T17-9 φ-意识量子坍缩定理 - 形式化规范

类型定义

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

@dataclass
class QuantumState:
    """量子态表示"""
    amplitudes: List[PhiComplex]  # 振幅系数
    basis_labels: List[str]  # 基态标签
    
    def normalize(self):
        """归一化量子态"""
        norm_squared = PhiReal.zero()
        for amp in self.amplitudes:
            norm_squared = norm_squared + amp.norm_squared()
        
        norm = norm_squared.sqrt()
        if norm.decimal_value > 1e-10:
            for i in range(len(self.amplitudes)):
                self.amplitudes[i] = self.amplitudes[i] / norm
    
    def get_probability(self, index: int) -> PhiReal:
        """获取特定基态的概率"""
        return self.amplitudes[index].norm_squared()
    
    def is_valid_no11(self) -> bool:
        """检查是否满足no-11约束"""
        # 检查非零振幅的基态索引
        active_indices = []
        for i, amp in enumerate(self.amplitudes):
            if amp.norm_squared().decimal_value > 1e-10:
                active_indices.append(i)
        
        # 验证相邻索引不同时激活
        for i in range(len(active_indices) - 1):
            if active_indices[i+1] - active_indices[i] == 1:
                return False
        return True

@dataclass
class ConsciousnessState:
    """意识状态"""
    self_reference_level: int  # 自指层级
    observation_history: List[int]  # 观察历史
    entropy: PhiReal  # 当前熵
    
    def observe(self, quantum_state: QuantumState) -> int:
        """意识观察导致坍缩"""
        # 增加自指层级
        self.self_reference_level += 1
        
        # 计算φ-坍缩概率
        collapse_probs = self._compute_phi_collapse_probabilities(quantum_state)
        
        # 选择坍缩结果
        collapsed_index = self._select_outcome(collapse_probs)
        
        # 更新观察历史
        self.observation_history.append(collapsed_index)
        
        # 增加熵
        self.entropy = self.entropy + OBSERVATION_ENTROPY_INCREASE
        
        return collapsed_index
    
    def _compute_phi_collapse_probabilities(self, state: QuantumState) -> List[PhiReal]:
        """计算φ-修正的坍缩概率"""
        # 基础Born概率
        born_probs = [state.get_probability(i) for i in range(len(state.amplitudes))]
        
        # φ-能量因子：E_n = E_0 * F_n (使用Fibonacci数作为能级)
        fibonacci_energies = self._compute_fibonacci_energies(len(born_probs))
        phi_factors = []
        for i in range(len(born_probs)):
            # P(n) ∝ φ^(-E_n/E_0) = φ^(-F_n)
            factor = PHI ** (-fibonacci_energies[i])
            phi_factors.append(factor)
        
        # 计算未归一化概率
        unnormalized = []
        for i in range(len(born_probs)):
            unnormalized.append(born_probs[i] * phi_factors[i])
        
        # 归一化
        total = PhiReal.zero()
        for p in unnormalized:
            total = total + p
        
        normalized = []
        for p in unnormalized:
            if total.decimal_value > 1e-10:
                normalized.append(p / total)
            else:
                normalized.append(PhiReal.zero())
        
        return normalized
    
    def _compute_fibonacci_energies(self, n: int) -> List[PhiReal]:
        """计算Fibonacci能级序列"""
        energies = []
        f_prev, f_curr = PhiReal.zero(), PhiReal.one()
        
        for i in range(n):
            energies.append(f_curr)
            f_next = f_prev + f_curr
            f_prev, f_curr = f_curr, f_next
        
        return energies
    
    def _select_outcome(self, probabilities: List[PhiReal]) -> int:
        """根据概率分布选择结果（完整随机采样）"""
        # 构建累积概率分布
        cumulative = []
        total = PhiReal.zero()
        
        for p in probabilities:
            total = total + p
            cumulative.append(total)
        
        # 生成φ-分布的随机数
        # 使用黄金分割生成伪随机数
        import time
        seed = PhiReal.from_decimal(time.time())
        random_phi = (seed * PHI) % PhiReal.one()
        
        # 根据累积分布选择结果
        for i, cum_prob in enumerate(cumulative):
            if random_phi.decimal_value <= cum_prob.decimal_value:
                return i
        
        return len(probabilities) - 1

@dataclass
class CollapseEvent:
    """坍缩事件"""
    initial_state: QuantumState
    final_index: int
    collapse_time: PhiReal
    entropy_increase: PhiReal
    consciousness_level: int

class PhiConsciousnessCollapse:
    """φ-意识量子坍缩系统"""
    
    def __init__(self):
        self.phi = PhiReal.from_decimal(1.618033988749895)
        self.consciousness = ConsciousnessState(
            self_reference_level=0,
            observation_history=[],
            entropy=PhiReal.zero()
        )
        self.collapse_events: List[CollapseEvent] = []
    
    def create_superposition(self, n_states: int) -> QuantumState:
        """创建量子叠加态"""
        # 创建等权叠加
        amplitudes = []
        for i in range(n_states):
            # 确保满足no-11约束
            if i == 0 or i >= 2:
                amp = PhiComplex(
                    PhiReal.one() / PhiReal.from_decimal(np.sqrt(n_states//2)),
                    PhiReal.zero()
                )
            else:
                amp = PhiComplex.zero()
            amplitudes.append(amp)
        
        state = QuantumState(
            amplitudes=amplitudes,
            basis_labels=[f"|{i}⟩" for i in range(n_states)]
        )
        state.normalize()
        return state
    
    def consciousness_observe(self, quantum_state: QuantumState) -> CollapseEvent:
        """意识观察导致坍缩"""
        initial_state_copy = QuantumState(
            amplitudes=quantum_state.amplitudes.copy(),
            basis_labels=quantum_state.basis_labels.copy()
        )
        
        # 计算坍缩时间
        collapse_time = self.compute_collapse_time(quantum_state)
        
        # 执行观察
        collapsed_index = self.consciousness.observe(quantum_state)
        
        # 记录事件
        event = CollapseEvent(
            initial_state=initial_state_copy,
            final_index=collapsed_index,
            collapse_time=collapse_time,
            entropy_increase=OBSERVATION_ENTROPY_INCREASE,
            consciousness_level=self.consciousness.self_reference_level
        )
        self.collapse_events.append(event)
        
        # 坍缩量子态
        for i in range(len(quantum_state.amplitudes)):
            if i == collapsed_index:
                quantum_state.amplitudes[i] = PhiComplex(PhiReal.one(), PhiReal.zero())
            else:
                quantum_state.amplitudes[i] = PhiComplex.zero()
        
        return event
    
    def compute_collapse_time(self, state: QuantumState) -> PhiReal:
        """计算坍缩时间 τ = ħ/ΔE · φ^N"""
        # 计算实际的纠缠熵作为复杂度度量
        entanglement_entropy = self._compute_entanglement_entropy(state)
        
        # 计算能级差
        energies = self._compute_fibonacci_energies(len(state.amplitudes))
        # 找到概率最大的两个态的能量差
        probs = [state.get_probability(i) for i in range(len(state.amplitudes))]
        sorted_indices = sorted(range(len(probs)), key=lambda i: probs[i].decimal_value, reverse=True)
        if len(sorted_indices) >= 2:
            delta_E = abs(energies[sorted_indices[0]].decimal_value - energies[sorted_indices[1]].decimal_value)
            if delta_E < 1e-10:
                delta_E = 1.0  # 避免除零
        else:
            delta_E = 1.0
        
        # τ = (ħ/ΔE) · φ^S，其中S是纠缠熵
        hbar = PhiReal.from_decimal(1.054571817e-34)  # 真实的约化普朗克常数
        tau_base = hbar / PhiReal.from_decimal(delta_E * 1.602176634e-19)  # 转换为焦耳
        collapse_time = tau_base * (self.phi ** entanglement_entropy)
        
        return collapse_time
    
    def _compute_entanglement_entropy(self, state: QuantumState) -> PhiReal:
        """计算量子态的纠缠熵"""
        entropy = PhiReal.zero()
        
        for i in range(len(state.amplitudes)):
            p = state.get_probability(i)
            if p.decimal_value > 1e-10:
                ln_p = PhiReal.from_decimal(np.log(p.decimal_value))
                entropy = entropy - p * ln_p
        
        return entropy
    
    def compute_zeno_survival(self, t: PhiReal, n_observations: int) -> PhiReal:
        """计算量子Zeno效应下的生存概率"""
        # P_survival = exp(-t/τ_Z · φ^(-n))
        tau_z = PhiReal.from_decimal(1.0)  # Zeno时间尺度
        
        exponent = -(t / tau_z) * (self.phi ** (-n_observations))
        
        # 近似计算指数
        if exponent.decimal_value > -10:
            survival_prob = PhiReal.from_decimal(np.exp(exponent.decimal_value))
        else:
            survival_prob = PhiReal.zero()
        
        return survival_prob
    
    def compute_collective_collapse_rate(self, n_observers: int) -> PhiReal:
        """计算集体意识坍缩率"""
        # Γ_N = Γ_1 · N^φ
        gamma_1 = PhiReal.one()  # 单意识坍缩率
        
        # N^φ的计算
        n_phi = PhiReal.from_decimal(n_observers ** self.phi.decimal_value)
        
        return gamma_1 * n_phi
    
    def compute_consciousness_quantum_entanglement(self, n_c_states: int, n_q_states: int) -> PhiMatrix:
        """计算意识-量子纠缠矩阵"""
        # β_ij = (1/√Z) exp(-E_ij / kT·φ)
        elements = []
        kT_phi = self.phi  # 归一化温度
        
        # 计算配分函数Z
        Z = PhiReal.zero()
        for i in range(n_c_states):
            for j in range(n_q_states):
                # 纠缠能量 = 意识能级 + 量子能级 + 相互作用能
                E_c = PhiReal.from_decimal(self._fibonacci_number(i))
                E_q = PhiReal.from_decimal(self._fibonacci_number(j))
                E_int = (E_c * E_q) / (E_c + E_q + PhiReal.one())  # 相互作用能
                E_total = E_c + E_q + E_int
                
                # 计算exp(-E/kT)
                exp_arg = (PhiReal.zero() - E_total) / kT_phi
                exp_val = PhiReal.from_decimal(np.exp(exp_arg.decimal_value))
                Z = Z + exp_val
        
        # 计算纠缠矩阵元素
        for i in range(n_c_states):
            row = []
            for j in range(n_q_states):
                E_c = PhiReal.from_decimal(self._fibonacci_number(i))
                E_q = PhiReal.from_decimal(self._fibonacci_number(j))
                E_int = (E_c * E_q) / (E_c + E_q + PhiReal.one())
                E_total = E_c + E_q + E_int
                
                # 纠缠振幅
                exp_arg = (PhiReal.zero() - E_total) / kT_phi
                exp_val = PhiReal.from_decimal(np.exp(exp_arg.decimal_value))
                beta = exp_val / PhiReal.from_decimal(np.sqrt(Z.decimal_value))
                row.append(PhiComplex(beta, PhiReal.zero()))
            elements.append(row)
        
        return PhiMatrix(elements=elements, dimensions=(n_c_states, n_q_states))
    
    def _fibonacci_number(self, n: int) -> int:
        """计算第n个Fibonacci数"""
        if n <= 1:
            return 1
        a, b = 1, 1
        for _ in range(n - 1):
            a, b = b, a + b
        return b
    
    def verify_self_reference(self) -> bool:
        """验证意识的自指性"""
        # 意识必须能观察自身的状态
        return self.consciousness.self_reference_level > 0
    
    def compute_consciousness_entropy(self) -> PhiReal:
        """计算意识系统的总熵"""
        return self.consciousness.entropy
    
    def get_collapse_statistics(self) -> Dict[str, PhiReal]:
        """获取坍缩统计信息"""
        if not self.collapse_events:
            return {}
        
        total_events = len(self.collapse_events)
        
        # 统计坍缩到各态的频率
        outcome_counts = {}
        for event in self.collapse_events:
            idx = event.final_index
            if idx not in outcome_counts:
                outcome_counts[idx] = 0
            outcome_counts[idx] += 1
        
        # 计算频率
        statistics = {}
        for idx, count in outcome_counts.items():
            freq = PhiReal.from_decimal(count / total_events)
            statistics[f"state_{idx}"] = freq
        
        # 平均坍缩时间
        total_time = PhiReal.zero()
        for event in self.collapse_events:
            total_time = total_time + event.collapse_time
        avg_time = total_time / PhiReal.from_decimal(total_events)
        statistics["avg_collapse_time"] = avg_time
        
        return statistics

# 物理常数
PHI = PhiReal.from_decimal(1.618033988749895)
OBSERVATION_ENTROPY_INCREASE = PhiReal.from_decimal(np.log(1.618033988749895))  # ΔS = k_B ln(φ)
PLANCK_TIME = PhiReal.from_decimal(5.39124e-44)  # 秒
CONSCIOUSNESS_TIMESCALE = PhiReal.from_decimal(0.1)  # 秒
BOLTZMANN_CONSTANT = PhiReal.from_decimal(1.380649e-23)  # J/K
REDUCED_PLANCK_CONSTANT = PhiReal.from_decimal(1.054571817e-34)  # J·s

# 验证函数
def verify_no11_collapse_pattern(events: List[CollapseEvent]) -> bool:
    """验证坍缩模式满足no-11约束"""
    indices = [e.final_index for e in events]
    
    # 检查连续坍缩不落在相邻态
    for i in range(len(indices) - 1):
        if abs(indices[i+1] - indices[i]) == 1:
            return False
    return True

def verify_entropy_increase(events: List[CollapseEvent]) -> bool:
    """验证每次观察都增加熵"""
    for event in events:
        if event.entropy_increase.decimal_value <= 0:
            return False
    return True

def verify_phi_probability_distribution(statistics: Dict[str, PhiReal]) -> bool:
    """验证坍缩统计符合φ-分布"""
    # 提取态频率
    state_freqs = []
    for key, freq in statistics.items():
        if key.startswith("state_"):
            state_freqs.append((int(key.split("_")[1]), freq))
    
    state_freqs.sort(key=lambda x: x[0])
    
    # 检查是否呈现φ^(-n)的趋势
    if len(state_freqs) >= 2:
        for i in range(len(state_freqs) - 1):
            if state_freqs[i][1].decimal_value > 0 and state_freqs[i+1][1].decimal_value > 0:
                ratio = state_freqs[i+1][1] / state_freqs[i][1]
                expected = PhiReal.one() / PHI
                # 允许20%误差
                if abs(ratio.decimal_value - expected.decimal_value) > 0.2 * expected.decimal_value:
                    return False
    
    return True

验证条件

1. 自指性: 意识系统C = C[C]
2. 熵增: 每次观察ΔS = k_B ln(φ)
3. no-11约束: 坍缩态和意识态都满足
4. φ-概率分布: P(n) ∝ φ^(-n)
5. 时间尺度: τ_collapse = τ_0 · φ^N