A Briefer History of Time by Stephen Hawking Read Free Book Online

you could distinguish the pull of gravity from uniform acceleration, in which everything does fall at the same rate. Einstein’s use of the equivalence of inertial and gravitational mass to derive his principle of equivalence, and eventually all of general relativity, amounts to a relentless march of logical reasoning unmatched in the history of human thought.
    Now that we know the principle of equivalence, we can start to follow Einstein’s logic by doing another thought experiment that shows why time must be affected by gravity. Imagine a rocket ship out in space. For convenience, imagine that the rocket ship is so long that light takes one second to traverse it from top to bottom. Finally, suppose there is an observer at the ceiling of the rocket ship and another at the floor, each with identical clocks that tick once each second.
    Suppose the ceiling observer w aits for the clock to tick, and then immediately sends a light signal down to the floor observer. The ceiling observer does this once more the next time the clock ticks. According to this setup, each signal travels for one second and then is received by the floor observer. So just as the ceiling observer sends two light signals a second apart, the floor observer receives two, one second apart.
    How would this situation differ if the rocket ship were resting on earth, under the influence of gravity, instead of floating freely out in space? According to Newton’s theory, gravity has no effect on this situation. If the observer on the ceiling sends signals one second apart, the observer will receive them one second apart. But the principle of equivalence does not make the same prediction. We can see what happens, that principle tells us, by considering the effect of uniform acceleration instead of the effect of gravity. This is an example of the way Einstein used the principle of equivalence to create his new theory of gravity.
    So let’s now suppose the rocket ship is accelerating. (We will imagine that it is accelerating slowly, so we don’t approach the speed of light!) Since the rocket ship is moving upward, the first signal will have less distance to travel than before and so will arrive sooner than one second later. If the rocket ship were moving at a constant speed, the second signal would arrive exactly the same amount of time sooner, so the time between the two signals would remain one second. But due to the acceleration, the rocket ship will be moving even faster when the second signal is sent than it was when the first signal was sent, so the second signal will have even less distance to traverse than the first and will arrive in even less time. The observer on the floor will therefore measure less than one second between the signals, disagreeing with the ceiling observer, who claims to have sent them exactly one second apart.
    This is probably not startling in the case of the accelerating rocket ship—after all, we just explained it! But remember, the principle of equivalence says that it also applies to a rocket ship at rest in a gravitational field. That means that even if the rocket ship is not accelerating but, say, is sitting on a launching pad on the earth’s surface, if the ceiling observer sends signals toward the floor at intervals of one each second (according to his clock), the floor observer will receive the signals at shorter intervals (according to his clock). That is startling!
    You might still ask whether this means that gravity changes time, or whether it merely ruins clocks. Suppose the floor observer climbs up to the ceiling, where he and his partner compare their clocks. They are identical clocks, and sure enough, both observers will find that they now agree on the length of a second. There is nothing wrong with the floor observer’s clock: it measures the local flow of time, wherever it happens to be. So just as special relativity tells us that time runs differently for observers in relative motion, general relativity tells us