# Upper bound on the momentum scale in noncommutative phase space of canonical type

## TL;DR

This paper establishes a very stringent upper bound on the momentum scale in noncommutative phase space by analyzing Mercury's perihelion shift, significantly tightening previous constraints.

## Contribution

It provides the first tight upper bound on the momentum noncommutativity parameter using planetary motion data, refining previous limits by many orders of magnitude.

## Key findings

- Upper bound for momentum noncommutativity parameter: 10^{-80} kg^2 m^2/s^2
- Analysis of Mercury's perihelion shift constrains noncommutative phase space
- Results are many orders less than previous literature bounds

## Abstract

We find stringent upper bound on the momentum scale in noncommutative phase space of canonical type on the basis of studies of perihelion shift of the Mercury planet with taking into account features of description of motion of macroscopic body in the space with noncommutativity of coordinates and noncommutativity of momenta. Using results for precession of perihelion of the Mercury planet from ranging to the MESSENGER spacecraft we obtain upper bound for parameter of momentum noncommutativity $10^{-80}\textrm{kg}^2\textrm{m}^2/\textrm{s}^2$ which is many orders less than known in the literature.