From Local Realistic Distribution to Global Coherent Possibility: A Unified Probabilistic Interpretation of Photon Polarization Under Continuous Decoherence Modulation

Classic physics and quantum mechanics construct distinct logical closures to describe macroscopically "unpolarized" light based on different foundational realisms. Classical local realism assumes definite yet unknown geometric directions of the electric field vector within a continuous probability space, whereas standard quantum mechanics advocates an uncertain state under coherent superposition prior to measurement. This study adopts a neutral, bottom-up perspective to construct a class of generalized first-order probability density function models modulated by a continuous coherence factor. By introducing an experimentally reproducible measurement procedure of identical single-photon time series, we demonstrate that under a completely decoherent statistical steady state, the indistinguishability constraint of identical photons erases the specificity of local hidden variables. Consequently, the integral statistical behavior of classical probability space becomes mathematically equivalent to the maximum mixed state in quantum mechanics. The proposed model demonstrates that classical local realistic distributions and quantum global coherent superpositions can be unified as a continuous transition of information representation under total probability conservation, providing a neutral modeling framework to resolve this long-standing controversy.