Gravitation and Acceleration

Einstein's Theories of Relativity and Gravitation by Albert Einstein, is part of the HackerNoon Books Series. You can jump to any chapter in this book here. Gravitation and Acceleration

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 [221]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 [222]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

Let us return for a moment to the moving ball. Four measures, three of distances and one of time, are required in specifying its position with reference [223]to some framework at each point and at each instant. All of these measures can be summed up in one compendious statement—the equations of motion showed how in changing from our room to his accelerated auto we found a new summary, “transformed equations,” which seemed to indicate that the ball had traversed a strong, variable field of force. Is there then in the chaos of observational disagreements anything which is independent of all observers? There is, but it is hidden at the very heart of nature.

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This book is part of the public domain. Albert Einstein (2020). Einstein's Theories of Relativity and Gravitation. Urbana, Illinois: Project Gutenberg. Retrieved October 2022.

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