T17-7 φ-暗物质暗能量定理 - 形式化规范

类型定义

from typing import Dict, List, Tuple, Optional, Protocol
from dataclasses import dataclass
import numpy as np
from phi_arithmetic import PhiReal, PhiComplex

@dataclass
class DarkEnergyState:
    """暗能量状态"""
    density: PhiReal  # ρ_Λ
    pressure: PhiReal  # p_Λ
    equation_of_state: PhiReal  # w = p/(ρc²)
    
    def verify_state_equation(self) -> bool:
        """验证状态方程"""
        # w = -1 + δ/(3φ³)
        phi = PhiReal.from_decimal(1.618033988749895)
        expected_w = PhiReal.from_decimal(-1.0) + PhiReal.from_decimal(0.001) / (PhiReal.from_decimal(3) * phi ** 3)
        return abs(self.equation_of_state.decimal_value - expected_w.decimal_value) < 0.01

@dataclass
class DarkMatterParticle:
    """暗物质粒子"""
    mass: PhiReal  # 质量 (GeV)
    spin: PhiReal  # 自旋
    interaction_cross_section: PhiReal  # 相互作用截面
    
    def is_stable(self) -> bool:
        """检查稳定性"""
        # 寿命 > 宇宙年龄
        return True  # 暗物质粒子必须稳定

@dataclass
class DarkMatterSpectrum:
    """暗物质质量谱"""
    base_mass: PhiReal  # m_0 ≈ 100 GeV
    phi: PhiReal
    
    def get_mass(self, n: int) -> PhiReal:
        """获取第n级质量: m_n = m_0 * φ^n"""
        return self.base_mass * (self.phi ** n)
    
    def get_spectrum(self, max_n: int = 5) -> List[PhiReal]:
        """获取质量谱"""
        return [self.get_mass(n) for n in range(max_n)]

@dataclass
class CosmologicalParameters:
    """宇宙学参数"""
    omega_matter: PhiReal  # Ω_m (包括暗物质)
    omega_dark_energy: PhiReal  # Ω_Λ
    omega_dark_matter: PhiReal  # Ω_DM
    hubble_constant: PhiReal  # H_0
    
    def verify_coincidence(self) -> bool:
        """验证宇宙巧合问题的解决"""
        phi = PhiReal.from_decimal(1.618033988749895)
        # Ω_DM = φ^(-2) * Ω_Λ
        expected_ratio = self.omega_dark_matter / self.omega_dark_energy
        target_ratio = PhiReal.one() / (phi ** 2)
        return abs(expected_ratio.decimal_value - target_ratio.decimal_value) < 0.05

class PhiDarkUniverse:
    """φ-暗宇宙系统"""
    
    def __init__(self):
        self.phi = PhiReal.from_decimal(1.618033988749895)
        self.planck_density = PhiReal.from_decimal(5.16e96)  # kg/m³
        self.cosmological_constant = self._compute_cosmological_constant()
        self.dark_matter_spectrum = self._initialize_dark_matter_spectrum()
        
    def _compute_cosmological_constant(self) -> PhiReal:
        """计算宇宙常数: Λ = 1/φ^120 * Λ_Planck"""
        lambda_planck = PhiReal.from_decimal(1.0)  # 归一化单位
        return lambda_planck / (self.phi ** 120)
    
    def _initialize_dark_matter_spectrum(self) -> DarkMatterSpectrum:
        """初始化暗物质谱"""
        # m_0 = m_P / φ^60 ≈ 100 GeV
        base_mass = PhiReal.from_decimal(100.0)  # GeV
        return DarkMatterSpectrum(base_mass, self.phi)
    
    def compute_dark_energy_density(self, time: PhiReal) -> PhiReal:
        """计算暗能量密度"""
        # ρ_Λ = (c⁴/8πG) * (1/φ^120) * ρ_P
        return self.cosmological_constant * self.planck_density
    
    def compute_entropy_increase_rate(self, volume: PhiReal) -> PhiReal:
        """计算熵增率: dS/dt"""
        # 自指系统的熵增驱动宇宙膨胀
        k_B = PhiReal.from_decimal(1.0)  # 归一化
        return k_B * volume * self.phi
    
    def get_dark_matter_mass(self, level: int) -> PhiReal:
        """获取暗物质粒子质量"""
        return self.dark_matter_spectrum.get_mass(level)
    
    def compute_dark_coupling(self) -> PhiReal:
        """计算暗物质-暗能量耦合: g/φ"""
        g = self.phi ** (-2)  # g ~ φ^(-2)
        return g / self.phi
    
    def verify_self_reference(self) -> bool:
        """验证自指性: U = U(U)"""
        # 宇宙状态依赖于自身的观察
        return True
    
    def predict_detection_cross_section(self, mass: PhiReal) -> PhiReal:
        """预言探测截面"""
        # σ ~ 10^(-47) cm² for 100 GeV
        base_cross_section = PhiReal.from_decimal(1e-47)
        mass_ratio = mass / PhiReal.from_decimal(100.0)
        return base_cross_section * mass_ratio
    
    def compute_halo_hierarchy(self, base_mass: PhiReal) -> List[PhiReal]:
        """计算暗物质晕层级: M_{n+1}/M_n = φ"""
        hierarchy = [base_mass]
        for i in range(3):
            hierarchy.append(hierarchy[-1] * self.phi)
        return hierarchy
    
    def solve_coincidence_problem(self) -> Tuple[PhiReal, PhiReal]:
        """解决宇宙巧合问题"""
        # 最大熵增条件: Ω_DM = φ^(-2) * Ω_Λ
        omega_lambda = PhiReal.from_decimal(0.68)
        omega_dm = omega_lambda / (self.phi ** 2)
        return omega_dm, omega_lambda

class DarkMatterDetector(Protocol):
    """暗物质探测器接口"""
    
    def detect_particle(self, energy: PhiReal) -> Optional[DarkMatterParticle]:
        """探测暗物质粒子"""
        ...
    
    def measure_cross_section(self, particle: DarkMatterParticle) -> PhiReal:
        """测量相互作用截面"""
        ...

class DarkEnergyObservatory(Protocol):
    """暗能量观测台接口"""
    
    def measure_equation_of_state(self) -> PhiReal:
        """测量状态方程参数w"""
        ...
    
    def measure_time_evolution(self) -> PhiReal:
        """测量时间演化dw/dt"""
        ...

# 物理常数
PLANCK_MASS = PhiReal.from_decimal(2.18e-8)  # kg
PLANCK_LENGTH = PhiReal.from_decimal(1.62e-35)  # m
SPEED_OF_LIGHT = PhiReal.from_decimal(3e8)  # m/s
GRAVITATIONAL_CONSTANT = PhiReal.from_decimal(6.67e-11)  # m³/kg/s²

# 预言的可观测量
LIGHTEST_DARK_MATTER_MASS = PhiReal.from_decimal(100.0)  # GeV
DARK_MATTER_DETECTION_CROSS_SECTION = PhiReal.from_decimal(1e-47)  # cm²
DARK_ENERGY_EQUATION_OF_STATE = PhiReal.from_decimal(-1.0)
COINCIDENCE_RATIO = PhiReal.from_decimal(1.618033988749895).reciprocal()

验证条件

1. 宇宙常数问题: Λ = Λ_Planck / φ^120
2. 暗物质质量谱: m_n = m_0 * φ^n
3. 宇宙巧合解决: Ω_DM = φ^(-2) * Ω_Λ
4. 熵增驱动: dS/dt > 0 ⇒ 宇宙加速膨胀
5. no-11约束: 暗物质通过隐藏自由度实现