Projection-Induced Decoherence and the Emergence of 1/f Noise

Scale-free 1/f noise appears across electronic devices, biological systems, and geophysical measurements. This paper shows that it is not a system-specific anomaly but the universal structural residue of a projection process that eliminates all coherent degrees of freedom prior to observation. When a bulk-to-boundary projection suppresses phase coherence while preserving long-range correlations, no deterministic observable survives — but correlations remain, and their only admissible form is scale-free. The absence of any privileged scale after projection uniquely selects spectra of the form S(f) ∝ 1/f. Three regimes are distinguished: (i) no projection — bulk information is fully observable; (ii) partial…