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arXiv:1412.1077

A model of virtual interference

Eduardo V. Flores, Michael Jay Young Lim, Jeffrey Scaturro

Published Dec 2, 2014• 1 citation
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Abstract

We set up an experiment with two independent laser beams that cross at a small angle, spatially separate, and end at detectors in front of each beam. The setup allows us to obtain maximum path or which-way information, K=1. However, when we scan a thin wire across the beam intersection the which-way information drops to K=0.985. The thin wire serves to verify the presence of an interference pattern with visibility, V=0.833, at the beam intersection. Our results appear to be in conflict with the complementarity inequality, V^2+K^2 smaller or equal to 1. We introduce a model that describes a virtual interference pattern. We resolve our paradoxical findings by proposing that the complementarity inequality does not apply to virtual interference patterns but only to physically real ones. We find that the interference pattern in our setup is virtual.

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We set up an experiment with two independent laser beams that cross at a small angle, spatially separate, and end at detectors in front of each beam. The setup allows us to obtain maximum path or which-way information, K=1. However, when we scan a thin wire across the beam intersection the which-way information drops to K=0.985. The thin wire serves to verify the presence of an interference pattern with visibility, V=0.833, at the beam intersection. Our results appear to be in conflict with the complementarity inequality, V^2+K^2 smaller or equal to 1. We introduce a model that describes a virtual interference pattern. We resolve our paradoxical findings by proposing that the complementarity inequality does not apply to virtual interference patterns but only to physically real ones. We find that the interference pattern in our setup is virtual.
Particle-like and wave-like behaviors of elementary particles are understood to be complementary. This can be expressed as K^2+V^2 is less or equal to 1, where K is the path information, and V is the visibility of an interference pattern. We explore this general constraint in an experiment using two independent yet phase-coherent laser beams. Our results appear to be in conflict with the complementarity inequality. We resolve our paradoxical findings by introducing the concept of a virtual interference pattern to describe interference that is present in the fields but is prevented from materializing due to lack of momentum. The visibility of such a virtual interference pattern is zero. However, when we scan a thin wire across the virtual interference pattern it becomes partially visible. We explain this phenomenon by realizing that the wire provides the momentum to deflect photons and form the pattern. Thus, the wire plays the role of an objective interactive observer by inducing the formation of a physical interference pattern on its surface.
We analyze the results of an experimental setup that consist of two statistically independent laser beams that cross, interfere and end at detectors. At the beam intersection we place a thin wire at the center of a dark interference fringe and analyze the complementarity inequality. We find that the complementarity inequality is fulfilled provided we include a scattering interaction. We find that this interaction is implicit in the formalism of quantum theory; however, this interaction is active only when the conservation laws are satisfied.
We analyze an experiment in which a thin wire is scanned across the overlap of two in phase photon beams. We find that unless the wire induces the formation of an interference pattern, the complementarity inequality is violated. Quantum electrodynamics accounts for this effect through photon deflections mediated by energy momentum exchange with the wire via virtual particles. This mechanism underscores the essential role of virtual particles in producing field effects and motivates an interpretation of quantum mechanics in which the wavefunction or field serves as information, a blueprint guiding virtual particles, whose exchanges with external sources shape the trajectories of real particles in accordance with field predictions. As an application, we propose a test of gravity quantum nature.
Bohr's principle of complementarity predicts that in a welcher weg ("which-way") experiment, obtaining fully visible interference pattern should lead to the destruction of the path knowledge. Here I report a failure for this prediction in an optical interferometry experiment. Coherent laser light is passed through a dual pinhole and allowed to go through a converging lens, which forms well-resolved images of the respective pinholes, providing complete path knowledge. A series of thin wires are then placed at previously measured positions corresponding to the dark fringes of the interference pattern upstream of the lens. No reduction in the resolution and total radiant flux of either image is found in direct disagreement with the predictions of the principle of complementarity. In this paper, a critique of the current measurement theory is offered, and a novel nonperturbative technique for ensemble properties is introduced. Also, another version of this experiment without an imaging lens is suggested, and some of the implications of the violation of complementarity for another suggested experiment to investigate the nature of the photon and its "empty wave" is briefly discussed.
We critically analyse the problem of formulating duality between fringe visibility and which-way information, in multibeam interference experiments. We show that the traditional notion of visibility is incompatible with any intuitive idea of complementarity, but for the two-beam case. We derive a number of new inequalities, not present in the two-beam case, one of them coinciding with a recently proposed multibeam generalization of the inequality found by Greenberger and YaSin. We show, by an explicit procedure of optimization in a three-beam case, that suggested generalizations of Englert's inequality do not convey, differently from the two-beam case, the idea of complementarity, according to which an increase of visibility is at the cost of a loss in path information, and vice versa.