# Kinetic energy properties and weak equivalence principle in a space with GUP

## TL;DR

This paper investigates how a generalized uncertainty principle (GUP) affects kinetic energy and the weak equivalence principle in a deformed space, revealing significant violations that can be mitigated by specific deformation parameters.

## Contribution

It demonstrates that GUP causes violations of fundamental principles in macroscopic bodies, and proposes a solution involving a deformation parameter inversely proportional to squared mass.

## Key findings

- GUP leads to violations of the weak equivalence principle for macroscopic bodies.
- Kinetic energy becomes non-additive and depends on composition under GUP.
- Adjusting the deformation parameter can resolve these issues.

## Abstract

A space with deformed commutation relations for coordinates and momenta leading to generalized uncertainty principle (GUP) is studied. We show that GUP causes great violation of the weak equivalence principle for macroscopic bodies, violation of additivity property of the kinetic energy, dependence of the kinetic energy on composition, great corrections to the kinetic energy of macroscopic bodies. We find that all these problems can be solved in the case of arbitrary deformation function depending on momentum if parameter of deformation is proportional inversely to squared mass.