Prequantum Classical Statistical Field Theory: Simulation of Probabilities of Photon Detection with the Aid of Classical Brownian Motion

TL;DR

This paper demonstrates through numerical simulations that Prequantum Classical Statistical Field Theory (PCSFT), combined with threshold detectors, can accurately reproduce quantum probabilities of photon detection and coherence, challenging semiclassical interpretations.

Contribution

The paper provides the first numerical validation that PCSFT, with classical Brownian motion and threshold detection, reproduces quantum detection probabilities and coherence measures.

Findings

PCSFT reproduces quantum detection probabilities.

Numerical results match quantum theory predictions.

PCSFT cannot be rejected based on $g^{(2)}(0)$ measurements.

Abstract

In this paper we present results of numerical simulation based on Prequantum Classical Statistical Field Theory (PCSFT), 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 fields model, PCSFT. Numerical modeling demonstrated that the classical Brownian motion (the Wiener process valued in complex Hilbert space) producing clicks when approaching the detection threshold gives probabilities of detection predcited by the formalism QM (as well as PCSFT). This numerical result is important, since the transition from PCSFT to the threshold detection has a complex mathematical structure (in the framework of classical random processes) and it was modeled only approximately. We also perform numerical simulation for the PCSFT-value of the coefficient of second order coherence. Our result matches well with the prediction of quantum theory. Thus, opposite to 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.