Uniformly accelerated reference frames in special relativity

Abstract

A uniformly accelerated reference frame S is defined as a set of observers who remain at rest with respect to a given observer A who is accelerating at a constant rate with respect to the instantaneously comoving inertial frames. The one-dimensional uniformly accelerated reference frame S is considered. The world lines of A and the other observers making up S are determined. Coordinates useful for describing events in S are carefully defined and the transformation equations between different sets of them are derived. The variation with position in S of the speed and frequency of light waves is determined. The motion of a free-particle in S is determined. Various phenomena in S, ordinarily associated with general relativity, are considered, in particular the asymmetric aging of twins at rest at different positions and the existence of horizons.

The Michelson–Morley experiment in an accelerated reference frame

“…The ability to detect absolute acceleration mechanically suggests the possibility of detecting absolute acceleration optically as well using, for example, a MichelsonMorley interferometer. This idea gains support from statements made by Desloge and Philpott [5],…”

“…We analyze a Michelson-Morley type experiment performed in a reference frame which is accelerating relative to this preferred reference frame at a rate which is constant relative to instantaneously co-moving inertial frames, otherwise known as constant proper acceleration. Reference frames with constant acceleration relative to instantaneously co-moving inertial frames have been thoroughly investigated [10,11,12,13,5]. The motion of a point object with constant proper acceleration g is referred to as hyperbolic motion and is described by the equation…”

Penrose–Carter diagram for a uniformly accelerated observer

“…Consequently, the asymptotes of the world line of the accelerated observer defines two event horizons [3,4,5,6,7,8,9,10,11]. In the conformal coordinates, equations of these horizons are…”

“…Its motion is such that it reaches the point x = 0 in the inertial frame at time t = 0 with a vanishing speed. The world line of the observer is given by [3,4,5,6,7,8,9,10,11]…”

“…In this framework, the very prominent notion of event horizon can be introduced in a simpler context than the one of black hole for instance. An uniformly accelerated observer can build his proper system of coordinates in a delimited, but infinite, sector of the flat Minkowski spacetime [7,8,9,10,11]. The corresponding time and position coordinate lines are respectively hyperbolas and straight lines in an ordinary diagram.…”