Quantum Mechanics as a RealVectorSpace Theory with a Universal Auxiliary Rebit Speaker(s): William Wootters
Abstract: In a 1960 paper, E. C. G. Stueckelberg showed how one can obtain the familiar complexvectorspace structure of quantum mechanics by starting with a realvectorspace theory and imposing a superselection rule. In this talk I interpret Stueckelberg’s construction in terms of a single auxiliary realvectorspace 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:quantph/0009063.
Date: 11/08/2009  2:30 pm
Collection: Reconstructing Quantum Theory  2009
