The Heisenberg limit at cosmological scales

TL;DR

This paper explores the fundamental quantum limits on measuring particle masses at cosmological scales, linking the Heisenberg principle to observable universe parameters and suggesting potential causes for cosmological parameter tensions.

Contribution

It introduces a cosmological application of the Heisenberg limit, connecting quantum measurement bounds to the observable universe's size and redshift.

Findings

Smallest measurable mass is 1.35 x 10^{-69} kg.

Corresponding length limit is 8.4 Gpc, with redshift 1.3.

Expansion constant H_0 exceeds the smallest measurable energy divided by Planck's constant.

Abstract

For an observation time {equal to} the universe age, the Heisenberg principle fixes the value of the smallest measurable mass at $m_{\rm H}=1.35 \times 10^{-69}$ kg and prevents to probe the masslessness for any particle using a balance. The corresponding reduced Compton length to $m_{\rm H}$ is $\lambdabar_{\rm H}$, and represents the length limit beyond which masslessness cannot be proved using a metre ruler. In turns, $\lambdabar_{\rm H}$ is equated to the luminosity distance $d_{\rm H}$ which corresponds to a red shift $z_{\rm H}$. When using the Concordance-Model parameters, we get $d_{\rm H} = 8.4$ Gpc and $z_{\rm H}=1.3$. Remarkably, $d_{\rm H}$ falls quite short to the radius of the {\it observable} universe. According to this result, tensions in cosmological parameters could be nothing else but due to comparing data inside and beyond $z_{\rm H}$. Finally, in terms of quantum quantities, the expansion constant $H_0$ reveals to be one order of magnitude above the smallest measurable energy, divided by the Planck constant