Abstract
A no-frills model of quantum theory can be constructed - a local realistic theory that has the same unitary evolution as a quantum field theory. On the other hand, evolution in this model is described by a partial differential equation in (3+1)-dimensional spacetime. Therefore, at any time point, information in this model can be stored in space in the form of electromagnetic field. In this sense, this is a legacy model of information storage and processing in nature, as it is very similar, in principle, to classical electrodynamics. The main premises and steps of construction of this model are as follows. Schr\"{o}dinger noted that the complex charged matter field in the Klein-Gordon equation or in scalar electrodynamics can be made real by a gauge transform. An extension of these results to the Dirac equation and spinor electrodynamics is proposed here: the Dirac equation is generally equivalent to one fourth-order partial differential equation for one complex component, which can also be made real by a gauge transform. Furthermore, the matter field can be algebraically eliminated both from scalar electrodynamics and from spinor electrodynamics in a certain gauge (for spinor electrodynamics, this is done after introduction of a complex electromagnetic four-potential, which leaves the electromagnetic fields unchanged). The resulting equations describe independent dynamics of the electromagnetic field. It is also shown that for these systems of equations, a generalized Carleman linearization (Carleman embedding) procedure generates systems of linear equations in the Hilbert space, which look like second-quantized theories and are equivalent to the original nonlinear systems on the set of solutions of the latter. Thus, the relevant local realistic models can be embedded into quantum field theories. Possible issues with the Bell theorem are discussed.
Andrey Akhmeteli