A Few Comments on Classical Electrodynamics

Abstract

In this article we will discuss a few aspects of the spacetime description of matter and fields. In Section:1 we will discuss the completeness of real numbers in the context of an alternate definition of the straight line as a geometric continuum. According to this definition, points are not regarded as the basic constituents of a line segment and a line segment is considered to be a fundamental geometric object. This definition is in particular suitable to coordinatize different points on the straight line preserving the order properties of real numbers. Geometrically fundamental nature of line segments are required in physical theories like the string theory. We will discuss the cardinality of rational numbers in the later half of Section:1. We will first discuss what we do in an actual process of counting and define functions well-defined on the set of all positive integers. We will follow an alternate approach that depends on the Hausdorff topology of real numbers to demonstrate that the set of positive rationals can have a greater cardinality than the set of positive integers. This approach is more consistent with an actual act of counting used in statistical mechanics. This article indicates that the axiom of choice is a better technique to prove theorems that use second-countability. This is important for the metrization theorems and physics of spacetime. In Section:2 we will discuss an improved proof of the Poisson's equation. We will show that the self energy of a point charge can be zero in the potential approach to evaluate it. In Section:3 we will discuss a few aspects of the equivalence of the Schwarzschild coordinates and the Kruskal-Szekeres coordinates. In Section:4 we will make a few comments on general physics including the special theory of relativity and hydrodynamics.