# Planck length challenges non-relativistic quantum mechanics of large masses

## TL;DR

This paper emphasizes the importance of quantum gravity effects in non-relativistic quantum mechanics for large masses, highlighting the necessity of gravity-related modifications to the Schrödinger equation at the Planck scale.

## Contribution

It demonstrates that quantum gravity considerations are essential even in non-relativistic regimes for large masses, and discusses possible autonomous Newtonian quantum-gravity theories.

## Key findings

- De Broglie wavelength approaches Planck length for large masses.
- Gravity influences non-relativistic quantum mechanics of massive objects.
- Modification of Schrödinger equation is necessary at the Planck scale.

## Abstract

With the simplest proof ever, we justify the significance of quantum-gravity in non-relativistic quantum mechanics together with the related theories and experiments. Since the de Broglie wave length is inverse proportional to the mass, it would descend towards and below the Planck scale 10^{-33} cm for large masses even at slow non-relativistic motion. The tricky relationship between gravity and quantum mechanics ---well-known in the relativistic case--- shows up in non-relativistic motion of massive objects. Hence the gravity-related modification of their Schr\"odinger equation is m a n d a t o r y. We also recall the option of an autonomous Newtonian quantum-gravity, a theory parametrized by hbar and G. On cancellation of c from the Newtonian limit of Planck scale metric fluctuations is given a new hint.