Difference between revisions of "TFNR - Elementary Relations"

Latest revision as of 18:22, 15 January 2026

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 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 arrive at the definition of "correlation", crucial to understanding the nature and function of Relations 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 and the distributions of Elementary Events self-organize, producing the basic forms, the dynamic building blocks that enable the construction of multiplicity and Complexity—I refer more to mathematics and statistics than to physics or other scientific disciplines. Specifically, I 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 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, or, more precisely, the volume of an infinitesimal region of the Field (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 us imagine that each event point in the Field behaves as a random harmonic oscillator in terms of spatial extension (amplitude of elementary spatial fluctuations, expansion-and-contraction of infinitesimal volumes), 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, 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, possibly exhibiting a square root power-law decay, where past evolution influences the current and future dynamics of the event point).

With this dynamic structure, in which the chaotic dynamics of event points influence other event points within a "causally connected" neighborhood (with quadratically decreasing intensity—spatially), and past dynamics influence the future evolution of each event point's dynamics (again with quadratically decreasing intensity—temporally), we obtain an Elementary Field characterized by the properties that are ideally required to enable the emergence of a Physical Reality compatible with the world we inhabit:

• connection and continuity (causal connection and variational, spatial and temporal, continuity)
• dynamism (a perturbed field)
• capacity for propagation (in Space) and conservation (in Time) of perturbations and structure
• capacity to create and evolve structure, which emerges from local dynamics and interactions

The Field thus tends to generate and evolve structures within itself, as a result of the formation, propagation, and conservation of spontaneous perturbations—an incessant evolution governed by the evolutionary operators: organization, transformation, and selection.

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 Relations 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 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. Elementary spatial fluctuations, which can be characterized not only in terms of their temporal distributions (Perturbation → (Metric / Mass)), but also by their spatial directionality (Translation → Motion), by the chirality of their vorticity (Rotation:Chirality → Charge), and by the spatial orientation of the axis of that vorticity (Rotation:AxisOrientation → Spin).

Correlations between the (local, pointwise) distributions of these fluctuations can be described by a combination of stochastic (new Action, new Information) and deterministic Processes (old Action, old Information). At the most elementary level of Reality—where the internal 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 organized by Relations in which the stochastic component is, "initially", overwhelmingly prevalent, and the deterministic part almost entirely marginal.

I call Emptiness the condition of the Elementary Field characterized by absent or modest and impermanent structuring (minimal level of Information / Energy).

As Time progresses, the Elementary Field—through the emergence of ever-new Relationships among Elementary Events and the accumulation of increasing Information / Energy—tends to form new and more stable structures, giving rise to a persistent, though still formless, turbulence. Gradually, this turbulence gives way to more defined, identifiable structures, persistent both causally and variationally (spatially and temporally). And so on, in an endless Evolution, from the earliest infinitesimal fluctuations to the vast structures of the Cosmic Web, and to the most complex biological architectures.

Emptiness gradually gives way to Somethingness. Absolute vacuum progressively yields to a Relative vacuum, and then to a Space-time increasingly populated by InfoStructures (Waves, Vortices/Chaos/Particles, Interactions) that constitute both Dark and Ordinary Matter—the invisible and the visible sides of the vastness of the Universe.

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"