Symbol Glossary
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Symbol Glossary
Notation on this page
Complete symbol reference for the Psionics cluster. Plain-language definitions of these terms are in Glossary_of_Psionics.
Core ψ-field symbols
| Symbol | LaTeX source | Name | SI units | Where it lives | Notes |
|---|---|---|---|---|---|
| $ \psi $ | \psi |
Psionic scalar field (amplitude) | $ {\sqrt {\mathrm {J/m} }} $ | Defined on (5D or 4D) spacetime | Real-valued; the fundamental object of the theory. |
| $ \partial _{\mu }\psi $ | \partial_\mu \psi |
4-gradient of ψ | $ {\sqrt {\mathrm {J/m} }}\,/\,\mathrm {m} $ | Covector | Components: $ \partial _{t}\psi ,\,\partial _{x}\psi ,\,\partial _{y}\psi ,\,\partial _{z}\psi $. Sets local "flow" direction. |
| $ \nabla \psi $ | \nabla \psi |
Spatial gradient of ψ | $ {\sqrt {\mathrm {J/m} }}\,/\,\mathrm {m} $ | 3-vector | Practitioners feel $ \nabla \psi $ as directional "push/pull". |
| $ \nabla ^{2}\psi $ | \nabla^2 \psi |
Spatial Laplacian of ψ | $ {\sqrt {\mathrm {J/m} }}\,/\,\mathrm {m} ^{2} $ | Scalar | Source of static Yukawa-screened solutions. |
| $ \Box \psi $ | \Box \psi |
d'Alembertian of ψ | $ {\sqrt {\mathrm {J/m} }}\,/\,\mathrm {m} ^{2} $ | Scalar | $ \Box =-\partial _{t}^{2}+\nabla ^{2} $; $ \Box \psi =0 $ is the massless wave equation. |
| $ \Psi $ | \Psi |
ψ-field energy density | $ \mathrm {J/m} ^{3} $ | Scalar | $ \Psi \equiv T^{00}(\psi ) $; the directly-felt quantity. |
| $ m $ | m |
ψ-field mass | $ \mathrm {eV} /c^{2} $ or $ 1/{\text{length}} $ | Scalar parameter | Sets Yukawa range $ 1/m $. $ m\to 0 $ gives infinite-range psi; $ m>0 $ gives finite-range shielding. |
| $ \lambda $ | \lambda |
ψ self-coupling | dimensionless (4D) | Scalar parameter | $ \lambda >0 $ stabilises against runaway; sources soliton solutions. |
| $ G_{\psi } $ | G_\psi |
Psionic coupling constant | $ \mathrm {m} ^{3}/(\mathrm {kg} \!\cdot \!\mathrm {s} ^{2}) $ (analog of G) | Scalar parameter | Empirically open. |
| $ \alpha $ | \alpha |
ψ–EM coupling (4D) | $ 1/(\mathrm {J} \!\cdot \!\mathrm {m} ) $ | Scalar parameter | Strength of the $ F_{\mu \nu }F^{\mu \nu } $ source term in the 4D ψ equation. |
| $ \kappa $ | \kappa |
ψ–EM coupling (5D) | $ 1/{\text{length}}^{3} $ | Scalar parameter | Companion of α in the 5D parent action. |
| $ k $ | k |
ψ–dilaton coupling | $ 1/{\sqrt {\mathrm {J/m} }} $ | Scalar parameter | Multiplies ψ inside the exponential $ e^{k\psi } $ that modulates EM coupling. Distinct from wavevector. |
| $ p $ | p |
Psionic charge | $ {\sqrt {\mathrm {J} \!\cdot \!\mathrm {m} }} $ | Scalar property of matter | $ F=-p\,\nabla \psi $. Ordinary matter $ p\approx 0 $; tuned matter $ p\neq 0 $. |
| $ J_{\psi } $ | J_\psi |
Psionic current (source) | $ {\sqrt {\mathrm {J/m} }}\,/\,\mathrm {m} ^{4} $ | Scalar field | Coherent neural firing, focused attention, tuned hardware. |
| $ \rho _{\psi } $ | \rho_\psi |
Psionic charge density | $ {\sqrt {\mathrm {J} \!\cdot \!\mathrm {m} }}\,/\,\mathrm {m} ^{3} $ | Scalar field | Spatial density of p; sources the static Poisson/Yukawa equation. |
| $ \mathbf {S} _{\psi } $ | \mathbf{S}_\psi |
ψ-field Poynting vector | $ \mathrm {W/m} ^{2} $ | 3-vector | $ \mathbf {S} _{\psi }=-(\partial _{t}\psi )\,\nabla \psi $; directional energy flux. |
| $ T_{\mu \nu }^{\psi } $ | T^\psi_{\mu\nu} |
ψ-field stress-energy tensor | $ \mathrm {J/m} ^{3} $ | Rank-2 tensor | See Psi_Field §"Stress-energy tensor". $ T^{00}=\Psi $. |
| $ \mathbf {F} _{\psi } $ | \mathbf{F}_\psi |
Psionic force | $ \mathrm {N} $ | 3-vector | $ \mathbf {F} _{\psi }=-p\,\nabla \psi $. |
Electromagnetic symbols
| Symbol | LaTeX source | Name | Notes |
|---|---|---|---|
| $ A_{\mu } $ | A_\mu |
EM 4-potential | $ (\Phi ,\mathbf {A} ) $ in 3+1 notation. |
| $ F_{\mu \nu } $ | F_{\mu\nu} |
EM field-strength tensor | $ F_{\mu \nu }=\partial _{\mu }A_{\nu }-\partial _{\nu }A_{\mu } $. |
| $ F^{2} $ | F^2 |
$ F_{\mu \nu }F^{\mu \nu } $ (Lagrangian density piece) | Proportional to $ E^{2}-B^{2} $. |
| $ \mathbf {E} $ | \mathbf{E} |
Electric field | $ \mathrm {V/m} $. |
| $ \mathbf {B} $ | \mathbf{B} |
Magnetic field | $ \mathrm {T} $. |
| $ \alpha _{\mathrm {EM} } $ | \alpha_{\mathrm{EM}} |
Fine-structure constant | $ \approx 1/137 $. Made ψ-dependent via the $ e^{k\psi } $ factor. |
Geometry symbols
| Symbol | LaTeX source | Name | Notes |
|---|---|---|---|
| $ g_{\mu \nu } $ | g_{\mu\nu} |
4D metric tensor | Signature $ (-,+,+,+) $. |
| $ {\tilde {g}}_{MN} $ | \tilde{g}_{MN} |
5D metric tensor | Tilde marks "lives in 5D". Also written $ {\hat {g}}_{AB} $ in some pages. |
| $ g,\ {\tilde {g}} $ | g,\ \tilde{g} |
Determinants of $ g_{\mu \nu },\ {\tilde {g}}_{MN} $ | Appear in $ {\sqrt {-g}} $ volume element. |
| $ \eta _{\mu \nu } $ | \eta_{\mu\nu} |
Minkowski metric | $ \operatorname {diag} (-1,+1,+1,+1) $. |
| $ R_{\mu \nu } $ | R_{\mu\nu} |
Ricci tensor | Contraction of Riemann tensor. |
| $ R $ | R |
Ricci scalar | $ R=g^{\mu \nu }R_{\mu \nu } $. |
| $ G_{\mu \nu } $ | G_{\mu\nu} |
Einstein tensor | $ G_{\mu \nu }=R_{\mu \nu }-{\tfrac {1}{2}}g_{\mu \nu }R $. |
| $ \Gamma _{\nu \rho }^{\mu } $ | \Gamma^\mu_{\nu\rho} |
Christoffel symbols | Affine connection from $ g_{\mu \nu } $. Not a tensor. |
| $ \nabla _{\mu } $ | \nabla_\mu |
Covariant derivative | Reduces to $ \partial _{\mu } $ in flat space. |
Gravitoelectromagnetism
| Symbol | LaTeX source | Name | Units | Notes |
|---|---|---|---|---|
| $ h_{\mu \nu } $ | h_{\mu\nu} |
Metric perturbation | dimensionless | $ g_{\mu \nu }=\eta _{\mu \nu }+h_{\mu \nu } $. |
| $ {\bar {h}}_{\mu \nu } $ | \bar{h}_{\mu\nu} |
Trace-reversed perturbation | dimensionless | $ {\bar {h}}_{\mu \nu }=h_{\mu \nu }-{\tfrac {1}{2}}\eta _{\mu \nu }h $. |
| $ \Phi _{g} $ | \Phi_g |
Gravitoelectric potential | $ \mathrm {m} ^{2}/\mathrm {s} ^{2} $ | Newtonian limit: $ \Phi _{g}=GM/r $. |
| $ \mathbf {A} _{g} $ | \mathbf{A}_g |
Gravitomagnetic vector potential | $ \mathrm {m/s} $ | Encodes frame-dragging. |
| $ \mathbf {E} _{g} $ | \mathbf{E}_g |
Gravitoelectric field | $ \mathrm {m/s} ^{2} $ | Gravity vector. |
| $ \mathbf {B} _{g} $ | \mathbf{B}_g |
Gravitomagnetic field | $ 1/\mathrm {s} $ | "Magnetic" analogue produced by mass currents. |
| $ \rho _{m} $ | \rho_m |
Mass density | $ \mathrm {kg/m} ^{3} $ | Source of $ \mathbf {E} _{g} $. |
| $ \mathbf {j} _{m} $ | \mathbf{j}_m |
Mass current density | $ \mathrm {kg} /(\mathrm {m} ^{2}\!\cdot \!\mathrm {s} ) $ | Source of $ \mathbf {B} _{g} $. |
Extra-dimensional / Kaluza–Klein
| Symbol | LaTeX source | Name | Notes |
|---|---|---|---|
| $ x^{5} $ | x^5 |
Coordinate along the compact 5th dimension | Periodic: $ x^{5}\equiv x^{5}+2\pi L $, where L is the compactification radius. |
| $ L $ | L |
Compactification radius | In natural units: $ 1/L $ is the KK mass gap. |
| $ \phi $ | \phi |
Dilaton | Scalar field describing the size of the compact dimension. Distinct from ψ. |
| $ {\tilde {A}}_{\mu },\ {\tilde {F}}_{MN},\ {\tilde {R}} $ | \tilde{A}_\mu, \tilde{F}_{MN}, \tilde{R} |
5D EM potential, EM field strength, Ricci scalar | Tildes mark 5D origin before KK reduction. |
Neuroscience and information
| Symbol | LaTeX source | Name | Notes |
|---|---|---|---|
| $ u(x,t) $ | u(x,t) |
Neural population firing-rate density | Wilson–Cowan variable. |
| $ W(x-x') $ | W(x-x') |
Synaptic weight kernel | Sets non-local coupling in Wilson–Cowan. |
| $ f(u) $ | f(u) |
Firing-rate function | Sigmoid: $ f(u)=1/(1+e^{-u}) $. |
| $ \beta $ | \beta |
Neural–ψ feedback coupling | Strength of the back-reaction term $ \beta \,\psi $ in the Wilson–Cowan equation. Bifurcation parameter. |
| $ \tau $ | \tau |
Neural relaxation time | Wilson–Cowan timescale. |
| $ \kappa _{J} $ | \kappa_J |
ψ-source efficiency | $ J_{\psi }=\kappa _{J}\int f(u(x',t))\,dx' $. |
| $ S=-\operatorname {Tr} ({\hat {\rho }}\ln {\hat {\rho }}) $ | S = -\operatorname{Tr}(\hat{\rho}\ln\hat{\rho}) |
Von Neumann entropy of the ψ density operator | See Quantization_of_the_Psi_Field. |
Common confusions
- $ \psi $ vs $ \Psi $. Lowercase $ \psi $ = field amplitude; uppercase $ \Psi =T^{00}(\psi ) $ = energy density. This wiki always uses both forms with this convention.
- $ \psi $ vs $ \phi $. $ \psi $ is the psionic scalar; $ \phi $ is the Kaluza–Klein dilaton (size of the compact extra dimension).
- $ k $ as ψ-dilaton coupling vs $ k $ as wavevector. Inside the $ e^{k\psi } $ factor, $ k $ is the dimensionful coupling. In wave-propagation formulas $ k $ is the usual wavevector. Disambiguated by context.
- $ m $ as ψ-field mass vs $ m_{e} $ as electron mass. Always disambiguated by subscript when both appear in the same equation.
- $ G $ vs $ G_{\psi } $. $ G $ is Newton's gravitational constant; $ G_{\psi } $ is the psionic coupling. Same dimensional category but different numerical value.
- $ \alpha $ as ψ–EM coupling vs $ \alpha _{\mathrm {EM} } $ 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: $ \Psi \sim 10^{-12}{\text{--}}10^{-9}\ \mathrm {J/m} ^{3} $
- Trained-meditator peak: $ \Psi \sim 10^{-7}{\text{--}}10^{-5}\ \mathrm {J/m} ^{3} $
- Macro-PK threshold: $ \Psi \gtrsim 10^{-5}\ \mathrm {J/m} ^{3} $
- Surface biophoton emission (Dotta et al. 2012): $ \sim 10^{-19}\ \mathrm {J/m} ^{3} $
- Brain magnetic field amplitude (MEG): $ \sim 10^{-13}\ \mathrm {T} $ (~100 fT)
- Schumann fundamental: $ 7.83\ \mathrm {Hz} $
- Microtubule resonance bands (Bandyopadhyay et al. 2014): kHz, MHz, GHz
- Earth gravitomagnetic field at pole: $ \sim 10^{-14}\ \mathrm {s} ^{-1} $
- 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)
