Abstract
The measurement problem in quantum mechanics strongly suggests that quantum theory is overcomplete and, strictly speaking, wrong, as it contains mutually contradictory parts - unitary evolution and measurement theory. Modification of the latter enables construction of "no drama" quantum theory - a local realistic theory that has the same unitary evolution as a quantum field theory. The main premises and steps of this construction 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, although it is generally believed that complex functions are required to describe charged fields. An extension of these results to the Dirac equation and spinor electrodynamics is proposed here: it is shown that 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. As the Dirac equation is one of the most fundamental, these results both belong in textbooks and can be used for development of new efficient methods and algorithms of quantum chemistry. 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