TFNR - An "extreme" example of Structures of Information

To give a concrete content to these words, especially to the expression "the correlations in the pre-temporal distributions of the pre-spatial sub-elementary fluctuations of the Elementary Field" or "the correlations of Elementary Action components in the Field", let us introduce an "extreme" example. It belongs to a domain of Reality close to us, which does not exhibit the quantum indeterminacy of the microscopic world, but whose simplicity can help us illustrate and better understand key aspects of the model.

Let us imagine a large football field (the Field), full of people (the Elementary Events, the point‑events of the Field). Let us imagine observing (or measuring) what happens on the field (observable) from the stands (observer). If we ask the people on the field to move freely in any direction, we will see spontaneous polydynamic chaotic motion: within certain limits each person will move independently of all the others. In probabilistic terms, each person's motion will be random and stochastically independent. In terms of correlations between the "movement" variables, this corresponds to zero correlation (stochastic independence). The movements can therefore be described as independent stochastic processes.

Some analogies:

• the football field is an analogy of the Elementary Field (or rather, of a finite portion of it, a volume of Space),
• the places where people stand at each instant are an analogy of the point‑events of the Elementary Field ("quasi-absolute" positions influenced by fluctuations of various length resonating around the Planck‑scale — infinitesimal local pre-spatial curvature — while macroscopic Space remains flat and only Time is curved: the local distances between individuals are always fluctuating around a mean value, while the extension of the entire field remains fixed);
• the people in the field are an analogy of the Elementary Events (tiny spatial fluctuations with their temporal distributions, defining the local Space‑Time Metric and Mass density);
• the spontaneous fluctuations that determine the movements of people (variations of mutual spatial distances) are an analogy of the spatial component of Elementary Events;
• the speed of people's movements is an analogy of the pre-temporal distribution of Elementary Events, representing the speed of propagation of the elementary fluctuations of / in the Elementary Field (analogous to the speed of light, though not constant in this model);
• the differences in spatial amplitudes and temporal speeds of people's movements are an analogy of the pre-temporal distributions of the sub-elementary pre-spatial fluctuations of the Elementary Field, which can be characterized in four main aspects: amplitude (extension/speed), leading to the Mode/Component of the Elementary Action called Perturbation; spatial orientation (direction of motion) -> Translation; chirality of vorticity (sense of intrinsic or self-rotation) -> Rotation:Chirality; axis orientation of vorticity (spatial orientation of the self rotation axis) -> Rotation:AxisOrientation (in this example, assuming that people stand in vertical or quasi‑vertical position, the orientation of the axis is obviously perpendicular to the ground, or close to it);
• the correlations between these differences, between these inhomogeneities, are an analogy of Information, the correlations between the inhomogeneities in the distributions of the elementary fluctuations, the correlations expressed in the terms of the Components of Elementary Action;
• the organizational patterns emerging from these correlations (groups of people exhibiting correlated behavior) are an analogy of the Structures of Information, while the correlated behavior itself is analogous to Information/Energy;
• groups of such groups, showing higher‑level correlated behavior (movement), are an analogy of Forms (object, systems, etc.).

Let's begin!

We will therefore have a football field, full of people moving in a random and stochastically independent way (spontaneous polydynamic fluctuations), with speeds varying around an average value and below a limit value — a conventional upper bound that we may associate, for the sake of analogy, with the maximum speed achievable by a human sprinter. Let's consider this value as an inviolable universal limit (like c, the speed of light in the vacuum in the case of Space-time in SR/GR).

This image serves as a metaphor for what happens at the most basic level of Reality, around the Planck scale and even below it, within the pre‑spatial domain. In such an ideal situation (stochastic independence of people's movements), the football field is homogeneous and non‑structured: there are no patterns of organization (no InfoStructures in the case of the Elementary Field), and the positions, speeds and "intentions" of all people are spontaneous, uncorrelated, and at maximum entropy. No higher‑level Information (InfoStructures and their dynamics) is present beyond the elementary level of individual movements (the Field and its dynamics). To describe this situation with full accuracy and maximum detail, the maximum amount of descriptive Information is required. Normally (even in physics), to describe such situations we use compact statistical representations — physical quantities such as temperature, which summarize the average speeds or impacts of the particles in the system — allowing us to represent a state with a minimal amount of Information (a single number, or a probability distribution of velocities, etc.).

Here we are using an example in the discrete (people moving on a field) to exemplify a dynamic situation that takes place in the continuum (elementary fluctuations of the Elementary Field, Planck‑scale fluctuations of spatial distances/areas/volumes in the time domain, their distributions, and the related correlations). We are an expression of the emerging discrete aspect of Reality; we live at discrete levels and therefore we can only find discrete examples, since everything in us and around us is made of atoms, particles, etc. (InfoStructures, Forms). But we must be aware that this is an oversimplification. These metaphors are useful for understanding, but we must not forget that the elementary level of Reality is continuous, and that the discrete is an emergent characteristic, dimension, property. With this clarification, let us delve into the example.

Let's go back to the football field. Now we provide instructions to a group of selected people who stand inside a circle in the center of the field. We tell them to start rotating on themselves while moving in more or less large circles around the center of the field while remaining within the identified circular area.

From the grandstand we will begin to see a movement that tends to be approximately swirling, which is basically / approximately centered in the center of the field, within the considered circle. A vortex-type Structure of Information has appeared! This structure — a pattern of correlations between the distributions of fluctuations / movements) is the manifestation of the information we have provided (= action of a force) to some people in the field (= elementary fluctuations of / in the field).

The potential Energy (the capacity to generate and sustain Structures, to manifest organizational schemes, to produce Information), which people possessed but did not express in their chaotic and independent motion, has—due to the action of a force (= the instructions provided), i.e., the transfer of Information/Energy from the platform to the people in the field (= the execution of an experiment)—transformed from potential into manifest or "effective" Energy, namely Information: a deformation of the state of perfect stochastic independence (dynamic homogeneity). If we observe the vortex and the field around the considered circle, we will see that the vortex movement, through impacts, "induction," imitation, etc., has propagated to the people in the areas immediately surrounding the vortex over time, and thus, little by little, all around, with an intensity that decreases as the distance from the center of the collective action increases.

And so on. We hypothesize that this "propagation of motion," which is in fact Propagation of Information, follows an inverse‑square law (the intensity of the propagation effect decreasing as the square of the distance from the center of the vortex structure). In this analogy, the situation is not perfectly defined, precise, or symmetrical (the dynamics of each person differ from all the others, as we well know; the grass on the pitch is not uniform; there may be small imperfections that slow down or speed up movements; people outside the circle may be more or less "receptive"; etc. — infinite variables...). But let us assume that the contributions of all these variables compensate, and that the real situation fluctuates slightly around a complex attractor that is stable and strong enough to make the situation ideal," or at least "near‑ideal."

And again, we can hypothesize that the Vortex motion widens, extending to the point where the new people reached by an increasingly rarefied Information (Energy) induce a "slight" variation in their movement, in the direction of motion in that part of the vortex — ever lighter the farther people are from the center of the vortex.

But how can we identify the center of the vortex? Is it an actual position (corresponding to the position of a person, or a point on the field)? Is it a stable position (absolute or relative)? Or is it a statistically calculated position, continuously variable over time, incessantly influenced by the position and dynamics of all the people present on the football field? And how can we measure and represent the contribution of each person — their position, extent of movement, and dynamics — to the position, extent, and dynamics of this (abstract?) structure we have called the vortex? Where can we place the boundaries of this structure? Are they static or dynamic?

In the answer to these questions essentially lies the representation of the InfoStructures that this model hypothesizes and proposes.

It is as if each person in the field took part in, participated in the Existence and Essence/Form of the structure (the Structure of Information) — of the vortex — to an individually variable extent, and as if the intensity of their participation fluctuated over time and in relation to the particular position they assumed in the field with respect to the structure. Everything changes incessantly: the people who participate in the Structure, the intensity of their participation, their characteristics, the speed of individual movements, their positions, and the evolution of trajectories and autorotations over time, etc. Yet the Structure is formed (Organization), evolves and changes (Transformation), and survives/persists in a causal and variational sense (Selection) until it reaches a condition of equilibrium that makes it sufficiently stable (an evolutionary adaptation — obviously unintentional, non‑direct, not designed, etc.).

I think — and here we hypothesize — that when the Structure, the approximated (imperfect) Vortex formed by people moving on the football field, is in (dynamical) equilibrium with the Field and its Dynamics, imagining a Field of infinite extension (to avoid interactions between the Structure and the boundaries of the Field), the absolute position has no relevance; it makes no sense at all. What is relevant is the mutual position of people (the relational aspect), the correlation between their dynamics with each other and with respect to the Field. Everything that matters is relative: the movement of individual people (the fact that people move — Elementary Events, individual behavior) and the correlations between people's movements (how people move collectively — Relations, collective behavior). From these two aspects arise the Existence and Essence/Form of this vortical structure, as a (complex) Process of Events and Elementary Relations. Always probabilities, or at least percentages — numbers in the continuum between 0 and 1 — the limit cases: 0 = no correlation, 1 = complete correlation. 0 = stochastic independence, independent stochastic processes. 1 = stochastic dependence, correlation, lack of independence.

If you suddenly took away the memories of the people on the ground (a metaphor for the elimination of Information, the nullification of Energy), or disoriented them with conflicting and misleading commands, the vortical structure would disappear rather quickly. The Field and the people would still be there, the movements would continue (Events → Action), but the correlation (Relations → Information) between them would vanish; the organization would dissolve, and we would no longer see the Vortex Structure. The biological energy available to each person individually remains intact, but its expression in movement is no longer directed by the previously received Information; therefore the collective Energy (so to speak) of the vortical motion in the field does not manifest (variational aspect → Structure) and is no longer expressed (causal aspect → induction of vortical motion in the surroundings).

Likewise, even if in another area of the Field we caused a similar vortex to form, with the opposite direction of rotation, and then pushed these two vortices to interact, here too — under the right conditions — both structures would disappear (annihilation). The interaction of the two structures would in fact lead to the gradual involvement of all the people participating in them, who would begin to experience the influence of the vortex dynamics of both structures, and would thus lose the set direction, returning to a condition of completely chaotic, independent, uncorrelated motion (in the case of the physical world: the Field in the absence of Structures: the Vacuum, the Quantum Vacuum). Or perhaps we would witness the analogue of photon emission in the annihilation of an electron and a positron — the generation of some tangential collective motion, for example.

Does the fact that there are no InfoStructures that give Form to the Vacuum mean that we are in the presence of Nothingness, that nothing exists? I would say no! The Field and the people (or the Elementary Events outside the metaphor) are always there; they simply do not manifest any identifiable configuration. There are no Relations, and therefore no Processes in progress — or rather, each person moves independently of the others: independent, uncorrelated stochastic processes. There is no collective Process resulting from the more or less intense correlation between individual Processes; InfoStructures do not exist or do not manifest themselves in the Field. In other words: no higher‑order Structure emerging from the underlying dynamism.

If, hypothetically, we wore glasses that prevented us from seeing the Field and the people, but allowed us to see only the organized patterns, what would we have seen in the mental experiment at the core of this "extreme example"? Nothing — until the gradual appearance of a Structure: trembling and uncertain at first, then little by little more delineated and stable, yet always dynamic. But when we say "Nothing," are we saying that there is Nothing, or that we see (observe, detect, measure) Nothing? This point is crucial for understanding Reality, and above all for understanding the fundamental concepts of Nothingness, Absolute Vacuum (no Dark or Visible Structures), and Relative Vacuum (Dark Structures present, Visible Structures absent).

For Dark or Visible Structures, as we will see in the continuation of this chapter, I mean:

• Dark Structures: Gravitational Waves; Dark-Matter/Dark-Energy Halos (large cosmic structures, giant voids, the cosmic dark web, super‑cluster and cluster‑complex dark halos, galactic halos, and the fine‑grained dark structure of the intra‑galactic medium down to the dark turbulences of space‑time around the smallest celestial bodies).
• Visible Structures: Electromagnetic Waves; Particles of Ordinary Matter and all their aggregates (states of Matter), which constitute the Visible Forms (observable because they emit/absorb electromagnetic radiation).

Returning to the vortex structure in the football field, we can imagine that the more or less organized movement (the pattern of correlations among the movements of individual people who participate in, or support the existence of the Structure) confers a sort of materiality, intangibility, a resistance to the movement of the Structure across the field. It is as if the vortex structure manifested — or rather, as if with the emergence of the Structure, specific properties and peculiar characteristics emerged.

One of these seems analogous to Mass: it attracts other people into the correlations that shape the Vortex, yet as they approach the center of the structure, further approach becomes more difficult. And this makes it "onerous" (it requires Energy, Work, or new Information) to try to move the center of the structure, to redirect its direction of motion, or to modify its speed (inertia: resistance to variation in motion or rest, to positive or negative acceleration). Think of how difficult it is to govern or direct the movement of a mass of frightened people trying to escape from a dangerous situation.

And again, we can see a tendency for displacement (change of position) emerge, which we can call Motion. And within the context of motion we can identify the two main phenomena: inertia (constancy of speed over time) and acceleration (variation of speed over time), or better: inertial and accelerated motion. We see this clearly in the vortex in the football field. In the absence of new instructions (Information, Energy, Work, no interactions), the Structure will continue either to remain still or to move with uniform motion, minimizing the Action, so to speak.

Each person (each Elementary Event) will spontaneously tend to follow the Principle of Least Action: partly trying to direct their movement according to the instructions received, and partly letting themselves be carried along by the flow of people, based on distances, contacts, pushes, pressure, etc. from the surrounding individuals. And thus the structure will involuntarily do the same, as the result of the collective behavior of the people who are supporting its existence at each moment and determining its essence/form (under the hypothesis of the absence of constraints in the Field or of the application of Forces, i.e., of new instructions).

But we still have two aspects to consider, two properties/phenomena that we would see emerge with the emergence of the vortex structure. Both are linked to the rotation of people on themselves, essential for initiating and maintaining the swirling rotary motion of the Structure (intrinsic rotation). In fact, if you recall, the instructions given to the people in the field were: "start rotating on yourselves while moving in more or less large circles around the center of the field, remaining within the identified circular area." Start rotating on yourselves, precisely.

The first aspect we discuss in this section is linked to each person's rotation on themselves. By analogy, this means that each Elementary Event, in addition to having a temporal component (the ratio between its own intrisic scalar movement speed and the average intrinsic scalar movement speed of all the other people in the region of the Field containing the structure → Mass) and a spatial component (the intrinsic vector movement speed that determines the vector speed of the Structure in its propagation through the field → Motion), has an intrinsic rotational component (each on itself) which we may call vorticity. This intrinsic rotational component, occurring around a rotation axis, can have two senses: right‑handed or left‑handed. We can call this component Charge (positive or negative depending on the sense of rotation).

The second aspect concerns the (dynamical) orientation — direction and sense — of the axis of that intrinsic rotational component. Every point‑event in/of the Field, in its rotational component, has a direction given by the rotation axis and a sense given by the right‑hand rule. We can call this component Spin (we may characterize the orientation as up/down, left/right, front/back, north/south, etc., depending on the direction and sense of the rotation axis).

Are we sure that this is precisely the last aspect in the characterization of the dynamics of Elementary Events? Modern physics tells us that the dynamics of point‑events — the Elementary Events of the Field — can take on more complex configurations and organizations. Here we enter a domain of derived forces, fields, action, and information/energy more complex than those that characterize Elementary Action and, in general, the dynamics of the Elementary Field under the incessant Action of the Fundamental Force.

We enter a level of Reality that concerns the dynamics of the Field and of Elementary Action in those domains of the Field that host or support vortex InfoStructures classifiable as massive Particles, such as leptons (Particles believed to be "elementary") and hadrons (Particles believed to be composed of quarks and gluons). We are now in the context of nuclear forces, fields, and phenomena (the Strong and Weak Nuclear Forces), which we consider here as forces and fields derived from the Elementary ones mentioned above.

Even if in mainstream physics these two forces/fields are considered fundamental, like the gravitational and electromagnetic ones, in the model I propose in this paper they are not. Strong Nuclear and Weak Nuclear are forces, fields, and Phenomena that pertain to InfoStructures and not to the Elementary Field directly.

In other words, in the absence of InfoStructures, the dynamics of the Elementary Field — spontaneous, under the incessant Action of the Fundamental Force, as described by the Uncertainty Principle — manifests the components of Elementary Action that I call Perturbation, Translation, and Rotation (in its two sub‑components, Chirality and AxisOrientation), respectively the roots of Metric/Mass, Motion, Charge, and Spin. But it does not manifest any dynamics that constitute the root components of nuclear forces and fields.

These arise from the complex organization of field dynamism in the presence of, or within the spatial domain that supports/hosts, a composite vortical Structure of Information (e.g., a proton). Nuclear forces, fields, and phenomena — although always derived forms of forces, fields, and phenomena such as gravity and electromagnetism — represent more complex forms that manifest only as aspects of the internal dynamics of composite InfoStructures, nuclear or similar (hadrons and leptons, nucleons, etc.).

Speaking of the orientation of the axis of Rotation, we must be careful not to refer to the rotation axis of the Structure, but to the axis of intrinsic rotation of each person who participates in or supports its Existence, its Essence/Form, its dynamics. Beyond the metaphor, this corresponds to the axis of intrinsic rotation arising from the dynamics of individual point‑events, the Elementary Events of/in the Field.

In the example that concerns us here, since a gravitational field binds people to the ground in a vertical posture (except for particular positions or movements), all the people on the field display the same orientation of their intrinsic rotation axis. In terms of the Dynamics of Elementary Action and its Modes/Components, we could say that in the Elementary Field — in the area/volume occupied moment by moment by the Vortex Structure — both the point value and the average area/volume value of the Rotation:AxisOrientation component appear non‑zero. Indeed, the level of correlation (Information/Energy) over the area or volume considered will appear very high.

In terms of mainstream physics, we could say that in the area/volume considered an intense magnetic field is present — or, in other words, that the Vortex Structure has a non‑zero Spin value.

If the football field, instead of being on Earth, were inside a space station in free fall, people could hover above the field, and each person would display a different orientation of their intrinsic rotation axis. If the orientations were independent — with no correlation among the axes of the people — then, continuing the usual analogy, we would have to say that in the area/volume considered no magnetic field would be observed; the Structure would not exhibit any Spin.

I think it is now clear that, as for Perturbation (Metric and Mass and related gravitational phenomena), Translation (Motion and related kinetic phenomena), Rotation:Chirality (Charge and related electrical phenomena), and also for Rotation:AxisOrientation (Spin and related magnetic phenomena), the key is the correlation between the components of Elementary Action. A correlation responsible for the manifestation of Information/Energy (gravitational, kinetic, electric, and magnetic respectively).

The Force and the Field (Source) are always there — always and forever. And so is their product, the Elementary Action, which is expressed in the Modes, with the Components mentioned (the discrepancies of the pre-temporal distributions over time of the amplitudes of the pre-spatial fluctuations of the Elementary Field around the Planck scale, of the directions of those fluctuations, the chirality and the spatial orientation of the axis of their vorticity). What changes and evolves is the organization of the Relations (correlations) between the distributions of these fluctuations — the Elementary Events, precisely.

Forces, fields, action, energy (information) that we see in the natural world — such as gravitational, electromagnetic, etc. forces and fields — are nothing more than forces, fields, action, and energy "derived" from the Fundamental Force, from the Elementary Field, from the Elementary Action, and from the Energy (Information) that represents the dynamics of the fundamental Processes that incessantly "form" Reality: the organization of the Relations between the Events of/in the Field. Specific views of the Field focused on different Modes/Components of the Elementary Action.

When we see a massive object that generates a gravitational field and a gravitational force that attracts other masses — or, in an equivalent representation (General Equivalence Principle), a deformation of the Space‑time Metric of the Field such that other masses move by following the curvature of Space‑Time generated by the first mass, and in turn produce curvature that influences that mass — here, in this case, we are observing the shape, the organization, the structure, the form of the Field in the Component of Elementary Action that I call Perturbation.

Perturbation, as we have seen in the sections dedicated to this concept, concerns the dynamics of the correlations between the pre-temporal distributions of the amplitudes of the sub-elementary pre-spatial fluctuations around the Planck scale. The power spectrum of these fluctuations (either pointwise or averaged over the considered volume of Space), which determines the distribution in Space of the rate at which Time locally flows, can — in concepts familiar to mainstream physics — be represented as the presence of a mass that produces a curvature of Space‑time or, in a more classical approach, as a gravitational field that attracts other masses.

In fact, according to the hypotheses advanced in this work, Perturbation — in terms of the behavior and the dynamics of the Field (in particular the Principle of General Equivalence) and the organization of Relations between Events — can be more precisely represented as a (local) deformation of the Field: a departure from homogeneity and the appearance of inhomogeneity; a variation in the density (over time) of Elementary Events; a curvature of Time, a variation in the speed of propagation of Causality / Action / Information (speed of light); a gradient in the temperature of the Field.

We said "curvature of time ", or "time warp" purposely. Not curvature of Space‑time, therefore, since the spatial distances at each event‑point in the (continuous) Elementary Field fluctuate around an average (universal) value determined by the properties of the Primary Source (essentially: the intensity of the Fundamental Force and the resistance of the Elementary Field to deformation — or rather, the resistances of the Field: resistance to stress → Perturbation = Metric Curvature/Mass; resistance to torsion → Rotation:Chirality = Charge; and resistance to variations in the orientation of the axis of torsion → Rotation:AxisOrientation = Spin).

Space, in this model of description of Reality, is curved only in the fluctuations that resonate around the Planck scale. At "wider" spatial distances — from those we consider infinitesimal (yet immense compared to the Planck scale) characteristic of elementary particles, to those specific to the objects of our everyday life, to our bodies, to the distances relating to the Earth, the solar system, the stars of our galaxy, up to the immense scales associated with the dark structures that host galaxies, clusters, super‑clusters, the fabric of the cosmic web, and ultimately the infinite Universe — at all these distances Space is not curved, but intrinsically flat, absolutely flat.

What we see as curvature, according to the hypotheses proposed here, is due to the curvature of Time, and therefore to the different speed of propagation of perturbations, of deformations of the Field (Action, Information/Energy, Structures, Forms). The "structured", non‑homogeneous Elementary Field, deformed by the incessant Action of the Force, can be viewed as a time‑field (where each point‑event can be associated with a clock that measures the pace of Time) and/or as a velocity‑field (where each point‑event can be associated with a tachometer that measures the speed of propagation of disturbances/deformations of the Field itself).

Translated into the terms of mainstream physics:

• no spatial curvature,
• yes curvature of Time,
• no constancy of the speed of light in vacuum,
• yes local variability of this speed.

In the light of this conceptual framework, all the phenomena we observe in the Universe — from Particles to the cosmos — take on a new and different light and meaning.

When we observe a curvature of the Space‑Time Metric, a gravitational field, a motion, an electric field, or a magnetic field, this is what is manifesting: a correlation between the distributions of the different aspects of the sub‑elementary pre‑spatial fluctuations whose discrepancies manifest as the corresponding Modes/Components of Action mentioned above. Through the "correlations" between the discrepancies in the distributions of the most elementary incessant fluctuations, the "dynamism" of the formless Elementary Field takes on "structure" and form, and therefore Information (or Energy, in its most elementary expression) appears. Mass emerge, then Gravity, and so do Motion, Charge, and Spin, and the corresponding Potentials (Metric, potential Motion -> Acceleration, electric potential, magnetic potential).

I repeat: these are properties and dynamics of the Elementary Field regardless of the presence of Vortex InfoStructures, or Waves, or Interactions. The Field is productive regardless. This is the effect that, in quantum physics, is described as the creation of virtual Particles (creation and annihilation). These virtual, ephemeral structures — which appear and disappear in extremely short times, a natural process connected to the Principle of Uncertainty — are in fact the fruit of the normal incessant dynamics of the Elementary Field, where the Field itself, under the incessant Action of the Fundamental Force, emits and reabsorbs "correlations" (Information, Energy) with dimensional resonances at various scales: from the Planck scale up to scales close to those of the elementary particles (InfoStructures, precisely) of ordinary/visible Matter. Correlations between discrepancies of distributions of sub-elementary pre-spatial fluctuations, with dimensional resonances around the Planck scale.

The presence of correlations is perceived or observed by us, and measured as gravitational field/force/action (attraction) (→ Mass), as Motion (by analogy we should say: kinetic field/force/action → inertial and accelerated Motion), as electric field/force/action (attraction or repulsion) (→ electric Charge), and as magnetic field/force/action (attraction or repulsion) (→ Spin, magnetic poles).

No correlation → no (derived) fields, no (derived) forces, no (derived) action!

The elementary, fundamental Force, Field, and Action — which incessantly create Reality and make it evolve ("Process of Formation of Reality") — are always there, inaccessible to us except through inhomogeneities/discrepancies, correlations, their organization, etc. (Information, Energy).

In quantum physics we talk a lot about entanglement — for better or for worse — in the sense that it is precisely the phenomenon of entanglement that constitutes one of the most interesting, distinctive, but also most emblematic and problematic aspects of the "weirdness" of the quantum world.

So: it is precisely the root, at the level of the Dynamics of the Elementary Field, of the entanglement that we observe (with such concern, disbelief, and wonder) at the level of Particles and quantum objects, that we are talking about here. The elementary root — in the causal and variational sense — of the phenomenon of quantum entanglement.

Let's go back to the football field on the space station and to the people who move on it, but are free to float and to rotate on themselves with orientations in all three spatial dimensions. We observe the people who participate in, who support, the vortex structure. Yes, it is true: there are some inconsistencies in the situation we are hypothesizing. There is a mix between 2D and 3D spatial conditions. We could resolve everything more rigorously, but we would complicate the description. Let us try to continue like this, although I am aware that in some respects this is an unrealistic example.

Let us look at the spatial orientation of the axis of intrinsic rotation of the vortex people. As we said, on Earth the axes would all be oriented (roughly) in the same direction, perpendicular to the ground (maximum correlation → very intense magnetic field, close to the theoretical maximum). In the space station, the axes — due to participation in the vortex structure, the relative rotation of people on themselves, weightlessness, etc. — could still be oriented in a direction perpendicular to the plane on which the vortex structure occurs (the rotation plane), but the probability that all the axes are aligned is less than one.

In the case of turbulence, also because of the interaction between the people of the structure and those in the border areas, and more generally because of the interaction with the set of chaotic (independent, uncorrelated) movements of all the people present in the field, the axes of intrinsic rotation, even if based on an aligned orientation, may exhibit a somewhat chaotic, random component. We could say that the correlation between the orientations of the intrinsic rotation axes of the people takes on a (variable) value between zero and one: with values close to one for the people near the center of the vortex structure, gradually decreasing toward zero for those on the periphery, and reaching zero for the people who, although present in the field, cannot be considered as participating in or supporting the vortex structure.

Yet, a simple instruction from the stand would be enough, the expression of a Force on the Field and on the people who metaphorically represent the Events, an Action, a transfer of Information from the stand to the people on the field, a transfer of Energy, Work. A simple instruction could make the vortex structure disappear in an instant, or it could trigger its movement in a defined direction, or the creation of a new structure next to the first, triggering phenomena of interaction, interference, etc. The field would always be the same, the people too, although not their individual movement. What would change if not the dynamic organization (Information / Energy) of correlations (Relations) between the behaviors (Action) of people (Events) within the field (the Elementary Field) animated by their force (the Fundamental Force)?

All of Reality is this: an infinite complexity and multiplicity in incessant evolution, incessantly created and recreated by a "Source", the Primary Source, the Source of Reality — a "Causal Agent" (the Force) acting through its power (Agency) on a "Variational Acted" (the Field), producing Action (Events) that takes Form as Information (Relations between Events → Processes).

The most elementary thing we can conceive gradually organizes itself into the most complex thing we can imagine: the physical and cognitive Universe, infinite, unlimited in the three fundamental dimensions — Cause, Space, and Time.

If suddenly all this organized Action — all the correlations between the discrepancies in the distributions of the sub-elementary fluctuations, all the Information/Energy at all levels of Complexity, the structured Field — were to disappear through a global "annihilation", only emptiness would remain: vacuum, the "Absolute Vacuum". All the sub-elementary fluctuations, with their stochastically independent distributions, would remain, but there would no longer be any correlation, not even the most insignificant, infinitesimal one.

Is this nothingness? For us — who are (for Existence and Essence/Form, therefore ontologically and phenomenologically, for Creation "and" Evolution) a set of multilevel correlations (of entanglement, as it is fashionable today to say, in an extended sense broader than that used in quantum physics, as I tried to mention above) — for us (who would no longer exist and would therefore be indifferent to any definition), this condition would effectively be equivalent to nothingness. Hence all the confusion we make about the terms Nothingness and Emptiness/Vacuum.

But here we need to broaden our vision. From the perspective of the Source (of the Force and the Field, and of their incessant product, the Elementary Action, the sub-elementary fluctuations, the Elementary Events), what would change? Nothing. A chilling conclusion? The "true" Nothing would exist only if the Source ceased to exist, ceased to express and manifest itself — if its active/causal aspect, the Fundamental Force, stopped acting (inner interaction) on its passive/variational aspect, the Elementary Field. No fluctuations, no Events, absolute homogeneity, no deformation, non‑existence. Nothingness.

Let us get back to the topic of this chapter. So, what is a Structure?

In the sense illustrated here, a Structure is essentially something that happens: a set of Relations between Events, positions, movements; a particular dynamic organization of Events and Relations; a Process; a set/net of interacting Processes — partly random, chaotic, independent (chaos, indeterminacy, the substrate of uncertainty that fuels Existence and supports the incessant renewal of Nature, the aspect, the "creative engine" of Reality), and partly deterministic, in some measure ordered, correlated (order, determination, the Information whose dynamics and conservation realize the incessant construction of Nature and give shape to its growing complexity, the appearance, the "evolutionary engine" of Reality).

The same thing happens in/to the Elementary Field. We can hypothesize that, in the continuum and with an average spatial extension of the Elementary Events equal to 10^−33 meters, about 10^54 Elementary Events participate in the Existence and Essence/Form of a "simple" electron, the most elementary Particle we can imagine (fluctuations of the Elementary Field which, given the characteristics/intensities/resistances of the Fundamental Force and the Elementary Field, resonate around the Planck Scale), together with all the correlations (Relations), variously intense and correctly organized, between all the discrepancies of the distributions of such sub-elementary fluctuations.

An immense spatial dimensional scale and an enormous complexity for a "simple" Particle... And we are surprised that we are unable to fully describe it, to precisely predict its Properties and Behaviors, to understand its nature and characteristics, its interactions with its peers and with other particles/forces, etc.

One final consideration, so it may be useful to play again with this example and with the metaphor/analogy that we used (and admittedly forced a little). In the Universe, it seems that ordinary/visible Matter is not really the most common "thing". Most of Matter/Energy appears to be made of something else. Even considering the inaccuracies in the proportions between Dark and Visible Matter, and Dark Energy — inevitable inaccuracies arising from the substantial incompleteness/incorrectness of the physical and cosmological models on which the calculations are based (Standard Particle Model and Quantum Field Theory, Big Bang/Inflation, Lambda‑CDM Concordance Cosmological Model, Cosmic Microwave Background, etc.) — it seems clear that the "Particles" of Matter and Radiation that we can observe in cosmic rays or in colliders represent only a small slice of the "Matter/Energy" that fills the Universe and makes the cosmos work, according to increasingly accurate (and increasingly problematic, for current models) observations and measurements.

How can we imagine a way out of this radical crisis? How can we use our "trivial" example to take a look at how we should observe the world both in here (microcosm, quanta and beyond) and out there (macrocosm, the cosmos and the Universe)?

Let's take the analogy of the football field once again. What we interpret as a Structure of Information (an elementary structure, a simple Vortex) in the small — which we associate with the physical concept of an elementary Particle (an electron, for example, as we said previously) — can be associated with the same kind of structure but with spatial (and temporal) dimensions — for the "slow" dynamics we observe in cosmological Phenomena — that are much, much more extensive.

Let us take for example a galactic Halo that hosts a normal, ideal kind of galaxy, one that shows no anomalies due to interaction with other structures, has not undergone mergers, does not interact with satellite dwarf galaxies, and does not interact with the dynamics of the surrounding cosmic‑web environment, of the cluster that contains it, and so on. Let us also imagine that the turbulence inside the galaxy — both in the visible/ordinary component (formed by Particles of baryonic Matter) and in the invisible/dark component (formed by a single, cohesive, spherical Halo of Dark Matter) — is minimal. An absolutely unrealistic situation, but useful for simplification.

Well, if we imagine extending the football field immensely, and going from a few thousand people to millions of billions of people, we might create an analogue representation of a dark Structure of Information corresponding to the galaxy above. The movements of this multitude of people would have to be organized through much more complex and precise, multi‑level instructions, as the individual and collective dynamics would be far more intricate, with an immense movement of all the billions of people on this immense football field.

It would require far more Information/Energy — therefore Force, Action — to produce all that correlation at all levels of Complexity: the organization of Particles into atoms, atoms into molecules, molecules into compounds, gases, dust, micro‑objects, rocks, satellites, planets, stars, star clusters, and so on, up to the complex immensity of a "small" galaxy in a tiny corner of an infinite Universe. Vertigo!

The same on the football field, with those people. Small, related groups that form the building blocks of larger, more complex groups. Correlations of correlations, correlations between the dynamic behaviors of interacting groups, and so on — ever more extensive groups, turbulence that organizes into turbulence of a wider and more complex level.

All the Information/Energy that a hypothetical director of the experiment, from the stand, would have to deliver to each person, to each group, to each group of groups, and so on, is the Information/Energy that that Structure possesses and manifests in its dynamism. Organization, correlation of something that exists at a more basic level — something that would continue to exist, albeit unmanifest, chaotic, formless — if that Information/Energy had not been transferred.

That's all there is. Existence (the product of the incessant sub-process of Creation by the Force acting on the Field, Elementary Action, Events) and Essence / Form (the product of the sub-process of Evolution, of incessant construction of correlations between inhomogeneities/discrepancies in the distributions of sub-elementary fluctuations, Information / Energy, Relations between Events, Processes).

Everything that makes up the world we live in (both Ordinary/visible Matter and Dark/invisible Matter) is Information/Energy — Action that takes on, that supports Form; Action with a Form; the Form of Action; In‑Form‑Action — in incessant evolution, Information/Energy supported by the elementary level of Action.

On the football pitch, in the great turbulence that a million billion people could produce simply by their presence, and through the incessant interaction with their most direct neighbors, small and more or less strictly/intensely organized groups — individuals and groups with more or less correlated dynamics, specially instructed — would compose an immense vortex structure (a Dark Halo). Within it, especially in the central areas, other smaller groups would compose structures that we could assimilate to celestial bodies: planets, stars, and so on. And at even lower levels of size and Complexity, much smaller groups would correspond to molecules and atoms, and even smaller Particles of Ordinary Matter.

Order in chaos. Organization in turbulence. Order within order. Organization within organization. Increasing Complexity.

All the Properties and dynamics, the deformation of the Metric or Mass, the Motion, the Charge, the Spin that we have illustrated above for the Vortex InfoStructures that we imagine as Particles of Ordinary/visible Matter, those same Phenomena can also be associated to the structures of Dark Matter, and above all to mixed structures (composed of dark parts and visible parts), which are the true structures that make up the Universe (mainly the galaxies). But with infinitely lower intensities of correlation (Information, Energy) compared to those of the Visible Matter.

We will thus have enormous masses, but distributed across immense spaces, with very low Mass densities — albeit variable, following the natural distributions linked to the shape of the Mass profiles of Vortex InfoStructures (a central peak of Mass density gradually decreasing toward the periphery of the Structure) and the chaotic turbulence that characterizes the dynamics of the Elementary Field, even at such low densities.

And then, internal motions and motions of the entire Vortex Structure which, under specific conditions of cosmic‑web dynamics (presence of "attractors," proximity to web nodes, positioning on highly dynamic filaments, internal dynamics of clusters/super‑clusters, etc.), can become highly relevant, with high velocities, accelerations, and sudden decelerations due to collisions with other Dark Halos.

High chirality arises from the vortex‑like rotational motion of Dark Halos around themselves; yet, because the Rotation:Chirality of the dynamics of the point‑events that support the Structure operates at extremely weak levels, the resulting electric‑charge densities remain extremely small.

Very low densities of Rotation:AxisOrientation — due to the vortex‑like shape of Dark Halos (the Halo's Spin), combined with the high turbulence within the various regions of the Structure (correlations among the Spins of the point‑events inside the Halo) — can give rise to intense magnetic fields capable of contributing decisively (alongside Mass and gravity) to shaping galactic structures (both their dark and visible components) and to guiding their interactions with surrounding Halos.

Magnetic fields do not arise (only, or primarily) from the alignment of the Spins of Ordinary/Visible‑Matter Particles, but above all from the weak — yet spatially vast — correlations of Rotation:AxisOrientation values (the root of the physical quantity that, for Particles, we call Spin) within the dynamism of the point‑events of the Elementary Field that, moment by moment, sustain the immense Structures (Dark‑Matter Halos) containing the visible parts of galaxies, or of clusters, or super‑clusters, and so on. These are rarefied magnetic fields, distributed across cosmic immensities, but which, through their sheer extension, can reach significant intensities and produce extremely relevant Phenomena, working alongside gravity in shaping astrophysical objects and the cosmological structures of the Universe.

This is a simplistic image of the Vortex Structure that we can imagine as a Dark Halo with a visible counterpart forming a galaxy as a whole. Reality is vastly more complex, due to the internal and external, dark and visible shapes and dynamics of the galaxy within the cluster that contains and influences it. Let me remember that, in this model, I hypothesize that at all levels of Physical Reality — from the Planck scale to the scale of elementary particles, to the entire cosmos — everything is turbulence, everything is dominated by turbulence, both in dynamism and in structure.

Unfortunately... this places severe limits on the knowledge and predictability of natural phenomena, on the observations we collect, and on the experiments we conduct. But we know: in the end, we must settle for probabilities, imperfect models, and summary statistical quantities of complex and turbulent dynamics that we cannot trace with infinite precision. It is indeterminacy — uncertainty raised to the nth degree. There is nothing we can do to achieve perfect knowledge of Reality as it is. Even where we believe Reality to be deterministic, ultimately it is an illusion. We can predict with great precision the motion of planets, stars, even galaxies under certain conditions. But it is always an illusion.

We are looking at Reality from afar. It's easy that way. If we push the required precision down to the individual Particles that compose those Forms, those objects, or if we wish to measure, for example, the Earth/Moon distance with infinite precision, we run into a series of important technical problems (where exactly is the center of the Earth and the Moon, where are stable test points on their surfaces, how can we eliminate the uncertainty of the light we must use to make a precise and stable measurement of distance, etc.), but above all into an inescapable intrinsic property of Nature: indeterminacy. There is no escape.

This is, in a sense, the tombstone of determinism — the ambition, given specific initial conditions, to predict the evolution of systems, and ultimately of "the" System, the Universe in its infinite entirety, with infinite, perfect certainty. A dream...

Returning to our "extreme" example, how could you predict the behavior of a million billion human beings moving freely, or bound by "generic" instructions, on a football field the size of a galaxy? Impossible. And this example is far simpler than the elementary reality of a Particle such as an electron. How can we expect "elementary," deterministic behavior, predictable with infinite precision? Turbulence and complexity (the Structure) within a turbulent and complex dynamical environment (the Field). Impossible!

One more effort, following the example we are using to try to make this model simpler and clearer (we hope). Let's try to hypothesize the Process of Formation of the InfoStructures in the Field: dark and then visible Vortex Structures, and perhaps later Wave Structures and Interactions between these two basic types. With this example, we could further explore the processes of formation of the InfoStructures of Dark/Invisible Matter and then of Ordinary/Visible Matter (baryonic Matter).

In the causal sequence (of cause‑effect relations, of Existence, ontological aspect) and in the variational sequence (of spatial and temporal relations, of Essence/Form, phenomenological aspect) of the formation of InfoStructures, we first find the InfoStructures (Waves, Vortices, and Interactions) that form Dark Matter, and then the Structures that make up Visible Matter. Or rather, the Structures of Visible Matter, in our hypotheses, can only have been formed through the complex dynamical interactions of the Structures of Dark Matter, which therefore — ontologically and phenomenologically — are their causal and variational precursors.

In extreme summary (we will examine the details in the next chapter, dedicated to Forms, Systems, the Cosmos, and the Universe), from the first organization of the temporal distributions of the infinitesimal elementary fluctuations of spatial distances — fluctuations that characterize the dynamism of the Elementary Field with relevant resonances around the Planck scale — extremely rarefied (very low‑density) yet increasingly extensive (micro-)gradients, (micro-)flows, and (micro-)torsions begin to form, gradually acquiring causal permanence and variational (spatio‑temporal) structure.

In particular, it is the alternating and interacting Vortex Structures that constitute the turbulence which, from the dimensional depths of the Planck Scale and below, progressively reach spatial extensions large enough to saturate the available Space and interact. It is precisely from the interactions between those Vortex Structures that — evolutionarily (we might say, by natural selection) — have "survived," from the "friction" of the boundary regions between the different Structures/Halos of this non-particle rarefied Matter (Dark Matter) — with very low Mass density yet extremely extensive — that Ordinary/Visible Matter is formed.

Turbulent micro‑vortices, formed by the accentuated turbulence of the friction zones in the peripheral regions of the gigantic Dark‑Matter Halos. The first elementary Particles — presumably electrons (or positrons) — accelerated by the extreme dynamism of the Elementary Field in these boundary regions, go on to form "cosmic rays" of immense energy. In unlikely yet inevitable high‑energy collisions (given the dimensions, quantity, extension of the phenomena, and the times and spaces involved), they produce other, more massive Particles (quarks, etc.), baryons or other hadrons, the first nucleons such as protons, which through further collisions/interactions — partly random, partly facilitated by the metric, gravitational, electric, and above all magnetic structure of the cosmos in a phase of ever‑increasing organization — form the first atoms and molecules.

The first gases that, from the formation zones in the outer regions of Dark Halos, due to gravitational attraction and magnetic interaction, tend to thicken in specific areas of galactic halos, precipitating more and more toward the center of gravity and forming dense clouds from which the first generations of stars arise. From their explosions, dust and additional gas fuel the formation of further generations of stars, and then planets, systems, star clusters, entire galaxies — all involved in spectacular fusion phenomena and in the complex gravitational dynamics within clusters of galaxies and clusters of clusters, immense cosmic structures in which the dark and visible components interact in intricate ways to form the infinite Cosmic Web of the evolving Universe.

This is the image that emerges from the hypotheses I have gradually formulated about the processes that lead from the infinitely small to the infinitely large. An overall image, because to understand the Universe — Reality — I believe it is absolutely necessary to keep the compass always oriented toward a synthetic vision of the whole, at all levels of Complexity of Reality. As stated several times in this work, analysis without synthesis can lead (and certainly leads, as we can see from the current state of research in physics and cosmology) into unproductive, if not outright mistaken, branches. Synthesis and analysis are two approaches, two complementary tools that cannot and must never be separated.

Returning to our football metaphor, I don't think we could define a good coach, a good football strategist, as someone who looks only at the individual players but not at the pitch and the team's play as a whole — nor as someone who looks only at the pitch and not at the individual players. The dynamics and properties of individual players, even if studied with infinite depth and precision, are not sufficient to guarantee good play and victory. We need knowledge of the pitch, of the team, an overall vision.

We could have used many other phenomena close to us (flocks of birds in flight, schools of fish in the sea, etc.) to provide a concrete example — as comprehensible as possible — of what we are trying to describe in this chapter and, more generally, in this work, even if it appears very abstract.

But I hope that this particular example has helped to clarify at least a little what we are talking about, beyond the formal and necessarily abstract definitions. Being able to imagine in a spatial/geometric/visual sense, and in a temporal/dynamic/evolutionary sense, helps us understand better. Modern physics — especially quantum field theory, with its abstract formalisms and concepts that often appear patently absurd and incomprehensible (even to physicists) — does not help us obtain a "realistic" idea of Reality, pardon the pun. But I’m sure we understand each other!

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"