Difference between revisions of "Paper Symbols"
From Evolutionary Knowledge Base
(→Geometric Projection) |
|||
| Line 140: | Line 140: | ||
<!--no latex--><span class="tex">𝓘[Ψ, Ξ] = 0</span><!--/no latex--><!--latex:\[\mathcal{I}[\Psi,\,\Xi] = 0\]--> | <!--no latex--><span class="tex">𝓘[Ψ, Ξ] = 0</span><!--/no latex--><!--latex:\[\mathcal{I}[\Psi,\,\Xi] = 0\]--> | ||
| − | + | == Geometric Projection == | |
| − | + | === Wave projection === | |
<!--no latex--><span class="tex">Proj(𝓦) → QM wave equations</span><!--/no latex--><!--latex: | <!--no latex--><span class="tex">Proj(𝓦) → QM wave equations</span><!--/no latex--><!--latex: | ||
| + | \[\mathrm{Proj}(\mathcal{W}) \;\longrightarrow\; \text{QM wave equations}\]--> | ||
| − | + | === Vortex projection === | |
| − | + | ||
| − | + | ||
| − | --> | + | <!--no latex--><span class="tex">Proj(𝓥) → spinor equations</span><!--/no latex--><!--latex:\[ |
| + | \mathrm{Proj}(\mathcal{V}) \;\longrightarrow\; \text{spinor equations}\]--> | ||
| − | === | + | === Interaction projection === |
| − | + | <!--no latex--><span class="tex">Proj(𝓘) → gauge equations</span><!--/no latex--><!--latex:\[ | |
| − | + | \mathrm{Proj}(\mathcal{I}) \;\longrightarrow\; \text{gauge equations}\]--> | |
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | <!--no latex--><span class="tex">Proj(𝓘) → gauge equations</span><!--/no latex--><!--latex: | + | |
| − | + | ||
| − | \[ | + | |
| − | \mathrm{Proj}(\mathcal{I}) \;\longrightarrow\; \text{gauge equations} | + | |
| − | \] | + | |
| − | + | ||
| − | --> | + | |
Revision as of 19:26, 13 July 2026
Contents
The Primary Source of Reality
Fundamental Force (FF)
F₀
Elementary Field (EF)
𝓕 = F₀(A, n, χ, u; kA, kn, kχ, ku)
Total resistances
k𝓲 = k𝓲intr + k𝓲dyn
Event-point(s) (EP)
nn
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)ist
Statistical configuration
(A(τ), n(τ), χ(τ), u(τ))
Elementary Action
EA = (ΔPA, ΔPn, ΔPχ, ΔPu)
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 Φ)
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
