Newtonian Quantum Gravity

TL;DR

This paper explores a Newtonian approximation to quantum gravity, suggesting it could address black hole issues, break certain principles of relativity, and be tested with current technology, with implications for planetary systems.

Contribution

It introduces a Newtonian quantum gravity framework that models planetary orbits and discusses its potential to resolve black hole singularities and testable predictions.

Findings

Newtonian quantum gravity can model planetary orbits consistent with Kepler's laws.

The theory suggests black holes could be prohibited, avoiding singularities.

Predictions are testable at scales above the Planck length with existing technology.

Abstract

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 $m \neq \pm l$). This is, in essence, a reflection of the "measurement problem" inherent in all quantum descriptions.