# Macroscopic body in Snyder space and minimal length estimation

## TL;DR

This paper investigates the motion of macroscopic bodies in Snyder space, demonstrating how effective parameters influence minimal length estimates and restoring classical physics principles within this quantum gravity framework.

## Contribution

It introduces an effective parameter for macroscopic body motion in Snyder space and shows how it addresses the minimal length problem while preserving classical physics properties.

## Key findings

- Effective parameter depends on particle parameters and masses.
- Reduction of the effective parameter resolves minimal length issues.
- Recovery of classical principles like the weak equivalence principle.

## Abstract

We study a problem of description of macroscopic body motion in the frame of nonrelativistic Snyder model. It is found that the motion of the center-of-mass of a body is described by an effective parameter which depends on the parameters of Snyder algebra for coordinates and momenta of particles forming the body and their masses. We also show that there is reduction of the effective parameter with respect to parameters of Snyder algebra for coordinates and momenta of individual particles. As a result the problem of extremely small result for the minimal length obtained on the basis of studies of the Mercury motion in the Snyder space is solved. In addition we find that relation of parameter of Snyder algebra with mass opens possibility to preserve the property of independence of the kinetic energy on composition, to recover the weak equivalence principle, to consider coordinates as kinematic variables, to recover proportionality of momenta to mass and to consider Snyder algebra for coordinates and momenta of the center-of-mass of a body defined in the traditional way.