Embedding the photon with its relativistic mass as a particle into the electromagnetic wave explains the Gouy phase shift as an energetic effect

A new aspect concerning the relationship between a photon and electromagnetic wave has been developed by considering the question why the energy and the mass density of an electromagnetic wave described by m=E/c² are propagating in the same direction. For instance, in optical resonators, the energy density usually propagates along curved lines. However, according to Newton’s first law the mass density should propagate along a straight line if no force is exerted it. In order to solve this problem, which represents a contradiction between fundamental physical laws, the assumption has been made that a transverse force is exerted on the mass density and in consequence on the mass of the photons forcing them to follow the propagating energy density. This force has been computed by considering the infi nitesimal change of the normalized Poynting vector with respect to an infi nitesimal propagation step.