Emergence of Quantum Dynamics and Electromagnetic Structure from Constrained Null Geometry

This work develops a minimal geometric framework in which key structures of quantum mechanics and electromagnetic interaction emerge from a system of null directions subject to a global closure constraint. Starting from a finite set of lightlike vectors in Minkowski space, it is shown that non-degenerate closed configurations generate a timelike resultant, providing an intrinsic notion of temporal evolution and effective mass without introducing these as fundamental inputs. The closure constraint defines a compact configuration space (simplex) with globally coupled degrees of freedom. This structure necessitates the emergence of a phase variable, leading to intrinsic oscillatory dynamics. Under coarse-graining, this dynamics gives rise to a Schrödinger-type evolution equation, while an associated Clifford algebra construction yields a Dirac-type structure in which mass is identified with the invariant magnitude of the closure. A central result is that the spinor current derived from this construction exhibits a radial inverse-square profile, leading to a Coulomb-type potential obtained directly from the global flux of the current, without assuming Maxwell’s equations. In this framework, electromagnetic-like interactions arise as effective manifestations of globally constrained geometry. Dimensionless parameters are interpreted as time-averaged invariants of the oscillatory dynamics, reflecting the interplay between geometric variance and phase coherence. The framework does not fix their numerical values but provides a minimal mechanism for their dynamical emergence. The results suggest a unifying perspective in which phase, spin, and interaction fields are not fundamental ingredients but effective descriptions of an underlying constrained null geometry.