A Possible Approach to Inclusion of Space and Time in Frame Fields of Quantum Representations of Real and Complex Numbers

TL;DR

This paper extends quantum-based reference frames to include space and time lattices, describing hybrid systems that represent numbers and physical states with an iterative, hierarchical structure.

Contribution

It introduces a novel framework integrating space and time into quantum reference frames using hybrid systems and an iterative hierarchical structure.

Findings

Frames include space and time lattices with hybrid systems.

Images of lattice points are associated with energy states.

The framework describes physical systems across multiple hierarchical frames.

Abstract

This work is based on the field of reference frames based on quantum representations of real and complex numbers described in other work. Here frame domains are expanded to include space and time lattices. Strings of qukits are described as hybrid systems as they are both mathematical and physical systems. As mathematical systems they represent numbers. As physical systems in each frame the strings have a discrete Schrodinger dynamics on the lattices. The frame field has an iterative structure such that the contents of a stage j frame have images in a stage j-1 (parent) frame. A discussion of parent frame images includes the proposal that points of stage j frame lattices have images as hybrid systems in parent frames. The resulting association of energy with images of lattice point locations, as hybrid systems states, is discussed. Representations and images of other physical systems in the different frames are also described.