Quote by Dickfore
So, in the first paragraph of the Introduction it says:
"...But the combined requirements of relativistic symmetry and manifest invariance may restrict the theory so severly that it is capable only of describing non interacting particles. We will show that this is in fact the case in a Lorentz symmetric classical mechanical theory of the motion of a pair of particles..."
So, I guess this goes in favor of my first post in this thread. The point is that, due to the finite speed of propagation of interactions, one ought to consider a field as a physical object carrying the interaction. A field has (innumerably) infinitely many degrees of freedom, and the Lorentz invariant twobody problem turns into a problem in continuum mechanics.

Thank you for taking the time and for your thoughtful response. I am looking at a copy of the paper right now. Let me spend the rest of the day reviewing it and collecting my thoughts and questions and I will get back with you tomorrow.
Heavywater