Difference between revisions of "TFNR - Elementary Relations"

Revision as of 22:23, 7 October 2025

By Elementary Relation we mean any Relation that emerges between Elementary Events in the dynamics of the Elementary Field, and is expressed in the fundamental Dimensions of Reality (Cause, Space and Time).

By Elementary Relation we mean any Relation that emerges between Elementary Events in the dynamics of the Elementary Field, and is expressed in the fundamental Dimensions of Reality (Cause, Space and Time).

At the most basic level of Reality, at the level of the dynamics of the Elementary Field, where Elementary Events and the inhomogeneities of their temporal distributions—Elementary Action—represent the most basic forms of Existence, manifestations of the Source's incessant causal pressure in a formless, variational ocean, rather than using the generic term "Relation," we should speak of "correlation," of "correlations."

At the most basic level of Reality—at the level of the dynamics of the Elementary Field, where Elementary Events and the inhomogeneities of their temporal distributions—Elementary Action—represent the most fundamental forms of Existence, manifestations of the Source's incessant causal pressure in a formless, variational ocean—rather than using the generic term "Relation," we should speak of "correlation," of "correlations."

We now come to the definition of "correlation," crucial to understanding the nature and function of Relationship in the construction of Reality. Correlation plays a crucial role here in the transition from formless Existence (the Unstructured Field, the Absolute Vacuum) to the emergence and evolution of the Essence/Form of Reality, albeit in its most elementary forms (the first, vaguest, impermanent hints of that dark turbulence that permeates the entire Elementary Field, and from its incessant transformation leads to the emergence of the first, evanescent InfoStructures (gradients, flows, and torsions, which will lead to the progressively more structured Waves and Vortices/Halos/Particles).

We now arrive at the definition of "correlation," crucial to understanding the nature and function of Relationship in the construction of Reality. Correlation plays a pivotal role in the transition from formless Existence (the Unstructured Field, the Absolute Vacuum) to the emergence and evolution of the Essence/Form of Reality—albeit in its most elementary manifestations: the first, vaguest, impermanent hints of that dark turbulence that permeates the entire Elementary Field, and through its incessant transformation gives rise to the first, evanescent InfoStructures (gradients, flows, and torsions), which will eventually lead to progressively more structured Waves and Vortices/Halos/Particles.

By correlation, especially in the context of the dynamics of the Elementary Field, where Elementary Action, the distributions of Elementary Events, organize themselves, producing the basic forms, the dynamic building blocks that allow the construction of Complexity. Referring more to mathematics and statistics than to physics and more generally to scientific disciplines, I mean "dependence" in the sense we attribute to the concept of stochastic dependence in the context of stochastic processes. This dependence recalls concepts of connection, covariance, and co-emergence, rather than causal link.

By correlation—especially in the context of the dynamics of the Elementary Field, where Elementary Action and the distributions of Elementary Events self-organize, producing the basic forms, the dynamic building blocks that enable the construction of Complexity—we refer more to mathematics and statistics than to physics or other scientific disciplines. Specifically, we mean "dependence" in the sense attributed to stochastic dependence within the framework of stochastic processes. This dependence evokes notions of connection, covariance, and co-emergence, rather than direct causal linkage.

Let's not forget that the dynamics of each event point in the Elementary Field is a Process, consisting of elementary spatial variations, where what varies is the spatial distance of a segment of infinitesimal extension (in dimensional resonance around the Planck scale). Given the uncertain nature (Uncertainty Principle) of the dynamics of the Field, this Process must be described by a stochastic process, a family of random variables indexed in Time. The connection between the stochastic processes describing the dynamics of individual event points can be viewed as a probabilistic trace of interaction.

Let us not forget that the dynamics of each event point in the Elementary Field constitutes a Process, composed of elementary spatial variations, where what varies is the spatial distance of a segment of infinitesimal extension (in dimensional resonance around the Planck scale). Given the inherent uncertainty (Uncertainty Principle) of the Field's dynamics, this Process must be described by a stochastic process—a family of random variables indexed in Time. The connection between the stochastic processes describing the dynamics of individual event points can be interpreted as a probabilistic trace of interaction.

Let's imagine that each event point in the Field consists of a random harmonic oscillator in spatial extension or distance (amplitude of elementary spatial fluctuations), spatial orientation of the fluctuations themselves, direction of chirality of the vorticity associated with the aforementioned fluctuations, and spatial orientation of the axis of the aforementioned vorticity. Let's assume an ideal condition of absolute stochastic independence of the behavior. of individual event points. This implies no interaction between event points, no stochastic dependence, independent dynamics. In essence, Elementary Events not linked by Relations.

Let us imagine that each event point in the Field behaves as a random harmonic oscillator in terms of spatial extension or distance (amplitude of elementary spatial fluctuations), spatial orientation of the fluctuations themselves, direction of chirality of the vorticity associated with said fluctuations, and spatial orientation of the axis of the aforementioned vorticity. Suppose an ideal condition of absolute stochastic independence among the behaviors of individual event points. This would imply no interaction between event points, no stochastic dependence, and entirely independent dynamics—in essence, Elementary Events not linked by Relations.

This is a purely hypothetical condition, as the Elementary Field is a continuous, connected, dynamic, and conservative field. The dynamics of each event point is in constant interaction with every other event point, with an intensity of interaction that decreases with the square of the distance. Since it is a conservative field, the dynamics of each event point depends not only on the interaction with other event points, but also on its past history (non-Markovian processes). The Field will therefore have a tendency to create and evolve structures within itself, as a result of the formation, propagation, and preservation of spontaneous perturbations, in an incessant evolution governed by the evolutionary operators: organization, transformation, and selection.

This, however, is a purely hypothetical condition, as the Elementary Field is a continuous, connected, dynamic, and conservative field. The dynamics of each event point are in constant interaction with every other event point, with an intensity of interaction that decreases with the square of the distance. Being a conservative field, the dynamics of each event point depend not only on interactions with other points, but also on its own past history (non-Markovian processes). The Field thus tends to generate and evolve structures within itself, as a result of the formation, propagation, and preservation of spontaneous perturbations—an incessant evolution governed by the evolutionary operators: organization, transformation, and selection.

This evolutionary tendency exerts a constant pressure toward the Creation and Evolution of increasingly extensive (Space), enduring (Time), and complex (Cause) Relations, which from the more complex correlations elementary ones go to the more complex relationships that link the macro-events at the basis, for example, of immense cosmic phenomena, or of intricate biological phenomena.

This evolutionary tendency exerts a continuous pressure toward the Creation and Evolution of increasingly extensive (Space), enduring (Time), and complex (Cause) Relations—progressing from elementary correlations to more intricate relationships that link macro-events underlying immense cosmic phenomena or intricate biological processes.

In summary, the most basic form of Relation is "correlation", which can be represented ad stochastic dependence, between the temporal distributions of the elementary spatial fluctuations of the Elementary Field in resonance around the Planck Scale (commonly called quantum fluctuations, quantum vacuum, quantum foam, etc.), the Elementary Events.

In summary, the most basic form of Relation is "correlation", which can be represented as stochastic dependence between the temporal distributions of the elementary spatial fluctuations of the Elementary Field in resonance around the Planck Scale (commonly referred to as quantum fluctuations, quantum vacuum, quantum foam, etc.)—the Elementary Events.

Correlations between the (local, point) distributions of those fluctuations, which can be described by a combination of stochastic and deterministic processes. At the most elementary level of Reality, where the inner interaction of the Fundamental Force and the Elementary Field incessantly occurs, producing the Elementary Events that form the Elementary Action, the correlations between the distributions can be described by Processes of Events in which stochastic component is almost completely prevalent, and the deterministic part absolutely marginal.

Correlations between the (local, pointwise) distributions of these fluctuations can be described by a combination of stochastic and deterministic processes. At the most elementary level of Reality—where the inner interaction of the Fundamental Force and the Elementary Field occurs incessantly, producing the Elementary Events that constitute Elementary Action—the correlations between distributions can be described by Processes of Events in which the stochastic component is overwhelmingly prevalent, and the deterministic part almost entirely marginal.

Links to the tables of contents of TFNR Paper

• Go to the contents list of the paper "The Fundamental Nature of Reality"

• Go to Chapter 2 "A first look"