Page:Benton 1959 The Clock Problem (Clock Paradox) in Relativity.djvu/14

 "In the particular case discussed by Eddington, a body B projected from the earth returns to find that he has lived a shorter time than a body A which has remained on the earth undisturbed. The author shows that B may have been disturbed in such a way as to leave the earth and return to find that he had lived a time than A who remained on earth. It is shown that time is increased over some disturbed paths and that the explicit effect of disturbances themselves on Time is zero. The special case is considered where B is disturbed so as to follow a cometary orbit with perihelion distance equal to the perihelion distance of the earth and with longitude of perihelion sufficiently different from that of the earth so that the earth would not appreciably perturb B's motion on subsequent near approaches, and at some later approach it is again projected to the earth at a perihelion passage. The effects of the following four factors are considered: (1) sun's gravitational field, (2) earth's gravitational field, (3) the projecting disturbances on B, (4) the disturbances (molecular bombardments by the earth) on A." Sci. Abs. 38A:1994, 1935.

The paradox depends on the theory of relativity and the strange phenomena that result when a body travels at a velocity near the velocity of light. An experimental verification one way or the other may be imminent.

Explains briefly the theory of relativity, and then discusses the special or restricted theory, "which is that part of the theory which deals with velocities, propounds and asserts the only simple hypothesis on which the theory can be made to agree with observational facts."

The author contends that proof is too long to include, but "the result is that the dimension of length in the direction of motion in the case of a body moving relative to an observer appears to that observer to be shortened in the ratio $$\sqrt{1 - v^2/c^2}$$ where v is the relative velocity between the two bodies and c is the velocity of light. The same ratio obtains on the moving body, as determined by the moving observer and the stationary observer respectively. This is not to say that either observer will see anything different from what is normally to be expected. Each observer will use his own length and time scales to determine their relative movement.