Imagine now that a man in an automobile looks in and observes the moving ball. Suppose he records the motion. To do so, he must refer to a timepiece and some body of reference. Say he selects his wrist-watch, the floor of his auto and two sides meeting in a corner. Fancy that just as he begins his series of observations his auto starts bucking and the main-spring of his watch breaks, so that he must measure “seconds” by the crazy running-down of his watch, and distances with reference to the sides of his erratic auto. Despite these handicaps he completes a set of observations, each of which consists of a time measured by his mad watch and three distances reckoned from the sides of his bucking machine. Let us assume him to have been so absorbed in his experiment that he noticed neither the disorders of his watch nor the motion of his auto. He gives us his sets of measurements. We remark that his seconds are only small fractions of ours, also his norths and wests are badly mixed. If we interpret his sets in terms of our stationary walls and sober clock we find the curious paradox that the ball zigzagged across the room like an intoxicated bee. He obstinately argues that we know no more than he about how the ball actually moved. For we got a smooth description, he asserts, by choosing an artificially simple reference framework, having no necessary relations whatever to the ball. The crooked path plotted from his observations proves, he declares, that the ball was subject to varying forces of which we in the room suspected nothing. He contends that our room was being jarred by a system of forces which exactly compensated and smoothed out the real jaggedness of path observed by himself. But if we know all about his watch and auto we can easily apply necessary corrections to his measurements, and, fitting the corrected set to our reference-framework of walls and clock, recover our own smooth description.
For consistency we must carry our readjustments farther. The path mapped from our measurements is a curve. Perhaps the curvature was introduced by some peculiarity of our reference framework? Possibly our own room is being accelerated upward, so that it makes the ball’s true path—whatever that may be—appear curved downward, just as the autoist’s zigzags made the path he mapped appear jagged. Tradition attributes the downward curving to the tug of gravity. This force we say accelerates the ball downward, producing the curved path. Is this the only possible explanation? Let us see.
Gravitation and Acceleration
Imagine a man in a room out of which he cannot see. He notices that when he releases anything it falls to the floor with a constant acceleration. Further he observes that all his objects, independently of their chemical and physical properties, are affected in precisely the same way. Now, he previously has experimented with magnets, and has remarked that they attract certain bodies in essentially the same way that the things which he drops are “attracted” to whatever is beneath the floor. Having explained magnetic attraction in terms of “forces,” he makes his first hypothesis: (A) He and his room are in a strong “field of force,” which he designates gravitational. This force pulls all things downward with a constant acceleration. Here he notes a singular distinction between magnetic and gravitational “forces”: magnets attract only a few kinds of matter, notably iron; the novel “force,” if indeed a force at all, acts similarly upon all kinds of matter. He makes another hypothesis: (B) His room and he are being accelerated upward.
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Either (A) or (B) describes the facts perfectly. By no experiment can he discriminate between them. So he takes the great step, and formulates the Equivalence Hypothesis:
A gravitational field of force is precisely equivalent in its effects to an artificial field of force introduced by accelerating the framework of reference, so that in any small region it is impossible to distinguish between them by any experiment whatever.
Next reconsidering his magnetic “forces,” he extends the equivalence hypothesis to cover all manifestations of force: The effects attributed to forces of any kind whatever can be described equally well by saying that our reference frameworks are accelerated; and moreover there is possible no experiment which will discriminate between the descriptions.
If the accelerations are null, the frameworks are at rest or in uniform motion relatively to one another. This special case is the “restricted” principle of relativity, which asserts that it is impossible experimentally to detect a uniform motion through the ether. Being thus superfluous for descriptions of natural phenomena, the ether may be abandoned, at least temporarily. The older physics sought this absolute ether framework to which all motions could be unambiguously referred, and failed to find it. The most exacting experiments, notably that of Michelson-Morley, revealed no trace of the earth’s supposed motion through the ether. Fitzgerald accounted for the failure by assuming that such motion would remain undetected if every moving body contracted by an amount depending upon its velocity in the direction of motion. The contraction for ordinary velocities is imperceptible. Only when as in the case of the beta particles, the velocity is an appreciable fraction of the velocity of light, is the contraction revealed. This contraction follows immediately from Einstein’s generalization constructed upon the equivalence hypothesis and the restricted relativity principle. We shall see that the contraction inevitably follows from the actual geometry of the universe.[1]