IS NO DRAMA QUANTUM THEORY POSSIBLE?

Abstract

The matter field can be naturally eliminated from the equations of the Klein-Gordon-Maxwell electrodynamics in the unitary gauge. The resulting equations describe independent dynamics of the electromagnetic field: if components of the 4-potential of the electromagnetic field and their first derivatives with respect to time are known in the entire space at some time point, the values of their second derivatives with respect to time can be calculated for the same time point, so the Cauchy problem can be posed, and integration yields the 4-potential in the entire space-time. This surprising result both permits mathematical simplification and can be useful for interpretation of quantum theory. For example, in the Bohm interpretation, the electromagnetic field can replace the wave function as the guiding field. Independent of the interpretation, quantum phenomena can be described in terms of electromagnetic field only. For the system of nonlinear partial differential equations of the Klein-Gordon-Maxwell electrodynamics, a generalized Carleman linearization procedure generates a system of linear equations in the Hilbert space, which looks like a second-quantized theory and is equivalent to the original nonlinear system on the set of solutions of the latter. Similar, but less general results are obtained for the Dirac-Maxwell electrodynamics.