2017 International Workshop: Collapse of the Wave Function

reduction and measurement in quantum mechanics

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    Arthur Jabs

    A conjecture concerning determinism, reduction, and measurement in quantum mechanics∗
    Arthur Jabs
    Alumnus, Technical University Berlin. Voßstr. 9, 10117 Berlin, Germany [email protected]
    (29 May 2017)
    Abstract. Determinism is established in quantum mechanics by tracing the probabilities in the Born rules back to the absolute (overall) phase constants of the wave functions and recognizing these phase constants as pseudorandom numbers. – The reduction process (collapse) is independent of measurement. It occurs when two wavepackets overlap in ordinary space and satisfy a certain criterion, which depends on the phase constants of both wavepackets. Reduction means contraction of the wavepackets to the place of overlap. – A measurement apparatus always fans out the incoming wavepacket into spatially separated eigenpackets of the chosen observable. When one of the eigenpackets and some wavepacket in the apparatus satisfy the criterion, the reduction associates the place of contraction with an eigenvalue of the observable. The theory is nonlocal and contextual.
    Keywords: determinism, overall phases, hidden variables, reduction, collapse, localization, quantum measurement, Born rule
    PACS: 01.70.+w; 03.65.–w; 03.65.Ta; 03.65.Vf
    1 Introduction 2
    2 The absolute phase constants 3
    3 Reduction 6
    4 The spacetime nature of measurements 8
    5 Reproducing the Born rules 13
    Appendix A. Valuation of the absolute phase 16 Appendix B. Approximation in Eq. (5.4) 17 Notes and references 18-21
    ∗An earlier version was paper-published in Quant. Stud.: Math. Found. 3 (4) 279-292 (2016). In the present version the content is the same but the presentation is improved.

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