Two-Particle Forces for Relativistic Newtonian Equations of Motion

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Abstract
Forces are found that satisfy the covariance condition of Currie and Hill for Newtonian equations of motion of two particles in four-dimensional space-time. Examples are given that can decrease, at any prescribed rate, for large particle separation. Unfortunately these latter forces become complex and even singular for certain regions of velocity space. The technique used is to simplify the covariance condition by using four-vector variables as much as possible.