  Based on an extended space-time symmetry a new attempt to search for links
between general relativity and quantum mechanics is proposed. A simplified
cylindrical model of gravitational geometrical dynamics leads to a microscopic
geodesic description of strongly curved extradimensional space-time which
implies a duality between an emission law of microscopic gravitational waves
and the quantum mechanical equations of free elementary particles.
Consequently, the Heisenberg indeterminism would originate from the time-space
curvatures.
