Uniqueness of the Isotropic Frame and Usefulness of the Lorentz Transformation

Abstract

According to the postulates of the special theory of relativity (STR), physical quantities such as proper times and Doppler shifts can be obtained from any inertial frame by regarding it as isotropic.Nonetheless many inconsistencies arise from the postulates, as shown in this paper. However, there are numerous experimental results that agree with the predictions of STR. It is explained why they are accurate despite the inconsistencies. The Lorentz transformation (LT), unless subject to the postulates of STR, may be a useful method to approach physics problems. As an example to show the usefulness of LT, the problem of the generalized Sagnac effect is solved by utilizing it.

Consistent Coordinate Transformation for Relativistic Circular Motion and Speeds of Light

“…We have obtained Eqs. (18) and 20based on the LT for the instantaneous transformation for inertial frames, as in Eqs. (13a) and (14b).…”

“…23is correct, Eqs. (18) and (20) would not be accurate because they have been derived from LT. We have used LT to find world lines, which are independent of synchronization procedures.…”

“…It seems to have been known to most physicists that SGR can resolve the Sagnac effect without contradictions, although it cannot provide consistent explanations on the speed of light in the rotating frame [2,3,[14][15][16][17][18]. We show that the difference between the travel times of two light beams traversing a circumference in opposition directions can be exactly obtained via the traditional methods utilizing GT and the invariant line element.…”

“…As clearly proven in Ref. 18, the equivalence of inertial frames under light speed constancy is mathematically infeasible, which one can readily see from the relationships of relative velocity between four arbitrary inertial frames.…”

Effects of Janus Oscillators in the Kuramoto Model with Positive and Negative Couplings

“…When this phase separation is less than π radians, the two clusters travel on the phase circle, maintaining an average separation angle. Recently, the dynamics of the traveling state in this model, as well as in a variant, has been studied in terms of the phase speed of clusters [7,8].…”