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arXiv:1807.03800 · Foundations of Physics

Position Measurement-Induced Collapse: A Unified Quantum Description of Fraunhofer and Fresnel Diffractions

Moncy V. John, Kiran Mathew

Published Mar 5, 2019• 2 citations
arXivHTMLPDF
DOI
10.1007/s10701-019-00248-0

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The quantum mechanical treatment of diffraction of particles, based on the standard postulates of quantum mechanics and the postulate of existence of quantum trajectories, leads to the `position measurement-induced collapse' (PMIC) states. An experimental set-up to test these PMIC states is proposed. The apparatus consists of a modified Lloyd's mirror in optics, with two reflectors instead of one. The diffraction patterns for this case predicted by the PMIC formalism are presented. They exhibit quantum fractal structures in space-time called `quantum carpets', first discovered by Berry (1996). The PMIC formalism in this case closely follows the `boundary bound diffraction' analysed in a previous work by Tounli, Alverado and Sanz (2019). In addition to obtaining their results, we have shown that the time evolution of these collapsed states also leads to Fresnel and Fraunhofer diffractions. It is anticipated that the verification of PMIC states by this experiment will help to better understand collapse of the wave function during quantum measurements.

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The quantum mechanical treatment of diffraction of particles, based on the standard postulates of quantum mechanics and the postulate of existence of quantum trajectories, leads to the `position measurement-induced collapse' (PMIC) states. An experimental set-up to test these PMIC states is proposed. The apparatus consists of a modified Lloyd's mirror in optics, with two reflectors instead of one. The diffraction patterns for this case predicted by the PMIC formalism are presented. They exhibit quantum fractal structures in space-time called `quantum carpets', first discovered by Berry (1996). The PMIC formalism in this case closely follows the `boundary bound diffraction' analysed in a previous work by Tounli, Alverado and Sanz (2019). In addition to obtaining their results, we have shown that the time evolution of these collapsed states also leads to Fresnel and Fraunhofer diffractions. It is anticipated that the verification of PMIC states by this experiment will help to better understand collapse of the wave function during quantum measurements.
This paper provides a complete physical model associated with mathematical analysis and formulation that is based on Schrödinger equation and Feynman path integral. This model answers to single Photon (electron) double slit experiment with high degree of accuracy. It also gives a new method of analysis and formulation for Fresnel and Fraunhofer diffractions that are completely according to the Schrödinger equation and Feynman path concept. The results of these methods are precisely in agreement with the near field and far field diffraction experiments. In other words the new formulation in all above mentioned phenomena i.e. single photon (electron) double slit experiment, Fresnel and Fraunhofer diffractions are completely confirmed by lab experiments(measurements). Lab experiments mean common intensity and pattern experiments resulting from Fresnel (near field) diffraction, Fraunhofer (far field) diffraction and patterns resulting in single photon (electron) lab experiment. The resultant formulas are sketched and calculated by matlab program, the resultant graphs and values are compared with lab experiments in each section. This analysis substitutes wave function and probability density function concepts instead of interference of light beams emitted from infinitesimal pinholes or classical interpretation of near field diffraction and far field diffraction phenomena. The ultimate goal of this paper is to give a very accurate answer to the single particle double slit experiment and also to unify diffraction concept of classical optics in to quantum mechanics, deleting the traditional concept of phases in classical optics and substituting the concept of deflection of Feynman paths. The above mentioned analysis may be a glad tiding to a reliable method to unify classical optics in to quantum mechanics.