Physics – Quantum Physics
Scientific paper
2004-04-07
Physics
Quantum Physics
Revised version, accepted for publication in Bulletin of the American Meteorological Society
Scientific paper
10.1175/BAMS-86-4-519
A not-too-technical version of the paper: "A Granular Permutation-based Representation of Complex Numbers and Quaternions: Elements of a Realistic Quantum Theory" - Proc. Roy. Soc.A (2004) 460, 1039-1055. The phrase "meteorological butterfly effect" is introduced to illustrate, not the familiar loss of predictability in low-dimensional chaos, but the much less familiar and much more radical paradigm of the finite-time predictability horizon, associated with upscale transfer of uncertainty in certain multi-scale systems. This motivates a novel reinterpretation of unit complex numbers (and quaternions) in terms of a family of self-similar permutation operators. A realistic deterministic kinematic reformulation of the foundations of quantum theory is given using this reinterpretation of complex numbers. Using a property of the cosine function not normally encountered in physics, that it is irrational for all dyadic rational angles between 0 and pi/2, this reformulation is shown to have the emergent property of counterfactual indefiniteness and is therefore not non-locally causal.
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