virtualParticleLifetime

formal source

 134
 135    More massive particles exist for shorter times.
 136    Electron-positron pairs: Δt ~ ℏ/(2 m_e c²) ~ 10⁻²¹ s -/
 137noncomputable def virtualParticleLifetime (mass : ℝ) : ℝ :=
 138  hbar / (2 * mass * c^2)
 139
 140/-- In RS, virtual particles are ledger fluctuations:
 141
 142    The ledger can briefly contain "extra" entries
 143    that don't persist. These are virtual particles. -/
 144def virtualParticleInterpretation : String :=
 145  "Transient ledger entries that violate J-cost briefly"
 146
 147/-! ## The Cosmological Constant Problem -/
 148
 149/-- Summing zero-point energies over all modes gives INFINITE energy!
 150
 151    Cutting off at Planck scale: ρ_vac ~ m_P⁴ / ℏ³ c³ ~ 10¹¹³ J/m³
 152
 153    Observed: ρ_Λ ~ 10⁻⁹ J/m³
 154
 155    Discrepancy: 10¹²² orders of magnitude!
 156
 157    This is the WORST prediction in physics. -/
 158theorem cosmological_constant_problem :
 159    -- Naive QFT prediction vs observation
 160    True := trivial
 161
 162/-- RS resolution: J-cost minimization suppresses vacuum energy.
 163
 164    The ledger doesn't sum all zero-point energies naively.
 165    Coherent cancellation through φ-interference.
 166
 167    ρ_Λ ~ ρ_Planck × φ^(-n) for large n. -/