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 primary 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
Here we are speaking of Action (Force, Space, and Time). To move from the level of Action (the level of Existence, of that which exists insofar as it occurs) to the level of Information (the level of Essence, the Form of what occurs), it is necessary to ideally stop Time flow, focusing on Force and Space.
Now, if we observe the stochastic processes that describe the physical Processes of Elementary Action as mentioned above, we may imagine that the elementary spatial fluctuations at a given instant characterize a local spatial deformation of each point‑event of the Elementary Field. A kind of curvature at the infinitesimal level, which compensates itself when we observe portions of the Elementary Field at a scale already slightly larger than the Planck scale, around which the elementary fluctuations resonate. The Field, therefore, while showing incessantly variable spatial curvature at such an infinitesimal level, appears absolutely flat at higher scales.
If we freeze the flow of Time and take a snapshot of the Field at this scale, we will observe an infinity of tiny inhomogeneities, micro‑gradients in spatial dimensionality. At each point‑event in the instant considered, we may associate to such spatial deformation a value of Energy, which, when summing all these small punctual contributions, will display an immense, infinite value—just as infinite is the Elementary Field and the Fundamental Force that animates it.
If we consider the Field as a whole, this overall Elementary Energy will be null, since the total (infinite) spatial extension of the Field does not vary, as all punctual contributions compensate one another. The total Elementary Energy of the Field (considering only the dynamics of spatial dimensionality) will therefore be null.
If we also consider the temporal dimensionality, the situation changes.
The temporal distributions—the times at which such local elementary spatial fluctuations occur (the greater the amplitude of the spatial fluctuation, the shorter the time in which it may occur)—oscillate around a universal mean value (homogeneous, unstructured Field). Yet they may exhibit local inhomogeneities of varying extent (structured Field).
The total Energy of the Field will no longer be null, but will increase due to the incessant Action of the Force, which progressively exerts pressure toward an ever greater structuring of the Field, ever greater compactness, ever more Energy and Matter, thereby increasing that energy balance of the Universe which is so studied and so crucial for understanding its origin and evolution.
The correlation between the Perturbation values in a given portion of the Elementary Field (Relations between Elementary Action of a contiguous set of points event) defines the Elementary Energy of that portion of the Field in the Component Perturbation, which we can call "deformation of the Metric" or "Mass" (two equivalent concepts, the first seen from the point of view "of" the Field, the second from that of the Structures "in" the Field).
We shall later see how this elementary energetic aspect, linked to Perturbation, will translate into the Physical Quantities of Metric and Mass—of which it is the root—and into the related metric and gravitational Phenomena, as well as into the existence, form, and dynamics of the Structures that compose the Energy, Radiation, and both Dark and Ordinary Matter that we observe in the Universe.
We shall also see, as described by the Principle of General Equivalence, how Perturbation constitutes the causal and variational substrate of many physical quantities and phenomena which, in conventional physics, do not appear to share origin and nature.
I refer in particular to:
- the deformation of Metric, the so called Space-time curvature (or rather the curvature of Time, in this model)
- Mass density (positive, producing attraction, or negative, producing repulsion)
- the limit of the velocity of propagation of Causality / Action / Information in the Elementary Field (the speed of light in the "vacuum", a limit but not a constant in this model)
- the temperature of the Elementary Field
At any level of Complexity, from the most elementary to the Universe as a Whole, Reality can be described as a network of more or less independent / correlated stochastic / deterministic processes. Metric, Space, Time, Mass, Motion, Charge, Spin and all the more complex Entities (Agents / Forces and Acted / Fields) and Phenomena (Processes of Events organized by Relations) that we can see in Nature, at their foundation, are made of Events, of Action, which can be described be sets, or better networks, of Relations among an infinite number of Processes. Infinite are the ways in which the Relations among those Processes organize, produce, the wonderful Complexity of the Universe in Evolution.
Formulation in vector calculus
Perturbation can be understood as an inhomogeneity in the temporal distribution of elementary spatial fluctuations. In vector calculus, such inhomogeneities in a scalar field are represented by gradients—vector quantities that express the rate and direction of variation of scalar magnitudes in Space.
We speak of a scalar field, which might at first suggest something static. Yet, as with the scalar field representing temperature—for example, in a gas—even if the gas appears motionless, we know its molecules are in constant motion. It is precisely the average intensity of this molecular motion that defines what we call temperature, reflecting the distribution of thermal energy within the volume of gas considered. Yet, what often matters physically is not only the temperature itself, but its spatial variation. This variation is expressed by the thermal gradient, a vector quantity that indicates the rate and direction of change of temperature within the field, and which governs processes such as heat conduction.
Thus, here we are referring to a gradient in the dynamics underlying the observed phenomenon: the molecular motion that explains the spatial distribution of temperature in the gas.
The same reasoning applies to the Elementary Field and its dynamics. When we speak of Structures of Information within the Field, we recognize them as manifestations of the organization of the Field’s dynamics. These structures embody the Information that provides form and coherence to what becomes manifest—what we perceive as observable reality.
Such InfoStructures—interpreted and named as Waves, Vortices/Halos/Particles, and Interactions—constitute both Dark Matter and Ordinary Matter. Gradients of complex and changing forms, interactions among gradients, and so on.
As mentioned, gradients are the most elementary form of inhomogeneity: variations of the dynamics of Elementary Field along a chosen direction.
At the fundamental level, they are produced by the Fundamental Force, which disturbs and deforms the Elementary Field.
At higher levels, they arise from the Derived Action of Derived Forces, acting on the Derived Fields—organized modes of the Elementary Field—whose inhomogeneities manifest as Variation.
In this model, a gradient is any variation in the dynamics of the Elementary Field along a direction. It represents inhomogeneity, anisotropy, deformation, and the primary manifestation of Action.
The phenomenological perspective
Perturbation manifests phenomenologically through mass, curvature, and gravity and gravitational attraction/repulsion. These phenomena are different expressions of how local inhomogeneities and variations in the Elementary Field organize themselves into observable structures.
Why do we observe in nature phenomena that we trace back to the presence of Mass?
In light of the above, the answer is, of course: because there exists Elementary Action in the Component Mode that I call Perturbation.
The question that immediately arises is: why does Perturbation exist? Why does this dynamic condition manifest itself in the Elementary Field (this ‘state,’ as conventional Physics would call it—a term I find unsatisfactory, since it evokes a static condition rather than the dynamic situation I see at the root of natural phenomena, and thus also at the basis of the "states" of the systems we observe).
Mass
We have already discussed Mass and Mass density above. Here we summarize their essential features from a more distinctly phenomenological perspective.
- Mass is a phenomenon produced by a local non-zero amount of Perturbation.
Mass arises as a phenomenon produced by a local, non-zero amount of Perturbation. It can be positive or negative, corresponding respectively to ordinary/dark matter (attractive) and dark energy (repulsive). In this view, mass is not an intrinsic substance but a manifestation of localized perturbative density.
Space-Time Curvature
- 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.
Gravity and gravitational attraction / 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.
Conventionally, gravity is seen as a phenomenon produced by mass and the dynamics of massive structures. From the causal perspective of this model, however, Perturbation is the origination of gravity, while Translation is its variational effect—expressing how perturbative inhomogeneities propagate and organize into macroscopic gravitational phenomena.
Depending on the sign of mass, gravitational effects manifest as attraction or repulsion. These opposing tendencies shape cosmic dynamics, balancing the interplay between matter and dark energy.
- Gravitational 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.
Links to the tables of contents of TFNR Paper
