Proof of the GM–GR parity theorem for the two-body problem.

One loosely defines Mechanics as a physical theory that rests on the concepts of mass and force and a law of inertia. In contrast, one loosely defines General Relativity as a physical theory that describes how mass and energy curve spacetime, causing objects to move along the straightest possible paths within that curved geometry. For a long time, scientists viewed Mechanics and General Relativity as fundamentally irreconcilable theories, with neither being a mere modification of the other, but rather grounded in distinct and incompatible physical principles. This theorem reshapes that understanding by proving that a modified Mechanics, called General Mechanics, fully aligns with General Relativity in the two-body problem. The trajectories in both theories are the same, and it follows that both adopt the same physical principles. NOTE FROM THE EDITOR-IN-CHIEF: In a blinded assessment, I asked five scientists to verify the mathematics of the parity theorem presented in this article before the article would undergo a review. All of them verified the mathematics. I took this additional step because of the theorem’s potentially significant impact on the fields of Mechanics and Relativity. [ABSTRACT FROM AUTHOR]