A Newtonian approach to quantum gravity is studied .
At least for weak gravitational fields it should be a valid approximation .
Such an approach could be used to point out problems and prospects inherent in a more exact theory of quantum gravity , yet to be discovered .
Newtonian quantum gravity , e.g. , shows promise for prohibiting black holes altogether ( which would eliminate singularities and also solve the black hole information paradox ) , breaks the equivalence principle of general relativity , and supports non-local interactions ( quantum entanglement ) .
Its predictions should also be testable at length scales well above the “ Planck scale ” , by high-precision experiments feasible even with existing technology .
As an illustration of the theory , it turns out that the solar system , superficially , perfectly well can be described as a quantum gravitational system , provided that the l quantum number has its maximum value , n - 1 .
This results exactly in Kepler ’ s third law .
If also the m quantum number has its maximum value ( \pm l ) the probability density has a very narrow torus-like form , centered around the classical planetary orbits .
However , as the probability density is independent of the azimuthal angle \phi there is , from quantum gravity arguments , no reason for planets to be located in any unique place along the orbit ( or even in an orbit for m \neq \pm l ) .
This is , in essence , a reflection of the “ measurement problem ” inherent in all quantum descriptions .