TITLE:
Separating Space and Time for Dimensional Analysis and Euclidean Relational Modeling
AUTHORS:
Steven D. P. Moore
KEYWORDS:
Spacetime, Relationalism, Quantum, Classical, Signal, Discrete Geometry
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.11 No.9,
September
28,
2023
ABSTRACT: The theory of relativity links space and time to account for observed events in four-dimensional space. In this article we describe an alternative static state causal discrete time modeling system using an omniscient viewpoint of dynamical systems that can express object relations in the moment(s) they are observed. To do this, three key components are required, including the introduction of independent object-relative dimensional metrics, a zero-dimensional frame of reference, and application of Euclidean geometry for modeling. Procedures separate planes of matter, extensions of space (relational distance) and time (duration) using object-oriented dimensional quantities. Quantities are converted into base units using symmetry for space (Dihedral360), time (Dihedral12), rotation (Dihedral24), and scale (Dihedral10). Geometric elements construct static state outputs in discrete time models rather than continuous time using calculus, thereby using dimensional and positional natural number numerals that can visually encode complex data instead of using abstraction and irrationals. Static state Euclidean geometric models of object relations are both measured and expressed in the state they are observed in zero-time as defined by a signal. The frame can include multiple observer frames of reference where each origin, point, is the location of a distinct privileged point of reference. Two broad and diverse applications are presented: a one-dimensional spatiotemporal orbital model, and a thought experiment related to a physical theory beyond Planck limits. We suggest that expanding methodologies and continued formalization, novel tools for physics can be considered along with applications for computational discrete geometric modeling.