Some people assume that because these two coordinate systems are empirically equivalent (classically) then any distinction between them is irrelevant, but that's not true. For example, there are some indications "...that a consistent formulation of quantum mechanics demands the existence of a preferred frame.":
From the abstract:
"In this paper the relativistic quantum mechanics (QM) is considered in the framework of the nonstandard synchronization scheme...Our results support expectations of other authors [J.S. Bell, in
Quantum Gravity, edited by C.J. Isham, R. Penrose, and D.W. Sciama (Oxford University Press, Oxford 1981), p. 611; P.H. Eberhard, Nuovo Cimento B
46, 392 (1978)] that a consistent formulation of quantum mechanics demands the existence of a preferred frame.",
and, from the first page:
"The formulation of the Poincare-covariant quantum mechanics presented here seems to have a number of advantages over the standard formulation. First of all, the conflict between the causality and the quantum theory disappears. Second, the localization problem is solved." -- P. Caban
et al.,
Lorentz-covariant quantum mechanics and preferred frame, Physical Review A
59(6), 4187 (1999);
http://www.arxiv.org/abs/quant-ph/9808013.
So, although these two coordinate systems are empirically equivalent as far as classical physics goes, the alternate system
may turn out to be ultimately superior.
If we were to assume that simply because these statements were published in Physical Review A then they are beyond questioning, then
relativity is toast.
Originally Posted by clj4
One-way lightspeed
transforms into a cutoff frequency in the absolute frame 
. Although this was proven using Eqs. (5), (6), and (7), please note that it is also fully consistent with Eqs. (1) and (4); and in fact, all frequencies transform between these two coordinate systems quite simply according to 
.
