The Mansouri–Sexl formalism for the Michelson–Morley experiment in nonvacuum media

In the present paper, we construct the complete Mansouri–Sexl formalism for the Michelson–Morley and Kennedy–Thorndike experiments executed in a refractive medium by extending their previous formalism derived for vacuum-based experiments. This is an important step since we will show that the experiments executed in a refractive medium give new possibilities for testing for Lorentz violations. In a previous paper, we developed the correct nonparametric treatment under the framework of special relativity, so no violation testing was possible. On the other hand, a parameterized theory, like that of Mansouri–Sexl is the standard way of testing for Lorentz symmetry violations. While other parameterized theories, like the Standard Model extension (SME) emerged in the late 1990s The Mansouri–Sexl formalism is still very much employed in experiments due to its relative simplicity and its lower number of parameters (three) versus the 19 parameters used in SME. This is why we are undertaking the novel step of constructing the corresponding Mansouri–Sexl formalism. Yet another novel attempt is to describe an unprecedented variation of the Kennedy–Thorndike experiment employing different refractive media for the interferometer arms. We will also demonstrate the advantages of deferring the expansion of the Mansouri–Sexl parameters a, b, and d as long as possible, thus obtaining a higher level of precision in deriving the violations.PACS No.: 03.30.+p