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Reyes G.E. and A. Royer (2003) On the law of motion in Special Relativiyt. arXiv: physics/0302065 v1 19 Feb 2003

Newton’s law of motion for a particle of a given mass subject to a force at a given time may formulated either as “force = rate of change of the quantity of motion” or, since the mass is constant, as “force = mass times acceleration”, where velocity and acceleration are relative to an inertial frame. This law may be interpreted in either of two ways: (1) The force acting on the particle at the given time during an infinitesimal lapse of time imparts to the laboratory a boost, while the particle maintains its velocity relative to the new frame. (2) The force acting on the particle at a given time during an infinitesimal lapse of time imparts to the particle a boost relative to its proper frame which moves with the same velocity relative to the laboratory. We show that the relativistic law of motion admits both interpretations, the first of which is in fact equivalent to this law. As a consequence, we show that the relativistic law of motion may also be formulated as “force = mass times acceleration” in analogy with Newton’s law, but with a relativistic mass and a relativistic acceleration defined in terms of the relativistic addition law of velocities, rather than ordinary mass and ordinary vectorial addition of velocities that lead to the classical acceleration and to Newton’s law.