Fermi coordinates and modified Franklin transformation: a comparative study on rotational phenomena

Abstract

Employing a relativistic rotational transformation to study and analyze rotational phenomena, instead of the rotational transformations based on consecutive Lorentz transformations and Fermi coordinates, leads to different predictions. In this article, after a comparative study between the Fermi metric of a uniformly rotating eccentric observer and the spacetime metric in the same observer’s frame obtained through the modified Franklin transformation, we consider rotational phenomena including the transverse Doppler effect and the Sagnac effect in both formalisms and compare their predictions. We also discuss length measurements in the two formalisms.