Appendix A: Relativity and Electromagnetism
Appendix A: Relativity and Electromagnetism In this appendix we examine and, relativistically, modify Newtonian particle mechanics; thus, it would be natural to look with the same intention at Maxwell’s electrodynamics, at first in a vacuum. That theory, however, turns out to be already “special-relativistic.” Unlike Newtonian mechanics, classical electrodynamics is consistent with special relativity. Maxwell’s equations and Lorentz’s force law can be applied legitimately in any inertial system (e.g., system S). The only two assumptions we need to make about the electromagnetic force are that it is pure force—in other words, rest mass is preserving—and that it acts on particles in proportion to point charge q, which they carry. Beyond that only “simplicity” and some analogies with Newton’s gravitational theory will guide us, which what this appendix is all about. A.1 Introduction With corrected Newtonian mechanics, we are now in a position to develop a complete and consistent formulation of relativistic electrodynamics. We will not be changing the rules of electrodynamics at all, however; rather, we will be expressing these rules in a notation that exposes and illustrates their relativistic character. As we said the at the beginning of this appendix, the intention is to look at Maxwell’s electrodynamics and its basic laws, as they have been summarized by the four Maxwell’s equations, plus Lorentz’s force law , are for an invariant condition under Lorentz transformations from one inertial frame to another. As also mentioned before, by inertial frame with only two assumptions: (1) the force induced from electromagnetics (EM) will be a pure force; and (2) the rest mass of moving particles persevere, and that it acts on particles in proportion to point charge q, which the particle carries.
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