Dale
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Yes, that is clear. It is not as trivial as I had thought at first glance, but it is still too poorly defined to discuss reasonably. Once you figure out what f_A and f_B are and can generate some testable predictions then you will have something worth discussing further.
My guess is that you will find any such transformation incompatible with the relativity postulate.
My guess is that you will find any such transformation incompatible with the relativity postulate.