Difference between revisions of "Paper Symbols"

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(→‎Elementary Action)
(→‎Elementary Action)
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== Elementary Action ==
 
== Elementary Action ==
  
−
<!--no latex--><span class="tex">EA = (ΔP<sub>A</sub>, ΔP<sub>n</sub>, ΔP<sub>χ</sub>, ΔP<sub>u</sub>)</span><!--/no latex--><!--latex:
+
<!--no latex--><span class="tex">EA = (ΔP<sub>A</sub>, ΔP<sub>n</sub>, ΔP<sub>χ</sub>, ΔP<sub>u</sub>)</span><!--/no latex--><!--latex:\[EA = (\Delta P_{A},\,\Delta P_{n},\,\Delta P_{\chi},\,\Delta P_{u})\]-->
−
 
+
−
\[
+
−
EA = (\Delta P_{A},\,\Delta P_{n},\,\Delta P_{\chi},\,\Delta P_{u})
+
−
\]
+
−
 
+
−
-->
+
  
 
Stochastically symmetric reference τ(σ) distribution
 
Stochastically symmetric reference τ(σ) distribution
Line 98: Line 92:
 
=== Modes / Components ===
 
=== Modes / Components ===
  
−
* Perturbation: <!--no latex--><span class="tex">ΔP<sub>A</sub> = τ<sub>A</sub><sup>actual</sup> − τ<sub>A</sub><sup>stochastically symmetric</sup></span><!--/no latex--><!--latex:
+
* Perturbation: <!--no latex--><span class="tex">ΔP<sub>A</sub> = τ<sub>A</sub><sup>actual</sup> − τ<sub>A</sub><sup>stochastically symmetric</sup></span><!--/no latex--><!--latex:\[\Delta P_{A} = \tau_{A}^{\mathrm{actual}} -
 +
\tau_{A}^{(\mathrm{stochastically\ symmetric})}\]-->
  
−
\[
+
* Translation: <!--no latex--><span class="tex">ΔP<sub>n</sub> = τ<sub>n</sub><sup>actual</sup> − τ<sub>n</sub><sup>stochastically symmetric</sup></span><!--/no latex--><!--latex:\[\Delta P_{n} =
−
\Delta P_{A} =
+
\tau_{n}^{\mathrm{actual}} -\tau_{n}^{(\mathrm{stochastically\ symmetric})}\]-->
−
\tau_{A}^{\mathrm{actual}} -
+
−
\tau_{A}^{(\mathrm{stochastically\ symmetric})}
+
−
\]
+
  
−
-->
+
* Rotation: Chirality: <!--no latex--><span class="tex">ΔP<sub>χ</sub> = τ<sub>χ</sub><sup>actual</sup> − τ<sub>χ</sub><sup>stochastically symmetric</sup></span><!--/no latex--><!--latex:\[\Delta P_{\chi} =
 +
\tau_{\chi}^{\mathrm{actual}} -\tau_{\chi}^{(\mathrm{stochastically\ symmetric})}\]-->
  
−
* Translation: <!--no latex--><span class="tex">ΔP<sub>n</sub> = τ<sub>n</sub><sup>actual</sup> − τ<sub>n</sub><sup>stochastically symmetric</sup></span><!--/no latex--><!--latex:
+
* Rotation: AxisOrientation: <!--no latex--><span class="tex">ΔP<sub>u</sub> = τ<sub>u</sub><sup>actual</sup> − τ<sub>u</sub><sup>stochastically symmetric</sup></span><!--/no latex--><!--latex:\[\Delta P_{u} =
−
 
+
\tau_{u}^{\mathrm{actual}} -\tau_{u}^{(\mathrm{stochastically\ symmetric})}\]-->
−
\[
+
−
\Delta P_{n} =
+
−
\tau_{n}^{\mathrm{actual}} -
+
−
\tau_{n}^{(\mathrm{stochastically\ symmetric})}
+
−
\]
+
−
 
+
−
-->
+
−
 
+
−
* Rotation: Chirality: <!--no latex--><span class="tex">ΔP<sub>χ</sub> = τ<sub>χ</sub><sup>actual</sup> − τ<sub>χ</sub><sup>stochastically symmetric</sup></span><!--/no latex--><!--latex:
+
−
 
+
−
\[
+
−
\Delta P_{\chi} =
+
−
\tau_{\chi}^{\mathrm{actual}} -
+
−
\tau_{\chi}^{(\mathrm{stochastically\ symmetric})}
+
−
\]
+
−
 
+
−
-->
+
−
 
+
−
* Rotation: AxisOrientation: <!--no latex--><span class="tex">ΔP<sub>u</sub> = τ<sub>u</sub><sup>actual</sup> − τ<sub>u</sub><sup>stochastically symmetric</sup></span><!--/no latex--><!--latex:
+
−
 
+
−
\[
+
−
\Delta P_{u} =
+
−
\tau_{u}^{\mathrm{actual}} -
+
−
\tau_{u}^{(\mathrm{stochastically\ symmetric})}
+
−
\]
+
−
 
+
−
-->
+
  
 
== Information / Energy (Potentials) ==
 
== Information / Energy (Potentials) ==

Revision as of 23:17, 14 July 2026

The Primary Source of Reality

Fundamental Force (FF)

F₀

Elementary Field (EF)

𝓕

𝓕 = F₀ (A, n, χ, u; kA, kn, kχ, ku)

Structure of resistances

k𝓲 = k𝓲(intrinsic) + k𝓲(dynamic), 𝓲 ∈ {A,n,χ,u}

Resistance parameters

kA, kn — proto‑stress resistances
kχ, ku — proto‑vorticity resistances

kA — intensity resistance

kn — linear‑orientation resistance

kχ — chirality‑reorientation resistance

ku — intrinsic‑angular‑orientation resistance

{kA — intensity‑resistance, kn — linear‑orientation resistance, kχ — chirality‑reorientation resistance, ku — intrinsic‑angular‑orientation resistance}

{kA, kn, kχ, ku}

Operational hypotheses (to be refined)

kχ ≈ ε0
ku ≈ μ0

Event-point(s) (EP)

EP = infinitesimal analytical sampling locus of the Field at label 𝑥

Elementary Events (EE)

EE(𝑥,τ)= δ𝓕(𝑥,τ)

Response of the Field

EE(𝑥,τ)= δ𝓕(𝑥,τ) = Resp𝓕 (𝑥,τ; F₀, kA, kn, kχ, ku)

Decomposition

EE = {A, n, χ, u}

Instantaneous configuration

σ = (A, n, χ, u)instantaneous

Statistical configuration

(A(τ), n(τ), χ(τ), u(τ))

Elementary Action

EA = (ΔPA, ΔPn, ΔPχ, ΔPu)

Stochastically symmetric reference τ(σ) distribution

ΔP𝓲 = τ𝓲actual − τ𝓲stochastically symmetric

Modes / Components

  • Perturbation: ΔPA = τAactual − τAstochastically symmetric
  • Translation: ΔPn = τnactual − τnstochastically symmetric
  • Rotation: Chirality: ΔPχ = τχactual − τχstochastically symmetric
  • Rotation: AxisOrientation: ΔPu = τuactual − τustochastically symmetric

Information / Energy (Potentials)

Equilibrium conditions

𝓒M = 𝓒(ΔPA) = 0

𝓒A = 𝓒(ΔPn) = 0

𝓒E = 𝓒(ΔPχ) = 0

𝓒B = 𝓒(ΔPu) = 0

Diffuse solutions

ΦM, ΦA, ΦE, ΦB ∈ Sol(𝓒)

InfoStructures

Wave‑like InfoStructures

Derived from

ΔPn, ΔPu

Equilibrium condition

𝓒wave (ΔPn, ΔPu) = 0

Proto‑wave equation

𝓦 [Ψ; ΔPn, ΔPu] = 0

Vortex‑like InfoStructures

Derived from

ΔPA, ΔPn, ΔPχ, ΔPu

Equilibrium condition

𝓒vortex (ΔPA, ΔPn, ΔPχ, ΔPu) = 0

Proto‑vortex equation

𝓥 [Ξ; ΔPA, ΔPn, ΔPχ, ΔPu] = 0

Interaction‑mediating InfoStructures

Relational equilibrium

𝓒int (Ψ, Ξ) = 0

Proto‑interaction equation

𝓘 [Ψ, Ξ] = 0

Geometric Projection

Wave projection

Proj(𝓦) → QM wave equations

Vortex projection

Proj(𝓥) → spinor equations

Interaction projection

Proj(𝓘) → gauge equations

Forms

No new fundamental equation

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