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
An observer in a closed compartment, moving with constant acceleration through empty space, finds that the “bottom” of his cage catches up with objects that he releases; that it presses on his feet to give him the sensation of weight, etc. It displays all the effects that he would expect if it were at rest in a gravitational field. On the other hand, if it were falling freely under gravitational influence, its occupant would sense no weight, objects released would not leave his hand, the reaction from his every [190]motion would change his every position in his cage, and he could equally well assume himself at rest in a region of space free from gravitational action. Accelerated motion may always be interpreted, by the observer on the system, as ordinary force effects on his moving system, or as gravitational effects on his system at rest.
An alternative statement of the Special Theory is that the observed phenomena of uniform motion may equally be accounted for by supposing the object in motion and the observer with his reference frame at rest, or vice versa. We may similarly state the General Theory: The observed phenomena of uniformly accelerated motion may in every case be explained on a basis of stationary observer and accelerated objective, or of stationary objective with the observer and his reference system in accelerated motion. Gravitation is one of these phenomena. It follows that if the observer enjoy properly accelerated axes (in time-space, of course), the absolute character of the world about him must be such as to present to him the phenomenon of gravitation. It remains only to identify the sort of world, of which gravitation as it is observed would be a fundamental characteristic.
Euclid’s and Newton’s systems stand as first and second approximations to that world. The Special Relativity Theory constitutes a correction of Newton, presumably because it is a third approximation. We must seek in it those features which we may most hopefully carry along, into the still more general case.
Newton’s system retained the geometry of Euclid. [191]But Minkowski’s invariant expression tells us that Einstein has had to abandon this; for in Euclidean geometry of four dimensions the invariant takes the form:
analogous to that of two and three dimensions. It is not the presence of the constant C in Minkowski’s formula that counts; this is merely an adjustment so that we may measure space in miles and time in the unit that corresponds to a mile. It is the minus sign where Euclidean geometry demands a plus that makes Minkowski’s continuum non-Euclidean.
The editor has told us what this statement means. I think he has made it clear that when we speak of the geometry of the four-dimensional world, we must not read into this term the restrictions surrounding the kind of geometry we are best acquainted with—that of the three-dimensional Euclidean continuum. So I need only point out that if we are to make a fourth (and we hope, final) approximation to the reality, its geometry must preserve the generality attained by that of the third step, if it goes no further.
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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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