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.

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 is, of course, focused on the active aspect of the Source, on its causal function, on the Force and on its expression in the incessant construction of Reality, from the most elementary levels to the most complex.

The causal perspective focuses on the active aspect 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 speaking, the Perturbation Operator should be defined as a sub-Entity, a functional derivation of the Primary Agent, the active aspect of the Primary Source of Reality, the Fundamental Force. In a broader and more descriptive sense of the Formation of Reality, we could say that Perturbation is the substrate of Existence in its most elementary form. As with all other Operators of Reality, we cannot say that Perturbation is something that exists, an Entity in the common sense. We may think of it as a Phenomenon, a portion of an immense phenomenon—the Universe in its incessant formation—produced by the dynamics of the internal interaction of the aforementioned two aspects of the Source of Reality.

Technically speaking, the Perturbation Operator should be defined as a sub-Entity, a functional derivation of the Primary Agent—the active aspect of the Primary Source of Reality, the Fundamental Force. In a broader and more descriptive sense of the Formation of Reality, we could say that Perturbation is the substrate of Existence in its most elementary form. As with all other Operators of Reality, we cannot say that Perturbation is something that exists, an Entity in the common sense. Rather, we may think of it as a Phenomenon: a portion of an immense phenomenon—the Universe in its incessant formation—produced by the dynamics of the internal interaction between the aforementioned two aspects of the Source of Reality.

Technically, the Perturbation Operator should be defined as a sub-Entity, a functional 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.

As with all other Operators of Reality, Perturbation is not an Entity in the common sense. It is a Phenomenon: 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

In terms of Elementary Events, Perturbation represents any inhomogeneity in the distributions of their intensities, namely the deformations of the Elementary Field under the incessant pressure of the Fundamental Force.

Elementary Events are the "substance" Reality is made of, produced by the inner interaction between the Fundamental Force and the Elementary Field, the unitary couple of the two aspects of the Source of Reality.

Perturbation transmutes the pressure of the Fundamental Force on the Elementary Field into an incessant flux of variations and fluctuations of the parameters that describe the same Field.

Variation is the root of the emergence of the Dimensionalities of Reality—Spatiality and Temporality—the fundaments of Space and Time.

The key question is: what varies? What varies is the distribution of the Elementary Events and the patterns of correlations among them. Any departure from homogeneity, any change in distribution or correlation, represents a perturbation.

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

Perturbation is associated with the Operator of Reality that bears the same name and expresses the Fundamental Principle we call Principle of Variation.

Everything that exists is in incessant mutation, variation—or better, everything that exists "is" incessant variation.

Modes of Action are intimately connected with the Dimensionalities of Reality: Physical Causality and Physical Variationality, which produce the Dimensions of Physical Reality: Cause, Space and Time.

The Operator Perturbation can be seen as the expression of Physical Causality, the active side of Physical Agency, while Translation and Rotation are expressions of its passive side, Physical Variationality: Physical Spatiality and Physical Temporality.

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).

The phenomenological perspective

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

• 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.

• 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.

• 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.

Parameter expressing "the intensity (and maybe the shape) of the temporal distribution (temporal durations) of the spatial fluctuations (spatial distances) of the Elementary Field" (intensity of the variational effects on the Elementary Field produced by the causal Action of the Fundamental Force, intensity of the Elementary Action, the most elementary form of Existence, primary manifestation of the Source of Reality).

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.

In term of Elementary Events, Perturbation represent any inhomogeneity in the distributions of the intensities of the Elementary Events, of the intensities of the deformations of the Elementary Field under the incessant pressure of the Fundamental Force. Elementary Events are the "substance" Reality in made of, produced by the inner interaction between the Fundamental Force and the Elementary Field, the unitary couple of the two aspects of the Source of Reality.

Perturbation is the substrate of Existence in its most elementary form. But we cannot say that Perturbation is something that exists, an entity. It is a phenomenon, a product of the dynamics of the inner interaction of the two aspects of the Source of Reality.

It is associated with the Operator of Reality that has the same name and is the expression of the Fundamental Principle that we call Principle of Variation (everything that exists is in incessant mutation, variation, or better, all that exist "is" incessant variation). Perturbation , as an Operator of Physical Reality, transmutes the pressure of the Fundamental Force on the Elementary Field in an incessant flux of variations, fluctuations, of the parameters that describe the same Elementary Field.

Perturbation is the way in which the Elementary Field react to the Elementary Action of the Fundamental Force, the way in which the Elementary 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 best question with respect to Variation undoubtedly is: what varies? What varies is the distribution of the Elementary Events and the patterns of correlations among them. Any departure from an homogeneous distribution of Events as any change in that distribution (and in their stochastic independence / correlation) represents a perturbation. 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. 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.

Modes of Action are intimately connected with the Dimensionalities of Reality: Physical Causality and Physical Variationality, that produce the Dimensions of Physical Reality: Cause, Space and Time. They represent three fundamental operators in the Formation of Physical Reality. The Operator Perturbation can be seen as the result of expression of Physical Causality, the active side of Physical Agency, while Translation and Rotation can be seen as expressions of the two aspects of its passive side, Physical Variationality: Physical Spatiality and Physical Temporality.

The Operator Perturbation is responsible for the formation of the gradients in the Elementary Field, inhomogeneities, anisotropies, in the Field and their dynamics in the inner interaction with the Fundamental Force as components of the Sources.

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.

Perturbation is:

• expression of the Principle of Uncertainty
• the root of Mass and gravitational phenomena
• 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.

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)

Gradients

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.

Mass

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

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.

Attraction / repulsion

Mass can be positive and negative (dark/ordinary matter and dark energy create respectively attraction or repulsion in the gravitational cosmic dance).

Gravity

Gravity is commonly seen as a natural phenomenon produced by Mass and the dynamics of massive objects (Structures and Forms).

Perturbation is causal origination of Gravity, while Translation is its variational effect.

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"