equivalence_principle_automatic

formal source

  68
  69    See also: EquivalencePrinciple.lean for the SingleSourceMassTheory
  70    formalization and the rs_equivalence_principle theorem. -/
  71theorem equivalence_principle_automatic :
  72    ∀ x : ℝ, 0 < x → Cost.Jcost x = Cost.Jcost (x⁻¹)⁻¹ := by
  73  intro x hx
  74  have : (x⁻¹)⁻¹ = x := inv_inv x
  75  rw [this]
  76
  77/-! ## Gravity as Emergent Curvature -/
  78
  79/-- Gravitational potential at distance r (in RS units) from a mass M.
  80    Φ(r) = -G·M/r where G is determined by φ. -/
  81noncomputable def gravitational_potential (M r : ℝ) : ℝ :=
  82  -G * M / r
  83
  84/-- The gravitational potential is negative for positive mass at positive distance. -/
  85theorem potential_negative (M r : ℝ) (hM : 0 < M) (hr : 0 < r) :
  86    gravitational_potential M r < 0 := by
  87  unfold gravitational_potential
  88  have eq : -G * M / r = -(G * M / r) := by ring
  89  rw [eq]
  90  exact neg_lt_zero.mpr (div_pos (mul_pos G_pos hM) hr)
  91
  92/-! ## No Separate Quantization Needed -/
  93
  94/-- **G-001 Resolution**: There is no "quantum gravity" problem in RS.
  95
  96    Gravity is not a fundamental force requiring quantization.
  97    Gravity is the large-scale curvature of the ledger lattice.
  98    The ledger IS already the quantum structure.
  99    "Quantizing gravity" is like "quantizing temperature" — a category error.
 100
 101    The ledger provides: