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Emergence of four dimensional quantum mechanics from a deterministic theory in 11 dimensions

A world model consisting of a matter field living in four dimensional spacetime and a gravitational field living in eleven dimensional spacetime is constructed. The seven hidden dimensions are compactified within a radius estimated by reproducing the particle - wave characteristic of diffraction experiments. In the presence of matter fields the gravitational field develops localized modes with elementary excitations called gravonons, which are induced by the sources (massive particles). The final world model contains only gravonons and a scalar matter field. The gravonons are localized in the environment of the massive particles which generate them. The solution of the Schroedinger equation for the world model yields matter fields which are localized in the 4 dimensional subspace.

The localization has the following properties:
(i) There is a chooser mechanism for the selection of the localization site.
(ii) The chooser selects one site on the basis of minor energy differences and differences in the gravonon structure between the sites, which at present cannot be controlled experimentally and therefore let the choice appear statistical.
(iii) The changes from one localization site to a neighbouring one take place in a telegraph-signal like manner.
(iv) The times at which telegraph like jumps occur dependent on subtleties of the gravonon structure which at present cannot be controlled experimentally and therefore let the telegraph-like jumps appear statistical.
(v) The fact that the dynamical law acts in the configuration space of fields living in 11 dimensional spacetime lets the events observed in 4 dimensional spacetime appear non-local.

In this way the phenomenology of Copenhagen quantum mechanics is obtained without the need of introducing the process of collapse and a probabilistic interpretation of the wave function. Operators defining observables need not be introduced. All experimental findings are explained in a deterministic way as a consequence of the time development of the wave function in configuration space according to Schroedinger's equation without the need of introducing a probabilistic interpretation.

G. Doyen and D. Drakova, Copenhagen Quantum Mechanics Emerges from a Deterministic Schroedinger Theory in 11 Dimensional Spacetime Including Weak Field Gravitation, Foundations of Physics 45, pp 959-999 (2015).