Universality of minimal length

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.