On the uncertainty principle in Rindler and Friedmann spacetimes

TL;DR

This paper revises the uncertainty relations in Rindler and Friedmann spacetimes, demonstrating their coordinate dependence and showing that apparent minimum uncertainties are artifacts of coordinate choice, thus clarifying their invariant nature.

Contribution

It reveals that previously reported minimum uncertainties are coordinate artifacts and connects these results to invariant uncertainty relations in spaces of constant curvature.

Findings

Uncertainty relations are coordinate dependent in Rindler and Friedmann spacetimes.

Non-zero minimum uncertainties are artifacts of coordinate choice.

Invariant uncertainty relations are derived for general 3D spaces of constant curvature.

Abstract

We revise the extended uncertainty relations for the Rindler and Friedmann spacetimes recently discussed by Dabrowski and Wagner in [9]. We reveal these results to be coordinate dependent expressions of the invariant uncertainty relations recently derived for general 3-dimensional spaces of constant curvature in [10]. Moreover, we show that the non-zero minimum standard deviations of the momentum in [9] are just artifacts caused by an unfavorable choice of coordinate systems which can be removed by standard arguments of geodesic completion.