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Central two-particle forces are not sufficient in relativistic Newtonian mechanics for particles with spin.

Another step is taken in an attempt to see if there are physically interesting two-particle forces, for particles with positive mass and nonzero spin, that satisfy both the Lorentz-invariance conditions for Newtonian equations of motion for two particles and the equations that follow from the additional assumption that sums of two-particle forces satisfy the Lorentz-invariance conditions for three-particle systems. It is shown that when each two-particle force is central in the rest frame of the source particle, there are no solutions that give nonzero accelerations for both particles in a two-particle system; then a particle can be accelerated only by forces from particles that do not accelerate. Thus for central two-particle forces for particles with spin, the situation is the same as for any two-particle forces for particles with no spin; many particle forces are needed.