Complementarity Paradox Solved: Surprising Consequences

Abstract

Afshar et al. claim that their experiment shows a violation of the complementarity inequality. In this work, we study their claim using a modified Mach-Zehnder setup that represents a simpler version of the Afshar experiment. We find that our results are consistent with Afshar et al. experimental findings. However, we show that within standard quantum mechanics the results of the Afshar experiment do not lead to a violation of the complementarity inequality. We show that their claim originates from a particular technique they use to analyze their results. In their analysis, they assume a classical concept, that particles have a definite trajectory before detection, thus, they obtain which-way information by particle detection plus path extrapolation by applying momentum conservation. This analysis technique is standard in experimental particle physics. Important discoveries such as the detection of vector bosons have been made through the application of this technique. We note that particle detection plus path extrapolation is a suitable technique within de Broglie-Bohm theory of quantum mechanics.