Jonnyb42 said:
Well the immense problem I am having is not getting solved, I am trying to learn enough physics to get to GR but people are telling me the answer does not lie in GR. I want a theory that explains the laws of physics in
any reference frame.
Does GR answer
https://www.physicsforums.com/showthread.php?t=404650"?
GR's field equations have the same form in any reference frame, but GR nevertheless has certain frames (Lorentz frames, i.e., free-falling, non-rotating frames) that are preferred, and that can be defined without reference to any external object.
You are basically expressing a dislike for this non-Machian feature of GR. There are other theories of gravity, such as Brans-Dicke gravity, that are more Machian than GR. In B-D gravity, it's quite possible that your two particles *will* collide. The theory was specifically constructed in order to give the "right" Machian behavior in cases similar to this one.
We then have several possibilities: (1) B-D gravity is right, GR is wrong, and your aesthetic distaste correctly steered you away from the theory that was wrong. (2) GR is right, B-D is wrong, and the universe works that way without concern for your aesthetic distaste. (3) Neither GR nor B-D is correct within their common domain of applicability (i.e., above the Planck scale).
The current empirical evidence leans toward #2, since the \omega parameter in B-D gravity is constrained by solar-system measurements to be very large.
Whether relational mechanics is a good candidate for #3, I can't say, not having studied it. Does it, for example, expose itself to falsification by making predictions of solar-system observation that differ from those of GR?