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Cause and Effect in Electromagnetic Theory

January 25, 2013

Consider a step electromagnetic wave incident on an initially stationary point charge. The charge will accelerate and emit an electromagnetic wave. Calculate the radius where the electric field of the emitted wave and incident wave are equal. Look familiar? It’s the “classical charge radius”. In fact, the emitted wave serves to cancel the tangential component of the incident wave’s electric field. Is this merely a mathematical tautology?

I believe this example shows how microscopic em theory is just an extension of macroscopic em theory. The cancellation of the tangential electric field is standard practice in macroscopic conductors. Does this mean that a charge is just some sort of conductor? No, that’s a circular argument and gets us no closer to the truth (conductor = point charges in a material, point charge = conductor).

It might be possible to eliminate mass as a concept using the above example. Note how the classical radius depends on the mass of the point charge. Conventionally, we would say that the mass regulates the acceleration due to the incident force, a = F/m. Let’s look at this example from a purely em viewpoint and start with a spherical charge of a given radius but no mass. The only physical law in this new em universe is that there can be no tangential electric field on a charge’s surface and that the charge will accelerate as needed to maintain that law. How it accelerates is unknown, just like it is in standard physics. How far can we get in constructing this em universe? Where does the theory break down?

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