JonoThora: Phase N (01b): LaTeX restoration — promote Unicode display-math to $; lint-clean per tools/wiki_latex_lint.py$

2026-05-11T20:08:00Z

Phase N (01b): LaTeX restoration — promote Unicode display-math to <math>; lint-clean per tools/wiki_latex_lint.py

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= Symbol Glossary =

{{Audience_Sidebar
| difficulty = Technical
| reading_time = 8 minutes
| prerequisites = [[Psionics_Primer]]; familiarity with relativistic field theory notation.
| if_too_advanced_see = [[Glossary_of_Psionics]]
}}

{{Notation
| psi_convention = ψ = field amplitude (lowercase Greek psi); Ψ = energy density of ψ, i.e. Ψ ≡ T<sup>00</sup>(ψ).
| signature = Mostly-plus: (−, +, +, +).
| units = ℏ = c = 1 unless explicitly noted. SI units used when dimensional values are quoted.
| index_convention = Greek μ,ν,ρ,σ run over 4D spacetime (0,1,2,3); capital M,N,P,Q run over 5D (0,1,2,3,5); Latin i,j,k run over spatial 3D (1,2,3).
}}

Complete symbol reference for the [[Psionics]] cluster. Plain-language definitions of these terms are in [[Glossary_of_Psionics]].

== Core ψ-field symbols ==

{| class="wikitable"
! Symbol !! LaTeX source !! Name !! SI units !! Where it lives !! Notes
|-
| <math>\psi</math> || <code>\psi</code> || Psionic scalar field (amplitude) || <math>\sqrt{\mathrm{J/m}}</math> || Defined on (5D or 4D) spacetime || Real-valued; the fundamental object of the theory.
|-
| <math>\partial_\mu \psi</math> || <code>\partial_\mu \psi</code> || 4-gradient of ψ || <math>\sqrt{\mathrm{J/m}}\,/\,\mathrm{m}</math> || Covector || Components: <math>\partial_t\psi,\,\partial_x\psi,\,\partial_y\psi,\,\partial_z\psi</math>. Sets local "flow" direction.
|-
| <math>\nabla \psi</math> || <code>\nabla \psi</code> || Spatial gradient of ψ || <math>\sqrt{\mathrm{J/m}}\,/\,\mathrm{m}</math> || 3-vector || Practitioners feel <math>\nabla\psi</math> as directional "push/pull".
|-
| <math>\nabla^2 \psi</math> || <code>\nabla^2 \psi</code> || Spatial Laplacian of ψ || <math>\sqrt{\mathrm{J/m}}\,/\,\mathrm{m}^2</math> || Scalar || Source of static Yukawa-screened solutions.
|-
| <math>\Box \psi</math> || <code>\Box \psi</code> || d'Alembertian of ψ || <math>\sqrt{\mathrm{J/m}}\,/\,\mathrm{m}^2</math> || Scalar || <math>\Box = -\partial_t^2 + \nabla^2</math>; <math>\Box\psi = 0</math> is the massless wave equation.
|-
| <math>\Psi</math> || <code>\Psi</code> || ψ-field energy density || <math>\mathrm{J/m}^3</math> || Scalar || <math>\Psi \equiv T^{00}(\psi)</math>; the directly-felt quantity.
|-
| <math>m</math> || <code>m</code> || ψ-field mass || <math>\mathrm{eV}/c^2</math> or <math>1/\text{length}</math> || Scalar parameter || Sets Yukawa range <math>1/m</math>. <math>m\to 0</math> gives infinite-range psi; <math>m>0</math> gives finite-range shielding.
|-
| <math>\lambda</math> || <code>\lambda</code> || ψ self-coupling || dimensionless (4D) || Scalar parameter || <math>\lambda > 0</math> stabilises against runaway; sources soliton solutions.
|-
| <math>G_\psi</math> || <code>G_\psi</code> || Psionic coupling constant || <math>\mathrm{m}^3/(\mathrm{kg}\!\cdot\!\mathrm{s}^2)</math> (analog of G) || Scalar parameter || Empirically open.
|-
| <math>\alpha</math> || <code>\alpha</code> || ψ–EM coupling (4D) || <math>1/(\mathrm{J}\!\cdot\!\mathrm{m})</math> || Scalar parameter || Strength of the <math>F_{\mu\nu}F^{\mu\nu}</math> source term in the 4D ψ equation.
|-
| <math>\kappa</math> || <code>\kappa</code> || ψ–EM coupling (5D) || <math>1/\text{length}^3</math> || Scalar parameter || Companion of α in the 5D parent action.
|-
| <math>k</math> || <code>k</code> || ψ–dilaton coupling || <math>1/\sqrt{\mathrm{J/m}}</math> || Scalar parameter || Multiplies ψ inside the exponential <math>e^{k\psi}</math> that modulates EM coupling. Distinct from wavevector.
|-
| <math>p</math> || <code>p</code> || Psionic charge || <math>\sqrt{\mathrm{J}\!\cdot\!\mathrm{m}}</math> || Scalar property of matter || <math>F = -p\,\nabla\psi</math>. Ordinary matter <math>p\approx 0</math>; tuned matter <math>p\ne 0</math>.
|-
| <math>J_\psi</math> || <code>J_\psi</code> || Psionic current (source) || <math>\sqrt{\mathrm{J/m}}\,/\,\mathrm{m}^4</math> || Scalar field || Coherent neural firing, focused attention, tuned hardware.
|-
| <math>\rho_\psi</math> || <code>\rho_\psi</code> || Psionic charge density || <math>\sqrt{\mathrm{J}\!\cdot\!\mathrm{m}}\,/\,\mathrm{m}^3</math> || Scalar field || Spatial density of p; sources the static Poisson/Yukawa equation.
|-
| <math>\mathbf{S}_\psi</math> || <code>\mathbf{S}_\psi</code> || ψ-field Poynting vector || <math>\mathrm{W/m}^2</math> || 3-vector || <math>\mathbf{S}_\psi = -(\partial_t\psi)\,\nabla\psi</math>; directional energy flux.
|-
| <math>T^\psi_{\mu\nu}</math> || <code>T^\psi_{\mu\nu}</code> || ψ-field stress-energy tensor || <math>\mathrm{J/m}^3</math> || Rank-2 tensor || See [[Psi_Field]] §"Stress-energy tensor". <math>T^{00} = \Psi</math>.
|-
| <math>\mathbf{F}_\psi</math> || <code>\mathbf{F}_\psi</code> || Psionic force || <math>\mathrm{N}</math> || 3-vector || <math>\mathbf{F}_\psi = -p\,\nabla\psi</math>.
|}

== Electromagnetic symbols ==

{| class="wikitable"
! Symbol !! LaTeX source !! Name !! Notes
|-
| <math>A_\mu</math> || <code>A_\mu</code> || EM 4-potential || <math>(\Phi, \mathbf{A})</math> in 3+1 notation.
|-
| <math>F_{\mu\nu}</math> || <code>F_{\mu\nu}</code> || EM field-strength tensor || <math>F_{\mu\nu} = \partial_\mu A_\nu - \partial_\nu A_\mu</math>.
|-
| <math>F^2</math> || <code>F^2</code> || <math>F_{\mu\nu}F^{\mu\nu}</math> (Lagrangian density piece) || Proportional to <math>E^2 - B^2</math>.
|-
| <math>\mathbf{E}</math> || <code>\mathbf{E}</code> || Electric field || <math>\mathrm{V/m}</math>.
|-
| <math>\mathbf{B}</math> || <code>\mathbf{B}</code> || Magnetic field || <math>\mathrm{T}</math>.
|-
| <math>\alpha_{\mathrm{EM}}</math> || <code>\alpha_{\mathrm{EM}}</code> || Fine-structure constant || <math>\approx 1/137</math>. Made ψ-dependent via the <math>e^{k\psi}</math> factor.
|}

== Geometry symbols ==

{| class="wikitable"
! Symbol !! LaTeX source !! Name !! Notes
|-
| <math>g_{\mu\nu}</math> || <code>g_{\mu\nu}</code> || 4D metric tensor || Signature <math>(-,+,+,+)</math>.
|-
| <math>\tilde{g}_{MN}</math> || <code>\tilde{g}_{MN}</code> || 5D metric tensor || Tilde marks "lives in 5D". Also written <math>\hat{g}_{AB}</math> in some pages.
|-
| <math>g,\ \tilde{g}</math> || <code>g,\ \tilde{g}</code> || Determinants of <math>g_{\mu\nu},\ \tilde{g}_{MN}</math> || Appear in <math>\sqrt{-g}</math> volume element.
|-
| <math>\eta_{\mu\nu}</math> || <code>\eta_{\mu\nu}</code> || Minkowski metric || <math>\operatorname{diag}(-1,+1,+1,+1)</math>.
|-
| <math>R_{\mu\nu}</math> || <code>R_{\mu\nu}</code> || Ricci tensor || Contraction of Riemann tensor.
|-
| <math>R</math> || <code>R</code> || Ricci scalar || <math>R = g^{\mu\nu}R_{\mu\nu}</math>.
|-
| <math>G_{\mu\nu}</math> || <code>G_{\mu\nu}</code> || Einstein tensor || <math>G_{\mu\nu} = R_{\mu\nu} - \tfrac{1}{2}g_{\mu\nu}R</math>.
|-
| <math>\Gamma^\mu_{\nu\rho}</math> || <code>\Gamma^\mu_{\nu\rho}</code> || Christoffel symbols || Affine connection from <math>g_{\mu\nu}</math>. Not a tensor.
|-
| <math>\nabla_\mu</math> || <code>\nabla_\mu</code> || Covariant derivative || Reduces to <math>\partial_\mu</math> in flat space.
|}

== Gravitoelectromagnetism ==

{| class="wikitable"
! Symbol !! LaTeX source !! Name !! Units !! Notes
|-
| <math>h_{\mu\nu}</math> || <code>h_{\mu\nu}</code> || Metric perturbation || dimensionless || <math>g_{\mu\nu} = \eta_{\mu\nu} + h_{\mu\nu}</math>.
|-
| <math>\bar{h}_{\mu\nu}</math> || <code>\bar{h}_{\mu\nu}</code> || Trace-reversed perturbation || dimensionless || <math>\bar{h}_{\mu\nu} = h_{\mu\nu} - \tfrac{1}{2}\eta_{\mu\nu}h</math>.
|-
| <math>\Phi_g</math> || <code>\Phi_g</code> || Gravitoelectric potential || <math>\mathrm{m}^2/\mathrm{s}^2</math> || Newtonian limit: <math>\Phi_g = GM/r</math>.
|-
| <math>\mathbf{A}_g</math> || <code>\mathbf{A}_g</code> || Gravitomagnetic vector potential || <math>\mathrm{m/s}</math> || Encodes frame-dragging.
|-
| <math>\mathbf{E}_g</math> || <code>\mathbf{E}_g</code> || Gravitoelectric field || <math>\mathrm{m/s}^2</math> || Gravity vector.
|-
| <math>\mathbf{B}_g</math> || <code>\mathbf{B}_g</code> || Gravitomagnetic field || <math>1/\mathrm{s}</math> || "Magnetic" analogue produced by mass currents.
|-
| <math>\rho_m</math> || <code>\rho_m</code> || Mass density || <math>\mathrm{kg/m}^3</math> || Source of <math>\mathbf{E}_g</math>.
|-
| <math>\mathbf{j}_m</math> || <code>\mathbf{j}_m</code> || Mass current density || <math>\mathrm{kg}/(\mathrm{m}^2\!\cdot\!\mathrm{s})</math> || Source of <math>\mathbf{B}_g</math>.
|}

== Extra-dimensional / Kaluza–Klein ==

{| class="wikitable"
! Symbol !! LaTeX source !! Name !! Notes
|-
| <math>x^5</math> || <code>x^5</code> || Coordinate along the compact 5th dimension || Periodic: <math>x^5 \equiv x^5 + 2\pi L</math>, where L is the compactification radius.
|-
| <math>L</math> || <code>L</code> || Compactification radius || In natural units: <math>1/L</math> is the KK mass gap.
|-
| <math>\phi</math> || <code>\phi</code> || Dilaton || Scalar field describing the size of the compact dimension. Distinct from ψ.
|-
| <math>\tilde{A}_\mu,\ \tilde{F}_{MN},\ \tilde{R}</math> || <code>\tilde{A}_\mu, \tilde{F}_{MN}, \tilde{R}</code> || 5D EM potential, EM field strength, Ricci scalar || Tildes mark 5D origin before KK reduction.
|}

== Neuroscience and information ==

{| class="wikitable"
! Symbol !! LaTeX source !! Name !! Notes
|-
| <math>u(x,t)</math> || <code>u(x,t)</code> || Neural population firing-rate density || Wilson–Cowan variable.
|-
| <math>W(x-x')</math> || <code>W(x-x')</code> || Synaptic weight kernel || Sets non-local coupling in Wilson–Cowan.
|-
| <math>f(u)</math> || <code>f(u)</code> || Firing-rate function || Sigmoid: <math>f(u) = 1/(1+e^{-u})</math>.
|-
| <math>\beta</math> || <code>\beta</code> || Neural–ψ feedback coupling || Strength of the back-reaction term <math>\beta\,\psi</math> in the Wilson–Cowan equation. Bifurcation parameter.
|-
| <math>\tau</math> || <code>\tau</code> || Neural relaxation time || Wilson–Cowan timescale.
|-
| <math>\kappa_J</math> || <code>\kappa_J</code> || ψ-source efficiency || <math>J_\psi = \kappa_J \int f(u(x',t))\,dx'</math>.
|-
| <math>S = -\operatorname{Tr}(\hat{\rho}\ln\hat{\rho})</math> || <code>S = -\operatorname{Tr}(\hat{\rho}\ln\hat{\rho})</code> || Von Neumann entropy of the ψ density operator || See [[Quantization_of_the_Psi_Field]].
|}

== Common confusions ==

* '''<math>\psi</math> vs <math>\Psi</math>.''' Lowercase <math>\psi</math> = field amplitude; uppercase <math>\Psi = T^{00}(\psi)</math> = energy density. This wiki always uses both forms with this convention.
* '''<math>\psi</math> vs <math>\phi</math>.''' <math>\psi</math> is the psionic scalar; <math>\phi</math> is the [[Kaluza-Klein_Unification|Kaluza–Klein dilaton]] (size of the compact extra dimension).
* '''<math>k</math> as ψ-dilaton coupling vs <math>k</math> as wavevector.''' Inside the <math>e^{k\psi}</math> factor, <math>k</math> is the dimensionful coupling. In wave-propagation formulas <math>k</math> is the usual wavevector. Disambiguated by context.
* '''<math>m</math> as ψ-field mass vs <math>m_e</math> as electron mass.''' Always disambiguated by subscript when both appear in the same equation.
* '''<math>G</math> vs <math>G_\psi</math>.''' <math>G</math> is Newton's gravitational constant; <math>G_\psi</math> is the psionic coupling. Same dimensional category but different numerical value.
* '''<math>\alpha</math> as ψ–EM coupling vs <math>\alpha_{\mathrm{EM}}</math> as fine-structure.''' Always disambiguated by subscript.

== Order-of-magnitude reference values ==

Approximate values used across the cluster (most are empirically open or rough estimates):

* Resting practitioner: <math>\Psi \sim 10^{-12}\text{--}10^{-9}\ \mathrm{J/m}^3</math>
* Trained-meditator peak: <math>\Psi \sim 10^{-7}\text{--}10^{-5}\ \mathrm{J/m}^3</math>
* Macro-PK threshold: <math>\Psi \gtrsim 10^{-5}\ \mathrm{J/m}^3</math>
* Surface biophoton emission (Dotta et al. 2012): <math>\sim 10^{-19}\ \mathrm{J/m}^3</math>
* Brain magnetic field amplitude (MEG): <math>\sim 10^{-13}\ \mathrm{T}</math> (~100 fT)
* Schumann fundamental: <math>7.83\ \mathrm{Hz}</math>
* Microtubule resonance bands (Bandyopadhyay et al. 2014): kHz, MHz, GHz
* Earth gravitomagnetic field at pole: <math>\sim 10^{-14}\ \mathrm{s}^{-1}</math>
* Tajmar superconductor anomaly: 28 orders of magnitude above GR prediction.

== See Also ==

* [[Glossary_of_Psionics]] (plain-language)
* [[Psionics]] (canonical equations)
* [[5D_Action_Principle]] (where most symbols are introduced)
* [[Neural_Field_Equations]] (next page in the Undergrad Physics reading path)
* [[Sanity_Check_Limits]] (limit-table)

[[Category:Psionics]]
[[Category:Reference]]

Symbol Glossary - Revision history

JonoThora: Phase N (01b): LaTeX restoration — promote Unicode display-math to ; lint-clean per tools/wiki_latex_lint.py

JonoThora: Phase N (01b): LaTeX restoration — promote Unicode display-math to $; lint-clean per tools/wiki_latex_lint.py$