James,
Wishes for a healthy, happy arrival of your grandchild!
Now, as to discussion of your deconstruction of Fitzgerald's contraction back to the Pythagorean basis of Michelson's design, without discussing relativistic spacetime; we open the Lorentzian can of worms. Specifically, it is constrained to only two dimensions, distance in space and duration of time. So does that necessarily mean that your 'corrected' gamma physically and realistically describes a true measurable length contraction even in a 3D+t Cartesian co-ordinates of absolute time everywhere in absolute space? You still would graph the form: C[1-{v^2/c^2)]^1/2 the same as that of the Lorentz Factor.
I have long argued that a real mass quantity being accelerated by application of an external force field should be regarded in four degrees of freedom, and the two dimensional factor should apply to the inductance reactance potential of the interaction. Velocity in this 4D paradigm, would equate directly with energy density of the mass, and the foreshortening would itself limit at a 'c' proportion, accompanied by a lateral expansion of 'c' proportion. The acceleration to light velocity would thereby 'dillute' the density of an electrostatic charge to the light velocity difference found by Maxwell for the coexistant magnetostatic intensity. Rather than infinite mass, or infinitely foreshortened, the Lorentz factor would limit out at a light velocity proportionate value; in four degrees of freedom conforming the shape and density of a mass in 4D, small enough to have a rest inertial density at core that would not inhibit its acceleration to light velocity. It would just require an infinite application of external force to maintain that velocity due to the 'c' proportionate decline in inductance reactance potential, while the coherent mass quantity would seek equilibrium at relative rest core inertial density.
In short, a unified field of energy precipitating as a coherent mass quantity would vary in rest density from an inelastic value commensurate with its relative inertial density, through an elastic electrostatic value, fluid magnetostatic, and an aetherial gravitational value to a lower bound limit of cohesion.
Note that this paradigm is profoundly background independent, as is does not prescribe either absolute space+time, or relativistic spacetime. The mass 'knows' its direction and velocity by its own density and shape, relative to a greatest density which translates as inertia across the entire energy volume. All spacetime is local. In an electromagnetic model it prescribes a cyclical acceleration/deceleration event, similar to the 'big bang - big crunch' modeling.
But here we come to the simplicity of preference. There is nothing that proves absolute time everywhere in space, either. There is the very human truth that time is inexorably slipping away.
'Well my soul checked out missing as I sat listening, To the hours and minutes tickin' away, Yeah just sittin' around waitin' for my life to begin, While it was all just slippin' away.' - Bruce Springsteen 'Better Days' 1992
On the GR arguments, I'll stay home and watch Tom. :-> jrc
