Comparing Relativistic and Newtonian Dynamics in First-Order Logic

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In this paper we introduce and compare Newtonian and relativistic dynamics as two theories of first-order logic (FOL). To illustrate the similarities between Newtonian and relativistic dynamics, we axiomatize them such that they differ in one axiom only. This one axiom difference, however, leads to radical differences in the predictions of the two theories. One of their major differences manifests itself in the relation between relativistic and rest masses, see Thms. 5 and 6.