Quantum Holographic Gravity: A Unified Theoretical Framework Based on a Core Constant Cluster

Abstract

Shen Hao, Zhang Qu and Ma Ruipeng

This paper constructs a unified theoretical framework based on first principles—i.e., how the universe generates from its most fundamental state—connecting quantum vacuum genesis, the origin of fundamental physical constants, the Standard Model of particle physics, and cosmic dynamics. The core breakthrough of the theory lies in identifying a mathematical-physical structure termed the” core constant cluster” from the physical mechanism of cosmic genesis. This structure consists of four mutually nested and constraining constants: the golden ratio φ ≈ 1.618, the core functional dimension n = 5, the fractal dimension Df ≈ 2.736, and the quantum error correction threshold pk ≈ 0.189. This paper demonstrates that these constants are inevitable products of the intrinsic holographic fractal geometry of the vacuum after spontaneous supersymmetry breaking, rather than being introduced through reverse artificial fitting.

On the basis of clarifying the origin and fundamental principles of this constant cluster, this paper forwardly deduces the fundamental physical constants—the speed of light c, Planck’s constant h, and the gravitational constant G—mediated via a Nambu-Goldstone scalar field derived from conformal symmetry breaking. Research indicates that these three constants possess scale-dependence compatible with Lorentz covariance, their evolution regulated by the role density ρR and the fractal dimension Df , while the universality of the fine-structure constant α is strictly maintained. Within this theoretical framework, gravity is redefined as a ”holographic tension field” emerging from the collective synergistic effects of quantum ”role basis vectors” (mathematically represented as |Li ⟩ = Γi ⊗ψi , where Γi is an irreducible representation of the SO(10) group). The observational phenomena of dark matter and dark energy are naturally explained as gravitational enhancement effects of this tension field at low role density and fractal synergistic repulsion effects at cosmological scales. This explanation does not require introducing any unknown particles or a cosmological constant; dark matter and dark energy are viewed as normal manifestations of gravity as defined herein under different scales and conditions, rather than being caused by undiscovered matter or energy.

This theory exhibits a high degree of consistency across multiple key observational tests: fitting the rotation curves of 153 galaxies in the SPARC sample yields a root mean square error of only 4.7km/s, with the Bayesian Information Criterion significantly outperforming mainstream models such as SIDM, FDM, and f(R) gravity; combined constraints from baryon acoustic oscillations and Type Ia supernova data yield a predicted Hubble constant H0 = 67.9 ± 0.4km/s/ Mpc, alleviating the current Hubble tension to the 2.1σ confidence level; the relative error of the predicted peak positions of the cosmic microwave background radiation power spectrum is less than 0.3%.

Through research on quantum origins, this paper compatibly embeds the core constant cluster with the Standard Model of particle physics. The theory provides natural explanationsforlong-standingunresolvedproblemssuchastheoriginofthre efermiongenerations, neutrino mass and mixing angles, and the Higgs mechanism. Finally, under the premise of strictly rigid calculation without modifying specific experimental conditions, this paper proposes five experimentally verifiable predictions covering microscopic, mesoscopic, strong-field, and cosmological scales, each with its own defined3σ statistical rejection line. This framework is mathematically self-consistent and complete, is in principle falsifiable by experiment, and provides a novel approach with a clear empirical path for exploring unified theories beyond the current scope of the standard cosmological model and quantum field theory. At the very least, even if this paper only serves to provide a new line of thought for related research, this work holds its own value.

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