A discussion is given of the uncertainty principle in view of the introduction of a Gravitational Planck Constant. The need for such a gravitational constant is shown first. A reduced electromagnetic Planck constant and the analogous reduced gravitational Planck constant are defined as h/e and H/m respectively. An attempt is made to reconcile the quantum uncertainty concepts with a deterministi...

The effect of introducing a fifth large-scale space-time dimension to the equations of orbital dynamics was analysed in an earlier paper by the authors. The results showed good agreement with the observed flat rotation curves of galaxies. This analysis did not require the modification of Newtonian dynamics, but rather only their restatement in a five dimensional framework. The same analysis der...

Multi-fractional theories with integer-order derivatives are models of gravitational and matter fields living in spacetimes variable Hausdorff spectral dimension, originally proposed as descriptions geometries arising quantum gravity. We derive the Poisson equation Newtonian potential these starting from their covariant modified Einstein's equations. In particular, case theory $T_v$ weighted sm...