148 lines
5.7 KiB
Python
148 lines
5.7 KiB
Python
#!/usr/bin/env python3
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"""
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Nuclear Scale Geometric Dominance Verification
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This script demonstrates the corrected calculation showing that geometric binding
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dominates over QCD confinement at nuclear scales when proper nuclear radii are used.
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Key insight from human collaborator: Use actual nuclear dimensions (~1 fm)
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rather than scaled atomic radii.
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Author: Andre Heinecke & AI Collaborators
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Date: June 2025
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License: CC BY-SA 4.0
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"""
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import numpy as np
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def verify_nuclear_geometric_dominance():
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"""Verify geometric dominance at nuclear scales with proper radii"""
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print("NUCLEAR SCALE GEOMETRIC DOMINANCE VERIFICATION")
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print("="*60)
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print("Testing F = ℏ²/(γm_q r³) vs F = σr at nuclear scales")
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print("Key insight: Use proper nuclear radii (~1 fm), not scaled atomic radii")
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print()
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# Physical constants (from scipy.constants or CODATA)
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hbar = 1.054571817e-34 # J·s (reduced Planck constant)
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c = 299792458 # m/s (speed of light, exact)
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eV_to_J = 1.602176634e-19 # J/eV (exact)
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# Nuclear parameters (PDG 2022)
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m_up_MeV = 2.16 # MeV/c² (up quark current mass)
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m_down_MeV = 4.67 # MeV/c² (down quark current mass)
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m_q_avg_MeV = (m_up_MeV + m_down_MeV) / 2
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m_q_kg = m_q_avg_MeV * 1e6 * eV_to_J / c**2 # Convert to kg
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# QCD string tension (Lattice QCD, FLAG 2021)
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sigma_GeV2_fm = 0.18 # GeV²/fm
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sigma_SI = sigma_GeV2_fm * (1e9 * eV_to_J)**2 / 1e-15 # Convert to N
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print("PARAMETERS:")
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print(f" Average light quark mass: {m_q_avg_MeV:.2f} MeV/c²")
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print(f" Quark mass in kg: {m_q_kg:.2e} kg")
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print(f" QCD string tension: {sigma_GeV2_fm:.2f} GeV²/fm")
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print(f" String tension in SI: {sigma_SI:.2e} N")
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print()
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# Test at different nuclear scales
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radii_fm = np.array([0.1, 0.5, 1.0, 2.0, 3.0]) # fm
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print("FORCE COMPARISON AT NUCLEAR SCALES:")
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print(f"{'r (fm)':<8} {'F_geom (N)':<12} {'F_conf (N)':<12} {'Ratio':<10} {'Dominant':<10}")
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print("-" * 60)
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for r_fm in radii_fm:
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r_m = r_fm * 1e-15 # Convert fm to meters
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# Geometric force: F = ℏ²/(m_q r³)
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F_geometric = hbar**2 / (m_q_kg * r_m**3)
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# Confinement force: F = σr
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F_confinement = sigma_SI * r_m
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# Calculate ratio
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ratio = F_geometric / F_confinement
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dominant = "Geometric" if ratio > 1 else "Confinement"
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print(f"{r_fm:<8.1f} {F_geometric:<12.2e} {F_confinement:<12.2e} {ratio:<10.1e} {dominant:<10}")
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print()
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# Calculate crossover point
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# F_geom = F_conf when ℏ²/(m_q r³) = σr
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# Solving: r⁴ = ℏ²/(m_q σ)
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r_crossover_m = (hbar**2 / (m_q_kg * sigma_SI))**(1/4)
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r_crossover_fm = r_crossover_m * 1e15
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print("CROSSOVER ANALYSIS:")
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print(f" Crossover radius: {r_crossover_fm:.1f} fm")
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print(f" Crossover radius: {r_crossover_m:.2e} m")
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print()
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if r_crossover_fm > 1000:
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print(" ⚠️ Crossover at unphysically large scale!")
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print(" This means geometric binding dominates at ALL nuclear scales")
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elif r_crossover_fm > 10:
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print(" ⚠️ Crossover beyond typical nuclear scales")
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print(" Geometric binding dominates within nucleons")
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else:
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print(" ✓ Crossover within nuclear range")
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print(" Both effects important at nuclear scales")
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print()
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# Test at typical nucleon size
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r_nucleon_fm = 0.8 # fm (proton charge radius)
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r_nucleon_m = r_nucleon_fm * 1e-15
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F_geom_nucleon = hbar**2 / (m_q_kg * r_nucleon_m**3)
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F_conf_nucleon = sigma_SI * r_nucleon_m
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ratio_nucleon = F_geom_nucleon / F_conf_nucleon
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print("AT TYPICAL NUCLEON SIZE:")
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print(f" Nucleon radius: {r_nucleon_fm} fm")
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print(f" Geometric force: {F_geom_nucleon:.2e} N")
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print(f" Confinement force: {F_conf_nucleon:.2e} N")
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print(f" Geometric/Confinement ratio: {ratio_nucleon:.1e}")
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print()
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if ratio_nucleon > 1e10:
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print(" 🚀 GEOMETRIC BINDING DOMINATES BY 10+ ORDERS OF MAGNITUDE!")
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print(" This suggests the 'strong force' may actually be geometric binding")
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print(" with confinement as a boundary condition preventing escape")
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elif ratio_nucleon > 100:
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print(" ✓ Geometric binding clearly dominates")
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print(" Confinement acts as secondary effect")
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else:
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print(" ≈ Both effects are comparable")
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print(" True competition between geometric and confining forces")
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print()
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print("IMPLICATIONS:")
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print("1. Geometric binding F = ℏ²/(m_q r³) dominates at nuclear scales")
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print("2. QCD confinement F = σr prevents escape but doesn't provide primary binding")
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print("3. 'Strong force' may be same geometric principle as electromagnetic force")
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print("4. Force hierarchy (strong >> EM) explained by geometric scaling r⁻³")
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print("5. All binding forces could be unified as centripetal requirements")
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return {
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'crossover_fm': r_crossover_fm,
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'nucleon_ratio': ratio_nucleon,
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'geometric_dominates': ratio_nucleon > 1e3
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}
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if __name__ == "__main__":
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result = verify_nuclear_geometric_dominance()
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print("\n" + "="*60)
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print("BOTTOM LINE:")
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if result['geometric_dominates']:
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print("🎯 Geometric binding dominates at nuclear scales!")
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print(" The geometric principle may be truly universal")
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print(" from quarks to planets via the same F = ℏ²/(γmr³)")
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else:
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print("📊 Mixed regime - both geometric and confinement important")
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print(" Nuclear physics requires careful treatment of both effects")
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