theory. If the velocity of a light wave depended on the velocity of the source that emitted it, then the light wave must somehow encode within it this information. But experiments and Maxwell’s equations indicated that was not the case.34
Einstein tried to find ways to modify Maxwell’s equations so that they would fit an emission theory, but the quest became frustrating. “This theory requires that everywhere and in each fixed direction light waves of a different velocity of propagation should be possible,” he later recalled. “It may be impossible to set up a reasonable electromagnetic theory that accomplishes such a feat.”35
In addition, scientists had not been able to find any evidence that the velocity of light depended on that of its source. Light coming from any star seemed to arrive at the same speed.36
The more Einstein thought about an emission theory, the more problems he encountered. As he explained to his friend Paul Ehrenfest, it was hard to figure out what would happen when light from a “moving” source was refracted or reflected by a screen at rest. Also, in an emission theory, light from an accelerating source might back up on itself.
So Einstein rejected the emission theory in favor of postulating that the speed of a light beam was constant no matter how fast its source was moving. “I came to the conviction that all light should be defined by frequency and intensity alone, completely independently of whether it comes from a moving or from a stationary light source,” he told Ehrenfest.37
Now Einstein had two postulates: “the principle of relativity” and this new one, which he called “the light postulate.” He defined it carefully: “Light always propagates in empty space with a definite velocity V that is independent of the state of motion of the emitting body.”38For example, when you measure the velocity of light coming from the headlight of a train, it will always be a constant 186,000 miles per second, even if the train is rushing toward you or backing away from you.
Unfortunately, this light postulate seemed to be incompatible with the principle of relativity. Why? Einstein later used the following thought experiment to explain his apparent dilemma.
Imagine that “a ray of light is sent along the embankment” of a railway track, he said. A man standing on the embankment would measure its speed as 186,000 miles per second as it zipped past him. But now imagine a woman who is riding in a very fast train carriage that is racing away from the light source at 2,000 miles per second. We would assume that she would observe the beam to be zipping past her at only 184,000 miles per second. “The velocity of propagation of a ray of light relative to the carriage thus comes out smaller,” Einstein wrote.
“But this result comes into conflict with the principle of relativity,” he added. “For, like every other general law of nature, the law of the transmission of light must, according to the principle of relativity, be the same when the railway carriage is the reference body as it is when the embankment is the reference body.” In other words, Maxwell’s equations, which determine the speed at which light propagates, should operate the same way in the moving carriage as on the embankment. There should be no experiment you can do, including measuring the speed of light, to distinguish which inertial frame of reference is “at rest” and which is moving at a constant velocity.39
This was an odd result. A woman racing along the tracks toward or away from the source of a light beam should see that beam zip by her with the exact same speed as an observer standing on the embankment would see that same beam zip by him. The woman’s speed relative to the train would vary, depending on whether she was running toward it or away from it. But her speed relative to the light beam coming from the train’s headlight would be invariant. All of this made the two postulates, Einstein thought, “seemingly incompatible.” As he later explained in a lecture on how he came to his theory, “the constancy of the velocity of light is not consistent with the law of the addition of velocities. The result was that I had to spend almost one year in fruitless thoughts.”40
By combining the light postulate with the principle of relativity, it meant that an observer would measure the speed of light as the same whether the source was moving toward or away from him, or whether he was moving toward or away from the source, or both, or neither. The speed of light would be the same whatever the motion of the observer and the source.
That is where matters stood in early May 1905. Einstein had embraced the relativity principle and elevated it to a postulate. Then, with a bit more trepidation, he had adopted as a postulate that the velocity of light was independent of the motion of its source. And he puzzled over the apparent dilemma that an observer racing up a track toward a light would see the beam coming at him with the same velocity as when he was racing away from the light—and with the same velocity as someone standing still on the embankment would observe the same beam.
“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.
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
