Classical signal model reproducing quantum probabilities for single and coincidence detections

We present a simple classical (random) signal model reproducing Born's rule. The crucial point of our approach is that the presence of detector's threshold and calibration procedure have to be treated not as simply experimental technicalities, but as the basic counterparts of the theoretic...

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Bibliographic Details
Published in:Journal of physics. Conference series 2012-01, Vol.361 (1), p.12030-10
Main Authors: Khrennikov, Andrei, Nilsson, Börje, Nordebo, Sven
Format: Article
Language:English
Subjects:
Applied Mathematics
Calibration
Coefficients
detection
Mathematical analysis
Mathematical models
Monitoring
Photons
Physics
quantum
Quantum mechanics
Random walk
Signal detection
signals
Similarity
Stationary processes
Thresholds
Tillämpad matematik
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Summary:We present a simple classical (random) signal model reproducing Born's rule. The crucial point of our approach is that the presence of detector's threshold and calibration procedure have to be treated not as simply experimental technicalities, but as the basic counterparts of the theoretical model. We call this approach threshold signal detection model (TSD). The experiment on coincidence detection which was done by Grangier in 1986 [22] played a crucial role in rejection of (semi-)classical field models in favour of quantum mechanics (QM): impossibility to resolve the wave-particle duality in favour of a purely wave model. QM predicts that the relative probability of coincidence detection, the coefficient g(2) (0), is zero (for one photon states), but in (semi-)classical models g(2)(0) ≥ 1. In TSD the coefficient g(2)(0) decreases as 1/ϵ2d, where ϵd > 0 is the detection threshold. Hence, by increasing this threshold an experimenter can make the coefficient g(2) (0) essentially less than 1. The TSD-prediction can be tested experimentally in new Grangier type experiments presenting a detailed monitoring of dependence of the coefficient g(2)(0) on the detection threshold. Structurally our model has some similarity with the prequantum model of Grossing et al. Subquantum stochasticity is composed of the two counterparts: a stationary process in the space of internal degrees of freedom and the random walk type motion describing the temporal dynamics.
ISSN:1742-6596
1742-6588
1742-6596
DOI:10.1088/1742-6596/361/1/012030