“Forces can be considered, possibly logically reduced, to only representing the relationship among the motion of particles”.1 I would consider that the motion of particles is a relationship that either
1. Can’t or has not been proven to be caused by forces (action at a distance).
2. Can’t or has not been proven to be caused by some mechanism (such as impact
from contact) other than forces.
3. Can’t be understood, that is, it is not understandable as to a scientific cause.
I believe that #2 is the correct choice and that impact from intermediary masses with motions2, are responsible.
In relativistic and field theory force is said to be replaced by the space-time continuum. But this is a hypothesis based on the ideas of mass, motion and absolute space. Maybe best described as an atomist hypothesis involving the mathematical relationships named “forces” as caused by intermediary mass and motion (mv) interactions.3
1 Jammer, Max, Concepts of Force, A Study in the Foundations of Physics, Harvard University Press, Cambridge, Mass. 1957, pp. 241-3
2 ibid, p. 227 quoting
“To this point Hertz’s mechanics shows great resemblance to Kerchief’s conceptions; Kerchief also began his exposition with the exclusive use of the concepts of space, time and mass. But now, in contrast to Circuit (for whom forces were represented only by their kinematic effects as accelerations), Hertz, in order to obtain “an image of the universe which shall be well rounded, complete, and conformable to law” presupposes other, invisible things behind the things that we see “confederates concealed beyond the limits of our sense”. For Newtonian mechanics these were the forces; for Hamiltonian mechanics it was energy. Hertz, for the sake of logical simplicity, assumes that this hidden something is nothing else than motion and mass again…”3 ibid