Understanding quantum interference in general nonlocality

Abstract

In this paper we attempt to give a new understanding of quantum double-slit interference of fermions in the framework of General Nonlocality (GN) [J. Math. Phys. 49, 033513 (2008)] by studying the self-(inter)action of matter wave. From the metric of the GN, we derive a special formalism to interpret the interference contrast when the self-action is perturbative. According to the formalism, the characteristic of interference pattern is in agreement with experiment qualitatively. As examples, we apply the formalism to the cases governed by Schrödinger current and Dirac current respectively, both of which are relevant to topology. The gap between these two cases corresponds to the fermion magnetic moment, which is possible to test in the near future. In addition, a general interference formalism for both perturbative and non-perturbative self-actions is presented. By analyzing the general formalism we predict that in the nonperturbative limit there is no interference at all. And by comparison with the special formalism of Schrödinger current, the coupling strength of self-action in the limit is found to be ∞. In the perturbative case, the interference from self-action turns out to be the same as that from standard approach of quantum theory. Then comparing the corresponding coefficients quantitatively we conclude that the coupling strength of self-action in this case falls in the interval [0, 1]. I. INTRODUCTIONUp to date, the experiments on quantum double-slit interference/diffraction have been realized with a series of single, separate fermions (electrons, neutrons etc.. A logical inference is that the interference pattern is created by each single particle interfering with itself. The given explanation is the Schrödinger description [5] using the analogy to the optical Young's experiment and Huygens-Fresnel principle. In this picture the fermion, one and the same quantum entity, has to be viewed as a local particle in the source and on the screen, but as a true matter wave for the propagating procedure in between [6]. Accordingly, the interference fringe is believed to be produced by the superposition of the waves from the two slits. It confuses us by introducing classically split paths to a matter wave. So far quantum interference has been always explained by utilizing a somewhat classical wave. In this paper we employ a realistic quantum nonlocal wave to describe the whole interference procedure, and the very same quantum entity can be viewed as a particle only when its charge(or one of other quantum numbers) is detected. Our nonlocal method and the given explanation differ in that the given explanation requires separate paths for a matter wave, whereas our nonlocality needs only one spreading path.The aim of this paper is to apply the theory of nonlocality [7] to the nonlocal phenomenon-double-slit interference. There are other works [5] [8] specifying the relationship between the nonlocality and the interference from different perspectives. In the reference [5] the authors attempt to link a set of locally me...