Notation Guide

The following table collects the principal symbols used throughout the monograph. Where a symbol has different meanings in different sections, all meanings are listed with section references.

Fundamental Constants and Ether Parameters

Symbol	Meaning	Section(s)	Units
$c$	Speed of light / ether EM wave speed	Throughout	m/s
$\hbar$	Reduced Planck constant	Throughout	J·s
$G$	Newton's gravitational constant	§3–4, §9	m³/(kg·s²)
$k_B$	Boltzmann constant	§4, §8	J/K
$\varepsilon_0$	Ether electric permittivity	§2, §5	F/m
$\mu_0$	Ether magnetic permeability	§2, §5	H/m
$Z_0 = \sqrt{\mu_0/\varepsilon_0}$	Ether vacuum impedance	§5	Ω
$\rho_e$, $\rho_0$	Ether mass density (unperturbed)	§2–4	kg/m³
$c_s$	Ether sound speed (longitudinal)	§3–4	m/s
$m_e$	Ether quantum mass (condensate)	§4, §9	eV/$c^2$
$\xi = \hbar/(m_e c_s)$	Healing length (phonon UV cutoff)	§4, §9	m
$\ell_e$	Transverse microstructure scale (EM UV cutoff)	§3, §5, §9	m
$a_0$	MOND acceleration scale	§4, §9	m/s²

Gravitational Sector (Sections 3–4)

Symbol	Meaning	Section(s)	Units
$\mathbf{v}_0$, $\mathbf{u}$	Ether background flow velocity	§3	m/s
$v_{\text{ff}} = \sqrt{2GM/r}$	Free-fall velocity	§3	m/s
$g_{\mu\nu}^{\text{eff}}$	Acoustic / effective metric	§3	—
$\mu_e(x)$	Gravitational permittivity	§4	—
$P(X)$	Superfluid pressure (Lagrangian)	§4	Pa
$\rho_{\text{ZPF}}$	Phonon zero-point energy density	§4	J/m³
$n_{\text{th}}$	Bose–Einstein thermal occupation	§4, §8	—

Electromagnetic / Plasma Sector (Section 5)

Symbol	Meaning	Section(s)	Units
$m_{\text{el}}$	Electron mass ($\neq m_e$)	§5	kg
$m_s$	Mass of charged species $s$	§5	kg
$q_s$	Charge of species $s$	§5	C
$n_s$	Number density of species $s$	§5	m⁻³
$\omega_p$	Electron plasma frequency	§5	rad/s
$\omega_{p,s}$	Plasma frequency of species $s$	§5	rad/s
$\Omega_s = q_s B_0/m_s$	Signed cyclotron frequency	§5	rad/s
$\boldsymbol{\varepsilon}_r(\omega)$	Dielectric tensor (Stix form)	§5	—
$S$, $D$, $P$	Stix parameters	§5	—
$v_A = B_0/\sqrt{\mu_0\rho}$	Alfvén velocity	§5	m/s
$f_s(\mathbf{r}, \mathbf{v}, t)$	Vlasov distribution function	§5	m⁻⁶·s³
$\varepsilon_L(\omega, k)$	Kinetic (longitudinal) dielectric	§5	—
$\lambda_D$	Debye length	§5	m
$v_{\text{th}}$	Electron thermal velocity	§5	m/s
$\gamma_L$	Landau damping rate	§5	rad/s

Quantum Sector (Sections 6–8)

Symbol	Meaning	Section(s)	Units
$\mathbf{E}_{\text{ZPF}}$	Zero-point electric field	§5–6	V/m
$\rho(\omega)$	ZPF spectral energy density	§6	J·s/m³
$\tau = e^2/(6\pi\varepsilon_0 mc^3)$	Radiation reaction time	§5–6	s
$D = \hbar/(2m)$	Nelson diffusion coefficient	§7	m²/s
$\mathbf{v}_+$, $\mathbf{v}_-$	Forward / backward Nelson velocities	§7	m/s
$\mathbf{v}_c$	Current velocity ($= \nabla S/m$)	§7	m/s
$\mathbf{u}$	Osmotic velocity ($= D\nabla\ln\rho$)	§7–8	m/s
$\psi = R\,e^{iS/\hbar}$	Wavefunction (Madelung form)	§7	m⁻³/²
$Q$	Quantum potential	§7	J
$|S_{\text{CHSH}}|$	Bell–CHSH parameter	§8	—

Conventions

• Metric signature: $(-,+,+,+)$
• Fourier convention: $e^{i(\mathbf{k}\cdot\mathbf{r} - \omega t)}$
• Cyclotron frequency: signed, $\Omega_e < 0$ for electrons
• SI units throughout except where eV or natural units are explicitly stated