Narrow Results

We define new coordinates using the family of accelerated Rindler observers in Minkowski space–time and study the spatial sections (hypersurfaces of simultaneity) adapted to the noninertial frame that arises from our definition. We show that the geometry of the spatial sections is not Euclidean. Owing to this feature, the new noninertial frame can be employed to illustrate, in a simple way, the connection between acceleration and non-Euclidean geometry in the relativistic context.

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.