A Unified Geometrical Theory of Emergent Space, Gravity, and Electromagnetism Based on a Two-Dimensional Graviton Membrane

A fundamental challenge in modern physics is the unification of gravity and electromagnetism within a single theoretical framework. General Relativity successfully describes gravity as the curvature of spacetime, whereas electromagnetism is formulated as a gauge interaction. Despite their successes, these interactions are described by fundamentally different mathematical structures.In this paper, we propose a speculative theoretical framework in which both gravity and electromagnetism emerge from different geometrical deformation modes of a fundamental two-dimensional graviton membrane. Three-dimensional physical space is assumed not to be fundamental but to emerge from a connected network of microscopic membranes embedded in a higher-dimensional background.Within this framework, gravity corresponds to membrane curvature and density variation, electric charge corresponds to membrane phase rotation, electric fields arise from spatial phase gradients, and magnetic fields originate from torsional deformation of the membrane generated by moving phase excitations. Matter is interpreted as localized membrane vibration states, while photons correspond to propagating coupled phase–torsion waves.Although the model is currently qualitative, it offers a unified geometrical interpretation of gravity and electromagnetism and suggests several experimentally testable predictions in strong gravitational environments.