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

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 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 transverse Doppler effect and Sagnac effect in both formalisms and compare their predictions. We also discuss length measurements in the two formalisms.Comment: 21 pages, 2 figures, replaced with the published versio

On Franklin’s relativistic rotational transformation and its modification

Unlike the Lorentz transformation which replaces the Galilean transformation among inertial frames at high relative velocities, there seems to be no such a consensus in the case of coordinate transformation between inertial frames and uniformly rotating ones. There have been some attempts to generalize the Galilean rotational transformation to high rotational velocities. Here we introduce a modified version of one of these transformations proposed by Philip Franklin in 1922. The modified version is shown to resolve some of the drawbacks of the Franklin transformation, specially with respect to the corresponding spacetime metric in the rotating frame. This new transformation introduces non-inertial eccentric observers on a uniformly rotating disk and the corresponding metric in the rotating frame is shown to be consistent with the one obtained through Galilean rotational transformation for points close to the rotation axis. Employing the threading formulation of spacetime decomposition, spatial distances and time intervals in the spacetime metric of a rotating observer's frame are also discussed.Comment: 30 pages, 2 figures, replaced with the published versio