Walter Isaacson - Einstein - His Life and Universe

“In view of this dilemma, there appears to be nothing else to do than to abandon either the principle of relativity or the simple law of the propagation of light,” Einstein wrote. 41

Then something delightful happened. Albert Einstein, while talking with a friend, took one of the most elegant imaginative leaps in the history of physics.

“The Step”

It was a beautiful day in Bern, Einstein later remembered, when he went to visit his best friend Michele Besso, the brilliant but unfocused engineer he had met while studying in Zurich and then recruited to join him at the Swiss Patent Office. Many days they would walk to work together, and on this occasion Einstein told Besso about the dilemma that was dogging him.

“I’m going to give it up,” Einstein said at one point. But as they discussed it, Einstein recalled, “I suddenly understood the key to the problem.” The next day, when he saw Besso, Einstein was in a state of great excitement. He skipped any greeting and immediately declared, “Thank you. I’ve completely solved the problem.” 42

Only five weeks elapsed between that eureka moment and the day that Einstein sent off his most famous paper, “On the Electrodynamics of Moving Bodies.” It contained no citations of other literature, no mention of anyone else’s work, and no acknowledgments except for the charming one in the last sentence: “Let me note that my friend and colleague M. Besso steadfastly stood by me in my work on the problem discussed here, and that I am indebted to him for several valuable suggestions.”

So what was the insight that struck him while talking to Besso? “An analysis of the concept of time was my solution,” Einstein said. “Time cannot be absolutely defined, and there is an inseparable relation between time and signal velocity.”

More specifically, the key insight was that two events that appear to be simultaneous to one observer will not appear to be simultaneous to another observer who is moving rapidly. And there is no way to declare that one of the observers is really correct. In other words, there is no way to declare that the two events are truly simultaneous.

Einstein later explained this concept using a thought experiment involving moving trains. Suppose lightning bolts strike the train track’s embankment at two distant places, A and B. If we declare that they struck simultaneously, what does that mean?

Einstein realized that we need an operational definition, one we can actually apply, and that would require taking into account the speed of light. His answer was that we would define the two strikes as simultaneous if we were standing exactly halfway between them and the light from each reached us at the exact same time.

But now let us imagine how the event looks to a train passenger who is moving rapidly along the track. In a 1916 book written to explain this to nonscientists, he used the following drawing, in which the long train is the line on the top:

Suppose that at the exact instant (from the viewpoint of the person on the embankment) when lightning strikes at points A and B, there is a passenger at the midpoint of the train, M t, just passing the observer who is at the midpoint alongside the tracks, M. If the train was motionless relative to the embankment, the passenger inside would see the lightning flashes simultaneously, just as the observer on the embankment would.

But if the train is moving to the right relative to the embankment, the observer inside will be rushing closer toward place B while the light signals are traveling. Thus he will be positioned slightly to the right by the time the light arrives; as a result, he will see the light from the strike at place B before he will see the light from the strike at place A. So he will assert that lightning hit at B before it did so at A, and the strikes were not simultaneous.

“We thus arrive at the important result: Events that are simultaneous with reference to the embankment are not simultaneous with respect to the train,” said Einstein. The principle of relativity says that there is no way to decree that the embankment is “at rest” and the train “in motion.” We can say only that they are in motion relative to each other. So there is no “real” or “right” answer. There is no way to say that any two events are “absolutely” or “really” simultaneous. 43

This is a simple insight, but also a radical one. It means that there is no absolute time. Instead, all moving reference frames have their own relative time. Although Einstein refrained from saying that this leap was as truly “revolutionary” as the one he made about light quanta, it did in fact transform science. “This was a change in the very foundation of physics, an unexpected and very radical change that required all the courage of a young and revolutionary genius,” noted Werner Heisenberg, who later contributed to a similar feat with his principle of quantum uncertainty. 44

In his 1905 paper, Einstein used a vivid image, which we can imagine him conceiving as he watched the trains moving into the Bern station past the rows of clocks that were synchronized with the one atop the town’s famed tower. “Our judgments in which time plays a part are always judgments of simultaneous events,” he wrote. “If, for instance, I say, ‘That train arrives here at 7 o’clock,’ I mean something like this: ‘The pointing of the small hand of my watch to 7 and the arrival of the train are simultaneous events.’ ” Once again, however, observers who are moving rapidly relative to one another will have a different view on whether two distant events are simultaneous.

The concept of absolute time—meaning a time that exists in “reality” and tick-tocks along independent of any observations of it—had been a mainstay of physics ever since Newton had made it a premise of his Principia 216 years earlier. The same was true for absolute space and distance.“Absolute, true, and mathematical time, of itself and from its own nature, flows equably without relation to anything external,” he famously wrote in Book 1 of the Principia. “Absolute space, in its own nature, without relation to anything external, remains always similar and immovable.”

But even Newton seemed discomforted by the fact that these concepts could not be directly observed. “Absolute time is not an object of perception,” he admitted. He resorted to relying on the presence of God to get him out of the dilemma. “The Deity endures forever and is everywhere present, and by existing always and everywhere, He constitutes duration and space.” 45

Ernst Mach, whose books had influenced Einstein and his fellow members of the Olympia Academy, lambasted Newton’s notion of absolute time as a “useless metaphysical concept” that “cannot be produced in experience.” Newton, he charged, “acted contrary to his expressed intention only to investigate actual facts.” 46

Henri Poincaré also pointed out the weakness of Newton’s concept of absolute time in his book Science and Hypothesis, another favorite of the Olympia Academy. “Not only do we have no direct intuition of the equality of two times, we do not even have one of the simultaneity of two events occurring in different places,” he wrote. 47

Both Mach and Poincaré were, it thus seems, useful in providing a foundation for Einstein’s great breakthrough. But he owed even more, he later said, to the skepticism he learned from the Scottish philosopher David Hume regarding mental constructs that were divorced from purely factual observations.

Given the number of times in his papers that he uses thought experiments involving moving trains and distant clocks, it is also logical to surmise that he was helped in visualizing and articulating his thoughts by the trains that moved past Bern’s clock tower and the rows of synchronized clocks on the station platform. Indeed, there is a tale that involves him discussing his new theory with friends by pointing to (or at least referring to) the synchronized clocks of Bern and the unsynchronized steeple clock visible in the neighboring village of Muni. 48