Eve:The Mother Of All Inertial Frames
Of course I understand the data Cahill is alleging. But neither you nor Cahill understand the real meaning of that data!
When there is a n =/= 1 (index of gas) "v =/= 0" absolute velocity detected, that means a vacuum symmetry breaking of O(1,3). It does not mean a return to t' = t absolute time of Galilean relativity. You still must use O(1,3) to get from one inertial frame to another even though there is a preferred frame which is to O(1,3) as the ferromagnetic order parameter is to O(3). There is a local vacuum order parameter just like there is a ferromagnetic order parameter.
Let Eve be in the preferred frame v = 0. This means that no fringe shifts on 90 degree rotations of the MM interferometer at rest in Eve's frame.
If Alice (Bob) measures v(Alice(Bob)) that means the Lorentz boost between Alice(Bob) and Eve is via [1 - (v(Alice(Bob))/c)^2]^-1/2 with the usual Lorentz transformations!
On the other hand the relative velocity between Alice and Bob (do 1 + 1 to keep it simple for now) directly measured in their Doppler radar is
v(Alice - Bob) = - v(Bob - Alice) = [v(Alice) - v(Bob)]/[1 - v(Alice)v(Bob)/c^2]
So that a direct boost between Alice and Bob (bypassing Eve) is via
[1 - (v(Alice - Bob)/c)^2]^-1/2
There is no problem with reciprocity as you incorrectly allege.
Apart from Alice and Bob seeing anomalous MM fringe shifts on 90 deg rotations if n =/= 1 and Eve seeing none, everything else is completely normal! Nothing else changes.
The anomaly is truly isolated! It is contingent not fundamental. No change of paradigm is required. A spontaneous broken O(1,3) vacuum symmetry in a finite space-time region simply means that the space of inertial frames is a vector space with an origin rather than an affine space with no origin, i.e. no preferred inertial Eve frame.
Ignoring GR curvature et-al for now, the kinematics of frame transforms is still O(1,3) and the dynamics is still O(1,3) covariant.
A revolution is not called for. There is no impending paradigm shift overturning Einstein as Cahill professes. There is no return to Galilean relativity. One simply punches an isolated hole in Einstein's affine space of inertial frames. End of story.
If you can find an inconsistency here show it. Cahill is the new Herbert Dingle even if his claims (and Consoli's in Catania) of the n =/= 1 Michelson-Morley fringe pattern shift on 90 degree rotations is confirmed. What he infers from that alleged fact is not justified by the evidence and the mainstream ideas of local gauge invariance with dynamics from compensating field and the "More is different" spontaneous breaking of vacuum (ground state) symmetries from the large-scale of cosmology to the shortest scales of high-energy physics.