Results Glossary Index Canonical physics Glossary for the τ-framework's physics domain — 95 canonical entries grouped by category.
Glossary IndexCanonical

Physics Glossary — 95 entries, 6 categories

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.

Glossary contract. Every entry below carries a 4-section structure: τ-definition (categorical invariant + primary registry anchor), τ-derivation (chain of registry steps), domain-specific Section 3, and Lean coverage. The structure is uniform across all three domains so cross-references resolve unambiguously.

Browse by category

Constant (19)

  • 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

  • Master constant ι_τ ι_τ

    ι_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

  • Speed of light c c

    The 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

  • Planck's reduced constant ℏ

    Planck'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

  • Fine-structure constant α α

    The 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

  • Elementary charge e e

    The 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

  • Vacuum permittivity ε₀ ε₀

    Vacuum 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

  • Vacuum permeability μ₀ μ₀

    Vacuum 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

  • Electron mass m_e m_e

    The 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

  • Proton mass m_p m_p

    The 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

  • Rydberg constant R_∞ 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

  • Bohr radius a_0 a_0

    The 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

  • Planck mass m_P m_P

    The 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

  • Gravitational fine-structure constant α_G α_G

    The 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

  • Boltzmann constant k_B k_B

    The 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

  • Weak mixing angle sin²θ_W sin²θ_W

    The 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

  • Strong coupling constant α_s α_s

    The 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

  • Gravity-sector coupling κ_τ κ_τ

    κ_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

  • Milgrom MOND acceleration a₀ 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

Law (13)

Object (13)

  • Hydrogen Atom H

    The 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

  • α-Particle (Helium-4 Nucleus) α

    The 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

  • Deuteron d

    The 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

  • Atomic Nucleus 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

  • Helium Atom He

    The 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

  • Electron Orbital 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

  • Finite-Stage Strong Vacuum 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

  • Crystal Regime (τ-Lattice) C_τ

    The 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

  • Macroscopic Compression κ_macro

    The 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

  • Fractional CR-Sublattice Λ_CR^q

    The 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

  • Black Hole BH

    A 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

  • Neutron Star NS

    A 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

  • Macro τ-Crystal C_τ^macro

    The 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

Particle (13)

  • τ-Neutron n

    The 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

  • τ-Proton p

    The 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

  • τ-Electron 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

  • τ-Photon γ

    The 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

  • τ-Neutrino ν

    The 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

  • τ-Up Quark u

    The 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

  • τ-Down Quark d

    The 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

  • τ-Muon 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-Tauon 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

  • τ-Higgs Boson H

    The 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

  • τ-Z Boson Z⁰

    The 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

  • τ-Gluon g

    The 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

Quantity (26)

  • Mass M

    Mass 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

  • Energy E

    Energy 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

  • Mass-Energy Relation E = Mc²

    The 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

  • Entropy S

    Entropy 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

  • Enthalpy H

    Enthalpy (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

  • Temperature T

    Temperature 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

  • Electric Charge Q

    Electric 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

  • Geometric Charge Q_geom

    Geometric 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

  • Frequency ν

    Frequency (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

  • Proper Time τ_proper

    Proper 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

  • Operational Distance d

    Operational 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

  • Spectral Distance √3 d_spec

    Spectral 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

  • Energy as CR-Tension E_CR

    Energy 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

  • Graph Energy Density ρ_E

    Graph 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

  • Holomorphic Entropy S_hol

    Holomorphic 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

  • Color Charge Q_color

    Color 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

  • Force as Boundary Mode F

    Force 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

  • Color Flux Tube Φ_color

    Color 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

  • Action (Crossing-Point Action Space) S_act

    Action (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

  • Yukawa Coupling y

    Yukawa 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

  • Coupling Ledger L_coup

    Coupling 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

  • Vacuum Energy E_vac

    Vacuum 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

  • Angular Momentum L

    Angular 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

  • Velocity v

    Velocity 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

  • Degeneracy Pressure P_deg

    Degeneracy 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

  • Spin (Intrinsic Angular Momentum) S

    Spin (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

Unit (11)

  • τ-Second s_τ

    The 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

  • τ-Meter m_τ

    The 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

  • τ-Kilogram kg_τ

    The 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

  • τ-Joule J_τ

    The 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

  • τ-Kelvin K_τ

    The 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

  • τ-Coulomb C_τ

    The 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

  • τ-Ampere A_τ

    The 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

  • τ-Newton N_τ

    The 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

  • τ-Pascal Pa_τ

    The 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

  • τ-Watt W_τ

    The 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

  • τ-Volt V_τ

    The 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

Save or share this page for inspection

Download a portable dossier, copy a reviewer note, or send this page to someone who can inspect it.

Email to expert