A neutron star is the compressed core of a dead star: a teaspoon of its material weighs a billion tons. You'd think quantum gravity would show up under such conditions. But between the star's density and the Planck density lies a chasm of $10^{80}$. It's like looking for a drop's trace at the bottom of the ocean.
There are three doors through which quantum gravity could enter. The first is the generalized uncertainty principle: if space ceases to be smooth at small lengths, particles have fewer available states. The second is noncommutative geometry: coordinates no longer multiply in the usual way, and matter gets smeared out. The third is corrections to gravity from higher curvature terms.
The author walks through each door and shows that to make the effect noticeable, the model parameters must be amplified by dozens of orders of magnitude. This means observations of neutron stars constrain not quantum gravity itself, but only models with artificially amplified parameters. The work provides a simple set of checks to distinguish reliable claims from artifacts.
The Planck density is about 10⁸⁰ times larger than the density of a neutron star. If a star had the Planck density, its mass would fit into a volume 10⁸⁰ times smaller than a proton — a vivid illustration of the gap between the laboratory and the fundamental scale.
The idea that spacetime at small scales ceases to be smooth and coordinates do not commute echoes the 'quantum foam' from Greg Egan's novels, where the structure of space at Planck lengths influences macroscopic phenomena.