The “Paradox” of Karl Popper and Its Connection with the Heisenberg Uncertainty Principle and Quantum Ghost Images

Abstract

An experiment to verify the adequacy of the Heisenberg uncertainty principle, as proposed by Karl Popper and implemented in practice, is considered. As in the Einstein–Podolsky–Rosen paradox, the quantum properties of an entangled pair of elementary particles are used. In this case, a ghost image of a narrow slit is actually formed. The results of the experiment, at first glance, support a violation of the uncertainty principle. However, analysis of the spatial resolution of the slit ghost image shows that this is not correct. A more correct description of diffraction in the case of spatially limited light beams, gives no violation of the uncertainty principle. The results can be also used to estimate the extreme quality of diffraction limited ghost images.