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 4-space. The question is partially answered in the affirmative by demonstrating that some motions cannot be expressed as geodesics in any 4-space under certain conditions. In particular, it is shown that the trajectories of the Newtonian equations of motion for any type of non-vanishing conservative force field cannot be expressed as geodesics in any static 4-space 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