Special Relativity, Energy and Measurement Part III

  From Maxwell’s equations or from a Newtonian definition of work involved assembling charge on a conductor or creating a spherically charged object of finite radius, it is known that energy carried in electric E and magnetic fields B, is given by:   .5 eo E dot E + .5/uo B dot B. In this note, we try to see if one may deduce the presence of energy in the E field without making use of the notion of of work associated with assembling charge (or Maxwell’s equations). In Part I, we called this a non-remeasurable type of energy. We argue here that the measurable is E, the electric field (and also B field)

  We use the notion of the energy of a core charge Q with electrostatic potential phi interacting with a test charge q as having an energy q phi(r vector). We suggest that the potential energy maps directly into a change in the electric field because the one adds the fields of Q and q. We suggest that this idea may be extended to any change in the electric field being associated with energy. The electric field, however, is governed by a change in phi and A (magnetic vector potential)  (4- vector) and it is this which dictates the new E field (and B) and hence the energy present. 

  We argue that the self-energy, i.e. the energy linked with an E field in the electrostatic case, is not a remeasurable quantity and that one must focus on the E field (and its link to phi). Thus,

without the notion of work (associated with assembling the charge), this field self-energy does not necessarily transform according to a Lorentz transformation. The reason seems to be that E (and B) fields are constrained to be associated with the change in (0, qphi) to (qAc, qphi’). No such constraint exists for a regular piece of rest mass or potential energy because it is not mapped to a changed E field. In other words, for an electrostatic charge, there exists a function f(E vector) =scalar = energy, but it is the E vector which changes when viewed from a moving frame, not the function f(E vector). E is an observable, while f(E vector) is not. These ideas are an extension of Part I.