Geometry and Newtonian Physics
Abstract
The question is raised whether there is any physical content in the requirement that freely moving particles move along geodesics in 4space. The question is partially answered in the affirmative by demonstrating that some motions cannot be expressed as geodesics in any 4space under certain conditions. In particular, it is shown that the trajectories of the Newtonian equations of motion for any type of nonvanishing conservative force field cannot be expressed as geodesics in any static 4space when it is required that the metric have the diagonal form (1,1,1, constant) at infinity.
 Publication:

Physical Review
 Pub Date:
 September 1966
 DOI:
 10.1103/PhysRev.149.1040
 Bibcode:
 1966PhRv..149.1040C