TFNR - Perturbation - Gradient

Perturbation is the instantiation through which "Variation" manifests at the most elementary level of Physical Reality.

It is the most fundamental Mode of manifestation of the Elementary Action, its first Component. The first of the Modes of Physical Action.

From a causal perspective, we can represent it as the Operator Perturbation, the Operational Agent responsible for the emergence of inhomogeneities / gradients in the temporal distributions of the elementary spatial fluctuations.

At the same time, from the variational point of view, Perturbation appears as inhomogeneities (gradients) in the temporal distributions of the Elementary Events, namely the tiny spatial fluctuations of the Elementary Field resonating around the Planck scale, emerging under the incessant Action of the Fundamental Force in its functional / operational form of the Operator Perturbation.

Perturbation is the way in which the Elementary Field react to the Action of the Fundamental Force, the way in which the Field receive the expression of the Fundamental Force, its the product of the expression of Causality at the most elementary level of Reality. Variation is the root of the emergence of the Dimensionalities of Reality that we call Spatiality and Temporality, the fundaments of Space and Time.

The Modes / Components of Action are intimately connected with the Dimensionalities of Physical Reality: Physical Causality and Physical Variationality, from which derive the Dimensions of Physical Reality: Cause, Space and Time.

The causal expression and the variational manifestation—two sides of the same coin—of this Mode of Elementary Action are described by the Principle of Uncertainty.

The causal perspective

The causal perspective focuses on the active aspect of the Agency of the Source, on its causal function, on the Force and its expression in the incessant construction of Reality, from the most elementary levels to the most complex.

Technically, the Perturbation Operator should be defined as a sub-Entity, a functional / operational derivation of the Primary Agent—the active aspect of the Primary Source of Reality, the Fundamental Force. In a broader sense, Perturbation is the substrate of Existence in its most elementary form.

Like all other Operators of Reality, Perturbation should not be regarded as an Entity in the common sense of the term. It is therefore not something that exists in and of itself. Rather, it must be conceived as a Phenomenon—something that occurs, something that exists in the very act of generating Existence: a portion of the immense Phenomenon—the Universe in its incessant formation—produced by the dynamics of the internal interaction between the two aspects of the Source of Reality.

The variational perspective

Symmetrically, the variational perspective focuses on the passive aspect of the Agency of the Source, on its variational function, on the Field and its manifestation in the incessant construction of Reality, from the most elementary levels to the most complex.

Here we must focus on what happens to the Field under the incessant Action of the Fundamental Force in the form of the Perturbation Operator. On the Variations produced by the internal interaction between Force and Field, between Agent and Acted, on what occurs in this interaction—on the Events I call Elementary precisely because they represent the most elementary form of Existence, the simplest occurrences that can manifest within Reality and that lie at the foundation of its very existence. This is the essence of the sub‑Process of Creation, as part of the Process of Formation of Reality.

As already stated countless times in this work, by Elementary Events I mean the tiny elementary spatial fluctuations of the Field resonating around the Planck scale. I use the term "spatial" even though Space, the spatial dimensions, technically emerge at an evolutionary stage of Reality that is temporally concurrent but causally subsequent to the expression of the Perturbation Operator. It is precisely this expression that produces the premises—the causal and variational substrate—for the emergence of the spatial dimension, of Space itself. We could say that spatial Dimensionality, inherent in the variational aspect of the Agency of the Source, through the expression of the Perturbation Operator, is the causal seed that enables the subsequent manifestation of Space and of the spatial dimension of Reality (as well as of Time and of the temporal dimension).

Everything occurs in parallel from the variational point of view (spatial and temporal), but from the causal point of view the order of expression of the Operators at the level of Elementary Action is crucial and fundamental for the creation of Physical Reality as we know it, in its causal, spatial, and temporal dimensions.

We will then see how Translation and Rotation represent, from the causal point of view, the subsequent steps in defining the dimensional framework of Physical Reality, the first being understood as Propagation and Conservation in Space and the second as Propagation and Conservation in Time. Taken together with Perturbation, all three constitute the elementary dynamic basis (the dynamism of the Elementary Field under the incessant Action of the Fundamental Force, the expression/manifestation of the Agency of the Primary Source) upon which the Fundamental Physical Quantities are founded: Metric/Mass, Motion, Charge, Spin, and the related phenomenological domains that combine in different forms within gravity, electromagnetism, and the more complex phenomenologies of the weak and strong nuclear interactions, as well as all the natural phenomena that contribute to the incessant Formation of Reality and to the complex life of the Universe.

From the point of view of the Elementary Events and the Dynamics of Elementary Action

Perturbation transmutes the active pressure of the Fundamental Force on the Elementary Field into an incessant Process of Variations of the same Field, in its dynamics at the most elementary level of organization. Causality produces Variationality (Spatiality and Temporality).

The key question is: what really varies? What varies is the temporal distribution of the Elementary Events, the tiny elementary spatial fluctuations of the Field resonating around the Planck scale.

The temporal distributions of the Elementary Events must be regarded as the "substance" Physical Reality is made of, the direct manifestation of the expression of the Action of the Force upon the Field.

All this lies beyond molecules and atoms, beyond particles; it dwells in the dimensional abysses, at infinitesimal scales where indetermination sketches a blurred boundary between here and there, between before and after, where Space and Time are but a faint hint, indistinguishable from the creative chaos out of which Reality incessantly emerges and evolves.

Here we are at an extremely elementary level, where we must consider the dynamics of the Field not in its entirety, nor over spatially extended portions or significant durations, but independently for each point‑event of the Field, with its own specific and peculiar dynamics.

We are in a dynamic condition (what in conventional physics is, in my view improperly, referred to as a "state" of the system) that is unstructured (an unstructured Elementary Field), characterized by separation and independence, and describable through an independent stochastic process.

This process could be assimilated to that of a "continuous random harmonic oscillator" (similar, for example, to a Damped Harmonic Oscillator with White Noise Forcing, as in the standard model for Brownian Motion with elastic return—confining potential), where what oscillates is the spatial distance, according to a temporal distribution around a mean value and with a given variance (confined random fluctuations). The amplitude of the fluctuations would depend on the intensity of the Fundamental Force, while the damping and rigidity would depend on the properties of the Elementary Field.

In this context, by inhomogeneity of the temporal distributions of Elementary Events I mean any deviation from the mean value of this dynamics.

It is evident that these temporal distributions define not only the rhythm of Time at the particular point‑event under consideration, but also the velocity of the elementary spatial fluctuations, and the variation of that velocity over Time, which we may call "acceleration". We shall later see how the relationship between the interactions among the dynamic conditions of point‑events in connected portions of the Elementary Field—describable as networks of interactions (correlation schemes) among the punctual stochastic processes mentioned above—will lead us to the concepts of Metric (Space‑Time) and Mass, and to the related metric phenomena (curvature, dilation‑contraction of Times, etc.) and gravitational phenomena (attraction‑repulsion of Structures endowed with Mass—ordinary Matter and Dark Matter/Energy). And we shall see how the equivalence between gravitational attraction and acceleration (the indistinguishability between an external gravitational field and the acceleration of one’s own reference system) is grounded in the properties and behaviors of the elementary dynamism of the Field, as outlined above and further integrated by what we shall discuss shortly concerning the Operator and the Mode/Component that I call Translation.

From the point of view of the Fundamental Principles of Evolutionary Dynamics

Perturbation is an instantiation of the Operator of Reality Variation that expresses the Fundamental Principle I call Principle of Variation: everything that exists is in incessant mutation, variation—or better, everything that exists "is" incessant variation.

The way Perturbation expresses and manifests itself in the construction of Reality is described by the Principle of Uncertainty, which is precisely an instantiation of the Principle of Variation.

This principle, in particular, describes how elementary variations—small spatial fluctuations at the Planck scale—are temporally distributed. It is precisely in the relation of indetermination that binds these two aspects of Variationality, which underlies all that exists, in the interplay between Spatiality and Temporality, that lies the foundation of the incessant creation of Elementary Action in its primary form, which I here call Perturbation. If, in response to the expression of the Fundamental Force, the Spatiality and Temporality manifested by the Field in the creation of Elementary Action were bound by a fixed, constant, determined relation, nothing could exist. It is only through differentiation, through inhomogeneity, that Existence and the Essence/Form of Reality in Formation can emerge.

The root of everything lies in this creative chaos, the primordial form of Existence, the raw material of the evolutionary organization that gradually emerges and shapes the Form of Reality.

Chaos, but not uncontrolled chaos. Chaos that follows a law, a principle—this very principle. Where the relation of indetermination binds Causality and Variationality, the expression of the Force and the manifestation of the Field, within the Action that is continuously expressed and manifested. Force, Space, and Time dance incessantly around a mean value, and this dance incessantly generates the dynamics upon which all of Reality is founded. If this dynamic—let me say "perfectly" indeterminate—were suddenly to cease, Reality would immediately vanish, and nothing would exist, as if Reality had never existed at all!

The Information / Energy perspective

The correlation between Perturbation values in a portion of the Elementary Field defines the Elementary Energy of that portion in the Perturbation Component. This is what we call "deformation of the Metric" or "Mass"—two equivalent concepts, the roots of metric and gravitational phenomena.

Perturbation is:

expression of the Principle of Uncertainty

the root of Mass and gravitational phenomena

connected with the intensity of the Elementary Action, the temperature of the Elementary Field, the curvature of Space-time, mass density, and the velocity of propagation of Information in the Field (limit of speed of light), as stated by the Principle of General Equivalence.

According to the Principle of General Equivalence, Perturbation corresponds to:

Mass density (positive, producing attraction, or negative, producing repulsion)

the curvature of space-time

the temperature of the Elementary Field, manifesting as gravitational, kinetic, electric, magnetic, weak and strong nuclear fields

the limit of the velocity of propagation of Information in the Elementary Field → the speed of light in the "vacuum" (a limit, not a constant).

intimately connected with the intensity of the Elementary Action, the temperature of the Elementary Field, the curvature of Space-time, mass density, the velocity of propagation of Information in the Field (limit of speed of light), as stated by the Principle of General Equivalence.

The correlation between the Perturbation values ​​in a given portion of the Elementary Field (Relationship between Elementary Action of a contiguous set of event points) defines the Elementary Energy of that portion in the Perturbation Component, which we call "deformation of the Metric" or "Mass" (two equivalent concepts), the roots of metric and gravitational phenomena.

According to the Principle of General Equivalence Perturbation corresponds to:

• Mass density (both positive mass density, that produces attraction, as that of baryonic or Ordinary matter and Dark matter, and negative mass density, that produces repulsion, as Dark energy),
• the curvature of space-time,
• the temperature of the Elementary Field, of which we can make experience as the many fields that we call space-time field, gravitational, kinetic, electric, magnetic, weak and strong nuclear fields, as complexity arises,
• the limit of the velocity of propagation of Information in the Elementary Field -> the speed of light in the "vacuum" (a limit, not a constant)

At any level of complexity, from the most elementary to the Universe as a Whole, Reality can be described as a net of more or less independent / correlated stochastic processes. Metric, Space, Time, Mass, Motion, charge, spin and all the more complex entities (Agents / Forces and Acted / Fields) and phenomena (Events and Relations) that we can see in Nature are made of Events, of Action, which can be described be sets, or better nets, of relations among an infinite number of stochastic processes. Infinite are the ways in which the relations among those stochastic processes organize, produce, the infinite complexity of the Universe in evolution.

Formulation in vector calculus

• Gradients are variations of the parameters that describe the Elementary Field along a chosen direction, the most elementary form of inhomogeneity. They are produced by the Fundamental Force at the elementary level, and by derived forces at higher levels.

In the context of Evolutionary Knowledge, gradient is any variation of the parameters that describe the Elementary Field along a chosen direction, the most elementary form of inhomogeneity, of anisotropy, of deformation of the Field.

Primary manifestation of Action. Elementary gradients are produced by the action of the Fundamental Force, which disturbs, deforms, the Elementary Field.

At more complex levels, the gradients are produced by the action of the derived forces, which perturb the Derived Acted / Fields, characterizations of the Elementary Field, different levels and modes of organization of the Events, whose inhomogeneities represent the Action.

In vector calculus, Perturbation is embodied by the vector operator called "Gradient" (GRAD), which represents the measure the rate and direction of change in a scalar field.

The phenomenological perspective

Perturbation manifests phenomenologically as gradients, mass, curvature, attraction/repulsion, and gravity.

• Mass is a phenomenon produced by a local non-zero amount of Perturbation.

• Space-time curvature can be explained through two equivalent models:
  • Curved spacetime with constant speed of light: lengths and durations vary with mass density and motion.
  • Curved time with flat space and variable speed of light: durations vary, while spatial extensions remain fixed.

In both models, mass density and distributions of Elementary Events determine curvature. Positive density (Dark energy) produces expansion of space and contraction of time; negative density (Ordinary/Dark matter) produces contraction of space and dilation of time.

• Attraction / repulsion: Mass can be positive or negative, generating gravitational attraction or repulsion, shaping the cosmic dynamics.

Mass can be positive and negative (dark/ordinary matter and dark energy create respectively attraction or repulsion).

Mass (positive or negative) is a phenomenon produces by a (local) non-zero amount of Perturbation.

• Gravity is commonly seen as a phenomenon produced by Mass and the dynamics of massive structures. From the causal perspective, Perturbation is the origination of Gravity, while Translation is its variational effect.

Space-time curvature

To explain the phenomena we observe as curvature of space-time we can imagine two models that are equivalent in some respects (even if the second offers more possibilities to explain some cosmological phenomena that otherwise remain mysterious):

• Curved spacetime and constant speed of light
  • What does it mean that Space is curved? Basically that the spatial extensions, the distances, and therefore the lengths, are not absolute, fixed, but can vary in space and time (rods can lengthen or shorten) as a result of two fundamental interconnected factors:
    • the density of Elementary Events otherwise called Mass (in terms of the Elementary Action: Perturbation, inhomogeneity in the distributions of Elementary Events, intensity of the tiny fluctuations at the Planck-scale)
    • the speed of the structure being measured / observed (Translation, inhomogeneity in the distributions of Elementary Events, orientation of the tiny fluctuations at the Planck-scale).
  • What does it mean that Time is curved? Basically that the temporal durations, the intervals, and therefore the times, are not absolute, fixed, but can vary in space and time (clocks can speed up or slow down) as a result of two fundamental interconnected factors:
    • the density of Elementary Events otherwise called Mass (in terms of the Elementary Action: Perturbation, inhomogeneity in the distributions of Elementary Events, intensity of the tiny fluctuations at the Planck-scale)
    • the speed of the structure being measured / observed (Translation, inhomogeneity in the distributions of Elementary Events, orientation of the tiny fluctuations at the Planck-scale).
  • Mass and and Space-time curvature are the same thing, produced by the same cause: the density of Elementary Events and their distributions. The more Mass (Ordinary matter) an object has (or the more massive a space-time region is, for example due to the organizational structure of the distributions of Elementary Events that we call Dark matter) the greater is what we call the curvature of Space-time in that object and its surroundings, or in the considered Space-time region. We can have:
    • no mass (zero mass density) = no curvature of the Space-time metrics (flat space and flat time): no massive structures, no Ordinary or Dark matter, no Ordinary or Dark energy (or rather, of an organizational structure of the distributions of Elementary Events that we call Dark Energy)
    • negative mass density = negative curvature: presence of Ordinary or Dark matter, or Ordinary energy -> negative curvature means
      • contraction of length, of spatial extension, of distance; space seems to shrink, to contract, objects seem to become smaller and so the distances between them
      • dilation of time, of temporal durations, of intervals; time seems to pass at a lower pace
    • positive mass density = positive curvature: presence of Dark energy -> positive curvature means
      • expansion of length, of spatial extension, of distance; space seems to grow, to expand, objects seem to become bigger and so the distances between them
      • contraction of time, of temporal durations, of intervals; time seems to pass at a faster pace.
• Curved time, flat space and variable speed of light
  • What does it mean that Space is flat (not curved and not bendable)? Basically that the spatial extensions, the distances, and therefore the lengths, even not absolute, fixed, cannot vary in space and time (rods cannot lengthen or shorten). Nothing can curve Space:
    • nor Mass, the density of Elementary Events otherwise called Mass (in terms of the Elementary Action: Perturbation, inhomogeneity in the distributions of Elementary Events, intensity of the tiny fluctuations at the Planck-scale)
    • nor Motion, the speed of the structure being measured / observed (Translation, inhomogeneity in the distributions of Elementary Events, orientation of the tiny fluctuations at the Planck-scale).
  • What does it mean that Time is curved? Basically that the temporal durations, the intervals, and therefore the times, are not absolute, fixed, but can vary in space and time (clocks can speed up or slow down) as a result of two fundamental interconnected factors:
    • the density of Elementary Events otherwise called Mass (in terms of the Elementary Action: Perturbation, inhomogeneity in the distributions of Elementary Events, intensity of the tiny fluctuations at the Planck-scale)
    • the speed of the structure being measured / observed (Translation, inhomogeneity in the distributions of Elementary Events, orientation of the tiny fluctuations at the Planck-scale).
  • What does it mean that the speed of light (the maximum velocity of causality and information in the Universe) is variable?
  • Mass and Time curvature with variable speed of light are the same thing, produced by the same cause: the density of Elementary Events and their distributions. The more Mass (Ordinary matter) an object has (or the more massive a space-time region is, for example due to the organizational structure of the distributions of Elementary Events that we call Dark matter) the greater is what we call the curvature of Space-time in that object and its surroundings, or in the considered Space-time region. We can have:
    • no mass (zero mass density) = no curvature of the Space-time metrics (flat space and flat time): no massive structures, no Ordinary or Dark matter, no Ordinary or Dark energy (or rather, of an organizational structure of the distributions of Elementary Events that we call Dark Energy)
    • negative mass density = negative curvature: presence of Ordinary or Dark matter, or Ordinary energy -> negative curvature means
      • contraction of length, of spatial extension, of distance; space seems to shrink, to contract, objects seem to become smaller and so the distances between them
      • dilation of time, of temporal durations, of intervals; time seems to pass at a lower pace
    • positive mass density = positive curvature: presence of Dark energy -> positive curvature means
      • expansion of length, of spatial extension, of distance; space seems to grow, to expand, objects seem to become bigger and so the distances between them
      • contraction of time, of temporal durations, of intervals; time seems to pass at a faster pace.

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"