Pete,
I see your distinction of proper and relative velocity, and it resolves from taking light velocity as the invariable rather than Newton's (et al) ubiquitous scalar increments as one or the other, time or space. Hence the relativities.
Your own dynamics of relative velocities methodology may well stem from your architectural training, live loads are just that. I climbed steel up to 50 feet above the millwrights on a one job, and in the States loads are in KIPS, that is; 1 pound of instantaneous applied force will propagate across structural members (seeking ground! center of earth!) at a rate of 1000 inches per second. So from a measuring method, comes our rationales.
The somewhat archaic 'free rest mass' simply means reducing to first principles in measures, the dynamics then can be examined from having a co-ordinate free, proper set of scalars as an invariable benchmark. But all dynamic models seem to fail to address a gap in understanding that Quants always point towards as segmenting the continuum. We treat inertia only in comparing one mass to another, and have not reasoned out what it is that makes inertia unique to all mass.
Typically: a body at rest tends to stay at rest..a body in motion tends to stay in motion So what is it about mass that is the same for either condition given that there is no way to determine motion or no motion except relative between two masses? And, keeping in mind that mass:energy equivalence is only that and says nothing about matter.
Addressing only that in terms of a free rest mass, meaning free of any influences save it's own self-gravitational parameters, and only one such free rest mass:energy quantity, it becomes nearly self-evident that inertia is the translation of response (at constant rate, c ) across a finite volume of energy. If we can say 'c' , the energy must seek to be existant at that ubiquitous velocity and have a continuum constant density. Physically, that would be a conceptually impossible state. Yet we also experience energy concentrations, as if we live in an energy supersaturate space which precipitates masses of energy concentrations to conserve space. There is not enough space for all the energy to exist in homogeneity at any given instant. There is therefore an equal tendency of energy to seek an existential deceleration from 'c' which is a cornerstone of John Merryman's thinking, ying and yang (sp?).
So we can hypothesize that inertia is relative to any size mass, but must be of the same proportional value for any relative size concentration, or different masses would fall in a gravitational field at different rates as each mass would have a different valued gravitational field of its own. That relative proportional constant value logically follows from the homogeneous continuum density paradox to a gradient of increasing density as deceleration piles up in front of itself, slowing the rate of decelerant energy in ever smaller spherical volume. It will seek nil velocity.
So we can conclude that for any mass to exhibit the characteristics of inertia, some portion of that energy quantity must exist at a constant density as the greatest density, in direct proportion to the quantity of energy itself. Given the established mass : energy equivalence of e = mc^2 , which can be taken as two dimensional, suggests that a 4D density gradient resolves from the existential deceleration of energy from 'c' to nil in four dimensions of measure consistent with the paradigm of two dimensional measure in equivalence. The proportional value sought as common to the characteristic of inertia would thereby obtain as the greatest and constant density concentration of energy, being X = ec^2 or its equivalence I = mc^4.
Quantum Mechanically, this classically defining energy density proportion is what determines whether a state of being exists or not. The 'Zero Point Particle' can exist in any relative location, however uncertain that location might be, within a spatial volume prescribed by that classical energy density parameter.
The trick will be to discover how that seed density volume relates through energy distribution to find true size of the full field volume and the inertial density volume, as well as the volume radial length of any specified density in a distinct, discrete field. Dynamic models are like schematics of experimental apparatus to detect how energy behaves. jrc
