Universality of minimal length

TL;DR

This paper proposes that the minimal length in quantum measurements can be understood as an effective variation of Planck's constant, linking it to fundamental physics concepts and cosmic evolution.

Contribution

It introduces a novel interpretation of the minimal length as an effective variation of ${h}$, connecting quantum measurement limits to cosmological and particle physics phenomena.

Findings

Charge radii support effective variation of ${h}$

Variation of ${h}$ and $G$ explains entropy corrections

Effective ${h}$ relates to nucleosynthesis epoch

Abstract

We present an argument reinterpreting the generalized uncertainty principle (GUP) and its associated minimal length as an effective variation of Planck constant ($\hbar$), complementing Dirac's large number hypothesis of varying $G$. We argue that the charge radii (i.e. the minimal length of a scattering process) of hadrons/nuclei along with their corresponding masses support an existence of an effective variation of $\hbar$. This suggests a universality of a minimal length in measurement of scattering process. Varying $\hbar$ and $G$ explains the necessity of Von Neumann entropy correction in Bekenstein-Hawking entropy-area law. Lastly, we suggest that the effective value of $\hbar$ derived from various elements may be related to the epoch of their creation via nucleosynthesis.