I'm working on researches in the area of Special and General Relativity (SR/GR) focused on time dilation and I have a question to pose. Lorentz transformations (LT) introduce a time transformation such that two events occurring at same time in one frame not being at same time in another frame (relative simultaneity).
A "special/singular" case for LT is when the clock in the frame at rest is also fixed. In this case the dependency on the position for transforming a delta time is dropped, and the conversion is only based on gamma (i.e. delta t' = gamma * delta t). This is the setup is fully equivalent to other relativity theories, based on absolute synchronization methods, and more specifically based on an absolute simultaneity. So this aspect is not a SR peculiarity anymore.
Looking at the SR literature for Earth and space time drift analysis real world experiments, all the models used are always based on the above "singular" case, i.e. an absolute-like frame is defined with a clock is at rest there. This allows to correlate delta times in different frames through coordinate vs. proper time comparisons, under certain assumptions for clock synchronization. But again it's not a specific feature of SR with respect to other theories! The same can be obtained with absolute frame & time models, with in some case much more easy and clear steps.
Does anyone know an example where the relative simultaneity is used for modeling a real experiment, i.e. where also the term -v*x/c^2 plays a role in the tranformation?