Necessary conditions for equivalence with the special theory of relativity
The Mansouri–Sexl theory is a well known test theory of relativity. Tangherlini  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  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