Internal structures of electrons and photons: The concept of extended particles revisited

The theoretical foundations of quantum mechanics and de Broglie–Bohm mechanics are analyzed and it is shown that both theories employ a formal approach to microphysics. By using a realistic approach it can be established that the internal structures of extended particles comply with a wave equation. Including external potentials yields the Schrödinger equation in this context, is arbitrary due to internal energy components. The statistical interpretation of wave functions in quantum theory as well as Heisenberg’s uncertainty relations are shown to be an expression of this, fundamental arbitrariness. Electrons and photons can be described by an identical formalism, providing formulations equivalent to the Maxwell equations. Electrostatic interactions justify the initial assumption of electron–wave stability: the stability of electron waves can be referred to vanishing intrinsic fields of interaction. The theory finally points out some fundamental difficulties for a fully covariant formulation of quantum electrodynamics, which seem to be related to the existing infinity problems in this field.