• A stepwise planned approach to the solution of Hilbert’s sixth problem. III: Measurements and von Neumann projection/collapse rule

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      https://www.ias.ac.in/article/fulltext/pram/077/06/1031-1051

    • Keywords

       

      Measurement problem; von Neumann projection rule; quantum–classical divide; supmech axioms; Hilbert’s sixth problem.

    • Abstract

       

      Supmech, the universal mechanics developed in the previous two papers (Dass, arXiv: 0909.4606[math-ph]; 1002:2061[math-ph]), accommodates both quantum and classical mechanics as subdisciplines (a brief outline is included for completeness); this feature facilitates, in a supmechbased treatment of quantum measurements, an unambiguous treatment of the apparatus as a quantum system approximated well by a classical one. Taking explicitly into consideration the fact that observations on the apparatus are made when it has ‘settled down after the measurement interaction’ and are restricted to macroscopically distinguishable pointer readings, the unwanted superpositions of (system + apparatus) states are shown to be suppressed; this provides a genuinely physics-based justification for the (traditionally postulated) von Neumann projection/collapse rule. The decoherence mechanism brought into play by the stated observational constraints is free from the objections against the traditional decoherence program.

    • Author Affiliations

       

      Tulsi Dass1

      1. Indian Statistical Institute, 7, S.J.S. Sansanwal Marg, New Delhi 110 016, India
    • Dates

       
  • Pramana – Journal of Physics | News

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