Nonequivalence of a uniformly accelerating reference frame and a frame at rest in a uniform gravitational field

Abstract

A general expression is obtained for the space-time interval between neighboring events in a one-dimensional space in which it is possible to set up a rigid reference frame. Particular expressions are then obtained for the interval for the special cases of a rigid frame at rest in a uniform gravitational field and a rigid frame uniformly accelerating in field-free space. The two expressions are not equivalent and are used to show why, how, and to what extent observations made in a rigid enclosure at rest in a gravitational field are not equivalent to observations made in a rigid enclosure that is uniformly accelerating in field-free space. Two facts of particular interest that are demonstrated in the course of the analysis are the following: (i) Two spatially separated particles that are simultaneously released from rest and allowed to fall freely in a uniform gravitational field will not remain at rest with respect to one another. (ii) Uniformly accelerating reference frames and inertial frames are the only possible one-dimensional rigid frames in flat space-time.