Tom,
I agree. That's precisely what we assume SR means, which I'm suggesting is not the only possible interpretation. The alternative recognises Einstein's 1952 analysis, and he and Minkowski's 'Proper Time' and the converse; co-ordinate time and undetectable ('imaginary') c+v (1908).
Consider carefully what you just wrote; "there is no objective third observer." I agree. There'can't be in current understanding. And it's not just that such an observer would 'see' different speeds, he cannot actually exist, as no possible frame exists for him to occupy! This is what Lorentz said he could not accept 'without reservation' in 1913. It means that if we, on Earth, observe light or objects approaching from each side of us at d/t = 0.6c then we must cease to exist!! I've now thrown a ring round that slippery soap bar so we can't keep chasing it away by slipping back to 'appearances' when faced with it.
But now consider the option. We don't remove the entire 3rd frame, we just remove it's privileged status, which means it's 'absolute' character. We treat everything as a 'medium', as diffuse as we like (which my essay showed space is anyway) bt allow media to move wrt each other, which again we already know they do anyway!! Now we recover Einstein's postulates WITHOUT any paradoxes, but WITH an underlying quantum mechanism (Raman atomic scattering) to explain them.
It's the tiniest adjustment to a hidden assumptions of SR, and one which Einstein knew and explained conceptually and was desperately trying to track down at the quantum level.
Even better. The structure of inertial systems and space-time gains Local Reality, and the precise hierarchical structure of Truth Functional Logic TFL;
Consider multiple 3D n body inertial systems; A, B, C, D, E, F, G, etc. (each equivalent to a 'proposition'). They are each of S spatial extent but bounded, and may be within or without each other. (Einstein's 1952; "space s in motion within space S"). Any two in the same state of motion become one.
Considered carefully, we find that each can only have ONE immediate larger neighbour. Each may have many different or compound spaces within it, but each of those still only has ONE adjoining 'background' frame. So if we 'nest' the spaces spatially up from A to G, The 'state of motion' of A is only relevant wrt to B, (A-B) which is only relevant to (A-B)-C, and on ad infinitum. B may leave the limits of C and move through D, but still only has that single relative motion B-D, and the compound proposition B/D only has a 'speed' wrt E so (B-D)-E.
This is the precise structure of propositions in TFL. Each proposition can only be logically resolved wrt it's immediate neighbour as a compound proposition, and then that can only be resolved wrt it's own immediate neighbour. Relative velocities are ALL limited to c. But that only applies to REAL velocities, in the local background, which are then 'Proper Speeds' or 'propagation' velocities.
Apparent velocities 'two frames removed' cannot be detected, only worked out trogonometrically as they are only apparent, and directly equivalent to 'co-ordinate time'. The light from any scattering evidence propagates at c, and has to cross the frame boundaries (so Doppler shifting) and arrive at the detector at c in it's local frame. So absolutely NOTHING breaches propagation speed c anywhere. The ontological construct treats each system is a discrete field (thus 'DFM')
Yet, we can now fire a bullet on Earth and have no problem reconciling that it's apparent velocity wrt some other planet at z=2, or a blob of plasma from a quasar at z-3, may be around 6c, which is exactly what we find in astronomy. (not logically resolved using current interpretation).
You rightly asked what proof. I pointed out it only had 3 proofs (though each seemingly irrefutable); Maths, Logical consistency and all available empirical evidence. As it agrees with most of SR and GR, then all the evidence for SR and GR is also consistent with this interpretation. All the stuff under the carpet is also now consistent, and I've pointed out a long string of unique predictions.
But unfortunately it doesn't seem to meet one other apparent requirement for an advancement of understanding; It isn't precisely the same as the previous understanding. I'm now not sure that can be overcome. If you can see how, or see any other remaining falsification with it do please identify it.
Many thanks
Peter