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. The Relativity of Uniform Motion

The Relativity of Uniform Motion

Let us consider some of the consequences which follow from this principle. An observer travelling with say one-half the velocity of light in the same direction as a ray of light would find that the latter has the usual velocity of 186,000 miles per second. Similarly an observer travelling in the opposite direction to that of the light-ray, with one-half the velocity of light, would obtain the same result.

Einstein has shown that these conclusions can be valid only if the units of time and space used by the two observers depend upon their relative motions. A careful calculation shows that the unit of length used by either observer appears to the other observer contracted when placed in the direction of their relative motion (but not, when placed at right angles to this direction), and the unit of time used by either observer appears to the other too great. Moreover, the ratio of the units of length or of time varies with the square of the relative speed of the two observers, according to a relation which is similar to that mentioned above for the swimmer in the current. This relation shows that as the relative speed approaches that of light the discrepancy between the units increases.

Thus, for an observer moving past our earth with a velocity which is nine-tenths that of light, a meter stick on the earth would be 44 centimeters as measured [234]by him, while a second on our clocks would be about two and a half seconds as marked by his clock. Similarly, what he calls a meter length would, for us, be only 44 centimeters and he would appear to us to be living about two and a half times slower than we are. Each observer is perfectly consistent in his measurements of time and space as long as he confines his observations to his own system, but when he tries to make observations on another system moving past his, he finds that the results which he obtains do not agree with those obtained by the other observer.

It is not surprising that in accordance with this conclusion it also follows that the mass of a body must increase with its velocity. For low velocities the increase is so small that we cannot ever hope to measure it, but as the velocity of light is approached the difference becomes more and more appreciable and a body having the velocity of light would possess infinite mass, which simply means that such a velocity cannot be attained by any material object. This conclusion has been experimentally confirmed by observations on the mass of the extremely small negatively charged particles which are emitted by radioactive elements. Some of these particles are ejected with velocities which are over nine-tenths that of light, and measurements show that the increase in mass is in accord with this theory.

The relativity theory also throws new light on the nature of mass itself. According to this view, mass and energy are equivalent. The absolute destruction of 1 gram of any substance, if possible, would yield an amount of energy which is one [235]hundred million times as much as that obtained by burning the same mass of coal. Conversely, energy changes are accompanied by changes in mass. The latter are ordinarily so inappreciably small as to escape our most refined methods of measurements, but in the case of the radioactive elements we actually observe this phenomenon. From this standpoint, also, the laws of conservation of energy and of mass are shown to be intimately related.

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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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The Relativity of Uniform Motion

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