Emergent Quantum Mechanics: How the Classical Laws Can Mimic Non-Local (“Spooky”) Interactions

In Feynman’s “Lectures on Physics” it is observed that close to an oscillating dipole the electromagnetic field is almost quasi-static, as if retardation is absent and the speed of transmission thus would approach infinity. Within the framework of Emergent Quantum Mechanics (Em.QM) non-singular electron models are being revisited, showing similar phenomena near a droplet of charge. In the literature, the matter has been called an as yet unsolved dilemma because – like the “spooky” non-local effects of Quantum Mechanics (QM) – it seems to be in conflict with relativity theory. In the present paper, an asymptotic expansion of the electromagnetic field around a moving and deforming droplet of charge is used to investigate the matter in detail. It is concluded that Feynman’s formulae are correct, be it _after_ initial conditions of the boundary value problem have been established by a field of normal travelling waves. When such a reset has been completed, the field of travelling waves can be written as a superposition of groups of standing waves. In each standing wave system, the variables belonging to it display synchronicity, which causes the illusion of non-retarded interactions. But in fact, there are no causal relations between the singularities (such as charges) and the other field variables (such as electromagnetic forces), even though the illusion may be given that superluminal signalling takes place. The conclusions are important for the theory of Em.QM, since they show that the classical laws are able to mimic non-local phenomena.