CHAPTER 2 - RELATIVISTIC MECHANICS

Abstract

Publisher Summary This chapter focuses on the relativistic mechanics of Einstein theory of relativity. The principle of least action asserts that the integral S must be a minimum only for infinitesimal lengths of the path of integration. For paths of arbitrary length, it can be said that S must be an extremum and not necessarily a minimum. For a closed system, in addition to conservation of energy and momentum, there is conservation of angular momentum, that is, of the vector M = ∑ r × p, where r and p are the radius vector and momentum of the particle; the summation runs over all the particles making up the system. The conservation of angular momentum is a consequence of the fact that because of the isotropy of space, the Lagrangian of a closed system does not change under a rotation of the system as a whole. In relativistic mechanics, the definition of the center of inertia of a system of interacting particles requires the explicit inclusion of the momentum and energy of the field produced by the particles. Although in the system K0 (in which Σ p = 0), the angular momentum is independent of the choice of the point with respect to which it is defined, in the K system (in which Σ p ≠ 0) the angular momentum does depend on this choice.