Emergence of Quantum Correlations as Macro-Time Correlations Derived from Underlying Micro-Time Correlations

This work introduces a rigorous mathematical approach for producing entangled quantum states from classical stochastic dynamics. We show that any density matrix ρAB describing a composite quantum system can be reconstructed from the correlations of two foundational stochastic processes, X(t) and Y(t), which model the random behavior of the individual subsystems. The framework employs a dual temporal scale—micro and macro time—where quantum correlations naturally arise as emergent macro-level correlations derived from fine-grained micro-level interactions. We formulate the Double Covariance Model (DCM), which captures the essential features of quantum mechanics by interpreting the quantum state as a fourth-order statistical structure within an underlying classical probabilistic model.