Diósi–Penrose Collapse Time ~25 ms and ~2×10¹⁰ Tubulins per Superposition — E8 Intelligence Research

FINDING: Diósi–Penrose objective reduction gives gravitational self-energy collapse time τ = ℏ/E_g, with tubulin dimer E_g ≈ 4.2×10⁻³³ J yielding τ ≈ 25 ms, and N = E_g/E_tubulin ≈ 2×10¹⁰ tubulins per coherent superposition. MATH: - Core collapse time: τ = ℏ/E_g (Penrose) ; Diósi form τ ≈ ℏ/E_g with E_g = gravitational self-energy of the mass-density difference between superposed states. - E_g = (G/2)∫∫ [ρ₁(r) − ρ₂(r)][ρ₁(r′) − ρ₂(r′)] / |r − r′| d³r d³r′ (Newtonian self-energy of the difference distribution). - Given values: ℏ = 1.0546×10⁻³⁴ J·s; E_g = 4.2×10⁻³³ J ⇒ τ = 1.05×10⁻³⁴ / 4.2×10⁻³³ ≈ 2.5×10⁻² s = 25 ms. - Tubulin count: N = E_g / E_tubulin ≈ 2×10¹⁰ (order-of-magnitude estimate of dimers needed for 25 ms collapse). - Consistency check: τ ∝ 1/E_g ∝ 1/(G m² N² / R) ⇒ τ ∝ R/(G m² N²). For fixed τ, N ∝ √(R/(G m² τ)). - GRW comparison: GRW rate λ ≈ 10⁻¹⁶ s⁻¹ per nucleon; DP is mass/energy-based, not particle-count-based — different scaling law (E_g ~ N² vs GRW ~ N). CONNECTION: Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com