Gravitational scattering of a quantum particle and the privileged coordinate system

TL;DR

This paper investigates how different coordinate systems affect the gravitational scattering of a quantum particle, suggesting the existence of a privileged coordinate system that aligns with experimental results.

Contribution

It evaluates Fourier-transforms of Schwarzschild metrics in various coordinate systems and explores their impact on scattering, proposing a criterion for selecting the optimal coordinate system.

Findings

Different coordinate systems yield different scattering results.

The choice of coordinate system influences the agreement with experimental data.

A potential privileged coordinate system may reconcile theory with observations.

Abstract

In gravitational scattering the quantum particle probes the Fourier-transforms of a metric. I evaluate the Fourier-transforms of Schwarzschild metrics in standard, harmonic and other coordinate systems in linear and $G^2-$approximations. In general different coordinate systems lead to different scattering. This opens up the possibility to choose the privileged coordinate system which should lead to scattering in agreement with experiment.