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The Clock Paradox in the Relativity Theory
並列摘要
A system S' (rocket) starts from rest in an inertial system S, and after a series of accelerated, uniform and decelerated motions, comes back to rest at its initial position in S. An exact calculation is carried out, from the standpoint of S, of the time intervals for the arrivals at S of light signals sent back by S'. From the standpoint of S', S has made a round trip after undergoing a series of free falls in gravitational fields and coasting motions. An exact calculation is carried out for the 'proper time' intervals in S from the standpoint of S'. It is shown that there is exact agreement between S and S' in their reckonings of the total time intervals for the two frames, namely, both S and S' agree quantitatively, to them, the time interval is longer for S than for S'.The accelerated motion of S' relative to S explicitly used in the treatment or the problem in the present work is that under time-independent field and subject to the condition of local Lorentz contraction and dilation; the resulting motion turns out to be that obtained earlier by M∅ller on entirely different considerations. The result or the present treatment is, however, more general than this particular motion seems to imply, since by an arbitrary coordinate transformation, it can be made to include an infinite number of accelerated frames including time-dependent fields, all within the framework or fiat space-time. General remarks are given for the clock problem in the general theory of relativity in the sense of Einstein's curved space.