Test theories of special relativity

Test theories of special relativity give a mathematical framework for analyzing results of experiments to verify special relativity.

An experiment to test the theory of relativity cannot assume the theory is true, and therefore needs some other framework of assumptions that are wider than those of relativity. For example, a test theory may have a different postulate about light concerning one-way speed of light vs. two-way speed of light, it may have a preferred frame of reference, and may violate Lorentz invariance in many different ways. Test theories predicting different experimental results from Einstein's special relativity, are Robertson's test theory (1949), and the Mansouri–Sexl theory (1977) which is equivalent to Robertson's theory. Another, more extensive model is the Standard-Model Extension, which also includes the standard model and general relativity.

Howard Percy Robertson (1949) extended the Lorentz transformation by adding additional parameters. He assumed a preferred frame of reference, in which the two-way speed of light, i.e. the average speed from source to observer and back, is isotropic, while it is anisotropic in relatively moving frames due to the parameters employed. In addition, Robertson used the Poincaré–Einstein synchronization in all frames, making the one-way speed of light isotropic in all of them.

A very similar model was introduced by Reza Mansouri and Roman Ulrich Sexl (1977). Contrary to Robertson, Mansouri–Sexl not only added additional parameters to the Lorentz transformation, but also discussed different synchronization schemes. The Poincaré–Einstein synchronization is only used in the preferred frame, while in relatively moving frames they used "external synchronization", i.e., the clock indications of the preferred frame are employed in those frames. Therefore, not only the two-way speed of light but also the one-way speed is anisotropic in moving frames.

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