COW test of the weak equivalence principle: A low-energy window to look into the noncommutative structure of space-time?

TL;DR

This paper models a COW experiment within a noncommutative space-time framework, showing that noncommutativity could mimic violations of the weak equivalence principle and setting new experimental bounds on noncommutative parameters.

Contribution

It introduces a quantum mechanical model of the COW experiment incorporating noncommutative space-time, revealing potential observable effects and tighter bounds on noncommutative parameters.

Findings

Time-space noncommutativity affects gravitational acceleration measurements.

Experimental bounds on noncommutative parameters are significantly improved.

Different particle species in COW experiments could reveal noncommutative space-time evidence.

Abstract

We construct the quantum mechanical model of the COW experiment assuming that the underlying space time has a granular structure, described by a canonical noncommutative algebra of coordinates $x^{\mu}$. The time-space sector of the algebra is shown to add a mass-dependent contribution to the gravitational acceleration felt by neutron deBrogli waves measured in a COW experiment. This makes time-space noncommutativity a potential candidate for an apparent violation of WEP even if the ratio of the inertial mass $m_{i}$ and gravitational mass $m_{g}$ is a universal constant. The latest experimental result based on COW principle is shown to place an upper-bound several orders of magnitude stronger than the existing one on the time-space noncommutative parameter. We argue that the evidence of NC structure of space-time may be found if the COW-type experiment can be repeated with several particle species.