A testable prediction from entropic gravity

TL;DR

This paper proposes a testable prediction linking quantum states to the gravitational constant through entropic gravity, suggesting experiments with matter-wave interferometry could validate the entropic gravity hypothesis.

Contribution

It introduces a novel conceptual connection between quantum states and gravity, enabling experimental testing of entropic gravity using current interferometry technology.

Findings

Quantum states relate directly to the gravitational constant.

Proposes using matter-wave interferometry for testing entropic gravity.

Provides a framework for experimental validation of entropic gravity theories.

Abstract

I have shown conceptually that quantum state has a direct relationship to gravitational constant due to entropic force posed by Verlinde's argument and part of the Newton-Schr\"odinger equation (N-S) in the context of gravity induced collapse of the wavefunction via Di\'osi-Penrose proposal. This direct relationship can be used to measure gravitational constant using state-of-the-art mater-wave interferometry to test the entropic gravity argument.