Free Einstein by Walter Isaacson

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.” 38 For 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, itmeant 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.
“The Step”
     
    It was a beautiful day in Bern,