We show that quantum mechanics can be interpreted as a modification of the Euclidean nature of 3-d space into a particular affine space, which we call Q-wis. This is proved using the Bohm–de Broglie causal formulation of quantum mechanics. In the Q-wis geometry, the length of extended objects changes from point to point. In this formu- lation, deformation of physical distances are in the core of quantum effects allowing a geometrical formulation of the uncertainty principle.
Authors: M. Novello, . M. Salim and F. T. Falciano.