Physical Science: New Insights and Developments Vol. 5

Aims: This chapter develops a speculative extremal/extremum-principle framework for interpreting the running gauge coupling constants of the Standard Model through gravitational and Bekenstein-like information-theoretic quantities. Generally, the extremum principle is a foundational concept in physics and mathematics, asserting that natural processes often follow paths that optimize a specific quantity. This principle underlies many laws in mechanics, optics, and thermodynamics. The elegance and previously recognized applications of the extremum principle in physics were the main motivations in writing this paper.

Study Design and Duration: This is a theoretical speculative study conducted between 2025 and 2026.

Methodology and Results: The central proposal is that the inverse value of a gauge coupling can be written as a base-2 logarithm of a sector-dependent gravitational microstate count. For the electromagnetic sector, the manuscript relates the fine-structure constant at low energy, alpha approximately 0.007297, to an electro-gravitational hierarchy and obtains a logarithmic value of about 136.92, close to alpha inverse approximately 137. The same construction is extended, in approximate form, to weak and strong interactions by defining analogous maximal quantities for each sector. The manuscript reports alpha_W approximately 0.034 with alpha_W inverse approximately 29.5 and an associated logarithmic estimate of about 108, and alpha_S approximately 0.118 with alpha_S inverse approximately 8.5 and an associated logarithmic estimate of about 127. A further quantitative refinement introduces effective sector-dependent gravitational constants, estimated as G_W approximately 10^23 G and G_S approximately 10^35 G, to improve the numerical matching, given that such hypothetical strong gravity sectors may be currently undetectable at LHC because of their relative weakness compared with the non-gravitational fields probed at the LHC. The proposed framework is then connected to a local Bekenstein-bound interpretation in which minimal neutral vacuum fluctuations saturate sectoral holographic entropy bounds at characteristic radii. The manuscript estimates radii of approximately 5.8 x 10^-12 m for the electromagnetic sector, 7.9 x 10^-18 m for the weak sector, and 0.87 x 10^-15 m for the strong sector. Finally, it explores a toy entropy-based renormalization-group model and discusses a possible relation between elementary-particle rest energies, the Planck scale, and the Higgs vacuum expectation value.

Conclusions: The work is intended as a theoretical hypothesis (a conceptual perspective) rather than an established extension of the Standard Model. EXP also offers a set of falsifiable predictions.