Reference Frame Fields based on Quantum Theory Representations of Real and Complex Numbers

Details Reference Frame Fields based on Quantum Theory Representations of Real and Complex Numbers Reference Frame Fields based on Quantum Theory Representations of Real and Complex Numbers

2007-09-17

arxiv.org/abs/0709.2664v2

Advances in Quantum Computation, K. Mahdavi and D. Koslover, Eds., Contemporary Mathematics Vol. 482, pp125-163, (2009)

Physics

Quantum Physics

Extensively revised and expanded, title changed. Submitted to Conference proceedings, NSF Conference, Tyler TX, Sept. 2007

Scientific paper

A quantum theory representations of real (R) and complex (C) numbers is given that is based on states of single, finite strings of qukits for any base k > 1. Both unary representations and the possibility that qukits with k a prime number are elementary and the rest composite are discussed. Cauchy sequences of qukit string states are defined from the arithmetic properties. The representations of R and C, as equivalence classes of these sequences, differ from classical kit string state representations in two ways: the freedom of choice of basis states, and the fact that each quantum theory representation is part of a mathematical structure that is itself based on the real and complex numbers. These aspects enable the description of 3 dimensional frame fields labeled by different k values, different basis or gauge choices, and different iteration stages. The reference frames in the field are based on each R and C representation where each frame contains representations of all physical theories as mathematical structures based on the R and C representation. Approaches to integrating this with physics are described. It is observed that R and C values of physical quantities, matrix elements, etc. which are viewed in a frame as elementary and featureless, are seen in a parent frame as equivalence classes of Cauchy sequences of qukit string states.

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