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" ... Instead, relativistic mechanics is treated with local field theories within the framework of Lagrangian or Hamiltonian mechanics. Instead of forces that particles exert on each other, we have interaction terms in L or H, that depend on the states of both a particle and a field, or two fields (or possibly more than two entities). The additivity of forces is equivalent to the linearity of these interaction terms. For example, the interaction term for classical electrodynamics is −JμAμ, where J contains the charge and current density, and A the field potentials; this describes both how charges and currents generate the field and how the field acts on charges and currents. Since it’s linear in both A and J, that guarantees that the field of multiple charges is the sum of the fields of the individual charges. When that field then acts on a particle, it does so in proportion to its own strength, so, overall, the force the particle feels is the sum of the forces due to the individual particles acting on it. ... "