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. Universal Relativity
Universal Relativity
So far we have dealt with what has been designated as the special theory of relativity. This, as we have seen, applies to uniform motion only. In extending the theory to include non-uniform or accelerated motion, Einstein has at the same time deduced a law of gravitation which is much more general than that of Newton.
A body falling towards the earth increases in velocity as it falls. The motion is said to be accelerated. We ascribe this increase in velocity to a gravitational force exerted by the earth on all objects. As shown by Newton, this force acts between all particles of matter in the universe, and varies inversely as the square of the distance, and directly as the product of the masses.
Of course, we have had a number of theories of gravitation, and none of them have proven successful. Einstein, however, was the first one to suggest a conception of gravitation which has proven extremely significant. He points out that a gravitational force is non-existent for a person falling [236]freely with the acceleration due to gravity. For this person there is no sensation of weight, and if he were in a closed box which is also falling with the same acceleration, he would be unable to decide as to whether his system were falling or situated in interplanetary space where there is no gravitational field. Furthermore, if he were to carry out any optical or electrical experiments in this box he would observe the same results as an experimenter on the earth. A ray of light would travel in a straight line so far as this observer can perceive, while an external observer would, of course, judge differently.
Einstein shows that this is equally true for all kinds of acceleration including that due to rotation. In the case of a rotating body there exists a centrifugal force which tends to make objects on the surface fly outwards, but for an external observer this force does not exist any more than gravity exists for the observer falling freely.
Thus we can draw the general conclusion that a gravitational field or any other field of force may be eliminated by choosing an observer moving with the proper acceleration. For this observer, however, the laws of optics and electricity must be just as valid as for an observer on the earth.
In postulating this equivalence hypothesis Einstein merely makes use of the very familiar observation that, independently of the nature of the material, all bodies possess the same acceleration in a given field of force.
The problem which Einstein now sets out to solve is that of determining the law which shall describe the motion of any system in a field of force in such [237]a general manner as to leave unaltered the fundamental relations of electricity and optics.
In connection with the solution of this problem he finds it necessary to discard the limitations placed on us by ordinary or Euclidean geometry. In this manner geometrical concepts as well as those of force are completely robbed of all notions of absoluteness, and the goal of a general theory of relativity is attained.
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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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