| > if you calculate the poynting vector you see energy is not really leaving the system in this case Isn't there? That wasn't what I learned. If you set the light charge in motion around the heavy charge, then space will fill with radiation that has energy. No? > As I said, I am willing to agree to calling Maxwell's equatins schizophrenic, but not because of their coupled equations nature, but because of its indeterministic nature Well, if you don't set a boundary condition then the solution isn't determined. So in some sense that's obviously demanding too much. Math can't tell you what a differential equation will do if you don't give it boundary conditions. The retarded/advanced potentials are Green's functions, and Green's functions depend on boundary conditions. The problem I'm talking about is in addition to this problem. If you somehow decided that you're only using the purely retarded potential, then you could calculate the EM field given the trajectories of the charges, but that still doesn't tell you how charges move. If you decide that a charge is affected by the entire EM field including its own field then you run into infinities, and if you decide that a charge is affected only by the combined field from all other charges in the universe then you run into the issue that I mentioned above. Simple ways to address the problem fail, e.g. if you replace the charges by a sphere with smeared out charge, then the solution is no longer relativistically invariant because rigid spheres aren't. > I since long suspect Maxwells Equations to contain quantum mechanical behaviour that has not been explored yet. I don't know about unexplored, but if I recall correctly, Schrodinger was highly influenced by Maxwell's equations. Basically, he noted the correspondence between ray optics (Fermat's least time principle) and classical mechanics (least action principle). Maxwell's equations are the wave version of ray optics, so he asked himself whether there is a wave version of mechanics. In other words, ray optics is to classical mechanics as Maxwell's equations are to what? So there's not just an analogy between Maxwell's equations and QM, but that's actually partially how QM came to be in the first place! Maybe you could even claim that Maxwell's equations should be classified as quantum physics not classical physics. After all, if the paradoxical nature of the double slit experiment is called quantum physics then surely Maxwell's equations are quantum physics because they correctly predict the result, as opposed to ray optics which does not. Maxwell's equations are a quantum theory of a single photon, ray optics are the classical theory of a single photon. |