Separating Space and Time for Dimensional Analysis and Euclidean Relational Modeling

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 zerodimensional 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 (Dihedral 360 ), time (Dihedral 12 ), rotation (Dihedral 24 ), and scale (Dihedral 10 ). 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.

Relational and Euclidean Temporal Space

“…(p179) [11] The recent introduction of Rt relationalism, a duration was defined as being related to a period between discrete cyclic events from object-oriented signals, consistent with ancient timekeeping systems. [1] The work aligns with Leibniz' comments whereby "…extension is to space as duration is to time. "(p261) [11] Relativity in context of Rt relationalism can be seen as the relativity of a network of independent durations, a methodology described as in more detail in this article.…”

“…We expand upon a recently introduced rishta (Rt) system that introduced new concepts for relationalism, capable of separating planes of matter, extensions of space (relational distance), and time (duration) for discrete Euclidean geometric modelling. [1] In this article, we describe independent and overlapping networks of object-oriented relational timelines, durations measurable by dimensional time that can be equated to a shared temporal space. Alternatively, relativity uses mathematical approaches that include continuums in time, or the speed of light as a measure that requires displacement through space to measure time.…”

“…These encompass Galilean relativity (Newtonian space-time) utilizing absolute time, Leibniz's descriptions based on relationalism [2]- [7] which stem from earlier work of Plato and Aristotle, and Einstein's relativistic Minkowski spacetime. Prior to the introduction of Rt relationalism [1], all systems relied on motion as a function of continuous time, encompassing inertial frames of reference.…”

“…[8] Taking a departure from conventional paths, the rishta system introduces the possibility of a universal frame characterized by zero-dimensional attributes and uses discrete geometry to model motion. [1] Relational durations and dimensional time is added into the model by utilizing shifts in relational space expressed using geometry, Euclidean translations, and time integrals of displacement, like absement [L•T] applying object-relational spatiotemporal units. Several characteristics are still in the early stages of development as Rt relationalism has only been recently introduced, including its formalization in set, group, and measurement theories.…”

“…Predictions into the future are computed using non-causal operations that leverage archival datasets from the past and present inputs from a causal system. [1] The causal-based system focuses on recording and communicating data from a dynamical system that can be used as inputs for modern functions, offering new tools for ongoing development.…”