Prequantum Classical Statistical Field Theory: Simulation of Probabilities of Photon Detection from Brownian Motion Interacting with Threshold Detectors

Abstract

Based on the prequantum classical statistical field theory (PCSFT), we present the results of numerical simulations of a model with hidden variables of the field-type reproducing probabilistic predictions of quantum mechanics (QM). PCSFT is combined with measurement theory based on detectors of the threshold type. The latter describes discrete events corresponding to the continuous field model. Using numerical modeling, we show that the classical Brownian motion (the Wiener process valued in the complex Hilbert space), producing clicks when approaching the detection threshold, gives the probabilities of detection predicted by the QM formalism (as well as PCSFT). This numerical result is important, since the transition from PCSFT to the threshold detection has a complex mathematical structure (within the framework of classical random processes) and it was modeled only approximately. Also we perform numerical simulation for the PCSFT value of the coefficient of the second-order coherence. Our result matches well with the prediction of quantum theory. Thus, in contrast to a semiclassical theory, PCSFT cannot be rejected as a consequence of measurements of g(2)(0). Finally, we analyze the output of the recent experiment performed in NIST questioning the validity of some predictions of PCSFT.