2001/01/02 by T. N. Palmer, Palmer, T. N.
Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Quantum Physics (quant-ph) #nlin.CD #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/0101007
27 pages, 1 eps figure
arxiv created 2001/01/02 · arxiv updated 2009/11/30
It is shown that in two-state quantum theory, a generic quantum state can be described by a non-computable real number. In terms of this, the criterion for measurement outcome is simply and deterministically defined. This demonstration is based on a construction of the Riemann sphere whose points represent, not complex numbers, but divergent sequences with bivalent elements. Complex structure arises from self-similar properties of a set of operators which generate these sequences. In general, a rotation of (the coordinates of) the sphere maps a computable real to a non-computable real. This is interpreted physically as a mapping of a physically-measurable state to a counterfactual state. Implications for non-locality, null measurements, many worlds and so on, are discussed. The possible role of the Euler equation as the counterpart of the Schrodinger equation for real-number quantum state evolution is also outlined.