EINSTEIN AND POINCARÉ (p4)

When I came back to the United States I started poking around old Swiss, British, German, and American patents and industrial records, and it turns out that there was an enormous industry in coordinated clocks in the late 19th century. Suddenly the famous metaphor with which Einstein begins his 1905 paper began to look not so peculiar. Einstein asks us to interrogate what we mean by simultaneity. He says, imagine a train comes into a station where you are standing. If the hour hand of your watch just touches 7:00 as the train pulls in front of your nose, then you would say that the train’s arrival and your watch showing 7:00 were simultaneous. But what does it mean to say that your clock ticks 7:00 at just the moment that a train arrives at a distant station? Einstein goes on to develop a technique for saying what it would mean to coordinate clocks, and explains that this is what simultaneity is. This quasi-operational definition of simultaneity becomes the foundation of his theory and leads to his startling conclusions that simultaneity depends on frame of reference, that therefore length measurements are different in different frames of reference, and to all of the other famous and amazing results of relativity theory. Suddenly I could see that Einstein’s seemingly abstract metaphor about trains and stations was actually both entirely metaphorical and yet altogether literal. Far from being the only person worried about the meaning of simultaneity—a lighthouse keeper in splendid isolation--there was a vast industry of people worrying about what it meant to say that a train was arriving at a distant train station. And they were determining simultaneity by sending electrical signals down telegraph lines to distant stations in ways very much like the way Einstein was describing in that fateful paper.

So I began to look further, wondering who else would have been worrying about simultaneity in the late 19th century. It turns out that the great French philosopher, mathematician, and physicist, Henri Poincaré, had much the same idea as Einstein. He also wanted to criticize the idea of absolute simultaneity and to make it something that could be measured. Instead of trains and stations, Poincaré chose for his key metaphor the exchange of a telegrapher’s signal down a line. In his famous philosophical article of January 1898, Poincaré says that simultaneity is really just the exchange of signals, like two telegraphers trying to determine how much longitudinal difference there is between them. You see, if the earth were stationary, we could find our longitude simply by looking up to see which stars were straight above us. But the earth turns, so to compare two longitudes, that is the stars above two different sites, you have to make the measurement at the same time. Consequently, for centuries map-makers have worried about simultaneity and how to determine it. By the late 19th century people were exchanging electrical time signals across the oceans via undersea cables, and what is interesting is that Poincaré was right in the middle of it — in 1899 he was elected president of the Bureau of Longitude in Paris. Then, in December 1900, he brought his new definition of time from philosophy and technology into the heartland of physics. He showed that if the telegraphers coordinated their clocks when moving through the ether, their clocks would “appear” to be simultaneous even though from the “true” ether-rest system they were not. But now the new definition of simultaneity stood central for Poincaré in all three domains: philosophy, technology, and physics.

Though Poincaré was as famous as any mathematician or philosopher of his time, he was also a man of enormous engineering skills, trained as a sophisticated engineer at the Polytechnique and Ecole des Mines in Paris and later becoming one of Polytechnique’s most illustrious professors. It is Poincaré’s situatedness that intrigues me: like Einstein, when Poincaré invoked the longitude-finding telegraphers, he was speaking both metaphorically and literally. He was changing a central concept for all physics and at the same time addressing the real practices of map-makers.

Though less well known by far than Einstein, at the turn of the century Poincaré’s popular philosophical books, Science and Hypothesis and Science and Values, were bestsellers in France. They had a profound effect on modern philosophy of science, and today are still read in philosophy courses. They were also translated into many other languages very early on, including German and English, and were widely distributed. He opened up whole new areas of mathematics, including the mathematics of topology. He helped invent the science of chaos, and all that we understand of the science of complexity owes an enormous amount to him. He contributed enormously to what became relativity theory, and is important in many other branches of physics. He was truly a polymath and went on to do things in engineering. He was one of the people who rescued the Eiffel Tower from being taken down after the International Exhibition for which it was built, because he saw a way of using it as a military antenna. In fact, in large measure under Poincaré’s direction, the Eiffel Tower itself became an enormous antenna that would send time signals all over the world, allowing longitude finders from Canada to the tip of Africa to do their work. Moving back and forth smoothly between high engineering and abstract mathematics, he left an enormous legacy across many fields, always reasoning concretely, visually—as an abstract engineer so to speak. His thoughts on time were no exception.