Violation of a Bell-like inequality by a combination of Rayleigh scattering with a Mach–Zehnder setup. (July 2016) - Rother, Tom
Abstract: In this paper I propose a classical optics experiment that results in a maximum violation of a Bell-like inequality. The first part is concerned with the Bell-like inequality (the so-called CHSH-inequality) itself. Its importance and its maximum violation in Quantum Mechanics (QM) are discussed in detail by employing an abstract probability state concept in a 4-dim. but classical event space. A T-matrix that represents the integral part of a corresponding Green׳s function as well as a statistical operator that contains a negative quasi-probability can be related to the corresponding quantum mechanical experiment. It is demonstrated that the derivation and usage of the T-matrix and the Green׳s function is equivalent to what is known from classical scattering theory. It is shown moreover that the negative quasi-probability of the statistical operator may be interpreted as a sink of probabilities related to two single events of the considered 4-dim. event space. A necessary condition for the violation of the CHSH-inequality is derived and discussed afterwards. In the second part of this paper I discuss a modification of the 4-dim. event space considered in the first part. It is shown that a combination of conventional Rayleigh scattering with a Mach–Zehnder setup would be able to put this modification into practice. Thus it becomes possible to achieve a maximum violation of the CHSH-inequality, if formulated in terms of intensities, on a pure classical way. The combination of classical light scattering with correlation experiments such as proposed in this paper may open new ways to study and to use the violation of Bell-like inequalities in modern optics. Abstract : Highlights: Consistent Green׳s function formulation of the quantum mechanical Bell׳s experiment and its classical counterpart. This description is closely related to what is known from electromagnetic wave scattering. This is achieved by introducing an abstract probability state concept. Discussion of a classical thought experiment to violate the CHSH inequality. Proposal of a classical optics experiment, based on the combination of Rayleigh scattering with a Mach–Zehnder interferometry, to put this thought experiment into practice.