Steps Towards a Unified Basis.

          @misc{ pirsa_PIRSA:09080008,
            doi = {10.48660/09080008},
            url = {https://pirsa.org/09080008},
            author = {Helland, Inge},
            keywords = {Quantum Foundations},
            language = {en},
            title = {Steps Towards a Unified Basis.},
            publisher = {Perimeter Institute},
            year = {2009},
            month = {aug},
            note = {PIRSA:09080008 see, \url{https://pirsa.org}}
          }
          

Abstract

A new foundation of quantum mechanics for systems symmetric under a compact symmetry group is proposed. This is given by a link to classical statistics and coupled to the concept of a statistical parameter. A vector \phi of parameters is called an inaccessible c-variable if experiments can be provided for each single parameter, but no experiment can be provided for \phi. This is related to the concept of complementarity in quantum mechanics, but more generally to contrafactual parameters. Using these concepts and some weak assumptions, the Hilbert space of quantum mechanics is constructed. The complete set of axioms for time-independent quantum mechanics is provided by proving Born`s formula under weak assumptions. 1. Helland, I.S. (2006) Extended statistical modeling under symmetry: the link towards quantum mechanics. Ann. Statistics 34, 1, 42-77. 2. Helland, I.S. (2008) Quantum Mechanics from Focusing and Symmetry. Found. Phys. 38, 818-842. Reference: arXiv 0801.2026. (http://arxiv.org/abs/0801.2026)