Eur. Phys. J. Plus (2016) 131: 296
https://doi.org/10.1140/epjp/i2016-16296-x

Regular Article

Coordinate transformation between rotating and inertial systems under the constant two-way speed of light

Department of Electrical and Electronic Engineering, Kangwon National University, 200-701, Kangwon-do, South Korea

^* e-mail: yhochoi@kangwon.ac.kr

Received: 13 June 2016
Accepted: 29 July 2016
Published online: 5 September 2016

Abstract

An observation system consists of the world lines of rest observers in the system. Recently a coordinate transformation between an isotropic and a rotating observation system has been presented which was derived through a relativistic circular approach based on the Lorentz transformation. It was formulated such that the relative speeds between the two systems are the same, but the two-way speed of light is not constant in the rotating observation system. The constancy of the two-way speed of light in inertial frames has been known to be experimentally verified. This paper presents the transformation that holds the constancy in the rotating system as well. Though the rotating system is in motion with acceleration, it can be regarded as locally inertial. Thus, in the limit, a transformation into a rotating system should be reduced to a transformation into an inertial systems. The transformation presented is consistent with the one between inertial systems so that the latter can be derived from the former in the limit. Moreover it allows us to theoretically analyze the generalized Sagnac effect, which involves rectilinear motion as well as circular motion. The theoretical analysis corresponds to the experimental results.