Uniqueness of the Isotropic Frame and Usefulness of the Lorentz Transformation

TL;DR

This paper examines the inconsistencies in the postulates of special relativity, discusses the Lorentz transformation's utility beyond STR, and demonstrates its application in solving the generalized Sagnac effect.

Contribution

It reveals inconsistencies in STR postulates, clarifies why experimental results still align with STR, and showcases the Lorentz transformation as a practical tool independent of STR postulates.

Findings

Experimental results agree with STR predictions despite inconsistencies.

Lorentz transformation can be useful without STR postulates.

Solved the generalized Sagnac effect using LT.

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.