Position measurement-induced collapse states and boundary bound diffraction: an idealised experiment
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Position measurement-induced collapse states and boundary bound diffraction: an idealised experiment Moncy V. John · Kiran Mathew
Received: 25 February 2020 / Accepted: 4 November 2020 © Chapman University 2020
Abstract In an earlier work, it was shown that single-slit diffraction of matter waves can be considered as position measurement of particles and that the Fresnel and Fraunhofer diffraction patterns result from the time evolution of the same collapsed quantum wave function. This 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. In the present work, an idealised 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. The PMIC formalism in this case closely follows the ‘boundary bound diffraction’ analysed in a previous work by Tounli, Alverado and Sanz. In addition to having obtained their results, we have identified that the Fresnel and Fraunhofer patterns are indeed present here. It is anticipated that the verification of fractal and nonfractal features of the wave function at various times and also the predicted revival distances to the screen by this experiment will help to better understand ‘quantum collapse’. Keywords Single slit diffraction · Matter waves · Wave function collapse · Quantum trajectories 1 Introduction With the advancement of technology in dealing with single-particle systems, quantum theory has now entered a new phase, namely that of ‘quantum measurement’ [1,2]. This has led to new operational interpretations of quantum mechanics. In classical mechanics of a system of particles, measurement of position is of prime concern. The case of quantum mechanics is not very different either. Heisenberg’s thought experiment, in which the position of a particle is measured with an idealised ‘gamma ray microscope’, has been central to its understanding. However, quantum M. V. John Department of Physics, St. Thomas College, Kozhencherri, Kerala 689641, India M. V. John School of Pure and Applied Physics, Mahatma Gandhi University, Kottayam, Kerala 686560, India e-mail: [email protected] K. Mathew (B) Department of Physics, Pavanatma College, Murickassery, Kerala 685604, India e-mail: [email protected]
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theory lacked a proper operational definition of ‘position measurement’ for a long time. Lamb [3] has made an attempt in this direction, observing that the above thought experiment by Heisenberg can only be considered as a scattering experiment. Recently operational approaches to quantum position measurement have gain
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