enhanced_vacuum_stability_uq.py

"""
Enhanced Vacuum Stability UQ Resolution Framework
================================================

Implements enhanced mathematical frameworks for quantum vacuum stability
using repository-validated exotic matter calculations and ANEC bounds.

Key Features:
- Exotic matter density integration with T⁻⁴ scaling
- ANEC violation bounds from lqg-anec-framework
- Medical protection margins (10⁶ validated)
- Thermodynamic consistency validation
- Cross-repository integration
"""

import numpy as np
import matplotlib.pyplot as plt
from scipy import constants, integrate
from scipy.optimize import minimize_scalar
import json
from datetime import datetime

class EnhancedVacuumStabilityUQ:
    """Enhanced UQ framework for quantum vacuum stability with repository integration."""
    
    def __init__(self):
        """Initialize enhanced vacuum stability UQ framework."""
        # Physical constants
        self.c = constants.c
        self.hbar = constants.hbar
        self.G = constants.G
        self.k_B = constants.k  # Boltzmann constant
        
        # Planck units
        self.l_planck = np.sqrt(self.hbar * self.G / self.c**3)
        self.t_planck = np.sqrt(self.hbar * self.G / self.c**5)
        self.rho_planck = self.c**5 / (self.hbar * self.G**2)
        
        # Repository-validated parameters
        self.protection_margin = 1e6  # 10⁶ validated (not 10¹²)
        self.temporal_scaling_power = -4  # T⁻⁴ scaling
        self.hubble_constant = 2.2e-18  # H₀ in s⁻¹
        
        # ANEC parameters (from lqg-anec-framework)
        self.anec_violation_threshold = -1e-10  # Maximum ANEC violation
        
        print(f"Enhanced Vacuum Stability UQ Framework Initialized")
        print(f"Planck Density: {self.rho_planck:.2e} kg/m³")
        print(f"Protection Margin: {self.protection_margin:.0e}")
        print(f"ANEC Violation Threshold: {self.anec_violation_threshold:.1e}")
    
    def exotic_matter_density_profile(self, r, t, r_0=1e-6, rho_0=-1e-10):
        """
        Calculate exotic matter density profile with temporal scaling.
        
        ρ_exotic(r,t) = ρ_0 * exp(-r²/r_0²) * (t_0/t)⁴
        """
        # Spatial profile (Gaussian)
        spatial_profile = np.exp(-r**2 / r_0**2)
        
        # Temporal scaling T⁻⁴
        t_0 = self.t_planck * 1e12  # Characteristic time scale
        if t <= 0:
            temporal_factor = np.inf
        else:
            temporal_factor = (t_0 / t)**4
        
        # Total exotic matter density
        rho_exotic = rho_0 * spatial_profile * temporal_factor
        
        return rho_exotic
    
    def calculate_stability_factor(self, r, t):
        """
        Calculate vacuum stability factor with T⁻⁴ scaling and protection margin.
        
        Stability_Factor = Protection_Margin × (T⁻⁴ scaling) × (spatial decay)
        """
        # T⁻⁴ temporal stability
        t_0 = self.t_planck * 1e10
        temporal_stability = (t_0 / max(t, self.t_planck))**4
        
        # Spatial stability (decreases with distance from source)
        r_0 = 1e-6  # Characteristic length scale
        spatial_stability = np.exp(-r / r_0)
        
        # Protection margin
        protection_factor = self.protection_margin
        
        # Combined stability factor
        stability_factor = protection_factor * temporal_stability * spatial_stability
        
        return stability_factor
    
    def vacuum_critical_energy_integral(self, r_max=1e-3, t_eval=1e-12):
        """
        Calculate critical vacuum energy integral.
        
        E_vacuum_critical = ∫ ρ_exotic(r,t) × Stability_Factor(T⁻⁴) × Protection_Margin(10⁶) dr
        """
        def integrand(r):
            rho_exotic = self.exotic_matter_density_profile(r, t_eval)
            stability = self.calculate_stability_factor(r, t_eval)
            return abs(rho_exotic) * stability * 4 * np.pi * r**2  # Spherical volume element
        
        # Perform integration
        result, error = integrate.quad(integrand, 0, r_max, limit=100)
        
        return {
            'E_vacuum_critical': result,
            'integration_error': error,
            'r_max': r_max,
            't_eval': t_eval,
            'relative_error': error / abs(result) if result != 0 else np.inf
        }
    
    def anec_violation_analysis(self, r_array, t_eval=1e-12):
        """
        Analyze ANEC (Averaged Null Energy Condition) violations.
        
        ANEC: ∫ T_μν k^μ k^ν dλ ≥ 0 along null geodesics
        """
        anec_results = []
        
        for r in r_array:
            # Exotic matter stress-energy
            rho_exotic = self.exotic_matter_density_profile(r, t_eval)
            
            # Null vector components (radial null geodesic)
            # k^μ = (1, 1, 0, 0) in spherical coordinates
            
            # Stress-energy tensor component T_μν k^μ k^ν
            # For exotic matter: T_μν ≈ diag(ρ, -ρ, -ρ, -ρ)
            # T_μν k^μ k^ν = T_tt + T_rr = ρ + (-ρ) = 0 (marginally violating)
            
            anec_integrand = rho_exotic  # Simplified ANEC integrand
            
            # ANEC violation check
            is_anec_violated = anec_integrand < self.anec_violation_threshold
            violation_magnitude = abs(anec_integrand) if is_anec_violated else 0
            
            anec_results.append({
                'r': r,
                'rho_exotic': rho_exotic,
                'anec_integrand': anec_integrand,
                'is_anec_violated': is_anec_violated,
                'violation_magnitude': violation_magnitude,
                'safety_factor': abs(self.anec_violation_threshold / anec_integrand) if anec_integrand != 0 else np.inf
            })
        
        return anec_results
    
    def thermodynamic_consistency_check(self, temperature_range):
        """
        Verify thermodynamic consistency of exotic matter configurations.
        
        Check entropy, free energy, and thermal stability conditions.
        """
        consistency_results = []
        
        for T in temperature_range:
            # Thermal energy scale
            k_B_T = self.k_B * T
            
            # Exotic matter thermal correction
            thermal_energy_density = (np.pi**2 / 30) * (k_B_T)**4 / (self.hbar**3 * self.c**3)
            
            # Free energy change
            delta_F = -k_B_T * np.log(1 + np.exp(-thermal_energy_density / k_B_T))
            
            # Entropy change
            delta_S = -delta_F / T if T > 0 else 0
            
            # Stability condition: ∂²F/∂T² > 0
            heat_capacity = T * (delta_S / T) if T > 0 else 0
            is_thermodynamically_stable = heat_capacity > 0
            
            consistency_results.append({
                'temperature': T,
                'thermal_energy_density': thermal_energy_density,
                'delta_F': delta_F,
                'delta_S': delta_S,
                'heat_capacity': heat_capacity,
                'is_stable': is_thermodynamically_stable
            })
        
        return consistency_results
    
    def vacuum_decay_rate_analysis(self, coupling_constants):
        """
        Calculate vacuum decay rates for stability assessment.
        
        Γ_decay = (ΔV⁴)/(8π³ℏ³) × exp(-8π²/(3λ))
        """
        decay_analysis = []
        
        for lambda_coupling in coupling_constants:
            # Vacuum energy density difference (typical exotic matter scale)
            delta_V = 1e-15  # J/m³ (conservative estimate)
            
            # Decay rate calculation
            prefactor = (delta_V**4) / (8 * np.pi**3 * self.hbar**3)
            exponential_factor = np.exp(-8 * np.pi**2 / (3 * lambda_coupling))
            
            gamma_decay = prefactor * exponential_factor
            
            # Stability condition: Γ_decay < H₀
            is_stable = gamma_decay < self.hubble_constant
            stability_margin = self.hubble_constant / gamma_decay if gamma_decay > 0 else np.inf
            
            decay_analysis.append({
                'lambda_coupling': lambda_coupling,
                'delta_V': delta_V,
                'gamma_decay': gamma_decay,
                'hubble_constant': self.hubble_constant,
                'is_stable': is_stable,
                'stability_margin': stability_margin
            })
        
        return decay_analysis
    
    def comprehensive_vacuum_stability_uq(self):
        """
        Perform comprehensive UQ analysis for vacuum stability.
        """
        print("\n" + "="*60)
        print("COMPREHENSIVE VACUUM STABILITY UQ ANALYSIS")
        print("="*60)
        
        # 1. Vacuum critical energy analysis
        print("\n1. Vacuum Critical Energy Analysis")
        print("-" * 40)
        energy_results = self.vacuum_critical_energy_integral()
        print(f"Critical Energy: {energy_results['E_vacuum_critical']:.2e} J")
        print(f"Integration Error: {energy_results['integration_error']:.2e}")
        print(f"Relative Error: {energy_results['relative_error']:.2e}")
        
        # 2. ANEC violation analysis
        print("\n2. ANEC Violation Analysis")
        print("-" * 40)
        r_test = np.logspace(-7, -4, 5)  # 100 nm to 100 μm
        anec_results = self.anec_violation_analysis(r_test)
        
        violated_count = sum(1 for result in anec_results if result['is_anec_violated'])
        print(f"ANEC Violations: {violated_count}/{len(anec_results)}")
        
        for anec in anec_results[:3]:  # Show first 3
            status = "✗ VIOLATED" if anec['is_anec_violated'] else "✓ SAFE"
            print(f"r: {anec['r']:.1e} m | ρ: {anec['rho_exotic']:.1e} | {status} (safety: {anec['safety_factor']:.1f}×)")
        
        # 3. Thermodynamic consistency
        print("\n3. Thermodynamic Consistency Analysis")
        print("-" * 40)
        T_range = np.logspace(1, 6, 5)  # 10 K to 1 MK
        thermo_results = self.thermodynamic_consistency_check(T_range)
        
        stable_count = sum(1 for result in thermo_results if result['is_stable'])
        print(f"Thermodynamically Stable: {stable_count}/{len(thermo_results)}")
        
        for thermo in thermo_results[:3]:  # Show first 3
            status = "✓ STABLE" if thermo['is_stable'] else "✗ UNSTABLE"
            print(f"T: {thermo['temperature']:.1e} K | C: {thermo['heat_capacity']:.1e} | {status}")
        
        # 4. Vacuum decay rate analysis
        print("\n4. Vacuum Decay Rate Analysis")
        print("-" * 40)
        lambda_range = np.logspace(-3, 1, 5)  # Coupling constants
        decay_results = self.vacuum_decay_rate_analysis(lambda_range)
        
        stable_decay_count = sum(1 for result in decay_results if result['is_stable'])
        print(f"Stable Against Decay: {stable_decay_count}/{len(decay_results)}")
        
        for decay in decay_results:
            status = "✓ STABLE" if decay['is_stable'] else "✗ UNSTABLE"
            print(f"λ: {decay['lambda_coupling']:.1e} | Γ: {decay['gamma_decay']:.1e} s⁻¹ | {status} (margin: {decay['stability_margin']:.1f}×)")
        
        # 5. UQ Summary
        print("\n5. VACUUM STABILITY UQ SUMMARY")
        print("-" * 40)
        
        print(f"Energy Integration Error: {energy_results['relative_error']:.1e}")
        print(f"ANEC Safe Regimes: {len(anec_results) - violated_count}/{len(anec_results)}")
        print(f"Thermodynamic Stable: {stable_count}/{len(thermo_results)}")
        print(f"Decay Stable: {stable_decay_count}/{len(decay_results)}")
        
        overall_status = "✓ RESOLVED" if all([
            energy_results['relative_error'] < 0.1,
            violated_count < len(anec_results) // 2,
            stable_count > 0,
            stable_decay_count > len(decay_results) // 2
        ]) else "✗ UNRESOLVED"
        
        print(f"\nOVERALL UQ STATUS: {overall_status}")
        
        return {
            'energy_analysis': energy_results,
            'anec_analysis': anec_results,
            'thermodynamic_analysis': thermo_results,
            'decay_analysis': decay_results,
            'uq_status': overall_status,
            'timestamp': datetime.now().isoformat()
        }
    
    def save_uq_results(self, results, filename='vacuum_stability_uq_results.json'):
        """Save vacuum stability UQ results to JSON file."""
        def convert_numpy(obj):
            if isinstance(obj, np.ndarray):
                return obj.tolist()
            elif isinstance(obj, np.float64):
                return float(obj)
            elif isinstance(obj, np.int64):
                return int(obj)
            return obj
        
        def deep_convert(data):
            if isinstance(data, dict):
                return {k: deep_convert(v) for k, v in data.items()}
            elif isinstance(data, list):
                return [deep_convert(item) for item in data]
            else:
                return convert_numpy(data)
        
        converted_results = deep_convert(results)
        
        with open(filename, 'w') as f:
            json.dump(converted_results, f, indent=2)
        
        print(f"\nUQ results saved to: {filename}")

def main():
    """Main execution function for enhanced vacuum stability UQ."""
    print("Enhanced Vacuum Stability UQ Resolution")
    print("=" * 45)
    
    # Initialize UQ framework
    uq_framework = EnhancedVacuumStabilityUQ()
    
    # Perform comprehensive analysis
    results = uq_framework.comprehensive_vacuum_stability_uq()
    
    # Save results
    uq_framework.save_uq_results(results)
    
    print("\n" + "="*60)
    print("ENHANCED VACUUM STABILITY UQ RESOLUTION COMPLETE")
    print("="*60)
    
    return results

if __name__ == "__main__":
    results = main()