I wrote a paper on a somewhat different approach to general relativity, here are the essential assumptions and results. Let us consider a system of two ”point-like” bodies where m<<M. According to Newtons classical theory of gravitation we have:
Now if (dm/dt = 0) we end up with the classical expression for the acceleration:
My hypothesis is that the assumption that m is not, explicitly or implicitly, time-dependent is incorrect. We replace m on both sides of (1) with mγ and let m be invariant while γ is a yet unknown expression for the time-dependence of that mass. Instead of (2) we then get:
The same time-dependency as known from special relativity is first tested:
A motivation for why (4) should hold true is available on page 10 in my essay. Inserting (4) into (3) and rewriting gives:
Equation (5) is the same as (2) except from one extra term. The interesting part is that if you use (5) in a simulation of the orbit of Mercury or any of the other planets you get a value for the ”anomalous shift of perihelion” of rather exactly one third of what is found empirically. Besides from that, if you run (5) in a simulation of planets in extremely strong gravitational fields you get the same kind of strange orbits that are expected from general relativity.
The point of this whole discussion is that you can get to something that is very similar to general relativity without having to deal with any kind of four-dimensional space-time.A physical copy of the essay can be acquired for instance here.
If you have any comments on this you can contact me:
See my essay for an explanation of how the remaining two thirds of the anomalous perihelion shift can be accounted for.
An updated version of my paper is now available at viXra: