Page:Benton 1959 The Clock Problem (Clock Paradox) in Relativity.djvu/13



Discusses the clock paradox based on Einstein's principle that an observer cannot detect uniform motion of his own system, and shows how Einstein's other basic principle - the constancy of the speed of light - resolves the paradox.

Clocks, time, motion, and relativity are discussed, in an attempt to "put into simple terms" the main points of Einstein's principle of relativity.

It is shown that the paradox can be resolved completely in terms of the restricted theory. It is also shown that the general theory can add nothing of physical significance to an analysis correctly made in terms of the restricted theory.

It is proved that if a clock X moves in a Galilean frame of reference (where gravitational fields are defined by their potentials) over any closed path and in any manner, then between any two passages through the same point with the same velocity, the gains, as seen by an observer moving with X, of all clocks at rest in the Galilean frame and not in the vicinity of matter are the same. These gains are precisely equal to the loss of the clock X as seen by observers stationed with the other clocks.

Clock problem treated for case of two observers, A and B. A remains at rest in Galilean frame of reference, while B moves relative to A with varying speed along radial straight line; problem is treated by another method: viz, that of moving axes.