Can someone give me reference about Newtonian (non-relativistic) quantum gravity like unifying Newtonian gravity with quantum mechanics?
1 Answer
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There is a study here, Newtonian Quantum Gravity, 2006, Johan Hansson:
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 $\textit{in}$ an orbit for $m\ne\pm l$). This is, in essence, a reflection of the "measurement problem" inherent in all quantum descriptions.
and here Newtonian Quantum Gravity, 1995, K. R. W. Jones:
We develop a nonlinear quantum theory of Newtonian gravity consistent with an objective interpretation of the wavefunction. Inspired by the ideas of Schrodinger, and Bell, we seek a dimensional reduction procedure to map complex wavefunctions in configuration space onto a family of observable fields in space–time. Consideration of quasi–classical conservation laws selects the reduced one–body quantities as the basis for an explicit quasi–classical coarse–graining. These we interpret as describing the objective reality of the laboratory. Thereafter, we examine what may stand in the role of the usual Copenhagen observer to localize this quantity against macroscopic dispersion. Only a tiny change is needed, via a generically attractive self–potential. A nonlinear treatment of gravitational self–energy is thus advanced.