sin2ThetaW

formal source

  61noncomputable def weinbergAngle : ℝ := Real.arccos massRatio
  62
  63/-- sin²(θ_W) - the key electroweak parameter. -/
  64noncomputable def sin2ThetaW : ℝ := 1 - massRatio^2
  65
  66/-- **THEOREM**: sin²(θ_W) ≈ 0.223. -/
  67theorem sin2_theta_w_value : sin2ThetaW > 0.22 ∧ sin2ThetaW < 0.23 := by
  68  unfold sin2ThetaW massRatio m_W m_Z
  69  constructor <;> norm_num
  70
  71/-! ## φ-Connection Hypotheses -/
  72
  73/-- Hypothesis 1: cos(θ_W) = √(1 - 1/φ²)
  74
  75    √(1 - 1/φ²) = √(1 - 0.382) = √0.618 ≈ 0.786
  76
  77    This is too small compared to observed 0.881. -/
  78noncomputable def hypothesis1 : ℝ := Real.sqrt (1 - 1/phi^2)
  79
  80/-- Hypothesis 2: cos(θ_W) = (φ + 1) / (φ + 2)
  81
  82    (1.618 + 1) / (1.618 + 2) = 2.618 / 3.618 ≈ 0.724
  83
  84    This is also too small. -/
  85noncomputable def hypothesis2 : ℝ := (phi + 1) / (phi + 2)
  86
  87/-- Hypothesis 3: cos(θ_W) = φ / √(φ² + 1)
  88
  89    1.618 / √(2.618 + 1) = 1.618 / 1.902 ≈ 0.851
  90
  91    Getting closer! -/
  92noncomputable def hypothesis3 : ℝ := phi / Real.sqrt (phi^2 + 1)
  93
  94/-- Hypothesis 4: cos(θ_W) = √(1 - 1/(φ² + 1))