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

arXiv comment8 pages, revtex4-2, 5 figures, 1 table, references added, added journal reference

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• Thermodynamics and Shadows of GUP-corrected Black Holes with Topological Defects in Bumblebee Gravity
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• Einstein-Rosen bridge from the minimal length
• A covariant tapestry of linear GUP, metric-affine gravity, their Poincaré algebra and entropy bound
• Theoretical and Observational Implications of Planck's Constant as a Running Fine Structure Constant
• The Mass Gap of the Space-time and its Shape
• Reconciling microscopic and macroscopic tests of the Compton-Schwarzschild correspondence
• Quantum corrections in general relativity explored through a GUP-inspired maximal acceleration analysis
• GUP/BEB correspondence