Quantum Mechanics as Statistical Geometry of Local Metrics

We propose a minimal physical framework in which quantum mechanics emerges from statistical fluctuations of local space–time metrics generated by matter itself. Instead of assuming a single smooth and uniform background space–time, we model reality as a dense network of overlapping local metrics. Quantum amplitudes arise as phase averages over microscopic metric fluctuations, and the Born rule follows naturally from Gaussian phase decoherence. In this picture, quantum uncertainty is not fundamental but reflects the breakdown of smooth geometry at small scales, while classical physics emerges through metric averaging.