# Necessary conditions for equivalence with the special theory of relativity

### Abstract

The Mansouri–Sexl theory is a well known test theory of relativity. Tangherlini [1] produced a theory that is a limit case for the Mansouri–Sexl theory. We will show that Tangherlin's theory disagrees with the waveguide theory, predicting a different result than special relativity (SR), so, the Tangherlini theory is not equivalent with SR. We will also show that for a theory to be equivalent to the special relativity, contrary to Robertson [2] it is not sufcient to predict the same results for the Michelson–Morley, Kennedy–Thorndike, and Ives–Stilwell experiments, it must also predict the same results for a waveguide-based experiment described in Section 4 of our paper.**Keywords:** Mansouri–Sexl test theory, SME, Tangherlini theory, Ives–Stilwell experiment, transverse Doppler effect, waveguide theory**PACS:** 03.30.+p