Nonlinear nonlocal classical field theory of quantum phenomena

Abstract

It is generally thought that there is a mysterious dividing line between classical physics and quantum physics: one objective, deterministic and continuous; the other discrete, indeterminate and subjective even at the single entity level. Such a division seems to be provisional and unsatisfactory in natural philosophy, and physicists never stopped to search for a deterministic and objective substratum of quantum phenomena. There is a recent revival of thought that matter and light and their interactions can be described by the ideas of classical field theories of continuous media and yet all the quantum effects can be reproduced, when the Dirac field for the electron is treated as a classical complex field. The discreteness in quantum physics is on the same footing as the discrete frequencies of a membrane due to the boundary conditions, and this discreteness disappears when radiative effects are included. The nonlinear nature of coupled matter and field equations plays a crucial role. Furthermore, the particle mechanics is a limit of a deterministic quantum theory of single events which is distinct from the quantum theory of repeated events for which we use probabilistic concepts.