The Schrödinger Equation from the Viewpoint of the Theory of Hidden Variables

акустика Механика

Mićo Đurđević, Milan Vujičić, Fedor Herbut

The three known demonstrations that there exist contextual hidden variables (HV) that reproduce quantum mechanics (the HV theories of Bohm–Bub, Wiener–Siegel, and Gudder) are shown to be special cases of a generalized Gudder’s theory defined in this work. Within this scheme, a symplectic HV theory is introduced for which it is argued that it is physically more useful than Gudder’s theory because it makes possible the definition of a Hamiltonian subquantum dynamical law that reproduces in a natural way the Schrödinger equation. On the other hand, the symplectic HV theory contains as concrete realizations a slightly modified theory of Bohm–Bub and the theory of Wiener and Siegel.

Salvatore Capozzıello, Wladimir-Georges Boskoff

Miloš V Lokajcek

It has been shown by us recently that Einstein was right in his controversy with Bohr or that the so called hidden-variable theory should be preferred to the Copenhagen quantum mechanics. In the following paper the corresponding arguments will be shortly repeated. The main attention will be then devoted to explaining main differences between these two quantum alternatives, differing in the access to the problem of chance, causality and locality of microscopic objects. The actual meaning of the mentioned hidden variables will be discussed, too, the essence of which remained practically unclear during all past discussions. It will be shown that the theory of hidden variables (or Schrodinger equation alone) is able to represent the properties of the whole known physical reality.

Jay Gambetta, Howard M. Wiseman

An important and well established area of quantum optics is the theory of Markovian stochastic Schr\"odinger equations (or by another name quantum trajectory theory). Recently stochastic Schr\"odinger equations have been developed for non-Markovian systems. In this paper we extend the current known stochastic Schr\"odinger equations for non-Markovian systems to include the position unraveling. We also discuss and illustrate that this stochastic Schr\"odinger equation can have an interpretation under both the orthodox and the de Broglie-Bohm hidden variable interpretation of quantum mechanics. We conclude that only the de Broglie-Bohm hidden variable theory provides a continuous-in-time interpretation of the non-Markovian stochastic Schr\"odinger equation.