def
definition
phi
show as:
view math explainer →
open explainer
Generate a durable explainer page for this declaration.
open lean source
IndisputableMonolith.QFT.Decoherence on GitHub at line 58.
browse module
All declarations in this module, on Recognition.
explainer page
depends on
formal source
55noncomputable def tau0_seconds : ℝ := 7.3e-15
56
57/-- Golden ratio (local alias for Constants.phi). -/
58noncomputable def phi : ℝ := Constants.phi
59
60/-- The Gap-45 threshold (approximate). -/
61noncomputable def gap45 : ℝ := 10^45
62
63/-- Planck time in seconds. -/
64noncomputable def tau_planck : ℝ := 5.4e-44
65
66/-- Biological/classical timescale in seconds. -/
67noncomputable def tau_bio : ℝ := 1.0
68
69/-- The logarithmic gap between biological and Planck timescales.
70 log₁₀(tau_bio / tau_planck) ≈ log₁₀(1 / 5.4e-44) ≈ 43.3
71
72 We prove this is approximately 43-44 orders of magnitude. -/
73def timescale_gap_log10 : ℚ := 43 -- Approximate value
74
75/-- **THEOREM**: The gap is between 43 and 45 orders of magnitude. -/
76theorem gap_range : 43 ≤ timescale_gap_log10 ∧ timescale_gap_log10 < 45 := by
77 unfold timescale_gap_log10
78 constructor <;> norm_num
79
80/-! ## Decoherence Time Formula -/
81
82/-- The number of environmental modes coupled to the system. -/
83structure EnvironmentCoupling where
84 /-- Number of modes. -/
85 modes : ℕ
86 /-- Coupling strength (0 to 1). -/
87 strength : ℝ
88 strength_bound : 0 ≤ strength ∧ strength ≤ 1