Page:Benton 1959 The Clock Problem (Clock Paradox) in Relativity.djvu/11

 coincidences; (2) that from a finite series of such determinations all other world-points can be determined. Here is found the minimum of theoretical knowledge required to make the knowledge of nature a possibility. As its consequence it appears that for the continuum to be measureable, it must contain infinitesimal congruent systems of world-points, or in other words, equidistant event-pairs must be capable of existing in every part of it." Sci. Abs. 26A:1777, 1923.

In German.

Translated title: The Lorenz contraction and the clock paradox.

"The author continues the investigation, begun in a former paper, of a rod moving in an inertial field in such a manner as to remain either unstrained or without change of strain, and illustrates graphically some of the conclusions. He obtains a general solution of the case in which a body receives acceleration not with consequent strains, but by the application of an impulse, such as might be communicated to a train by a push from a locomotive, so that after the dissipation of the resulting strain waves, the motion becomes steady. As a consequence of this general solution, it is shown that a moving body, on becoming free from strain, immediately undergoes the exact Lorentz contraction, without the intervention of any forces of unknown origin, the necessity of which has been postulated by some relativists. The author next proceeds to deal with the so-called clock paradox. He takes the case of the observer A at rest in an inertial system, his world-line being OA, perpendicular to OX, the x-axis. Then OA is the time axis, and an observer B, moving along an arbitrary course in the space-time, is supposed to meet the observer A at O and A, and at each point they compare their clocks. The space-time interval OA is then common to the two tracks, so that it must be the same for each observer. The author verifies this by a rather lengthy analysis, using the formulae obtained in the paper and embodying the assumptions that A measures his time so that the light velocity in any inertial system is constant, while B measures his so that the backward and forward velocities are everywhere equal to each other. He then explains the rate of B's clock appears to A to be determined by: (1) the retardation due to the uniform motion of special relativity together with the parallel displacement of the time-plane; (2) the retardation of the rate wherever B's motion is retarded, both accompanied by corresponding rotations in the time-plane." Sci. Abs. 26A:824, 1923.