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 (ħ), 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 ħ. This suggests a universality of a minimal length in measurement of scattering process. Varying ħ and G explains the necessity of Von Neumann entropy correction in Bekenstein-Hawking entropy-area law. Lastly, we suggest that the effective value of ħ derived from various elements may be related to the epoch of their creation via nucleosynthesis.