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Artificial Radioactivity

principle of equivalence, uniform motion, sec2, world line, great circles

In 1915 Einstein developed the general theory of relativity in which he considered objects accelerated with respect to one another. He developed this theory to explain apparent conflicts between the laws of relativity and the law of gravity. To resolve these conflicts he developed an entirely new approach to the concept of gravity, based on the principle of equivalence.

The principle of equivalence holds that forces produced by gravity are in every way equivalent to forces produced by acceleration, so that it is theoretically impossible to distinguish between gravitational and accelerational forces by experiment. In the theory of special relativity, Einstein had stated that a person in a closed car rolling on an absolutely smooth railroad track could not determine by any conceivable experiment whether he was at rest or in uniform motion. In general relativity he stated that if the car were speeded up or slowed down or driven around a curve, the occupant could not tell whether the forces so produced were due to gravitation or whether they were acceleration forces brought into play by pressure on the accelerator or on the brake or by turning the car sharply to the right or left.

Acceleration is defined as the rate of change of velocity. Consider an astronaut standing in a stationary rocket. Because of gravity his or her feet are pressed against the floor of the rocket with a force equal to the person's weight, w. If the same rocket is in outer space, far from any other object and not influenced by gravity, the astronaut is again being pressed against the floor if the rocket is accelerating, and if the acceleration is 9.8 m/sec2 (32 ft/sec2) (the acceleration of gravity at the surface of the earth), the force with which the astronaut is pressed against the floor is again equal to w. Without looking out of the window, the astronaut would have no way of telling whether the rocket was at rest on the earth or accelerating in outer space. The force due to acceleration is in no way distinguishable from the force due to gravity. According to Einstein's theory, Newton's law of gravitation is an unnecessary hypothesis; Einstein attributes all forces, both gravitational and those associated with acceleration, to the effects of acceleration. Thus, when the rocket is standing still on the surface of the earth, it is attracted toward the center of the earth. Einstein states that this phenomenon of attraction is attributable to an acceleration of the rocket. In three-dimensional space, the rocket is stationary and therefore is not accelerated; but in four-dimensional space-time, the rocket is in motion along its world line. According to Einstein, the world line is curved, because of the curvature of the continuum in the neighborhood of the earth.

Thus, Newton's hypothesis that every object attracts every other object in direct proportion to its mass is replaced by the relativistic hypothesis that the continuum is curved in the neighborhood of massive objects. Einstein's law of gravity states simply that the world line of every object is a geodesic in the continuum. A geodesic is the shortest distance between two points, but in curved space it is not generally a straight line. In the same way, geodesics on the surface of the earth are great circles, which are not straight lines on any ordinary map.

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