Relativistic Classical Mechanics with Time as a Dynamical Variable

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Abstract
A relativistically invariant classical Hamiltonian mechanics is presented, in which each particle is described by the eight dynamical variables of position, time, momentum, and energy. The two-particle scattering problem which consists of both inelastic scattering and elastic scattering is completely solved and reduced to quadratures. Special attention is given to elastic scattering, and it is shown that the two particles participating in elastic scattering remain at a spacelike separation with respect to each other throughout their trajectories. It is also shown that this theory is capable of describing the decay of one particle into two particles.