planckTime_rs

formal source

 240
 241/-- Planck time in RS units: τ_P = √(ħG/c⁵).
 242    In RS-native units, this is a dimensionless φ-expression. -/
 243noncomputable def planckTime_rs : Time :=
 244  -- Using the gate identity: τ_P = τ₀ · √(G/c³) where G,c are in RS units
 245  -- Since c = 1, and G is derived, this is pure φ-structure
 246  tick * Real.sqrt (Constants.G / (c ^ 3))
 247
 248/-- Planck length in RS units: ℓ_P = c · τ_P. -/
 249noncomputable def planckLength_rs : Length :=
 250  c * planckTime_rs
 251
 252/-- Planck mass in RS units: m_P = √(ħc/G).
 253    This is the mass at which gravitational and quantum scales meet. -/
 254noncomputable def planckMass_rs : Mass :=
 255  Real.sqrt (hbarQuantum * c / Constants.G)
 256
 257/-- Planck energy in RS units: E_P = m_P · c² = m_P (since c = 1). -/
 258noncomputable def planckEnergy_rs : Energy := planckMass_rs
 259
 260/-! ## Dimensionless Ratios (Fixed by φ)
 261
 262These ratios are the same in any unit system - they are the "physics" of RS.
 263-/
 264
 265/-- Fine structure constant inverse: α⁻¹ ≈ 137.036. -/
 266noncomputable def alphaInv_rs : ℝ := Constants.alphaInv
 267
 268/-- The K-gate ratio: K = π/(4 ln φ). -/
 269noncomputable def K_rs : ℝ := Constants.RSUnits.K_gate_ratio
 270
 271/-- Coherence scaling: E_coh = φ⁻⁵. -/
 272noncomputable def E_coh_rs : ℝ := phiRung (-5)
 273