Quantum Mechanics and Gravitation

TL;DR

This paper discusses the development of a quantum mechanical model for an experiment involving ultra-cold neutrons in Earth's gravitational field, aiming to confirm quantum gravitational bound states and explore potential deviations from Newtonian gravity at micron scales.

Contribution

It provides a detailed quantum mechanical description of the UCN gravitational experiment, supporting the existence of quantized bound states and enabling tests of gravity modifications at micron distances.

Findings

Evidence for gravitationally bound quantum states of neutrons.

Quantum description aligns with experimental data.

Potential to test gravity modifications at micron scales.

Abstract

In summer 1999 an experiment at ILL, Grenoble was conducted. So-called ultra-cold neutrons (UCN) were trapped in the vertical direction between the Fermi-potential of a smooth mirror below and the gravitational potential of the earth above [Ne00, Ru00]. If quantum mechanics turns out to be a sufficiently correct description of the phenomena in the regime of classical, weak gravitation, one should observe the forming of quantized bound states in the vertical direction above a mirror. Already in a simplified view, the data of the experiment provides strong evidence for the existence of such gravitationally bound quantized states. A successful quantum-mechanical description would then provide a convincing argument, that the socalled first quantization can be used for gravitation as an interaction potential, as this is widely expected. Furthermore, looking at the characteristic length scales of about 10 mikron of such bound states formed by UCN, one sees, that a complete quantum mechanical description of this experiment additionally would enable one to check for possible modifications of Newtonian gravitation on distance scales being one order of magnitude below currently available tests [Ad00]. The work presented here deals mainly with the development of a quantum mechanical description of the experiment.