matter_gravity_coherence.py

#!/usr/bin/env python3
"""
Matter-Gravity Coherence: Quantum Entanglement-Based Energy Extraction with LV
==============================================================================

This module implements quantum coherence-based energy extraction through
matter-gravity entanglement, enhanced with Lorentz-violating modifications.
The system exploits quantum coherence preservation in curved spacetime when
LV parameters exceed experimental bounds.

Key Features:
1. Quantum entanglement between matter and gravitational fields
2. Coherence preservation in curved spacetime
3. LV-enhanced entanglement stability
4. Macroscopic quantum coherence effects
5. Energy extraction through decoherence control

Physics:
- Based on matter-wave interferometry and gravitational decoherence
- Incorporates Lorentz violation in quantum field coupling
- Exploits coherence-energy uncertainty relations
- LV suppresses decoherence when μ, α, β > experimental bounds

Author: Quantum Geometry Hidden Sector Framework
"""

import numpy as np
from scipy.special import hermite, factorial, erf, dawsn
from scipy import integrate, optimize, linalg
from typing import Dict, List, Tuple, Optional, Union, Callable
from dataclasses import dataclass
import matplotlib.pyplot as plt

@dataclass
class MatterGravityConfig:
    """Configuration for matter-gravity coherence calculations."""
    
    # Quantum system parameters
    particle_mass: float = 1e-26      # Test particle mass (kg)
    coherence_length: float = 1e-6    # Initial coherence length (m)
    coherence_time: float = 1e-3      # Initial coherence time (s)
    
    # Gravitational parameters
    gravitational_gradient: float = 1e-6  # Gravitational gradient (m/s²/m)
    spacetime_curvature: float = 1e-10    # Spacetime curvature (m⁻²)
    gravitational_coupling: float = 1e-15 # Matter-gravity coupling
    
    # Entanglement parameters
    entanglement_depth: int = 10       # Number of entangled particles
    entanglement_fidelity: float = 0.95 # Initial entanglement fidelity
    decoherence_rate: float = 1e3      # Base decoherence rate (s⁻¹)
    
    # LV parameters
    mu_lv: float = 1e-18               # CPT-violating coefficient
    alpha_lv: float = 1e-15            # Lorentz violation in matter fields
    beta_lv: float = 1e-12             # Gravitational LV coupling
    
    # Energy extraction parameters
    extraction_efficiency: float = 1e-6  # Energy extraction efficiency
    extraction_volume: float = 1e-6      # Extraction volume (m³)
    extraction_time: float = 1.0         # Extraction time (s)
    
    # Computational parameters
    time_steps: int = 1000             # Time evolution steps
    spatial_grid_points: int = 100     # Spatial discretization
    evolution_time: float = 1.0        # Total evolution time (s)

class MatterGravityCoherence:
    """
    Matter-gravity coherence system with Lorentz violation enhancements.
    
    This class implements energy extraction through quantum coherence preservation
    in matter-gravity entangled systems with LV modifications.
    """
    
    def __init__(self, config: MatterGravityConfig):
        self.config = config
        self.experimental_bounds = {
            'mu_lv': 1e-19,      # Current CPT violation bounds
            'alpha_lv': 1e-16,   # Lorentz violation bounds
            'beta_lv': 1e-13     # Gravitational LV bounds
        }
        
        # Physical constants
        self.hbar = 1.055e-34  # J⋅s
        self.c = 3e8           # m/s
        self.G = 6.674e-11     # m³/kg⋅s²
        self.k_B = 1.381e-23   # J/K
        
    def is_pathway_active(self) -> bool:
        """Check if LV parameters exceed experimental bounds to activate pathway."""
        return (self.config.mu_lv > self.experimental_bounds['mu_lv'] or
                self.config.alpha_lv > self.experimental_bounds['alpha_lv'] or
                self.config.beta_lv > self.experimental_bounds['beta_lv'])
    
    def lv_coherence_enhancement(self, time: float) -> float:
        """
        Calculate LV enhancement factor for coherence preservation.
        
        Parameters:
        -----------
        time : float
            Evolution time (s)
            
        Returns:
        --------
        float
            Coherence enhancement factor from LV effects
        """
        # Energy scale from coherence time
        energy_scale = self.hbar / time if time > 0 else self.hbar / 1e-10
        
        # LV-modified decoherence suppression
        mu_suppression = self.config.mu_lv * (energy_scale / self.hbar)**2
        alpha_suppression = self.config.alpha_lv * (energy_scale / self.hbar)
        beta_suppression = self.config.beta_lv * np.sqrt(energy_scale / self.hbar)
        
        # Total suppression factor (reduces decoherence)
        suppression = 1.0 + mu_suppression + alpha_suppression + beta_suppression
        
        return 1.0 / suppression  # Lower values mean better coherence preservation
    
    def gravitational_decoherence_rate(self, time: float) -> float:
        """
        Calculate gravitational decoherence rate with LV modifications.
        
        Parameters:
        -----------
        time : float
            Evolution time (s)
            
        Returns:
        --------
        float
            Modified decoherence rate (s⁻¹)
        """
        # Base decoherence from gravitational coupling
        base_rate = self.config.decoherence_rate
        
        # Gravitational enhancement
        gravitational_factor = (self.config.gravitational_gradient * 
                              self.config.coherence_length / self.c**2)**2
        
        # LV coherence enhancement (suppresses decoherence)
        lv_enhancement = self.lv_coherence_enhancement(time)
        
        return base_rate * gravitational_factor * lv_enhancement
    
    def entanglement_fidelity_evolution(self, time: float) -> float:
        """
        Calculate entanglement fidelity evolution with time.
        
        Parameters:
        -----------
        time : float
            Evolution time (s)
            
        Returns:
        --------
        float
            Entanglement fidelity at time t
        """
        # Decoherence rate
        gamma = self.gravitational_decoherence_rate(time)
        
        # Fidelity decay with LV protection
        decay_factor = np.exp(-gamma * time)
        
        # Multi-particle entanglement scaling
        n_particles = self.config.entanglement_depth
        scaling_factor = decay_factor**(n_particles - 1)
        
        return self.config.entanglement_fidelity * scaling_factor
    
    def coherence_length_evolution(self, time: float) -> float:
        """
        Calculate coherence length evolution with gravitational effects.
        
        Parameters:
        -----------
        time : float
            Evolution time (s)
            
        Returns:
        --------
        float
            Coherence length at time t (m)
        """
        # Gravitational spreading
        gravitational_spreading = 0.5 * self.config.gravitational_gradient * time**2
        
        # LV-modified spreading (can be suppressed or enhanced)
        lv_factor = 1.0 / self.lv_coherence_enhancement(time)
        
        # Total coherence length
        total_spreading = gravitational_spreading * lv_factor
        coherence_length = self.config.coherence_length + total_spreading
        
        return max(coherence_length, 1e-12)  # Minimum coherence length
    
    def quantum_fisher_information(self, time: float) -> float:
        """
        Calculate quantum Fisher information for coherence estimation.
        
        Parameters:
        -----------
        time : float
            Evolution time (s)
            
        Returns:
        --------
        float
            Quantum Fisher information
        """
        # Fidelity and coherence parameters
        fidelity = self.entanglement_fidelity_evolution(time)
        coherence_length = self.coherence_length_evolution(time)
        
        # Fisher information scaling
        n_particles = self.config.entanglement_depth
        
        # Quantum Fisher information with Heisenberg scaling
        fisher_info = n_particles**2 * fidelity / (coherence_length**2 + 1e-20)
        
        return fisher_info
    
    def coherence_energy_uncertainty(self, time: float) -> float:
        """
        Calculate energy uncertainty from coherence preservation.
        
        Parameters:
        -----------
        time : float
            Evolution time (s)
            
        Returns:
        --------
        float
            Energy uncertainty (J)
        """
        # Coherence time with LV enhancement
        coherence_time = self.config.coherence_time / self.lv_coherence_enhancement(time)
        
        # Time-energy uncertainty relation
        energy_uncertainty = self.hbar / (2 * coherence_time)
        
        return energy_uncertainty
    
    def extractable_energy_density(self, time: float) -> float:
        """
        Calculate extractable energy density from coherence effects.
        
        Parameters:
        -----------
        time : float
            Evolution time (s)
            
        Returns:
        --------
        float
            Energy density (J/m³)
        """
        if not self.is_pathway_active():
            return 0.0
        
        # Energy uncertainty
        energy_uncertainty = self.coherence_energy_uncertainty(time)
        
        # Coherence volume
        coherence_length = self.coherence_length_evolution(time)
        coherence_volume = coherence_length**3
        
        # Number density of coherent particles
        particle_density = self.config.entanglement_depth / coherence_volume
        
        # Extractable energy density
        energy_density = particle_density * energy_uncertainty * self.config.extraction_efficiency
        
        return energy_density
    
    def total_extractable_power(self, volume: float = None) -> float:
        """
        Calculate total extractable power from matter-gravity coherence.
        
        Parameters:
        -----------
        volume : Optional[float]
            Extraction volume (m³)
            
        Returns:
        --------
        float
            Total extractable power (Watts)
        """
        if not self.is_pathway_active():
            return 0.0
        
        if volume is None:
            volume = self.config.extraction_volume
        
        # Time-averaged energy density
        def integrand(t):
            return self.extractable_energy_density(t)
        
        # Integrate over extraction time
        avg_energy_density, _ = integrate.quad(
            integrand,
            0,
            self.config.extraction_time,
            limit=100
        )
        avg_energy_density /= self.config.extraction_time
        
        # Power = Energy density × Volume / Time
        power = avg_energy_density * volume / self.config.extraction_time
        
        return power
    
    def decoherence_control_efficiency(self, time: float) -> float:
        """
        Calculate efficiency of decoherence control mechanisms.
        
        Parameters:
        -----------
        time : float
            Evolution time (s)
            
        Returns:
        --------
        float
            Control efficiency (0-1)
        """
        # LV-enhanced coherence preservation
        lv_enhancement = 1.0 / self.lv_coherence_enhancement(time)
        
        # Fidelity maintenance
        fidelity = self.entanglement_fidelity_evolution(time)
        
        # Combined efficiency
        efficiency = fidelity * min(lv_enhancement, 1.0)
        
        return efficiency
    
    def optimize_coherence_parameters(self, target_power: float = 1e-15) -> Dict[str, float]:
        """
        Optimize coherence parameters for target power extraction.
        
        Parameters:
        -----------
        target_power : float
            Target power extraction (Watts)
            
        Returns:
        --------
        Dict[str, float]
            Optimized parameters
        """
        def objective(params):
            coherence_length, coherence_time, coupling = params
            
            # Update configuration
            old_length = self.config.coherence_length
            old_time = self.config.coherence_time
            old_coupling = self.config.gravitational_coupling
            
            self.config.coherence_length = coherence_length
            self.config.coherence_time = coherence_time
            self.config.gravitational_coupling = coupling
            
            # Calculate power
            power = self.total_extractable_power()
            
            # Restore configuration
            self.config.coherence_length = old_length
            self.config.coherence_time = old_time
            self.config.gravitational_coupling = old_coupling
            
            return abs(power - target_power)
        
        # Optimization bounds
        bounds = [
            (1e-9, 1e-3),    # coherence_length
            (1e-6, 1e0),     # coherence_time
            (1e-18, 1e-12)   # gravitational_coupling
        ]
        
        # Initial guess
        x0 = [self.config.coherence_length, self.config.coherence_time, 
              self.config.gravitational_coupling]
        
        # Optimize
        result = optimize.minimize(objective, x0, bounds=bounds, method='L-BFGS-B')
        
        return {
            'coherence_length': result.x[0],
            'coherence_time': result.x[1],
            'gravitational_coupling': result.x[2],
            'optimized_power': target_power,
            'success': result.success
        }
    
    def coherence_dynamics_simulation(self) -> Dict[str, np.ndarray]:
        """
        Simulate coherence dynamics over time.
        
        Returns:
        --------
        Dict[str, np.ndarray]
            Simulation results
        """
        # Time array
        times = np.linspace(0, self.config.evolution_time, self.config.time_steps)
        
        # Calculate dynamics
        fidelity_evolution = []
        coherence_lengths = []
        energy_densities = []
        fisher_information = []
        control_efficiency = []
        
        for t in times:
            fidelity_evolution.append(self.entanglement_fidelity_evolution(t))
            coherence_lengths.append(self.coherence_length_evolution(t))
            energy_densities.append(self.extractable_energy_density(t))
            fisher_information.append(self.quantum_fisher_information(t))
            control_efficiency.append(self.decoherence_control_efficiency(t))
        
        return {
            'times': times,
            'fidelity_evolution': np.array(fidelity_evolution),
            'coherence_lengths': np.array(coherence_lengths),
            'energy_densities': np.array(energy_densities),
            'fisher_information': np.array(fisher_information),
            'control_efficiency': np.array(control_efficiency)
        }
    
    def visualize_coherence_dynamics(self, save_path: Optional[str] = None):
        """
        Visualize matter-gravity coherence dynamics.
        
        Parameters:
        -----------
        save_path : Optional[str]
            Path to save the plot
        """
        # Get simulation data
        dynamics = self.coherence_dynamics_simulation()
        
        fig, ((ax1, ax2), (ax3, ax4)) = plt.subplots(2, 2, figsize=(12, 10))
        
        # Entanglement fidelity evolution
        ax1.plot(dynamics['times'], dynamics['fidelity_evolution'], 'b-', linewidth=2)
        ax1.set_xlabel('Time (s)')
        ax1.set_ylabel('Entanglement Fidelity')
        ax1.set_title('Fidelity Evolution with LV Enhancement')
        ax1.grid(True, alpha=0.3)
        ax1.set_ylim(0, 1)
        
        # Coherence length evolution
        ax2.semilogy(dynamics['times'], dynamics['coherence_lengths'], 'r-', linewidth=2)
        ax2.set_xlabel('Time (s)')
        ax2.set_ylabel('Coherence Length (m)')
        ax2.set_title('Coherence Length Evolution')
        ax2.grid(True, alpha=0.3)
        
        # Energy density evolution
        ax3.semilogy(dynamics['times'], dynamics['energy_densities'], 'g-', linewidth=2)
        ax3.set_xlabel('Time (s)')
        ax3.set_ylabel('Energy Density (J/m³)')
        ax3.set_title('Extractable Energy Density')
        ax3.grid(True, alpha=0.3)
        
        # Quantum Fisher information
        ax4.semilogy(dynamics['times'], dynamics['fisher_information'], 'm-', linewidth=2)
        ax4.set_xlabel('Time (s)')
        ax4.set_ylabel('Quantum Fisher Information')
        ax4.set_title('Coherence Estimation Precision')
        ax4.grid(True, alpha=0.3)
        
        plt.tight_layout()
        
        if save_path:
            plt.savefig(save_path, dpi=300, bbox_inches='tight')
        plt.show()
    
    def generate_report(self) -> Dict[str, Union[float, bool, str]]:
        """
        Generate comprehensive analysis report.
        
        Returns:
        --------
        Dict[str, Union[float, bool, str]]
            Analysis report
        """
        # Dynamics simulation
        dynamics = self.coherence_dynamics_simulation()
        
        # Time-averaged quantities
        avg_fidelity = np.mean(dynamics['fidelity_evolution'])
        avg_coherence_length = np.mean(dynamics['coherence_lengths'])
        avg_energy_density = np.mean(dynamics['energy_densities'])
        
        report = {
            'pathway_active': self.is_pathway_active(),
            'total_extractable_power': self.total_extractable_power(),
            'lv_parameters': {
                'mu_lv': self.config.mu_lv,
                'alpha_lv': self.config.alpha_lv,
                'beta_lv': self.config.beta_lv
            },
            'experimental_bounds': self.experimental_bounds,
            'coherence_configuration': {
                'particle_mass': self.config.particle_mass,
                'initial_coherence_length': self.config.coherence_length,
                'initial_coherence_time': self.config.coherence_time,
                'entanglement_depth': self.config.entanglement_depth,
                'gravitational_coupling': self.config.gravitational_coupling
            },
            'average_fidelity': avg_fidelity,
            'average_coherence_length': avg_coherence_length,
            'average_energy_density': avg_energy_density,
            'lv_coherence_enhancement': self.lv_coherence_enhancement(self.config.extraction_time),
            'decoherence_control_efficiency': self.decoherence_control_efficiency(self.config.extraction_time),
            'quantum_fisher_information': self.quantum_fisher_information(self.config.extraction_time)
        }
        
        return report

def demo_matter_gravity_coherence():
    """Demonstrate matter-gravity coherence functionality."""
    print("=== Matter-Gravity Coherence Demo ===")
    
    # Create configuration with LV parameters above bounds
    config = MatterGravityConfig(
        mu_lv=1e-18,     # Above experimental bound
        alpha_lv=1e-15,  # Above experimental bound
        beta_lv=1e-12,   # Above experimental bound
        particle_mass=1e-26,
        coherence_length=1e-6,
        coherence_time=1e-3,
        entanglement_depth=10,
        gravitational_coupling=1e-15
    )
    
    # Initialize coherence system
    coherence_system = MatterGravityCoherence(config)
    
    # Generate report
    report = coherence_system.generate_report()
    
    print(f"Pathway Active: {report['pathway_active']}")
    print(f"Total Extractable Power: {report['total_extractable_power']:.2e} W")
    print(f"Average Fidelity: {report['average_fidelity']:.3f}")
    print(f"Average Coherence Length: {report['average_coherence_length']:.2e} m")
    print(f"Average Energy Density: {report['average_energy_density']:.2e} J/m³")
    print(f"LV Coherence Enhancement: {report['lv_coherence_enhancement']:.3f}")
    
    # Optimization
    print("\n=== Parameter Optimization ===")
    optimal = coherence_system.optimize_coherence_parameters(target_power=1e-15)
    print(f"Optimization Success: {optimal['success']}")
    print(f"Optimal Coherence Length: {optimal['coherence_length']:.2e} m")
    print(f"Optimal Coherence Time: {optimal['coherence_time']:.2e} s")
    print(f"Optimal Gravitational Coupling: {optimal['gravitational_coupling']:.2e}")
    
    # Dynamics simulation
    print("\n=== Coherence Dynamics ===")
    dynamics = coherence_system.coherence_dynamics_simulation()
    print(f"Final Fidelity: {dynamics['fidelity_evolution'][-1]:.3f}")
    print(f"Final Coherence Length: {dynamics['coherence_lengths'][-1]:.2e} m")
    print(f"Final Energy Density: {dynamics['energy_densities'][-1]:.2e} J/m³")
    
    # Visualization
    print("\n=== Generating Visualization ===")
    coherence_system.visualize_coherence_dynamics('matter_gravity_coherence_analysis.png')
    
    return coherence_system, report

if __name__ == "__main__":
    demo_matter_gravity_coherence()