Bell's Experiment in Quantum Mechanics and Classical Physics

TL;DR

This paper compares quantum and classical Bell's experiments, analyzing probability differences, superposition effects, and negative quasi probabilities, and discusses their implications for entanglement and the complementarity principle.

Contribution

It provides a detailed analysis of Bell's experiments in both quantum and classical contexts, highlighting the role of superposition and negative quasi probabilities without requiring entanglement.

Findings

Negative quasi probabilities are neither necessary nor sufficient for entanglement.

Superposition causes interference effects in quantum Bell's experiments.

Classical Bell's experiments can be modeled with similar probability structures.

Abstract

Both the quantum mechanical and classical Bells experiment are within the focus of this paper. The fact that one measures different probabilities in both experiments is traced back to the superposition of two orthogonal but nonentangled substates in the quantum mechanical case. This superposition results in an interference term that can be splitted into two additional states representing a sink and a source of probabilities in the classical event space related to Bells experiment. As a consequence, a statistical operator can be related to the quantum mechanical Bells experiment that contains already negative quasi probabilities, as usually known from quantum optics in conjunction with the Glauber-Sudarshan equation. It is proven that the existence of such negative quasi probabilities are neither a sufficient nor a necessary condition for entanglement. The equivalence of using an interaction picture in a fixed basis or of employing a change of basis to describe Bells experiment is demonstrated afterwards. The discussion at the end of this paper regarding the application of the complementarity principle to the quantum mechanical Bells experiment is supported by very recent double slit experiments performed with polarization entangled photons.