The traditional One-Body Problem is solving the equation of motion for a single body in space, often where the space has an energy potential, described by an equation, that affects the body. What’s artificial about this is that space and the potential surface are taken as one unified thing. Or the potential surface is changing slowly vis-a-vis the body motion. These are relatively tractable situations.

In reality the potential surface is determined by the interaction of the test body and all outside objects, with the material of space as the intermediary transmitting those interactions. So separate the potential surface from space itself, then are the solutions absolute in space or only relative to other outside objects (which together with the test particle, create the potential surface)?

The One-Body Problem, Classical Version: given an object/particle in space, can we know and/or does it have an absolute position and momentum (not merely relative to the rest of the objects out there)?

Answer: in classical physics, yes.

The One-Body Problem, Quantum Relativistic Version: given a wave function in relativistic space, can we know and/or does it have an absolute position and momentum (not merely relative to the rest of the objects out there)?

Answer: in quantum physics, either yes or it’s irrelevant.

Answer: in relativistic physics, no. There are no absolute positions or velocities in space, only relative to other objects (or the center of mass of a group of objects or whatever).

The One-Body Problem, Very Universe Version: given a wave in the aether, can we know and/or does it have an absolute position and momentum (not merely relative to the rest of the objects out there)?

Answer: working this out elsewhere. I’m pretty sure there are absolute speeds, but only the aether knows them, the waves only know their relative speeds, or what they believe their relative speeds to be. (All waves always travel at c, but the direction can be in the perpendicular microscopic dimension we identify with time). There are not absolute directions or positions – directions and positions are only relative.

Examples

 Just about anything!