Results Glossary Entry Canonical physics τ-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 Newtonian Poisson equation ∇²Φ = 4πGρ, with Newton's constant G = (c…
Results · Physics Glossary · Law PG-L05-tau-newton-gravity ∇²Φ = 4πG ρ, G = (c³/ℏ) · ι_τ² Canonical Lean · formalized

τ-Newton's Law of Gravity

τ-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 Newtonian Poisson equation ∇²Φ = 4πGρ, with Newton's constant G = (c³/ℏ) · ι_τ² derived (not fitted) from the τ-cascade. The full derivation chain is `V.R69` Newton-from-τ.

Physics Glossary Primary: V.T28 dynamical law gravity newtonian limit categorical theorem

τ-Definition

τ-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 Newtonian Poisson equation ∇²Φ = 4πGρ, with Newton's constant G = (c³/ℏ) · ι_τ² derived (not fitted) from the τ-cascade. The full derivation chain is `V.R69` Newton-from-τ.

Categorical invariant. Chart-shadow of V.D52 (linearized τ-Einstein) in the weak-field regime: ∇²Φ = 4πGρ, F = −m∇Φ.

Primary registry anchor: V.T28

Supporting items: V.R69, V.D52, V.D46

τ-Derivation Chain

  1. I.K0 — Universe Postulate
  2. V.D46 — Gravitational coupling κ_τ = 1 − ι_τ
  3. V.D51 — τ-Einstein equation R^H = κ_τ · T^mat
  4. V.D52 — Linearized τ-Einstein equation (weak-field expansion)
  5. V.T28 — Newtonian limit recovery — ∇²Φ = 4πGρ with G = (c³/ℏ) · ι_τ²
  6. V.R69 — Newton-from-τ — full derivation chain from K0–K6 to Poisson equation

Lean modules referenced: TauLib.BookV.GravityField.LinearEinstein

SI Translation

Calibration anchor: PG-P01-neutron

Calibration chain:

  1. ι_τ from K0–K6 ladder
  2. G = (c³/ℏ) · ι_τ² (Newton's constant cascade)
  3. SI bridge via m_n anchor for mass and length units

Manuscript reference: manuscript-sources/book-05/part02/ch14-linear-tau-einstein.tex

Lean Coverage

Status: Formalized

Module: TauLib.BookV.GravityField.LinearEinstein

Lean kind: theorem

Lean symbol: Tau.BookV.GravityField.NewtonianLimitRecovery

Related glossary entries

Referenced by

Cross-domain bridges

This glossary term sits on the boundary between domains. The τ-framework's cross-domain pivots are the structural junctions where physics, life, and metaphysics readouts meet.

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