Relation Between Gravitation and Permittivity in the Yin–Yang Model

This article presents the geometric derivation and physical interpretation of the relationship between the gravitational constant G and the vacuum permittivity epsilon_0 within the framework of the Yin–Yang Model (YY). The model describes the observable Universe as the three-dimensional interface — called the Now — between two complementary four-dimensional domains: Yin (phase, torsion) and Yang (space, curvature). In the YY framework, gravitation and electromagnetism are not independent forces but orthogonal deformation modes of the same cosmic membrane. G quantifies the radial curvature of the Now (the Yang resistance to compression), while epsilon_0 quantifies the tangential torsion (the Yin resistance to phase variation). Both arise from the same geometric thickness delta, equal to (127/6) times the Planck length, approximately 3.421×10⁻³⁴ meters. From this geometry, the canonical expression for G emerges as proportional to (c³ * delta²) divided by (hbar * eta²), showing that the gravitational constant depends only on the geometric structure of the Now. By introducing the fine-structure constant alpha and the elementary charge e, G can also be expressed in terms of the vacuum permittivity epsilon_0, revealing that gravitation is directly proportional to the same property that defines the electromagnetic field. Using the official physical constants (eta = 127/6, c, hbar, epsilon_0, alpha, e), the model reproduces the experimental value of G = 6.6743×10⁻¹¹ m³·kg⁻¹·s⁻² with no adjustable parameters. This establishes a quantitative bridge between curvature and torsion, suggesting that gravity is the same geometric phenomenon as the electric field when observed along the radial axis of the cosmic interface.