# Space-time: Commutative or noncommutative ?

## TL;DR

This paper investigates whether spacetime coordinates are commutative or noncommutative, proposing that the noncommutativity scale could be larger than the Planck length and exploring experimental ways to test this.

## Contribution

It applies deformation theory and the principle of stability to distinguish between coordinate and generator noncommutativity, suggesting new experimental approaches.

## Key findings

- Noncommutativity scales of coordinates and generators are independent.
- Possible larger noncommutativity scale than Planck length.
- Experimental strategies for testing spacetime noncommutativity.

## Abstract

Noncommutativity of the spacetime coordinates has been explored in several contexts, mostly associated to phenomena at the Planck length scale. However, approaching this question through deformation theory and the principle of stability of physical theories, one concludes that the scales of noncommutativity of the coordinates and noncommutativity of the generators of translations are independent. This suggests that the scale of the spacetime coordinates noncommutativity could be larger than the Planck length. This paper attempts to explore the experimental perspectives to settle this question, either on the lab or by measurements of phenomena of cosmological origin.