TFNR - Perturbation - Gradient - Revision history

Paolo: /* The variational perspective */

2026-09-06T17:19:24Z

‎The variational perspective

Paolo at 16:53, 21 May 2026

2026-05-21T16:53:14Z

Paolo at 14:15, 7 April 2026

2026-04-07T14:15:55Z

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Paolo at 18:06, 11 March 2026

2026-03-11T18:06:58Z

Paolo at 18:05, 11 March 2026

2026-03-11T18:05:23Z

Paolo at 18:03, 11 March 2026

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Paolo at 17:32, 11 March 2026

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Paolo at 17:25, 11 March 2026

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Paolo at 17:19, 11 March 2026

2026-03-11T17:19:46Z

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 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 pre-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)'''.
-From the variational perspective, Perturbation manifests as the '''re-Action of the Field to the incessant Action of the Fundamental Force, reaction that deforms the originally uniform basic sub-elementary dynamism of the Field in the form of Elementary Events. This reaction produces gradients (Micro-gradients) in the temporal distributions of the minute elementary spatial fluctuations resonating near the Planck scale.
+From the variational perspective, Perturbation manifests as the '''re-Action of the Field to the incessant Action of the Fundamental Force''', reaction that deforms the originally uniform basic sub-elementary dynamism of the Field in the form of Elementary Events. '''This reaction produces gradients''' (Micro-gradients) in the temporal distributions of the minute elementary spatial fluctuations resonating near the Planck scale.
 In other words, Perturbation manifests as '''discrepancies in the tau-distributions of Elementary Events'''. Crucially, Perturbation focuses exclusively on the '''pre-spatial amplitude of the sub-elementary fluctuations''', the basic dynamism of the Field, distinguishing it from the directional aspects of other Modes of Elementary Action. This focus on the pre-temporal distribution of the amplitudes of pre-spatial fluctuations '''underlies the nature and structure of Space and Time, and therefore of Metric and Mass''' — respectively the potential and the actual manifestations of Spacetime curvature, in particular of Time, given the hypothesis (adopted in this research) that Space is flat at scales far larger than the Planck scale.

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 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 Events that characterize the elementary dynamism of the Elementary Field''' near the Planck scale. '''The tiny sub-elementary pre-spatial sigma-fluctuations of the Field in their pre-temporal tau-distributions'''. Sometimes, for brevity, in this work I use the term "spatial", instead of "pre-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. The same consideration applies to the use of the term ‘temporal’ instead of "pre temporal".
+As already stated countless times in this work, '''by Elementary Events I mean the Events that characterize the elementary dynamism of the Elementary Field''' near the Planck scale. '''The tiny sub-elementary pre-spatial sigma-fluctuations of the Field in their pre-temporal tau-distributions'''. Sometimes, for brevity, in this work I use the term "spatial", instead of "pre-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. The same consideration applies to the use of the term ‘temporal’ instead of "pre-temporal".
 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 pre-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)'''.
@@ Line 104: / Line 104: @@
 From the variational perspective, Perturbation manifests as the '''re-Action of the Field to the incessant Action of the Fundamental Force, reaction that deforms the originally uniform basic sub-elementary dynamism of the Field in the form of Elementary Events. This reaction produces gradients (Micro-gradients) in the temporal distributions of the minute elementary spatial fluctuations resonating near the Planck scale.
-In other words, Perturbation manifests as '''discrepancies in the tau-distributions of Elementary Events'''. Crucially, Perturbation focuses exclusively on the '''pre-spatial amplitude of the sub-elementary fluctuations''', the basic dynamism of the Field, distinguishing it from the directional aspects of other Modes of Elementary Action. This focus on the pre temporal distribution of the amplitudes of pre spatial fluctuations '''underlies the nature and structure of Space and Time, and therefore of Metric and Mass''' — respectively the potential and the actual manifestations of Spacetime curvature, in particular of Time, given the hypothesis (adopted in this research) that Space is flat at scales far larger than the Planck scale.
+In other words, Perturbation manifests as '''discrepancies in the tau-distributions of Elementary Events'''. Crucially, Perturbation focuses exclusively on the '''pre-spatial amplitude of the sub-elementary fluctuations''', the basic dynamism of the Field, distinguishing it from the directional aspects of other Modes of Elementary Action. This focus on the pre-temporal distribution of the amplitudes of pre-spatial fluctuations '''underlies the nature and structure of Space and Time, and therefore of Metric and Mass''' — respectively the potential and the actual manifestations of Spacetime curvature, in particular of Time, given the hypothesis (adopted in this research) that Space is flat at scales far larger than the Planck scale.
 Micro-gradients define the primitive dynamic elements of the informational scaffold from which temporal Dimensionality arises. As said, in this model, while Space remains flat at macroscopic scales, Time is conceived as "curvable"—undergoing contraction or dilation according to the local value of Perturbation. Thus, the "curvature of Spacetime" is more accurately described as the curvature of Time.
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 The Operator '''Perturbation''', as a derived causal expression of the Force, transmutes the active pressure of the Fundamental Force on the Elementary Field into an incessant Process of Variation of the dynamism of the same Field at the most elementary level of Complexity. At the same time, Perturbation, as a variational manifestation, is the result of that Process of Variation. Causality produces Variationality (Spatiality and Temporality).
-The key question is: what really varies? '''What varies are the pre-temporal distributions of the amplitude of [[Elementary Events]]''', the tiny sub-elementary sigma-fluctuations of the Field. Or, more precisely, what varies is the pre temporal aspect of the amplitudes of Elementary Events.
+The key question is: what really varies? '''What varies are the pre-temporal distributions of the amplitude of [[Elementary Events]]''', the tiny sub-elementary sigma-fluctuations of the Field. Or, more precisely, what varies is the pre-temporal aspect of the amplitudes of Elementary Events.
 Elementary Events, and precisely their pre-temporal distributions of the pre-spatial fluctuations, must be regarded as the '''pre-physical substance''' Reality is based on, the direct manifestation of the expression of the Action of the Force upon the Field.
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 These inhomogeneities constitute the Elementary Action, which manifests in Modes / Components of which Perturbation is the most elementary. These inhomogeneities are the true support, the true ‘physical substance’ from whose organizational correlations Information/Energy emerges—the Structures of Information that compose the Material Forms.
-'''Here we are at an extremely elementary level'''. I call it '''sub elementary''' precisely to highlight that we are at the most elementary level of Reality, and that we are examining its most basic aspects (from a speculative and entirely hypothetical conceptual perspective). Here '''we must consider the dynamism of the Field not in its entirety''', nor over spatially extended portions or significant durations, '''but independently for each event-point of the Field''', with its own independent, specific and peculiar dynamics.
+'''Here we are at an extremely elementary level'''. I call it '''sub-elementary''' precisely to highlight that we are at the most elementary level of Reality, and that we are examining its most basic aspects (from a speculative and entirely hypothetical conceptual perspective). Here '''we must consider the dynamism of the Field not in its entirety''', nor over spatially extended portions or significant durations, '''but independently for each event-point of the Field''', with its own independent, specific and peculiar dynamics.
 A way of looking (so to speak) at the most elementary aspects of Physical Reality that is '''entirely unrealistic and purely theoretical'''. The Elementary Field is not a collection of independent event‑points. It is an interconnected continuum, exhibiting features both of the classical continuous fields found in General Relativity and of the quantum fields found in Quantum Field Theory and in the Standard Model of Particles.
@@ Line 136: / Line 136: @@
 To do this, we must attempt to picture how the dynamism of the Field manifests at the level of a single event‑point of infinitesimal extension (both spatial and temporal—or rather, pre‑spatial and pre‑temporal) at the aforementioned sub‑elementary level, a conceptual level that is, as noted, purely descriptive.
-'''The next step is to imagine the dynamics of the pre temporal distributions of the pre spatial fluctuations that I call Elementary Events'''—the units of Existence—and then to contextualize this dynamics within the continuous dynamism of larger regions of the Field, with the corresponding correlations that lead us from the plane of Action to that of Information, Energy, and the patterns that emerge and evolve within the Field, the patterns I call InfoStructures: Waves, Particles, Dark Halos, and so on, which compose the Forms—the objects we observe in the Universe.
+'''The next step is to imagine the dynamics of the pre-temporal distributions of the pre-spatial fluctuations that I call Elementary Events'''—the units of Existence—and then to contextualize this dynamics within the continuous dynamism of larger regions of the Field, with the corresponding correlations that lead us from the plane of Action to that of Information, Energy, and the patterns that emerge and evolve within the Field, the patterns I call InfoStructures: Waves, Particles, Dark Halos, and so on, which compose the Forms—the objects we observe in the Universe.
-Returning to the Process that unfolds at the sub elementary level within each event point we can imagine in the Elementary Field, I remind the reader that this is '''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.
+Returning to the Process that unfolds at the sub-elementary level within each event-point we can imagine in the Elementary Field, I remind the reader that this is '''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 are the pre-spatial distances, area and volume, according to a pre-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.
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 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 / Energy''' (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 sub-elementary sigma-fluctuations at a given instant characterize''' a local pre-spatial deformation of each event point 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 a few orders of magnitude larger than the Planck scale, around which the elementary fluctuations resonate. The Field, therefore, while showing incessantly variable pre-spatial curvature at such an infinitesimal level, appears absolutely flat at higher scales.
+Now, if we observe the stochastic processes that describe the physical Processes of Elementary Action as mentioned above, we may imagine that the sub-elementary sigma-fluctuations at a given instant characterize''' a local pre-spatial deformation of each event-point 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 a few orders of magnitude larger than the Planck scale, around which the elementary fluctuations resonate. The Field, therefore, while showing incessantly variable pre-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 pre-spatial dimensionality. At each event point in the instant considered, '''we may associate to such pre-spatial deformation a value of proto-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 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 pre-spatial dimensionality. At each event-point in the instant considered, '''we may associate to such pre-spatial deformation a value of proto-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 pre-spatial dimensionality) will therefore be null.
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 Elementary Action, in its simplest form—Perturbation—exists because the internal interaction of Force with the Field, the ceaseless expression and manifestation of the Agency of the Primary Source of Reality, occurs in a way that can be synthesized through the Principle of Uncertainty, in the general form stated in this model: '''everything varies incessantly, and even variation itself varies''', to use a hyperbolic image. '''The rate of variation also varies''', and the result of the variation of variation is a change that does not follow a deterministic law, but instead expresses and manifests chaos—uncertainty itself.
-'''Within the complexity of the interaction among an immense number of event points''', even considering the quadratic decrease of reciprocal interaction intensity with distance, '''this characteristic of indeterminacy and chaoticity is further amplified'''. The outcome is '''an omnipresent turbulence''', spanning from the most infinitesimal scales to the most extended cosmic ones, '''with dimensional resonances that lead to the emergence and manifestation of  Vortex type Structures of Information''', which we observe as Particles of Ordinary Matter and Halos of Dark Matter/Energy.
+'''Within the complexity of the interaction among an immense number of event-points''', even considering the quadratic decrease of reciprocal interaction intensity with distance, '''this characteristic of indeterminacy and chaoticity is further amplified'''. The outcome is '''an omnipresent turbulence''', spanning from the most infinitesimal scales to the most extended cosmic ones, '''with dimensional resonances that lead to the emergence and manifestation of  Vortex type Structures of Information''', which we observe as Particles of Ordinary Matter and Halos of Dark Matter/Energy.
 This turbulence arises from the spontaneous dynamics of the Elementary Field. '''Structures emerge from such turbulence, organizing, expanding, contracting'''. Some are "real"—more or less stable and permanent—while others are "virtual", ephemeral and impermanent. All participate in an incessant cosmic dance of Creation and Evolution, contributing to the Formation of the building blocks of the immense Complexity of Physical Reality.

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 <!--/no latex-->
 <!--latex:
-TABLE
+INSERT TABLE
 -->

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      </tr>
      <tr>
-       <td>Combined field reactions (composed counter-forces) produced by the interaction of divergences</td>
+       <td>Combined field reactions (composed counter-forces) produced by the manifested divergences</td>
        <td>Interaction of divergences, tendency to conservation of homogeneities in the density of τ-distributions of σ-fluctuations -> vorticity -> chirality and axis orientation</td>
        <td>Rotation / Curl formation</td>

@@ Line 30: / Line 30: @@
      </tr>
      <tr>
-       <td>Combined field reactions (composed counter-forces) produced by the manifestation of divergences</td>
+       <td>Combined field reactions (composed counter-forces) produced by the interaction of divergences</td>
        <td>Interaction of divergences, tendency to conservation of homogeneities in the density of τ-distributions of σ-fluctuations -> vorticity -> chirality and axis orientation</td>
        <td>Rotation / Curl formation</td>

@@ Line 9: / Line 9: @@
 <table class="wikitable">
      <tr>
@@ Line 35: / Line 36: @@
      </tr>
 </table>

@@ Line 10: / Line 10: @@
 <table class="wikitable">
      <tr>
        <th>Cause (expression of force)</th>
@@ Line 17: / Line 16: @@
        <th>Observed variation of the micro-dynamism of event-points and its geometric implications</th>
      </tr>
      <tr>
        <td><b>Internal interaction between the Force and the Field</b></td>
@@ Line 37: / Line 34: @@
        <td>Vorticity of σ-fluctuations within the micro-dynamism of event-points</td>
      </tr>
 </table>

@@ Line 20: / Line 20: @@
    <tbody>
      <tr>
-       <td>Internal interaction between the Force and the Field</td>
+       <td><b>Internal interaction between the Force and the Field</b></td>
-       <td>Local inhomogeneities in the density of τ-distributions of σ-fluctuations -> amplitude</td>
+       <td><b>Local inhomogeneities in the density of τ-distributions of σ-fluctuations -> amplitude</b></td>
-       <td>Perturbation / Gradient formation</td>
+       <td><b>Perturbation / Gradient formation</b></td>
-       <td>Variation of the infinitesimal event-point volume (local dilation or contraction) within the micro-dynamism of event-points</td>
+       <td><b>Variation of the infinitesimal event-point volume (local dilation or contraction) within the micro-dynamism of event-points</b></td>
      </tr>
      <tr>
@@ Line 32: / Line 32: @@
      </tr>
      <tr>
-       <td><b>Combined field reactions (composed counter-forces) produced by the manifestation of divergences</b></td>
+       <td>Combined field reactions (composed counter-forces) produced by the manifestation of divergences</td>
-       <td><b>Interaction of divergences, tendency to conservation of homogeneities in the density of τ-distributions of σ-fluctuations -> vorticity -> chirality and axis orientation</b></td>
+       <td>Interaction of divergences, tendency to conservation of homogeneities in the density of τ-distributions of σ-fluctuations -> vorticity -> chirality and axis orientation</td>
-       <td><b>Rotation / Curl formation</b></td>
+       <td>Rotation / Curl formation</td>
-       <td><b>Vorticity of σ-fluctuations within the micro-dynamism of event-points</b></td>
+       <td>Vorticity of σ-fluctuations within the micro-dynamism of event-points</td>
      </tr>
    </tbody>

← Older revision		Revision as of 17:19, 11 March 2026
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	At the same time, '''from a variational point of view''', Perturbation appears as '''inhomogeneities (gradients) in the tau-distributions of the Elementary Events''', namely the tiny sigma-fluctuations of the Elementary Field resonating around the Planck scale (discrepancies in the amplitudes of the sub-elementary sigma-fluctuations), emerging under the incessant Action of the Fundamental Force in its functional / operational form of the Operator Perturbation.		At the same time, '''from a variational point of view''', Perturbation appears as '''inhomogeneities (gradients) in the tau-distributions of the Elementary Events''', namely the tiny sigma-fluctuations of the Elementary Field resonating around the Planck scale (discrepancies in the amplitudes of the sub-elementary sigma-fluctuations), emerging under the incessant Action of the Fundamental Force in its functional / operational form of the Operator Perturbation.
		+
		+
		+	<table class="wikitable">
		+	<thead>
		+	<tr>
		+	<th>Cause (expression of force)</th>
		+	<th>Sub-elementary dynamism</th>
		+	<th>Dynamic effect</th>
		+	<th>Observed variation of the micro-dynamism of event-points and its geometric implications</th>
		+	</tr>
		+	</thead>
		+	<tbody>
		+	<tr>
		+	<td>Internal interaction between the Force and the Field</td>
		+	<td>Local inhomogeneities in the density of τ-distributions of σ-fluctuations -> amplitude</td>
		+	<td>Perturbation / Gradient formation</td>
		+	<td>Variation of the infinitesimal event-point volume (local dilation or contraction) within the micro-dynamism of event-points</td>
		+	</tr>
		+	<tr>
		+	<td>Field reaction (counter-force) produced by the manifestation of gradients</td>
		+	<td>Tendency to restoration of homogeneity of the density of τ-distributions of σ-fluctuations -> orientation</td>
		+	<td>Translation / Divergence formation</td>
		+	<td>Stretching of σ-fluctuations along the direction of divergence within the micro-dynamism of event-points</td>
		+	</tr>
		+	<tr>
		+	<td><b>Combined field reactions (composed counter-forces) produced by the manifestation of divergences</b></td>
		+	<td><b>Interaction of divergences, tendency to conservation of homogeneities in the density of τ-distributions of σ-fluctuations -> vorticity -> chirality and axis orientation</b></td>
		+	<td><b>Rotation / Curl formation</b></td>
		+	<td><b>Vorticity of σ-fluctuations within the micro-dynamism of event-points</b></td>
		+	</tr>
		+	</tbody>
		+	</table>
		+

	These gradients in the tau-distributions of Elementary Events, precisely because they occur on extremely small scales and at the level of individual event points of the Field, can be called [[Micro-gradients]].		These gradients in the tau-distributions of Elementary Events, precisely because they occur on extremely small scales and at the level of individual event points of the Field, can be called [[Micro-gradients]].