Speculation on the Photon Solution from Maxwell's EM Equations Part II

As noted in Part I, the mathematical derivation of the existence of a photon in Maxwell’s EM equations is demonstrated through the existence of two wave equations, one for E (electric field) and the other for B (magnetic field).  This, in turn, is based on two specific Maxwell equation.

    In Part I, we argued that the form:  E = -grad phi - dA/dt partial already suggests a wave solution because there exists a periodic function f(-wt+kx) which makes E=0 and B=0, namely phi= f(-wt+xk) and A= f(-wt+kx) (1,0,0). This may be readily altered to:  phi= f(-wt+kx) and A = phi (1,1,1) to obtain E and B fields of the same magnitude and perpendicular to each other and the direction of motion. We also suggested that a solution exp(-iwt+ikx) is associated with conservation of energy, momentum and spatial probability, a feature which is not apparent from E=cos(-wt+kx) ei (example) from the wave equation.

     In Part I, we noted that the form E= -grad phi - dA/dt partial follows from a desire to have the vector part of E depend on the natural vector in the moving frame, namely: { (x-vt), y,z }. If one uses -grad phi (which holds in the rest frame of a point charge), the vector portion is: { gg(x-vt) , y,z) where gg=1/ (1-vv/cc). This is not the spatial vector that a person in the moving frame would see or measure, but E is in fact measured.  In order to remove gg, one requires the addition of - dA/dt partial. 

   Although conservation of energy, momentum and spatial probability are key and linked with exp(-iwt+ikx), we suggest that there is an extra feature which is directly linked to the use of E= -grad phi - dA/dt partial. This form ensures a usual measurement of an r vector in the moving frame and at the same time provides for a mathematical solution of an entity which is able to provide both a ruler and clock, namely exp(-iwt+ikx), because:  w=2*3.14 f  and T=1/f and wavelength = 1/k. Thus, the suggestion that E= -grad phi - dA/dt partial existing because of a measurement criterion (usual r vector) is actually physically linked to a measurement entity. Thus, one does not simply have an abstract condition requiring a usual vector, but it is enforced physically by the existence of a photon which provides for this measurement, we argue.