Newton's gravitational constant G G
Newton's gravitational constant G is, in the τ-framework, a derived structural ratio that emerges from the gravity-sector embedding of ι_τ in the categorical bridge. It is not a…
PG-C01-newton-g
Glossary for the τ-framework's physics domain — 95 canonical entries grouped by category.
The 95-entry physics glossary covers quantities, units, constants, laws, particles, and objects, all calibrated to the neutron mass anchor PG-P01-neutron. Every entry carries an SI translation with a numerical value, uncertainty, and calibration cascade rooted at m_n.
GNewton's gravitational constant G is, in the τ-framework, a derived structural ratio that emerges from the gravity-sector embedding of ι_τ in the categorical bridge. It is not a…
PG-C01-newton-g
ι_τι_τ = 2/(π + e) is the master algebraic constant of the τ-framework — the unique dimensionless number that governs every dimensionless ratio of physics. It is not measured; it i…
PG-C02-iota-tau
cThe speed of light c is, in the τ-framework, the dimensional unit-conversion factor between τ-native length and τ-native time at enrichment layer E₁. It is a Tier-I (Established…
PG-C03-speed-of-light
ℏPlanck's reduced constant ℏ is, in the τ-framework, the dimensional unit-conversion factor M · L² · H that closes the (M, L, ℏ) triple at E₁. It is a Tier-I (Established) entry …
PG-C04-planck-hbar
αThe fine-structure constant α is, in the τ-framework, the τ-effective dimensionless coupling of the electromagnetic sector — derived as α = (11/15)² · ι_τ⁴ at enrichment layer E…
PG-C05-fine-structure-alpha
eThe elementary charge e is, in the τ-framework, a Layer-3 SI quantity built from the dimensionless EM coupling α (a τ-prediction) and the Tier-I unit conversions (c, ℏ, ε₀). It …
PG-C06-elementary-charge
ε₀Vacuum permittivity ε₀ is, in the τ-framework, a Tier-I (Established) unit-conversion entry of the constants ledger — the dimensional factor Q²/(M L³ H²) that, together with c a…
PG-C07-vacuum-permittivity
μ₀Vacuum permeability μ₀ is, in the τ-framework, a Tier-I (Established) unit-conversion entry of the constants ledger — the dimensional factor M L / Q² that, together with ε₀ and …
PG-C08-vacuum-permeability
m_eThe electron mass m_e is, in the τ-framework, the τ-effective Layer-2 readout m_e = m_n / R, where R = ι_τ⁻⁷ − (√3 + π³ α²) ι_τ⁻² is the τ-predicted neutron-to-electron mass rat…
PG-C09-electron-mass
m_pThe proton mass m_p is, in the τ-framework, the τ-effective Layer-2 readout m_p = m_n − δ_A, where δ_A is the β-decay differential between the neutron and proton sectors of the …
PG-C10-proton-mass
R_∞The Rydberg constant R_∞ is, in the τ-framework, a Layer-4 verification readout of the cascade — derived as R_∞ = α² m_e c / (2h) from the τ-predicted α and m_e. It inherits the…
PG-C11-rydberg-constant
a_0The Bohr radius a_0 is, in the τ-framework, a Layer-4 verification readout of the cascade — derived as a_0 = ℏ/(α m_e c) from the τ-predicted α and m_e. It inherits the 0.025 pp…
PG-C12-bohr-radius
m_PThe Planck mass m_P is, in the τ-framework, the τ-effective Layer-2 readout m_P = m_n / ι_τ — the gravity-sector partner of the neutron-mass anchor. It exhibits the gauge hierar…
PG-C13-planck-mass
α_GThe gravitational fine-structure constant α_G is, in the τ-framework, the dimensionless gravity-sector coupling, derived as α_G = α¹⁸ √3 (1 − (3/π)α). It is the right-hand side …
PG-C14-gravitational-fine-structure
k_BThe Boltzmann constant k_B is, in the τ-framework, a Layer-3 SI unit-conversion entry — exact by 2019 SI definition (k_B fixes the kelvin) and adopted verbatim by the τ-cascade.…
PG-C15-boltzmann-constant
sin²θ_WThe weak mixing angle sin²θ_W (Weinberg angle) is, in the τ-framework, the τ-effective dimensionless coupling of the electroweak crossing — derived as sin²θ_W = ι_τ (1 − ι_τ). I…
PG-C16-weinberg-angle
α_sThe strong coupling constant α_s is, in the τ-framework, the τ-effective dimensionless coupling of the strong (C) sector — derived as α_s = 2 κ(C; 3) = 2 ι_τ³/(1 − ι_τ). It is a…
PG-C17-strong-coupling
κ_τκ_τ = 1 − ι_τ is the τ-effective dimensionless coupling of the dual (D) sector — the gravitational complement of the master constant ι_τ at depth 1. It is one of the two complem…
PG-C18-kappa-tau
a₀^{MOND}The Milgrom MOND acceleration a₀ ≈ 1.2 × 10⁻¹⁰ m s⁻² is, in the τ-framework, derived as the gravity-sector readout a₀ = c²/(2 ℓ_τ), where ℓ_τ is the τ-derived horizon length anc…
PG-C19-milgrom-acceleration
iℏ ∂_t ψ = Ĥ ψThe τ-Schrödinger equation is the τ-categorical statement of unitary time evolution on the holomorphic state space of the τ-framework. It emerges as a structural theorem from th…
PG-L01-tau-schrodinger
Δx · Δp ≥ ℏ_τ / 2The τ-Heisenberg uncertainty inequality is a τ-categorical theorem (`IV.T102`) stating that for every ontic defect bundle and every refinement level n, Δx · Δp ≥ ℏ_τ / 2. It is …
PG-L02-tau-heisenberg-uncertainty
dF = 0, d⋆F = ⋆JThe complete τ-Maxwell system is a τ-categorical theorem (`IV.T44`) assembling all four Maxwell equations: the homogeneous pair dF = 0 (from the Bianchi identity, kinematic) and…
PG-L03-tau-maxwell-system
R^H(x) = κ_τ · T^mat(x)The τ-Einstein equation is the boundary-character identity R^H(x) = κ_τ · T^mat(x) in H_∂[ω], where R^H is the curvature character, κ_τ = 1 − ι_τ is the gravitational coupling, …
PG-L04-tau-einstein-equation
∇²Φ = 4πG ρ, G = (c³/ℏ) · ι_τ²τ-Newton's law of gravity is the τ-categorical theorem (`V.T28`) that, in the weak-field, slow-motion regime, the chart shadow of the linearized τ-Einstein equation is the Newto…
PG-L05-tau-newton-gravity
∂_[μ F_νρ] = 0 (i.e. dF = 0)The τ-Bianchi identity (`IV.T234`) states that the curvature 2-form F of any U(1) connection on the τ-EM gauge bundle automatically satisfies ∂_[μ F_νρ] = 0 (equivalently, dF = …
PG-L06-tau-bianchi-identity
∂_t u + (u·∇)u = −∇p + ν∇²u (chart shadow); ‖u‖_{H^s} bounded for all tτ-Navier–Stokes regularity (`IV.R161`) is the τ-categorical statement that the τ-NS flow on τ-admissible fluid data preserves regularity globally in time: the defect-transport o…
PG-L07-tau-navier-stokes-regularity
symmetry ⇄ conservation law (both faces of categorical naturality)τ-Noether's theorem (`IV.R180`) is a corollary of the categorical structure of τ: in Category τ, the natural transformations are determined by the structure, each automatically …
PG-L08-tau-noether-theorem
□ A^μ = 0 (source-free, Lorenz gauge), c = L · HThe τ-EM wave equation (`IV.T47`) is the τ-categorical theorem that, in the source-free Lorenz gauge, the τ-Maxwell system reduces to □ A^μ = 0, with plane-wave solutions propag…
PG-L09-tau-em-wave-equation
d⋆F = ⋆J (Gauss + Ampère–Maxwell)The τ-inhomogeneous Maxwell equations (`IV.T43`) are the τ-categorical theorem that the source equation d⋆F = ⋆J on the τ-EM gauge bundle is the Euler–Lagrange equation of the B…
PG-L10-tau-inhomogeneous-maxwell
conservation law = naturality squareτ-Conservation as Naturality (`IV.T247`) is the τ-categorical theorem that every conservation law in the τ³ framework is a naturality condition: the conserved current is the dia…
PG-L11-tau-conservation-as-naturality
δΔ_k^{(n)} satisfying R^H_lin = 0 (vacuum perturbation)A τ-gravitational wave (`V.D53`) is a propagating perturbation δΔ_k^{(n)} of the holonomy-gap elements satisfying the linearized τ-Einstein equation with vanishing matter source…
PG-L12-tau-gravitational-wave
δφ = 6π G M_⊙ / (a (1 − e²) c²) per orbitτ-Mercury perihelion precession (`V.T29`) is the τ-categorical theorem that the τ-Einstein equation predicts a per-orbit precession δφ = 6π G M_⊙ / (a(1−e²)c²) for a planet in a…
PG-L13-tau-mercury-precession
HThe τ-hydrogen atom is the simplest composite object in the τ-framework: a τ-proton (β-decay-differentiated τ-neutron) bound to a τ-electron via the electromagnetic sector at E₁…
PG-O01-hydrogen-atom
αThe τ-α-particle is the smallest doubly-saturated T² nucleon bundle: 2 protons + 2 neutrons whose proton and neutron T² shells are both closed at the magic number N_magic = 2. A…
PG-O02-alpha-particle
dThe τ-deuteron is the simplest non-trivial nuclear bundle: a single proton + single neutron bound on T² × R³ via the strong sector. It is the unique stable two-nucleon T² compos…
PG-O03-deuteron
N(A,Z)The τ-atomic nucleus is the general multi-defect-bundle composite of Z τ-protons and (A − Z) τ-neutrons bound on T² × R³ via the strong sector. Its T²-shell occupancy is governe…
PG-O04-atomic-nucleus
HeThe τ-helium atom is the simplest two-electron composite: an α-particle nucleus (PG-O02) bound to two τ-electrons via the EM sector at E₁. It is the cleanest τ-native test of mu…
PG-O05-helium-atom
ψ_{n,ℓ,m}A τ-electron orbital is a single-particle eigenmode of the τ-Schrödinger operator in an EM-sector central potential — the τ-categorical projection of the Bohr-style structure th…
PG-O06-electron-orbital
Γ_s*[n]The τ-finite-stage strong vacuum Γ_s*[n] is the stage-n argmin of the strong-sector defect functional Δ_n^s over the admissible class Adm_s[n], with NFMin tie-breaking. It is th…
PG-O07-finite-stage-strong-vacuum
C_τThe τ-crystal regime is the many-body matter phase characterized by μ ≈ 0 (locked) — a lattice-ordered configuration of T² defect bundles whose translational degree of freedom i…
PG-O08-crystal-regime
κ_macroThe τ-macroscopic-compression κ_macro(C) is the bulk compression observable for an N-defect configuration C: the average single-defect compression plus an interaction term. Defi…
PG-O09-macroscopic-compression
Λ_CR^qThe τ-fractional CR-sublattice Λ_CR^q is a sub-lattice of the strong-sector CR-address lattice with rational denominator q — the categorical home of fractional charges in confin…
PG-O10-fractional-cr-sublattice
BHA τ-black-hole is a maximal topological defect of the cosmological τ-base whose horizon is canonically a 2-torus T² (V.T109/V.T110), not a 2-sphere — the τ-categorical replaceme…
PG-O11-black-hole
NSA τ-neutron-star is a TOV-bound compact object — a macroscopic τ-bundle of τ-neutrons whose phase sequence (V.P55) and TOV maximum mass (V.R93) are τ-categorical theorems. It si…
PG-O12-neutron-star
C_τ^macroThe τ-macro-crystal is the cosmological-scale crystalline regime — the macroscopic phase counterpart of the microscale crystal regime (PG-O08), arising in book-V's macro-phase-t…
PG-O13-macro-tau-crystal
nThe τ-neutron is the minimal stable ontic defect bundle on the toroidal T² fiber: the lightest persistent T² defect with non-trivial winding data, unpolarized (zero charge, zero…
PG-P01-neutron
pThe τ-proton is the β-decay-differentiated sibling of the τ-neutron: a stable T²-defect bundle obtained by replacing one down-mode of the (udd) neutron with an up-mode, yielding…
PG-P02-proton
e⁻The τ-electron is the lightest stable lepton-class T²-defect: a charged, spin-½ winding bundle whose mass is generated by the τ-Yukawa overlap integral on the linkage modes of t…
PG-P03-electron
γThe τ-photon is the unique massless boundary character of the EM (B-)sector: a phase-quantum mode with no T²-fiber rest-mass content, propagating as a null transport on the boun…
PG-P04-photon
νThe τ-neutrino is the lightest lepton-class T²-defect on the τ¹-dimensional time eigenmode: a charge-zero, near-massless winding bundle whose suppressed mass and three-flavor st…
PG-P05-neutrino
uThe τ-up quark is the lighter member of the first-generation quark mode pair on the T² fiber: a fractional-charge (+2/3) winding mode that, together with the down mode, composes…
PG-P06-up-quark
dThe τ-down quark is the heavier member of the first-generation quark mode pair on the T² fiber: a fractional-charge (−1/3) winding mode that, paired with the up mode, supplies t…
PG-P07-down-quark
μ⁻The τ-muon is the second-generation lepton-class T²-defect: the second rung of the τ-Yukawa overlap ladder, sharing the electron's charge and chirality structure but with a heav…
PG-P08-muon
τ⁻The τ-tauon (tau lepton) is the third-generation lepton-class T²-defect: the heaviest rung of the τ-Yukawa overlap ladder, sharing the electron and muon's charge and chirality s…
PG-P09-tauon
HThe τ-Higgs is the radial breathing mode of the τ-framework's E₁ sector: not a separate "mass-giving field" but the diagonal scalar excitation of the linkage geometry whose vacu…
PG-P10-higgs-boson
Z⁰The τ-Z boson is the neutral weak gauge mode: a massive boundary character of the W (weak) sector whose mass arises from the window-universality theorem and whose mixing with th…
PG-P11-z-boson
gThe τ-gluon is the family of eight massless color-carrier modes of the strong (S-)sector: bi-color boundary characters of the strong holonomy algebra that mediate quark-mode exc…
PG-P12-gluon
c, s, t, bThe τ-heavy quark families (charm, strange, top, bottom) are the second- and third-generation quark modes on the T² fiber: rungs 3–6 of the Epstein-zeta quark spectrum, sharing …
PG-P13-heavy-quarks
MMass is a τ-categorical invariant that quantifies the dimensional load carried by a stable defect bundle on the toroidal T² fiber. It is the structural cost of persistence — the…
PG-Q01-mass
EEnergy is the τ-categorical Energy Index (IV.D21): a dimensional invariant assigned to every τ-state that measures the integrated CR-tension carried by its defect configuration.…
PG-Q02-energy
E = Mc²The τ-Mass-Energy Relation (IV.D23) is the categorical identity that locks the Mass Index (IV.D11) and the Energy Index (IV.D21) via the speed-of-light constant in relational un…
PG-Q03-mass-energy-relation
SEntropy is the τ-categorical mode-counting invariant (IV.D466): for any thermodynamic τ-state it counts the breathing-mode multiplicity of the underlying defect configuration. I…
PG-Q04-entropy
HEnthalpy (IV.D465) is the τ-categorical Energy Index plus the work-conjugate term carried by the τ-pressure on the bundle's volume mode. It is the natural energy quantity on a d…
PG-Q05-enthalpy
TTemperature in the τ-framework is the defect-gradient quantity (IV.D228): the τ-internal gradient of the breathing-mode population on a defect bundle. It is not fundamental — it…
PG-Q06-temperature
QElectric Charge (IV.D84) is the τ-categorical winding-number quantity on the U(1)-electromagnetic sector. It is a topological invariant of the defect bundle's holonomy around th…
PG-Q07-electric-charge
Q_geomGeometric Charge (IV.D58) is the τ-categorical generalization of charge: the winding-number / topological holonomy invariant of a defect bundle on any closed fiber loop. Special…
PG-Q08-geometric-charge
νFrequency (IV.D79) is the τ-categorical Base Circulation rate: the rate at which a defect bundle traverses its base loop on T². It is the natural conjugate to τ-time and the ope…
PG-Q09-frequency
τ_properProper Time (V.D17) is the τ-categorical arc-length of a defect bundle's worldline on the τ-base. It is not a coordinate but an intrinsic invariant — the cumulative phase carrie…
PG-Q10-proper-time
dOperational Distance (V.D28) is the τ-categorical spatial separation between defect bundles, defined as the arc-length on the spatial complement of the τ-base. It is the spatial…
PG-Q11-operational-distance
d_specSpectral Distance √3 (IV.D43) is the τ-categorical fixed spectral separation arising from the three-fold internal-fiber structure. It is a dimensionless invariant equal to √3, f…
PG-Q12-spectral-distance-sqrt3
E_CREnergy as CR-Tension (IV.D76) is the τ-categorical operational form of the Energy Index: the integrated holomorphic strain (Cauchy-Riemann tension) that a defect bundle exerts a…
PG-Q13-energy-cr-tension
ρ_EGraph Energy Density (IV.D77) is the local-density form of the τ-Energy Index: the CR-tension integrand evaluated pointwise on the τ-graph (the discrete approximant of T²). It i…
PG-Q14-graph-energy-density
S_holHolomorphic Entropy (IV.D80) is the holomorphic sector of the τ-Entropy Splitting (IV.D24): the count of breathing modes of a defect bundle that are compatible with holomorphic …
PG-Q15-holomorphic-entropy
Q_colorColor Charge (IV.D154) is the SU(3)-sector specialization of the τ-Geometric Charge (IV.D58): the winding-number invariant of a defect bundle's holonomy on the strong/SU(3) sub-…
PG-Q16-color-charge
FForce in the τ-framework (IV.D402) is not a mediated push or pull, but a τ-categorical Boundary Mode: the rate-of-change of a defect bundle's CR-tension at the τ-boundary, equal…
PG-Q17-force-as-boundary-mode
Φ_colorColor Flux Tube (IV.D475) is the τ-categorical defect-bundle topology connecting color-charged sub-bundles. Its quantized cross-sectional flux (IV.P138) and confined topology (V…
PG-Q18-color-flux-tube
S_actAction (IV.D115) is the τ-categorical Crossing-Point Action Space: the integrated CR-tension along a τ-trajectory, evaluated at every crossing point of the underlying defect-gra…
PG-Q19-action-space
yYukawa Coupling (IV.D142) is the τ-categorical coupling strength between a fermion defect-bundle and the Higgs-sector mode, fixed by the ι_τ-structured generation hierarchy. It …
PG-Q20-yukawa-coupling
L_coupCoupling Ledger (IV.D300) is the τ-categorical lookup table of dimensionless coupling constants — α, α_s, α_W, Yukawa entries, mixing angles — all expressible as ι_τ-fixed ratio…
PG-Q21-coupling-ledger
E_vacVacuum Energy (IV.D572) is the τ-categorical Energy Index of the no-defect ground state, computed as the defect functional (IV.D274) evaluated on the empty bundle. In τ it is fi…
PG-Q22-vacuum-energy
LAngular Momentum (V.D118) is the τ-categorical Angular-Momentum Character: the cohomology-class-valued quantity that records a defect bundle's net rotation around the τ-base, eq…
PG-Q23-angular-momentum
vVelocity in the τ-framework (V.D262) is the Linearized Velocity Scale: the rate of change of operational distance with respect to proper time on a defect bundle's worldline, eva…
PG-Q24-velocity
P_degDegeneracy Pressure (V.D124) is the τ-categorical Degeneracy-Pressure Character: the τ-pressure quantity arising from defect-bundle exclusion (no two fermion bundles share the s…
PG-Q25-degeneracy-pressure
SSpin (IV.T17) is the τ-categorical half-integer correction to the Angular-Momentum Character: the intrinsic rotational invariant of a fermion defect-bundle, equal to ±ℏ/2 by vir…
PG-Q26-spin
s_τThe τ-second is the natural unit of time in the τ-framework: a structural duration derived from the master constant ι_τ and the dimensional bookkeeping of the calibration cascad…
PG-U01-tau-second
m_τThe τ-meter is the natural unit of length in the τ-framework: a structural extent derived from the master constant ι_τ and the dimensional bookkeeping of the calibration cascade…
PG-U02-tau-meter
kg_τThe τ-kilogram is the natural unit of mass in the τ-framework: a structural mass scale rooted in the calibration anchor m_n. Unlike the other τ-natural units, mass is the single…
PG-U03-tau-kilogram
J_τThe τ-Joule is the natural unit of energy in the τ-framework: a structural energy scale derived from the master constant ι_τ and the dimensional bookkeeping of the calibration c…
PG-U04-tau-joule
K_τThe τ-Kelvin is the natural unit of temperature in the τ-framework: a structural temperature scale derived from the τ-Joule via the Boltzmann constant analog. SI kelvins are rec…
PG-U05-tau-kelvin
C_τThe τ-Coulomb is the natural unit of electric charge in the τ-framework: a structural charge scale derived from the master constant ι_τ via the fine-structure cascade α = (11/15…
PG-U06-tau-coulomb
A_τThe τ-Ampere is the natural unit of electric current in the τ-framework: charge per unit τ-time, A_τ = C_τ / s_τ. SI amperes are recovered by multiplying the τ-Ampere by a dimen…
PG-U07-tau-ampere
N_τThe τ-Newton is the natural unit of force in the τ-framework: a structural force scale derived from the master constant ι_τ via energy-per-length composition. SI newtons are rec…
PG-U08-tau-newton
Pa_τThe τ-Pascal is the natural unit of pressure in the τ-framework: force per unit τ-area, Pa_τ = N_τ / m_τ². SI pascals are recovered by multiplying the τ-Pascal by a dimensionles…
PG-U09-tau-pascal
W_τThe τ-Watt is the natural unit of power in the τ-framework: energy per unit τ-time, W_τ = J_τ / s_τ. SI watts are recovered by multiplying the τ-Watt by a dimensionless ι_τ-chai…
PG-U10-tau-watt
V_τThe τ-Volt is the natural unit of electric potential in the τ-framework: energy per unit τ-charge, V_τ = J_τ / C_τ. SI volts are recovered by multiplying the τ-Volt by a dimensi…
PG-U11-tau-volt
Download a portable dossier, copy a reviewer note, or send this page to someone who can inspect it.