  The problem of quantum gravity is treated from a radically new viewpoint
based on a detailed mathematical analysis of what the constitution of physical
space is, which has been carried out by Michel Bounias and the author. The
approach allows the introduction of the notion of mass as a local deformation
of space regarded as a tessellation lattice of founding elements, topological
balls, whose size is estimated as the Planck one. The interaction of a moving
particle-like deformation with the surrounding lattice of space involves a
fractal decomposition process that supports the existence and properties of
previously postulated inerton clouds as associated to particles. The cloud of
inertons surrounding the particle spreads out to a range \Lambda = \lambda c /
v from the particle where v and c are velocities of the particle and light,
respectively, and \lambda is the de Broglie wavelength of the particle. Thus
the particle's inertons return the real sense to the wave \psi-function as the
field of inertia of the moving particle. Since inertons transfer fragments of
the particle mass, they play also the role of carriers of gravitational
properties of the particle. The submicroscopic concept has been verified
experimentally, though so far in microscopic and intermediate ranges.
