Electron as a Complex-Dynamical Interaction Process
  A system of two initially homogeneous, physically real fields uniformly attracted to each other is considered as the simplest basis of the self-developing world structure. It is shown that the system is unstable against periodic cycles of self-amplified, essentially nonlinear squeeze of its extended part to a small volume around randomly chosen centre, followed by the reverse extension. The resulting spatially random pulsation, or "quantum beat", is observed as (massive) elementary particle such as the electron. The property of mass is then universally and consistently defined as temporal rate of such dynamically chaotic and essentially nonlinear quantum beat, without introduction of any additional entities. The obtained picture can be considered as complex-dynamical completion of the "double solution" concept of Louis de Broglie. The dynamically emerging wave-particle duality, quantum discreteness, indeterminacy, space, and time lead to the equations of special relativity and quantum mechanics, providing their causal explanation and explicit unification. The elementary particle structure, its intrinsic properties, quantum and relativistic behaviour are obtained thus all together, within the unified analysis of the unreduced interaction process leading to the universal concept of dynamic complexity. The same complex-dynamical process accounts for the universal gravitation and general relativity. The electromagnetic, weak, and strong types of interaction between particles also constitute integral, dynamically unified parts of quantum beat processes inside elementary particles. The classical, dynamically localised behaviour emerges in a closed system as a higher complexity level corresponding to formation of elementary bound systems (like atoms). 
Andrei P. Kirilyuk