Quantum Reality, Complex Numbers and the Meteorological Butterfly Effect
摘要
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.
引用
@article{arxiv.quant-ph/0404041,
title = {Quantum Reality, Complex Numbers and the Meteorological Butterfly Effect},
author = {T. N. Palmer},
journal= {arXiv preprint arXiv:quant-ph/0404041},
year = {2009}
}
备注
Revised version, accepted for publication in Bulletin of the American Meteorological Society