Unification of Mass and Charge through Entropic Gravity and Diagram Hilbert Space

We propose a framework where gravity and electromagnetism emerge from the statistical behavior of microscopic degrees of freedom. Building upon Erik Verlinde’s entropic gravity [1–3], we introduce a complex quantity Z = m + i q, combining mass m and charge q. In a diagram Hilbert space, Z serves as an eigenvalue of a combined mass-charge operator, linking the emergent gravitational and electromagnetic interactions. We show that the Einstein field equations arise from the real part of the entropy structure, while the complex nature of Z provides a unified description of mass and charge.