Page:Benton 1959 The Clock Problem (Clock Paradox) in Relativity.djvu/7



In French.

Translated title: Physical space- and space-time of an observer in relation to other observers.

Continuing an investigation of the structure of the space-time of a solitary observer, a discussion in general terms is now given of the restrictions imposed if this observer exchanges signals with other observers.

In Spanish. Not examined.

"The equations of motion in Birkoff's flat space-time theory of gravitation are solved to the first order of approximation for small velocities. A particle moving approximately in a circular orbit is found to have a small acceleration perpendicular to the plane of the orbit. The effect is too small for observation, but might have applications in cosmology." Sci. Abs. 56A:595, 1953.

A space-space representation is developed for nonrelativistic wave mechanics as was done for classical mechanics, by adding to the system a rotating body to serve as a clock, and applying the time-independent forms of the equations of motion. The usual Schrödinger equation is obtained in this way, however, only in the limit as the energy of the clock becomes very large. The reason for this restriction is found in an appendix, by comparison with the classical equations. Other appendixes deal with certain aspects of the Hamiltonian representation of the problem.

Refers to the clock paradox controversy and suggests use of a clock whose behavior is totally unaffected by motion and as easily