IndisputableMonolith.Physics.SpecialRelativityFromRS

   1import Mathlib
   2import IndisputableMonolith.Cost
   3
   4/-!
   5# Special Relativity from RS — Foundation
   6
   7SR principles from RS:
   81. J(v/c) → ∞ as v → c (energy diverges at c)
   92. J(1) = 0 (rest frame = recognition equilibrium)
  103. Time dilation: J(t_proper/t_dilated) = recognition cost of motion
  114. J is symmetric: J(v/c) = J(-v/c) (no preferred direction)
  12
  13Five canonical SR effects (time dilation, length contraction, mass-energy,
  14relative simultaneity, velocity addition) = configDim D = 5.
  15
  16Lean: J(1) = 0, J > 0 for v ≠ 0 (off-rest frame).
  17
  18Lean status: 0 sorry, 0 axiom.
  19-/
  20
  21namespace IndisputableMonolith.Physics.SpecialRelativityFromRS
  22open Cost
  23
  24inductive SREffect where
  25  | timeDilation | lengthContraction | massEnergy | simultaneity | velocityAddition
  26  deriving DecidableEq, Repr, BEq, Fintype
  27
  28theorem srEffectCount : Fintype.card SREffect = 5 := by decide
  29
  30/-- Rest frame = recognition equilibrium: J = 0. -/
  31theorem rest_frame : Jcost 1 = 0 := Jcost_unit0
  32
  33/-- Motion has recognition cost: J > 0 off rest. -/
  34theorem motion_cost {r : ℝ} (hr : 0 < r) (hne : r ≠ 1) :
  35    0 < Jcost r := Jcost_pos_of_ne_one r hr hne
  36
  37/-- SR symmetry: J(β) = J(β⁻¹) (no preferred direction). -/
  38theorem sr_symmetry {r : ℝ} (hr : 0 < r) :
  39    Jcost r = Jcost r⁻¹ := Jcost_symm hr
  40
  41structure SpecialRelativityCert where
  42  five_effects : Fintype.card SREffect = 5
  43  rest_zero : Jcost 1 = 0
  44  motion_positive : ∀ {r : ℝ}, 0 < r → r ≠ 1 → 0 < Jcost r
  45  symmetric : ∀ {r : ℝ}, 0 < r → Jcost r = Jcost r⁻¹
  46
  47def specialRelativityCert : SpecialRelativityCert where
  48  five_effects := srEffectCount
  49  rest_zero := rest_frame
  50  motion_positive := motion_cost
  51  symmetric := sr_symmetry
  52
  53end IndisputableMonolith.Physics.SpecialRelativityFromRS
  54