On a Special Transformation to a Non-Inertial, Radially Rigid Reference Frame

TL;DR

This paper derives a special coordinate transformation connecting an inertial frame to a non-inertial, radially rigid frame in Minkowski space, revealing effects like desynchronization and length contraction.

Contribution

It introduces a series expansion of a generalized Lorentz transformation for non-inertial frames that maintain their size, detailing the resulting coordinate and physical effects.

Findings

Desynchronization of clocks in the non-inertial frame

Kinematic length contraction observed in the inertial frame

Dependence of transformation parameters on proper coordinates

Abstract

We discuss the conditions under which a body, moving non-inertially in Minkowski space, can preserve its size. Under these conditions, using a series expansion of the generalized Lorentz transformation, we find a coor- dinate transformation connecting the laboratory inertial reference frame S and the rigid non-inertial reference frame s which moves without its own rotation with respect to S. Direct consequences of this transformation are: (a) desynchronization, in system s, of the coordinate clocks of s which were previously synchronized in S, and (b) a kinematic contraction of a ruler of system s observed in S. We also consider the dependence of the transfor- mation vector parameter on the proper coordinates of s.