author={M. Novello and J. Salim and F. Falciano},
  journal={International Journal of Geometric Methods in Modern Physics},
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 formulation, deformation of physical distances are in the core of quantum effects allowing a geometrical formulation of the uncertainty principle. 
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