The potential energy field model of objective gravity and inertia is simple and coherent. Inertia and the force of gravity are the same thing - energy gradients of a particle and of the field, respectively. We can compute their interactions with high school math.
Here is a comparison of classical versus relativistic formulas and outcomes, to show where Newton quite understandably went wrong. Throughout, θ is the gradient angle, and speeds are measured as a fraction of c, the speed of light. All calculations are for collinear motion to simplify and clarify.
Classical acceleration:
sfinal = sa + sb
0.5c + 0.75c = 1.25c
0.5c - 0.75c = -0.25c
Relativistic acceleration:
sfinal = sin(atan(tan(asin sa) + tan(asin sb))) = sin(atan(tan θa + tan θb))
0.5c + 0.75c = 0.863c
0.5c - 0.75c = -0.486c
Classical relative motion:
sapparent = sthem - syou
0.75c - 0.5c = 0.25c
-0.75c - 0.5c = -1.25c
Relativistic relative motion:
sapparent = sin(atan(tan(asin sthem) - tan(asin syou))) = sin(atan(tan θthem - tan θyou))
0.75c - 0.5c = 0.486c
-0.75c - 0.5c = -0.863c
With this new relativistic formula, it is mathematically impossible for a massive particle to ever reach the speed of light. (Photons have neither a mass nor a gradient.) Since all particles have a fixed width, the gradient angle can never reach the vertical. The speed of a particle is determined by the sine of the gradient angle. The tangent of the angle is the gradient, the change in energy levels across the particle.
This doesn’t really do anything much different from special relativity. It just does it from the starting assumption that there is such a thing as objective time and flat, Euclidean space. Plus, it uses the exact same formula for gravity (once you figure out the energy gradients), so it is much simpler than general relativity.
QED
