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Chapter 2 Symbols, Terms & Units
I. Abstract & Scope
This chapter defines global and cross-chapter symbols, terms, and SI units; enforces symbol uniqueness and do-not-confuse rules; fixes explicit path gamma(ell) and measure d ell for all integrals; standardizes statistical notation and uncertainty reporting; and specifies the division of labor between the centralized symbol table and chapter-local tables. All equations and symbols use English notation wrapped in backticks; SI units with a default of 3 significant figures are required. Momentum-space measure is d^3k/(2π)^3. For any time-of-arrival (ToA) statement both forms must be given and delta_form recorded: T_arr = ( 1 / c_ref ) * ( ∫ n_eff d ell ) and T_arr = ( ∫ ( n_eff / c_ref ) d ell ), with explicit gamma(ell) and d ell.
II. Dependencies & References
- Terms & notation: EFT.WP.Core.Terms v1.0 P10-*.
- Metrology & dimensional analysis: EFT.WP.Core.Metrology v1.0 Ch.1–3.
- Path & ToA formulations: EFT.WP.Core.Equations v1.1 Ch.2 S20-*.
- Timebase & path corrections: EFT.WP.Metrology.TimeBase v1.0, EFT.WP.Metrology.PathCorrection v1.0.
III. Normative Anchors (added in this chapter)
- P12-1 (Symbol Uniqueness): Global, cross-chapter symbols are registered in the centralized table; chapter-local temporary symbols must be listed in a “Local Symbol Table” at the chapter start and must not leak across chapters. Vectors use the _vec suffix; fields use _fld. Energy and path dependencies must be explicit, e.g., f(E), g(gamma(ell)).
- P12-2 (Units & Dimensions): SI is mandatory. Momentum-space measure is d^3k/(2π)^3. Tables must contain a “Unit/Dim” column and be auditable by check_dim.
- P12-3 (Do-Not-Confuse List): T_fil (tension) vs. T_trans (transmittance); n (number density) vs. n_eff (effective refractive index); Gamma (Lorentz factor) vs. gamma(ell) (path function); Pi (polarization fraction) vs. constant π; DM (dispersion measure) is not a differential operator.
- P12-4 (Statistics & Uncertainty): Use E[·], Var[·], Med[·]. Report 68% and 95% intervals; declare priors in symbol tables or parameter cards.
IV. Body Structure
I. Centralized Symbol Table (cross-chapter)
Table 2-1 Central Symbols & Units (global)
Symbol | Meaning | Unit (SI) | Dim | Scope | See |
|---|---|---|---|---|---|
c_ref | reference speed | m·s^-1 | L·T^-1 | global | Core.Metrology |
e_charge | elementary charge | C | I·T | global | Core.Terms |
m_e | electron mass | kg | M | global | Core.Terms |
m_p | proton mass | kg | M | global | Core.Terms |
k_B | Boltzmann constant | J·K^-1 | M·L^2·T^-2·Θ^-1 | global | Core.Terms |
T_fil | tension (magnitude) | N | M·L·T^-2 | global | Core.Tension |
T_fil_fld | tension field | N | M·L·T^-2 | field | Core.Tension |
T_trans | transmittance coefficient | 1 | 1 | global | Propagation |
n | number density | m^-3 | L^-3 | medium | Core.Density |
n_eff | effective refractive index | 1 | 1 | path | Packets.Light |
B_vec | magnetic field | T | M·T^-2·I^-1 | field | Core.Sea |
E_vec | electric field | V·m^-1 | M·L·T^-3·I^-1 | field | Core.Sea |
v_vec | velocity | m·s^-1 | L·T^-1 | flow | Kinematics |
R_rec | reconnection rate | s^-1 | T^-1 | accel | STG/TBN |
sigma_shear | shear strain rate | s^-1 | T^-1 | accel | Shear |
D(E) | diffusion coefficient | m^2·s^-1 | L^2·T^-1 | transport | Transport |
N(E) | particle number vs energy | 1 | 1 | spectra | Spectra |
dN/dE | differential spectrum | eV^-1 | E^-1 | spectra | Spectra |
Phi(E) | differential flux | m^-2·s^-1·sr^-1·eV^-1 | L^-2·T^-1·E^-1 | obs | Spectra |
alpha_spec | spectral index | 1 | 1 | obs | Spectra |
Pi | polarization fraction | 1 | 1 | obs | Polarimetry |
DM | dispersion measure | m^-2 (astro: pc·cm^-3) | L^-2 | obs | FRB |
T_arr | time of arrival | s | T | path | Packets.Light |
tau_loss(E) | loss timescale | s | T | loss | Transport |
tau_acc(E) | acceleration timescale | s | T | accel | S-series |
z | redshift | 1 | 1 | cosmology | Propagation |
gamma(ell) | path curve | — | — | path | Path |
d ell | line element | m | L | path | Path |
d^3k/(2π)^3 | momentum-space measure | m^-3 | L^-3 | k-space | Methods |
k_STG | STG mechanism weight | 1 | 1 | model | Falsification |
beta_TPR | TPR coupling weight | 1 | 1 | model | Falsification |
gamma_Path | path-correction strength | 1 | 1 | model | Falsification |
Notes
- Symbols in the centralized table are unique across the volume. Any chapter-local redefinition must be explicitly scoped in the Local Symbol Table and must not propagate across chapters.
- All ToA statements must carry explicit path and measure, e.g., T_arr = ( 1 / c_ref ) * ( ∫_{gamma(ell)} n_eff d ell ) and T_arr = ( ∫_{gamma(ell)} ( n_eff / c_ref ) d ell ).
- SI is primary; if astrophysical convenience units (e.g., pc·cm^-3) are used, list them alongside SI in the “Unit” column.
II. Units & Dimensionality (audit rules)
- SI only; derived units follow ISO symbols (N, Pa, T, V·m^-1).
- Spectral/flux units must include steradians and energy, e.g., m^-2·s^-1·sr^-1·eV^-1.
- All integrals include explicit path and measure: real space d ell; wavevector space d^3k/(2π)^3.
- Dimensional consistency is auditable via check_dim; each table includes a “Dim” column.
- Statistical reports provide point estimates plus 68% and 95% intervals; priors and likelihoods are declared.
III. Do-Not-Confuse & Prohibited Usages (enforcement)
- Do not interchange T_fil and T_trans; never omit required subscripts/suffixes.
- Do not use n to mean n_eff, or vice versa.
- Keep Gamma distinct from gamma(ell); keep Pi distinct from π.
- Do not omit path or measure in ToA or any ∫///convolution expression; wrap composite expressions in parentheses.
- Chapter-local symbols must remain local; cross-chapter reuse requires registration in the centralized table.
IV. Statistical Notation & Uncertainty (reporting stance)
- Use E[·], Var[·], Med[·], and quantiles Q_p[·].
- Clearly distinguish credible vs confidence intervals; when reporting Bayes factors or information criteria, state priors and data dependence.
- Propagate uncertainty in M-series flows via error-budget tables; energy E and frequency ν dependencies must be explicit.
V. Summary & Handoff
This chapter finalizes centralized symbols and units, the do-not-confuse list, and statistical conventions. Chapter 3 builds on this to establish frames and acceleration kinematics, define tau_acc(E), and close notation for coherence windows and scattering models.
V. Figures & Tables (this chapter)
- Tab. 2-1 Central Symbols & Units (global).
- Tab. 2-2 Local Symbol Table template (fields: Symbol / Meaning / Unit / Validity(Ch.#) / Range or Prior / Notes / See).
- Tab. 2-3 Statistical conventions and interval examples (point + 68% / 95%).
- Tab. 2-4 Dimensional audit examples (equation—unit—dimension—result).
Copyright & License (CC BY 4.0)
Copyright: Unless otherwise noted, the copyright of “Energy Filament Theory” (text, charts, illustrations, symbols, and formulas) belongs to the author “Guanglin Tu”.
License: This work is licensed under the Creative Commons Attribution 4.0 International (CC BY 4.0). You may copy, redistribute, excerpt, adapt, and share for commercial or non‑commercial purposes with proper attribution.
Suggested attribution: Author: “Guanglin Tu”; Work: “Energy Filament Theory”; Source: energyfilament.org; License: CC BY 4.0.
First published： 2025-11-11｜Current version：v5.1
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