Fundamental Constants from Holographic Information: An Informational Approach

Testing Holographic Constraints Across Cosmology, Atomic Structure, and Elementary Particles: Validation of $\lambda_C/r_{\mathrm{hol}} = 4\pi/\alpha$ from Neutrinos to Higgs

 

This work develops a holographic information framework in which spacetime and interactions emerge from a discrete information-processing substrate characterised by four primitive postulates and two experimental inputs.

 

The primitives are the Planck length $l_P$, the speed of light $c$, the reduced Planck constant $\hbar$, and the maximum holographic information density $\eta_P = 1/(4\ln 2)$, constrained by black hole thermodynamics. The electromagnetic sector is anchored by the fine-structure constant $\alpha$ and the elementary charge $e$, treated as high-precision experimental inputs.

 

Within this architecture, Newton's constant is defined as $G = l_P^2 c^3/\hbar$, the vacuum permittivity and permeability $(\varepsilon_0,\mu_0)$ are reconstructed from $(\alpha,e,\hbar,c)$, and the hierarchy between electromagnetic and gravitational forces is rewritten as $F_{\text{em}}/F_{\text{grav}} = \alpha (m_P/m_p)^2$, making the role of mass and charge ratios explicit.

 

 

1.  UNIVERSAL SCALING LAW: The framework is generalized beyond the electron to all massive Standard Model particles. We derive a universal scaling law governing the ratio between the Compton wavelength $\lambda_C$ and the holographic radius $r_{\mathrm{hol}}$:

$\frac{\lambda_C}{r_{\mathrm{hol}}} = \frac{4\pi}{\alpha}\left(\frac{m_e}{m}\right)^{3/2}$

This relation demonstrates that the predicted cosmic expansion rate $H_0$ is invariant with respect to the probe mass, validated across 11 orders of magnitude from neutrinos to the Higgs boson.

 

2.  COSMOLOGICAL PREDICTION: Linking the informational structure of the electron to the present expansion rate yields a predictive value $H_0 \simeq 74.7\ \text{km s}^{-1}\text{Mpc}^{-1}$ for an observational matter fraction $\Omega_m \simeq 0.30$, resolving the tension with local measurements without using distance ladders.

 

3.  ATOMIC STRUCTURE CORRECTION: The application to atomic systems is refined by explicitly correcting the binding energy relation to $E_{\text{binding}} = \frac{1}{2}\alpha^2 \mu c^2$ (correcting a transcription error in previous versions). This ensures exact agreement with the Rydberg energy and spectroscopic data for Positronium and Muonium without adjustable parameters.

 

In the present model, cosmological holographic bookkeeping is referenced to the present-epoch Hubble scale

$R_H=c/H_0$, while alternative horizon choices are discussed. The framework emphasises parametric reduction, explicit separation between inputs and derived quantities, and the avoidance of circularity.

 

It does not attempt to derive the strong and weak interactions, the cosmological constant, or the value of $\alpha$, but provides a coherent informational architecture that can be tested against future high-precision measurements of $H_0$ and further theoretical developments.

 

RELATED RECORDS:

• Unified & Empirical Tests: https://zenodo.org/records/18304386

• Comprehensive Framework: https://zenodo.org/records/18207461

• Executive Summary: https://zenodo.org/records/18213776

• All Version: https://zenodo.org/records/18207460