New-proof-of-Einstein's-clock-paradox-by-general-relativity (original) (raw)

A proof is given based entirely on Einstein's general relativity to successfully explain an old problem, namely the clock paradox of Einstein which originated in his 1905 paper on special relativity. Essentially the problem involves time intervals which are said to dilate by the Lorentz factor. Recall that this factor applies only in inertial systems to relative motion at velocities constant in both magnitude and direction. Einstein, however, applied it to a clock situated on the earth's surface which obviously is not at constant velocity, since its direction is changing continually; the clock is therefore in a noninertial system. Yet tests show that this factor accounts for the time dilation perfectly for all cases of circular motion; this calls for an explanation. In the paper it is explained that the true reason for the time dilation is that the clock is moving not with constant velocity but with an acceleration (centripetal) due to a change in direction. Using Einstein's Equivalence Principle and his general relativity, it is shown that time dilation in motion will occur only when the velocity is continually changing either in magnitude or in direction. Remarkably the time dilation factors in the several different kinds of motion we have analyzed all turn out to be similar in algebraic form to the Lorentz factor, a pure coincidence. The clock paradox and the related twin paradox are therefore true but only in noninertial accelerating systems. This is confirmed by all observed cases of time dilation in clocks and mesons which are in motion.

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