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T16-2 φ-引力波理论形式化规范

1. 基础数学对象​

1.1 φ-度量扰动张量​

class PhiMetricPerturbation:
    def __init__(self, dimensions: int = 4):
        self.dimensions = dimensions
        self.phi = (1 + np.sqrt(5)) / 2
        self.components = {}  # (μ,ν) -> PhiNumber
        
    def get_component(self, mu: int, nu: int) -> 'PhiNumber':
        """获取h_{μν}^φ分量"""
        
    def set_component(self, mu: int, nu: int, value: 'PhiNumber'):
        """设置h_{μν}^φ分量，确保对称性"""
        
    def verify_gauge_condition(self) -> bool:
        """验证TT规范条件"""
        
    def verify_no_11_constraint(self) -> bool:
        """验证所有分量满足no-11约束"""

1.2 φ-引力波模式​

class PhiGravitationalWaveMode:
    def __init__(self, fibonacci_index: int):
        self.n = fibonacci_index
        self.F_n = self._fibonacci(fibonacci_index)
        self.amplitude = None  # PhiNumber
        self.polarization = None  # (+, ×)
        self.wave_vector = None  # PhiVector
        self.frequency = None  # PhiNumber
        
    def _fibonacci(self, n: int) -> int:
        """计算第n个Fibonacci数"""
        
    def verify_dispersion_relation(self) -> bool:
        """验证φ-色散关系"""
        
    def compute_energy_density(self) -> 'PhiNumber':
        """计算该模式的能量密度"""

1.3 φ-波函数​

class PhiWaveFunction:
    def __init__(self):
        self.modes = []  # List[PhiGravitationalWaveMode]
        self.phi = (1 + np.sqrt(5)) / 2
        
    def add_mode(self, mode: PhiGravitationalWaveMode):
        """添加一个满足no-11约束的模式"""
        
    def evaluate(self, x: 'PhiVector', t: 'PhiNumber') -> 'PhiMetricPerturbation':
        """计算时空点(x,t)处的度量扰动"""
        
    def fourier_decomposition(self) -> Dict[int, PhiGravitationalWaveMode]:
        """返回Fibonacci模式分解"""

2. 核心算法​

2.1 φ-d'Alembert算子​

class PhiDAlembert:
    def __init__(self, metric: 'PhiMetric'):
        self.metric = metric
        self.phi = (1 + np.sqrt(5)) / 2
        
    def apply(self, field: 'PhiTensor') -> 'PhiTensor':
        """应用φ-d'Alembert算子: □^φ = -1/φ² ∂²/∂t² + ∇²_φ"""
        
    def solve_wave_equation(self, source: 'PhiTensor') -> 'PhiWaveFunction':
        """求解φ-波动方程"""

2.2 模式选择器​

class PhiModeSelector:
    def __init__(self):
        self.allowed_modes = set()  # 满足no-11约束的模式
        self._compute_allowed_modes()
        
    def _compute_allowed_modes(self, max_n: int = 100):
        """计算满足no-11约束的Fibonacci指标"""
        
    def is_allowed(self, n: int) -> bool:
        """检查模式n是否允许"""
        
    def get_mode_spectrum(self) -> List[int]:
        """返回允许的模式谱"""

2.3 φ-能量动量张量​

class PhiGravitationalWaveStressTensor:
    def __init__(self, wave: 'PhiWaveFunction'):
        self.wave = wave
        self.phi = (1 + np.sqrt(5)) / 2
        
    def compute_energy_density(self) -> 'PhiNumber':
        """计算引力波能量密度ρ_GW^φ"""
        
    def compute_energy_flux(self) -> 'PhiVector':
        """计算能量通量S_GW^φ"""
        
    def verify_conservation(self) -> bool:
        """验证φ-能量守恒"""

3. 物理过程​

3.1 双星系统辐射​

class PhiBinarySystem:
    def __init__(self, m1: 'PhiNumber', m2: 'PhiNumber', a: 'PhiNumber'):
        self.m1 = m1  # 质量1
        self.m2 = m2  # 质量2
        self.a = a    # 轨道半径
        self.phi = (1 + np.sqrt(5)) / 2
        
    def orbital_frequency(self) -> 'PhiNumber':
        """计算轨道频率"""
        
    def gravitational_wave_power(self) -> 'PhiNumber':
        """计算引力波辐射功率"""
        
    def chirp_mass(self) -> 'PhiNumber':
        """计算chirp质量"""
        
    def evolution_timescale(self) -> 'PhiNumber':
        """计算演化时标"""

3.2 引力波探测器响应​

class PhiDetectorResponse:
    def __init__(self, arm_length: 'PhiNumber'):
        self.L = arm_length
        self.phi = (1 + np.sqrt(5)) / 2
        
    def strain_response(self, wave: 'PhiWaveFunction', 
                       direction: 'PhiVector') -> 'PhiNumber':
        """计算探测器应变响应"""
        
    def antenna_pattern(self, theta: float, phi: float, psi: float) -> Tuple[float, float]:
        """计算天线方向图F+, F×"""
        
    def sensitivity_curve(self, frequencies: List['PhiNumber']) -> List['PhiNumber']:
        """计算灵敏度曲线"""

3.3 φ-引力波记忆效应​

class PhiMemoryEffect:
    def __init__(self):
        self.phi = (1 + np.sqrt(5)) / 2
        
    def compute_memory(self, wave: 'PhiWaveFunction') -> 'PhiNumber':
        """计算永久应变"""
        
    def verify_quantization(self, memory: 'PhiNumber') -> bool:
        """验证记忆效应的φ-量子化"""

4. 数值方法​

4.1 φ-快速傅里叶变换​

class PhiFFT:
    def __init__(self):
        self.phi = (1 + np.sqrt(5)) / 2
        
    def forward(self, signal: List['PhiNumber']) -> List['PhiNumber']:
        """φ-FFT正变换，只保留允许的Fibonacci模式"""
        
    def inverse(self, spectrum: List['PhiNumber']) -> List['PhiNumber']:
        """φ-FFT逆变换"""
        
    def power_spectrum(self, signal: List['PhiNumber']) -> List['PhiNumber']:
        """计算功率谱"""

4.2 模板匹配​

class PhiTemplateMatching:
    def __init__(self, templates: List['PhiWaveFunction']):
        self.templates = templates
        self.phi = (1 + np.sqrt(5)) / 2
        
    def match_filter(self, data: List['PhiNumber'], 
                    template: 'PhiWaveFunction') -> 'PhiNumber':
        """计算匹配滤波器输出"""
        
    def find_best_match(self, data: List['PhiNumber']) -> Tuple[int, 'PhiNumber']:
        """找到最佳匹配模板"""

5. 验证函数​

5.1 理论一致性检查​

def verify_no_11_constraint(wave: PhiWaveFunction) -> bool:
    """验证波函数所有分量满足no-11约束"""
    
def verify_gauge_invariance(perturbation: PhiMetricPerturbation) -> bool:
    """验证规范不变性"""
    
def verify_energy_conservation(system: PhiBinarySystem) -> bool:
    """验证能量守恒"""

5.2 数值精度检查​

def check_dispersion_relation(mode: PhiGravitationalWaveMode, 
                            tolerance: float = 1e-10) -> bool:
    """检查色散关系的数值精度"""
    
def check_wave_equation_solution(wave: PhiWaveFunction, 
                                source: PhiTensor) -> float:
    """检查波动方程解的误差"""

6. 关键常数​

# 物理常数（φ-单位制）
PHI = (1 + np.sqrt(5)) / 2
G_PHI = 1.0  # φ-引力常数
C_PHI = PHI   # φ-光速

# Fibonacci数列
FIBONACCI_SEQUENCE = [1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ...]

# 允许的模式集合（示例）
ALLOWED_MODES = {1, 3, 4, 6, 8, 9, 11, 12, 14, 16, 17, 19, ...}  # 无连续11

# 探测器参数
LIGO_ARM_LENGTH_PHI = PhiNumber("4000.0")  # 米，φ-编码
MIN_DETECTABLE_STRAIN = PhiNumber("1e-23")

7. 错误处理​

class PhiGravitationalWaveError(Exception):
    """引力波计算错误基类"""
    
class No11ConstraintViolation(PhiGravitationalWaveError):
    """违反no-11约束"""
    
class DispersionRelationError(PhiGravitationalWaveError):
    """色散关系不满足"""
    
class EnergyConservationError(PhiGravitationalWaveError):
    """能量不守恒"""