Origin of Planck's Constant from Realization Geometry

This work presents a geometric derivation of Planck’s constant based on the framework of null orientation fields. Instead of treating Planck’s constant as a fundamental empirical parameter, the theory shows that it emerges naturally from the structure of realization. In this approach, light is interpreted as a null geometric relation carrying phase rather than as a propagating particle. Physical events arise when multiple null orientations form a non-collinear closure, producing a timelike realization. The requirement that such a realization must be phase-consistent leads to a fundamental condition: phase closure over a complete cycle. This condition introduces a minimal unit of realization, corresponding to a full phase cycle of 2π. From this, a minimal time interval of realization is defined, and energy emerges as the rate of realization. This directly yields the relation E = ℏω, with Planck’s constant appearing as the proportionality factor. Within this framework, Planck’s constant is interpreted as the minimal unit of action associated with a complete realization cycle. Frequency determines the rate of realization, energy measures the density of realization, and ℏ sets the fundamental scale linking them. The theory further connects this geometric interpretation to standard quantum mechanics by recovering the Schrödinger equation from phase relations and showing that the wave function represents the geometric structure of possible realizations rather than a physical field. This work provides a minimal and unified geometric interpretation of quantization, in which Planck’s constant arises from phase closure in null orientation geometry, bridging quantum theory with an underlying spacetime structure.