A Unified Geometric Framework for Light Deviation: From Refraction to Gravitational Lensing

This work proposes a unified geometric framework in which both optical refraction and gravitational lensing are interpreted as angular projections of light paths onto structured space. Instead of treating these phenomena through separate physical mechanisms—one relying on refractive index gradients and the other on spacetime curvature—this theory demonstrates that both can be described using a single trigonometric structure based on projection angles. By modeling space and time as orthogonal vectors , and interpreting deviations in velocity (Δv≠0) as a rupture of that orthogonality, the theory postulates that matter arises from the geometric closing of space into surfaces. These "closed surfaces" behave as light itself, giving rise to both particles and macroscopic structures. Central to the theory is the reinterpretation of Lorentz contraction and time dilation as simple trigonometric projections: v/c=sin⁡θ,γ=cos⁡θ These relations, visualized through a unit-circle geometry, unify light deflection, relativistic transformation, and wave propagation into a single angular principle. The paper further extends this model to electromagnetic and gravitational waves, field behavior, and general curvature dynamics, culminating in a proposed master equation: where Φrepresents the generative structure of space itself. An epilogue imagines a philosophical and mathematical dialogue with Einstein, exploring the potential that this framework offers as a deeper geometric reformulation of spacetime. Name: Tetsuo Konno(今野哲夫) ORCID: https://orcid.org/0009-0002-1842-7865 [email protected]