The amplitude of the gravitational de Broglie waves

TL;DR

This paper calculates the amplitude of gravitational de Broglie waves within Einstein's General Relativity, showing they vanish as Planck's constant approaches zero and proposing a method to measure their effects on test particles.

Contribution

It provides a theoretical calculation of gravitational de Broglie wave amplitude and suggests experimental approaches to detect their influence.

Findings

Amplitude vanishes as 7 o 0

Amplitude decreases with large mass and volume of source

Proposes measuring a unique, time-invariant shift angle

Abstract

We calculate the amplitude of the de Broglie gravitational waves using the standard Einstein General Relativity. We find that these waves disappear in the limit $\hbar \to 0$ and when their source has a large mass and volume. From the experimental point of view, the knowledge of the amplitude allows to estimate the magnitude of the effect of the wave on a sphere of test particles. We propose also to measure a very special shift angle that does not change with time.