P-12: The Geometric Origin of Quantum Tunneling — From Nonlinear Dynamics to Spatial Mirror Coupling

Abstract:Quantum tunneling is one of the most iconic and counterintuitive phenomena in quantum mechanics. The standard quantum mechanical description treats it as the wave-like behavior of a particle penetrating a classically forbidden barrier with a certain probability, but offers no ontological picture of "how" the penetration occurs. Based on the framework of Space Ontology, starting from the spatial orientation field equation, we establish a nonlinear dynamical theory of tunneling and further reveal its deep geometric essence. We demonstrate that tunneling is not a particle "passing through" a barrier, but a geometric coupling process in which a spatial ripple excites a mirror ripple at the barrier interface. The "perception range" of a ripple is determined by its geometric entanglement entropy, with correlation length ξ = ξ₀ e^{E_geo}. The tunneling probability satisfies T = T₀ exp(-d/ξ), where d is the barrier width. Nonlinear self-interaction modulates the tunneling strength by changing the ripple shape: repulsive nonlinearity (g>0) flattens the ripple, enhancing tunneling; attractive nonlinearity (g<0) sharpens the ripple, suppressing tunneling. There exists a critical nonlinear strength g_c, beyond which the ripple "sees through" the barrier and the tunneling behavior undergoes a qualitative change. For double-barrier structures, the ripple accumulates a geometric phase of π in a round trip, leading to a 1/2 factor shift in resonance levels. The theoretical predictions are in quantitative agreement with cold-atom BEC tunneling experiments and superconducting circuit double-barrier resonance data, and may provide new principles for quantum information devices. The core physical picture of this paper can be condensed into a concise metaphor: the barrier is not a wall, but a mirror. Tunneling is not passing through the wall, but looking into the mirror. This study reduces quantum tunneling from a statistical rule to the mirror-coupling dynamics of spatial modes, marking the completion of the systematic geometric reduction of the "three great mysteries" of quantum mechanics by Space Ontology. This paper is the twelfth in the first series (17 papers total) of Space Ontology, establishing the geometric origin of quantum tunneling from nonlinear dynamics to spatial mirror coupling.