Howard Percy Robertson (1949) extended the Lorentz transformation by adding additional parameters.
[1] 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.
[3][6] A similar model was introduced by Reza Mansouri and Roman Ulrich Sexl (1977).
[2][8][9] Contrary to Robertson, Mansouri–Sexl not only added additional parameters to the Lorentz transformation, but also discussed different synchronization schemes.
[3][6] Since the two-way speed of light in moving frames is anisotropic in both models, and only this speed is measurable without synchronization scheme in experimental tests, the models are experimentally equivalent and summarized as the "Robertson–Mansouri–Sexl test theory" (RMS).
By evaluating the RMS parameters, this theory serves as a framework for assessing possible violations of Lorentz invariance.
is the factor by which the interval between ticks of a clock increases when it moves (time dilation) and
(Notice that Newtonian physics, which has been conclusively excluded by experiment, results from
Mansouri–Sexl discussed the following synchronization schemes: By giving the effects of time dilation and length contraction the exact relativistic value, this test theory is experimentally equivalent to special relativity, independent of the chosen synchronization.
So Mansouri and Sexl spoke about the "remarkable result that a theory maintaining absolute simultaneity is equivalent to special relativity."
To second order in v/c, the parameters of the RMS framework have the following form:[9] Deviations from the two-way (round-trip) speed of light are given by: where
To verify that special relativity is correct, the expected values of the parameters are
The fundamental experiments to test those parameters, still repeated with increased accuracy, are:[1][9] The combination of those three experiments,[1][9] together with the Poincaré–Einstein convention to synchronize the clocks in all inertial frames,[4][5] is necessary to obtain the complete Lorentz transformation.
In addition to those second order tests, Mansouri and Sexl described some experiments measuring first order effects in v/c (such as Rømer's determination of the speed of light) as being "measurements of the one-way speed of light".
They emphasize that the negative results of those tests are also consistent with aether theories in which moving bodies are subject to time dilation.
[2][8] However, even though many recent authors agree that measurements of the equivalence of those two clock-synchronization schemes are important tests of relativity, they don't speak of "one-way speed of light" in connection with such measurements anymore, because of their consistency with non-standard synchronizations.
RMS is fully included in SME, though the latter has a much larger group of parameters that can indicate any Lorentz or CPT violation.
[15] For instance, a couple of SME parameters was tested in a 2007 study sensitive to 10−16.
It employed two simultaneous interferometers over a year's observation: Optical in Berlin at 52°31'N 13°20'E and microwave in Perth at 31°53'S 115°53E.
A preferred background (leading to Lorentz Violation) could never be at rest relative to both of them.
[16] A large number of other tests has been carried out in recent years, such as the Hughes–Drever experiments.