Quantum Mechanics as a Real-Vector-Space Theory with a Universal Auxiliary Rebit

          @misc{ pirsa_PIRSA:08080100,
            doi = {10.48660/08080100},
            url = {https://pirsa.org/08080100},
            author = {Wootters, William},
            keywords = {Quantum Foundations},
            language = {en},
            title = {Quantum Mechanics as a Real-Vector-Space Theory with a Universal Auxiliary Rebit},
            publisher = {Perimeter Institute},
            year = {2009},
            month = {aug},
            note = {PIRSA:08080100 see, \url{https://pirsa.org}}
          }
          

Abstract

In a 1960 paper, E. C. G. Stueckelberg showed how one can obtain the familiar complex-vector-space structure of quantum mechanics by starting with a real-vector-space theory and imposing a superselection rule. In this talk I interpret Stueckelberg’s construction in terms of a single auxiliary real-vector-space binary object—a universal rebit, or “ubit." The superselection rule appears as a limitation on our ability to measure the ubit or to use it in state transformations. This interpretation raises the following questions: (i) What is the ubit? (ii) Could the superselection rule emerge naturally as a result of decoherence? (iii) If so, could one hope to see experimentally any effects of imperfect decoherence? Background reading: E. C. G. Stueckelberg, "Quantum Theory in Real Hilbert Space," Helv. Phys. Acta 33, 727 (1960). P. Goyal, "From Information Geometry to Quantum Theory," arXiv:0805.2770. C. M. Caves, C. A. Fuchs, and P. Rungta, "Entanglement of Formation of an Arbitrary State of Two Rebits," arXiv:quant-ph/0009063.