Authors: Steven Kenneth Kauffmann
The generic single-particle relativistic dynamical principle is usually taken to be that the time derivative of the particle's momentum is equal to the applied force. That relativistic momentum itself, however, is the particle's rest mass times the proper-time derivative of its position, so this dynamical principle is easily reverted to the original Newtonian one of the particle's mass times acceleration being equal to the force, provided that the time derivatives always refer to proper time and the force is amended by a relativistic factor of gamma, which we denote as proper force; the Lorentz covariance of the result is greatly aided by the Lorentz invariance of proper time. It is shown that the purely relativistic fourth component of this Lorentz-covariant Second Law extension pertains to the particle's power, as would be expected. Its full electromagnetic case emerges directly from a certain entirely Lorentz-invariant Lagrangian.
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