Open Access
Subscription or Fee Access

### On the Physical Interpretation of the Velocity Parameter in the Formula for Gravitational Planck Constant

#### Abstract

Nottale's formula for the gravitational Planck constant

*ħ*=_{gr}*GMm*/*v*involves parameter_{0}*v*with dimensions of velocity. I have worked with the quantum interpretation of the formula but the physical origin of_{0}*v*- or equivalently the dimensionless parameter_{0}*β*=_{0}*v*/_{0}*c*(to be used in the sequel) appearing in the formula has remained open hitherto. In the following, a possible interpretation based on many-sheeted space-time concept, many-sheeted cosmology, and zero energy ontology (ZEO) is discussed. In ZEO, the non-changing parts of zero energy states are assigned to the passive boundary of CD and*β*should be assigned to it. There are two measures for the size of the system. The_{0 }*M*size^{4}*L*is identifiable as the maximum of the radial_{M4}*M*distance from the tip of CD associated with the center of mass of the system along the light-like geodesic at the boundary of CD. System has also size^{4 }*L*defined in terms of the induced metric of the space-time surface, which is space-like at the boundary of CD. One has_{ind}*L*<_{ind}*L*. The identification_{H}*β*=_{0 }*L*/_{M4}*L*does not allow the identification of_{H}*L*=_{H}*L*._{M4}*L*would however naturally corresponds to the size of the magnetic body of the system in turn identifiable as the size of CD. One can deduce an estimate for_{H}*β*by approximating the space-time surface as Robertson-Walker cosmology expected to be a good approximation near the passive light-like boundary of CD. The resulting formula is tested for planetary system and Earth. The dark matter assignable to Earth can be identified as the innermost part of inner core with volume, which is .01 per cent of the volume of Earth._{0 }