A Geometric Model of Spacetime Emerging from Pure Wave Dynamics: A Theoretical Prototype / 基于纯波动力学的时空涌现几何模型:一个理论原型

This paper proposes a theoretical prototype deriving spacetime structure from pure wave dynamics. Taking the discreteness of spacetime and the ontology of de Broglie waves as its two core axioms, it constructs a self-consistent geometric model. Through the"dragging"picture, the starting point of a probability wave is fixed at the origin and extends in all directions, with the outermost contour of its probability amplitude distribution (the wavefront) subject to the Orthogonality Constraint Principle—no non-zero probability amplitude can touch the Y-axis. The shape of the wavefront is determined by frequency and amplitude; therefore, a wave's Maximum Activity Angle is the diffusion limit of its probability cloud in spacetime, jointly determined by its frequency and amplitude. Among all waves satisfying this constraint, light is identified as a special wave possessing intrinsic locked-ness. This absolute invariance, locked by Planck's constant, is geometrically defined as 90 degrees. Light's 90-degree Activity Angle"opens up"a light-cone, a new reference frame, in spacetime. Within this light-cone framework, the light-speed limit principle, time dilation effect, and the geometric origin of the Lorentz transformation are further derived. This model reveals the geometric unity of classical and quantum mechanics: classical mechanics describes the deterministic boundary of the probability cloud, while quantum mechanics describes the probabilistic behavior within that boundary. The model provides a unified geometric perspective on wave-particle duality, the difficulty of the many-worlds interpretation, and the decoherence problem.