Relativistic Nature of Wave-particle Duality

A new wave of relativistic nature is derived from the classical Hamilton-Jacobi equation on a curved space-time. The gravitational time dilation in the neighbourhood of an almost point-like mass is responsible for its existence. In order to obtain such type of wave (interpretable as a matter field), one has to resort to an old idea due to de Broglie according to which the physical 3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\textbf {3}}$$\end{document}-dimensional space behaves as if it were covered with an infinity of clocks. The resulting particle field, that propagates in the physical 3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\textbf {3}}$$\end{document}-dimensional space and is due to the interaction with the (classic) gravitational field of the mass, is shown to be associated with the usual scalar particle wave function of quantum mechanics. Therefore, the model here described, by linking Einstein's general relativity to the wave-like behaviour of particles via the viewpoint of de Broglie's Double Solution Theory rather than via the standard mechanisms of field quantisation, provides a new approach to quantum gravity. Finally, it is shown that this model provides a new interpretation of the single-particle interference and explains non-locality in terms of a novel quantum communication channel.