmetries in austerity |
| Simplicity | For human convenience | Because "nature is the realization of the simplest conceivable mathematical ideas" |
| Heuristics | Threaten intelligibility (quanta) | Legitimate stop-gap machines |
| Style of modernism | Constructive: build up complex relations to the last white space | Critical: strip to principles reflecting the natural order |
Einstein's depth had a theology: not a personal God but "a rapturous amazement at the harmony of natural law," a scientist "possessed by the sense of universal causation." "In a certain sense I hold it true that pure thought can grasp reality, as the ancients dreamed." The magnet-and-coil symmetry demanded a symmetric theory; later he complained of quantum mechanics that predictable features of the world lacked corresponding theoretical elements. Neither man was a naive realist or anti-realist: Poincaré's conventions were anchored in objective "true relations" and non-negotiable simplicity; Einstein, who asked whether a theory was "the true Jacob," also held that the fertile part of theory lay in revisable links between coordinates and perceptions.
Reading back from Einstein makes Poincaré look like a failed precursor, as if Picasso were "antimodern" for not being Pollock or Proust for not being late Joyce. Reading forward shows two great modernisms of physics, "too close and too far to speak," no more able to engage each other than "Freud could read Nietzsche."
Priority is the dull question
Galison calls "who discovered relativity" "as tedious as they are fruitless," a debate first propelled by Nazi-era attacks on Einstein and continued over what relativity's essence is: dropping the ether, the transformation formulas, the universal relativity principle, deriving the transformations from clock synchronization, or correct predictions. This sidesteps rather than settles the dispute; readers wanting the technical comparison should note that Poincaré's 1905–06 mathematics was in places more complete than Einstein's (group structure, four-vector invariant), while Einstein's 1905 kinematics was the first to treat all frames' times as equally physical and to derive contraction and dilation from two postulates.
Rare moments of critical opalescence
Such moments are rarer than "revolutions." Galison names two parallels:
- Energy and entropy in the nineteenth century: steam engines, thermodynamics and quasi-theological talk of the universe's heat death.
- Information sciences in the mid-twentieth: wartime feedback devices from weapons production, information theory and models of mind, giving cybernetics, computer science and cognitive science.
In each, "it became impossible to think abstractly without invoking machines or to think materially without grasping for world-spanning concepts." The analogy he prefers to chess (grandmasters winning simultaneous games with one move) is meteorology: isobars and isotherms made predictive weather science possible; the electric world array of clocks made distant synchronization a modern problem solvable by a machine-like procedure, "even if that machine turned out to be both infinite and theoretical."
Galison's lens transfers to any moment where infrastructure, concepts and institutions co-evolve. When a technical standard (a clock protocol, a data format, a model-evaluation convention) is negotiated across competing networks, look for the three arcs: the practice that already does it routinely and anonymously, the philosophy that names it, and the theory that makes it fundamental. The people who stand at the junction, like a Bureau president or a patent examiner, are where the new concept gets snapped into the circuit.
Looking up, looking down
Einstein left the patent office on 15 October 1909 for the University of Zurich, went to Prague on 1 April 1911, and to Berlin in spring 1914, where he completed general relativity and opposed the war. After the war Favarger's 550-page third edition of his treatise on electric timekeeping lamented "a heap of ruins, miseries and suffering." Time "cannot be defined in substance; it is, metaphysically speaking, as mysterious as matter and space"; to escape anarchy and "physical, intellectual and moral misery," precision time must leave the observatory: "we must democratize time," making everyone "maître du temps," master of the second and even the millionth of a second.
| Reading | Claim | What it sees in Einstein |
|---|---|---|
| Empiricist (1920s–1950s) | Things structure thoughts | The last inductive step: ether tests at first order in v/c (about 1 in 10,000), then second order (about 1 in 100 million), so ether "superfluous" |
| Antipositivist (1960s–1970s) | Thoughts structure things | The philosophical innovator of symmetry and operational definitions, sceptical of supposed experimental refutations |
| Galison | Critical opalescence | Literal and metaphorical seen through each other; neither reduction holds |
Galison does not split the difference: clocks, maps, telegraphs, steam engines and computers refuse the either/or of things versus thoughts. "Staring through the metaphorical we can find the literal; through the literal we can see the metaphorical." The Bern patent office was no "lonely deep-sea lightboat" but "a grandstand seat for the great march of modern technologies"; Einstein seized the world-spanning simultaneity machine, generalized it to every inertial frame, and eliminated the master clock.
Two academies
- Poincaré co-authored What Books Say, What Things Say, joining the Académie Française and the Académie des Sciences: Hugo, Voltaire and Bossuet beside his chapters on stars, gravity, heat, coal mining, batteries and dynamos.
- Einstein became a world figure after Eddington's 1919 eclipse confirmed light bending; his later work moved to abstract unification, away from the machine culture of the patent office. Days after the 1933 Albert Hall speech he left for the Institute for Advanced Study in Princeton, "half seer, half mascot."
- April 1953, to Solovine: "To the immortal Olympia academy... You took a childish delight in all that was clear and reasonable"; "fidelity and devotion until my last learned breath," signed "A.E.," a "corresponding member."
- Besso died on 15 March 1955. Einstein to his family, 21 March: "it was the Patent Office that reunited us... Our conversations on the way home had an incomparable charm... For us devout physicists, the division between past, present, and future is only an illusion, if a stubborn one." Einstein died a month later.
Einheitszeit "never emerged from contestation among imperial empire, democracy, world citizenship, and antianarchism"; each clock came to stand for the individual, and coordination for a logic of linkage among people and peoples. A medieval saying linking alchemy and astronomy gives Galison his close: in looking down, we see up; in looking up, we see down. Down at the regulated clock networks, we see empire, metaphysics and civil society; up at Einstein's and Poincaré's procedural time, we see the wires, gears and pulses of the Bern patent office and the Paris Bureau des Longitudes.
We find metaphysics in machines, and machines in metaphysics. Modernity, just in time.Peter Galison
Master Takeaways
- Simultaneity became a procedure: two distant events are simultaneous if clocks synchronized by signal exchange, corrected for transit time, read the same; this replaced Newton's absolute time with an operation.
- The procedure was already routine before physics needed it: telegraph longitude-finders computed transit time = ½ (east-to-west − west-to-east apparent difference) for decades, anonymously, from Valentia to Dakar.
- Critical opalescence: around 1860–1910 clock coordination flickered between abstract and concrete at every scale, so neither "ideas condense into machines" nor "machines sublime into ideas" explains it.
- Poincaré made the surveyors' rule philosophical (1898) and physical (1900): Lorentz's fictional local time is what signal-synchronized clocks in a moving frame actually show.
- Einstein made clock synchronization the capstone: with no ether and no privileged frame, each inertial frame's synchronized clocks give an equally real time, from which contraction and dilation follow.
- Einstein completed and subverted the master-clock project: he extended unified time to an infinite universe while abolishing the mother clock and any metaphysical centre.
- Conventions are political: the meter, the Greenwich meridian (1884), decimal time and zones were fought over by empires; French reason lost to Anglo-American commerce and cables on time, but won on length.
- Railways and markets, not astronomers, unified time in North America: 79,041 track miles voted in zones in 1883, and cities followed.
- Precision outran need: Boston's watch owners complained of fractions of a second; a culture of precision preceded any practical demand for it.
- Poincaré's method was variants plus invariants: choose the most convenient representation, then hold to the relations that survive every choice.
- Convenience can be computed: Poincaré's conversion-factor table chose the 400-grad circle as least inconvenient, an engineer's settlement of a cultural war.
- Poincaré kept the ether and "true" time as aids to intuition; the observable predictions matched Einstein's, but the meaning differed.
- Einstein's principles were pillars made probable by experience, not Poincaré's "conventions and definitions in disguise."
- The patent office was a school of critical reading: Haller's "think that anything the inventor says is wrong" fitted Einstein's iconoclasm, and Bern's clock patents peaked in 1904.
- The 1905 paper reads like a patent: no citations, a modelable device, consequences laid out like claims; suggestive, not proven.
- Theory became machine: GPS satellite clocks gain a net 38 μs/day from relativity, against a 50 ns/day budget.
- Two modernisms: Poincaré's constructive repair of an elastic frame versus Einstein's critical stripping to principles; priority disputes miss this difference.
- Look up and look down: in machines we find metaphysics and in metaphysics machines; history must hold both.
Frameworks & mental models
| Name | What it says | Use it when |
|---|---|---|
| Critical opalescence | At rare moments technology, philosophy and science interpenetrate at every scale | Explaining an innovation that seems to have "context" everywhere and no single cause |
| Signal-exchange simultaneity | Set the distant clock to the sender's time plus half the round trip | Reasoning about synchronization, latency or distributed time |
| Transit-time correction | Average opposite-direction readings to cancel delay; halve their difference to get delay | Any two-way measurement with unknown symmetric lag |
| Variants and invariants | Choose representations freely; trust only what survives the choice | Comparing models, coordinate systems or framings |
| Convention, triple sense | Treaty, agreement and the revolutionary Convention fused | Reading French standards politics |
| Arcs and moves | Concepts change through sequences of moves in several fields that intersect | Tracing how one idea functions in different communities |
| Constructive vs principle theories | Build from mechanisms vs start from general principles | Diagnosing why rival theories with equal predictions feel different |
| Looking up / looking down | Material networks reveal ideals; ideals reveal material networks | Avoiding reductionism in either direction |
On the whole book. Galison's archival reconstruction of Poincaré's world is overwhelming, and the case that Poincaré's 1898 essay grew from Bureau practice is strong. The case for Einstein is circumstantial: no surviving document shows him examining a clock-synchronization patent or citing one; his own accounts credit Hume, Mach and Besso. The "critical opalescence" metaphor resists falsification: almost any outcome can be described as fluctuation across scales. The narrative also centres France, Switzerland and the United States, with Britain and Germany seen largely through French eyes; colonial subjects appear mostly as obstacles in expedition reports. A few numbers slip (the 1884 vote counts, the Magny interval, the Eiffel signal date). Read it as a powerful reframing of context, not as proof of a causal pathway into Einstein's head.
Who's who
| Person | Role | Why they matter |
|---|---|---|
| Henri Poincaré (1854–1912) | Mathematician, physicist, philosopher; Bureau des Longitudes | Simultaneity as convention (1898); local time as clock time (1900); relativity with ether (1905–06) |
| Albert Einstein (1879–1955) | Bern patent examiner | 1905 relativity built on clock synchronization; no ether, no centre |
| Hendrik A. Lorentz | Dutch theorist | Electron theory, contraction, "local time" (1895, 1904) |
| Hermann Minkowski | Göttingen mathematician | Spacetime (1908): "space by itself and time by itself... Shadows" |
| Alfred Cornu | Polytechnique physicist | Mentor; electric clock theory; critic of the decimal compromise |
| Auguste Calinon | Polytechnician philosopher | Psychological and conventional analysis of time and simultaneity |
| Urbain Le Verrier | Paris Observatory director | Failed electric unification of Paris time (1875–83) |
| Leonard Waldo | Harvard time-service manager | Sold precision time across New England |
| William F. Allen | Railway time convention secretary | Engineered the 1883 North American zones |
| Sandford Fleming | Canadian engineer | Cosmopolitan 24-letter time; Greenwich advocate |
| Frederick Barnard, Cleveland Abbe | American Metrological Society | Lobbied for uniform and zone time |
| George Airy | Astronomer Royal | Sceptic of universal time |
| Jules Janssen, Albert Lefaivre | French delegates, 1884 | Fought for a neutral meridian and decimal time |
| Charles Lallemand | Bureau member | French advocate of Greenwich-based zones |
| Benjamin Gould, George Dean | U.S. Coast Survey | First transatlantic cable longitude (1866) |
| Francis Green | U.S. Navy | Cable longitude of the Caribbean and South America |
| Octave de Bernardières | French naval astronomer | South American polygon; global geodetic network |
| Helmuth von Moltke | Prussian field marshal | 1891 plea for German unified time |
| Mathias Hipp, Albert Favarger | Swiss clock engineers | Electric clock networks; "time anarchy" and "democratize time" |
| Friedrich Haller | Patent office director | Taught Einstein critical examination |
| Michele Besso | Einstein's friend | May 1905 conversation that unlocked time |
| Maurice Solovine, Conrad Habicht | Olympia Academy | Reading Mach, Pearson, Hume, Poincaré with Einstein |
| Emil Cohn | German theorist | Light-signal local time (1904); popular clock models (1913) |
| Gustave Ferrié | French army engineer | Eiffel Tower radio time |
| Gösta Mittag-Leffler, Edvard Phragmén | Acta Mathematica | Prize and the discovery of Poincaré's error (1889) |
Connect it
- Distributed systems. Einstein's round-trip rule is the logic of network clock protocols (NTP, PTP), which assume symmetric delay exactly as the longitude-finders did; asymmetric paths produce the same systematic errors the Paris–Greenwich teams fought.
- Standards as power. The meter, Greenwich and zone time show that whoever owns the network (cables then, platforms and data formats now) tends to set the convention; enterprise architecture standards are negotiated the same way, by "track miles" of installed base.
- Banking time. Trading and payment systems depend on synchronized timestamps (European MiFID II rules require traceability to UTC within microseconds for high-frequency trading), a direct descendant of Waldo's time service and GPS's relativistic clocks.
- Concepts at junctions. In AI as in 1900, decisive concepts (benchmarks, evaluation protocols) often begin as anonymous engineering practice before being named philosophically and made fundamental in theory.
About this book
Einstein’s Clocks, Poincaré’s Maps: Empires of Time by Peter Galison, 2003. This is a chapter-by-chapter study of the book, with summaries, maps, tables and diagrams; short quotations keep their page references. It is shared free for personal study, is not for sale, and is not endorsed by the author or publisher. Please read and buy the original.
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