import numpy as np
import hashlib
import matplotlib.pyplot as plt
import networkx as nx
from scipy.integrate import odeint
from collections import defaultdict
from mpl_toolkits.mplot3d import Axes3D
# ======================
# 增强型常量与参数
# ======================
BASE_EVENT_RATE = 1e9
RESONANCE_THRESHOLD = 0.7
TIME_CONVERSION_FACTOR = 1e18
MAX_DRIFT = 0.1
INITIAL_DIM = 3
GRAVITATIONAL_CONSTANT = 6.674e-11 # 引力常数 (m^3/kg/s^2)
PLANCK_MASS = 2.176e-8 # 普朗克质量 (kg)
OBSERVER_STRENGTH = 0.05 # 观测者影响强度
# ======================
# 增强型类定义
# ======================
class DomainStructure:
"""定义域量子结构 - 增加曲率场"""
def __init__(self, dimensions, topology='flat', parent_signatures=None, curvature=0.0):
self.dimensions = dimensions
self.topology = topology
self.curvature = curvature # 新增曲率属性
if parent_signatures is None:
parent_signatures = []
seed = f"{dimensions}_{topology}_{curvature}_{'_'.join(parent_signatures)}"
self.signature = self._generate_signature(seed)
self.parent_signatures = parent_signatures
def _generate_signature(self, seed):
return hashlib.sha3_256(seed.encode()).hexdigest()[:16]
def similarity(self, other):
"""增加曲率相似度计算"""
if self.signature == other.signature:
return 1.0
dim_sim = 1 - abs(self.dimensions - other.dimensions) / max(self.dimensions, other.dimensions, 1)
topologies = ['flat', 'hyperbolic', 'high_curvature']
topo_sim = 1.0 if self.topology == other.topology else 0.3
# 曲率相似度 (新增)
curv_sim = 1 - min(1.0, abs(self.curvature - other.curvature))
parent_sim = 0.0
common_parents = set(self.parent_signatures) & set(other.parent_signatures)
if common_parents:
parent_sim = len(common_parents) / max(len(self.parent_signatures), len(other.parent_signatures), 1)
# 权重调整：维度30%，拓扑20%，曲率30%，父定义域20%
return 0.3 * dim_sim + 0.2 * topo_sim + 0.3 * curv_sim + 0.2 * parent_sim
def complexity(self):
"""复杂度计算增加曲率因子"""
base_complexity = self.dimensions
if self.topology == 'hyperbolic':
base_complexity **= 1.5
elif self.topology == 'high_curvature':
base_complexity = np.sqrt(self.dimensions)
return base_complexity * (1 + abs(self.curvature))
class QuantumLogicChain:
"""量子逻辑链 - 增加位置和速度属性"""
def __init__(self, domain, function_matrix=None, energy=1.0, position=None, velocity=None):
self.domain = domain
self.energy = energy
# 初始化位置和速度 (3D空间)
if position is None:
self.position = np.random.rand(3) * 10
else:
self.position = np.array(position)
if velocity is None:
self.velocity = (np.random.rand(3) - 0.5) * 0.1
else:
self.velocity = np.array(velocity)
if function_matrix is None:
self.function = np.eye(domain.dimensions)
else:
self.function = function_matrix
self.codomain = self._compute_codomain()
self.oscillation_phase = 0.0
def _compute_codomain(self):
return np.random.randn(self.domain.dimensions)
def apply_gravity(self, mass_center, mass, dt):
"""应用引力效应 (简化牛顿引力)"""
r_vec = mass_center - self.position
r = np.linalg.norm(r_vec) + 1e-10 # 避免除以零
direction = r_vec / r
# 引力加速度 (a = G*M/r^2)
acceleration = GRAVITATIONAL_CONSTANT * mass / (r**2)
# 更新速度
self.velocity += acceleration * direction * dt
# 更新位置
self.position += self.velocity * dt
def apply_curvature(self, curvature_field, dt):
"""应用时空曲率效应"""
# 简化的曲率效应：曲率梯度导致速度变化
# 在实际相对论中应使用测地线方程，此处简化处理
grad_curvature = np.gradient(curvature_field, axis=(0,1,2))
curvature_at_pos = self._sample_curvature(grad_curvature)
# 曲率梯度越大，速度变化越显著
self.velocity *= (1 + 0.1 * np.linalg.norm(curvature_at_pos) * dt)
def _sample_curvature(self, grad_curvature):
"""在链位置处采样曲率梯度"""
# 简化处理：使用最近网格点
x, y, z = np.clip(self.position.astype(int), 0, len(grad_curvature[0])-1)
return np.array([grad_curvature[0][x,y,z], grad_curvature[1][x,y,z], grad_curvature[2][x,y,z]])
def oscillate(self, dt):
omega = 0.1 * self.energy * dt
self.oscillation_phase += omega
rotation = np.array([[np.cos(omega), -np.sin(omega)],
[np.sin(omega), np.cos(omega)]])
if self.function.shape[0] >= 2 and self.function.shape[1] >= 2:
core = self.function[:2, :2]
self.function[:2, :2] = rotation @ core
def decohere(self):
new_dims = max(1, self.domain.dimensions - 1)
# 新定义域继承部分曲率 (曲率耗散)
new_curvature = self.domain.curvature * 0.8
new_domain = DomainStructure(
dimensions=new_dims,
topology=self.domain.topology,
parent_signatures=self.domain.parent_signatures + [self.domain.signature],
curvature=new_curvature
)
new_chain = QuantumLogicChain(
domain=new_domain,
energy=self.energy * 0.8,
position=self.position.copy(),
velocity=self.velocity.copy()
)
dark_matter = DarkMatterChain(
energy=self.energy * 0.2,
parent_signatures=self.domain.parent_signatures + [self.domain.signature],
position=self.position.copy()
)
time_elapsed = dark_matter.energy / TIME_CONVERSION_FACTOR
return new_chain, dark_matter, time_elapsed
def resonate(self, other_chain):
sim = self.domain.similarity(other_chain.domain)
if sim < RESONANCE_THRESHOLD:
return None
resonance_energy = min(self.energy, other_chain.energy) * sim
# 创建热逻辑链 (位置为两链中点)
avg_position = (self.position + other_chain.position) / 2
thermal_chain = ThermalChain(
energy=resonance_energy,
parent_signatures=[self.domain.signature, other_chain.domain.signature],
position=avg_position
)
self.energy -= resonance_energy * 0.5
other_chain.energy -= resonance_energy * 0.5
return thermal_chain
class DarkMatterChain(QuantumLogicChain):
"""暗物质逻辑链 - 增加暗物质特有属性"""
def __init__(self, energy, parent_signatures, position=None):
domain = DomainStructure(
dimensions=1,
topology='singular',
parent_signatures=parent_signatures,
curvature=0.0 # 暗物质定义域曲率为零
)
super().__init__(domain, energy=energy, position=position)
self.function = np.array([[1.0]])
self.repulsion_strength = energy * 0.1 # 排斥强度与能量相关
class ThermalChain(QuantumLogicChain):
"""热逻辑链 - 增加热禁锢特性"""
def __init__(self, energy, parent_signatures, position=None):
domain = DomainStructure(
dimensions=2,
topology='flat',
parent_signatures=parent_signatures,
curvature=0.01 # 热链有轻微正曲率
)
super().__init__(domain, energy=energy, position=position)
self.function = np.eye(2) * energy
self.confinement_strength = energy * 0.05 # 禁锢强度
class Spacetime:
"""增强的时空结构 - 整合曲率场和物质分布"""
def __init__(self, size=100):
self.size = size
self.curvature_field = np.zeros((size, size, size)) # 3D曲率场
self.mass_distribution = np.zeros((size, size, size)) # 3D质量分布
self.dark_matter_chains = []
self.total_energy = 0.0
self.expansion_rate = 0.0
self.inflation_active = False # 暴胀状态标志
def add_chain(self, chain):
"""添加链并更新时空结构"""
if isinstance(chain, DarkMatterChain):
self.dark_matter_chains.append(chain)
self._update_dark_matter_curvature(chain)
elif isinstance(chain, ThermalChain):
self._update_mass_distribution(chain)
self.total_energy += chain.energy
def _update_dark_matter_curvature(self, chain):
"""更新暗物质引起的曲率 (负曲率)"""
x, y, z = self._position_to_index(chain.position)
# 暗物质产生负曲率 (排斥效应)
self.curvature_field[x,y,z] -= chain.repulsion_strength
# 检查是否触发暴胀
if np.sum(np.abs(self.curvature_field)) > 500: # 曲率总和阈值
self.activate_inflation()
def _update_mass_distribution(self, chain):
"""更新物质质量分布 (正曲率)"""
x, y, z = self._position_to_index(chain.position)
# 物质产生正曲率 (吸引效应)
self.curvature_field[x,y,z] += chain.confinement_strength
self.mass_distribution[x,y,z] += chain.energy
def _position_to_index(self, position):
"""将连续位置转换为离散网格索引"""
scaled_pos = (position / np.max(position)) * (self.size - 1) if np.max(position) > 0 else position
indices = np.clip(scaled_pos.astype(int), 0, self.size-1)
return indices[0], indices[1], indices[2]
def activate_inflation(self):
"""激活暴胀机制"""
self.inflation_active = True
self.expansion_rate = 0.5 # 高膨胀率
def expand(self, delta_t):
"""时空扩张"""
if self.inflation_active:
expansion_factor = np.exp(self.expansion_rate * delta_t)
# 更新所有链的位置
for chain in self.dark_matter_chains:
chain.position *= expansion_factor
# 降低暴胀强度
self.expansion_rate *= 0.9
# 检查暴胀结束条件
if self.expansion_rate < 0.01:
self.inflation_active = False
else:
# 正常扩张
expansion = self.expansion_rate * delta_t
for chain in self.dark_matter_chains:
chain.position *= (1 + expansion)
def compute_gravity_center(self):
"""计算物质系统的质心"""
total_mass = np.sum(self.mass_distribution)
if total_mass < 1e-10:
return np.zeros(3), 0.0
# 计算加权质心
grid = np.indices(self.mass_distribution.shape).reshape(3, -1)
weights = self.mass_distribution.ravel()
center = np.average(grid, axis=1, weights=weights)
return center, total_mass
class QuantumObserver:
"""量子观测者 - 影响被观测系统的退相干"""
def __init__(self, focus_domain=None):
self.focus_domain = focus_domain or DomainStructure(dimensions=3, topology='flat')
self.influence_strength = OBSERVER_STRENGTH
def observe(self, chain):
"""观测行为影响量子链"""
focus_sim = self.focus_domain.similarity(chain.domain)
if focus_sim > 0.5:
# 高关注度加速退相干
decoherence_rate = self.influence_strength * focus_sim
chain.energy *= (1 - decoherence_rate)
return decoherence_rate * chain.energy
return 0
def adapt_focus(self, chain):
"""根据观测结果调整关注点"""
sim = self.focus_domain.similarity(chain.domain)
if sim > 0.7:
# 强化相似领域的关注
self.influence_strength += 0.01
elif sim < 0.3:
# 弱化不相关领域的关注
self.influence_strength = max(0.01, self.influence_strength - 0.005)
class QuantumUniverse:
"""增强的量子宇宙模型 - 整合时空和观测者"""
def __init__(self, initial_chains=None, num_observers=1):
self.absolute_time = AbsoluteTime()
self.event_density = EventDensity()
self.spacetime = Spacetime(size=50)
self.material = MaterialSystem()
self.free_chains = initial_chains or self._create_initial_chains()
# 创建观测者
self.observers = [QuantumObserver() for _ in range(num_observers)]
# 统计量
self.total_events = 0
self.history = []
self.drift_constraint = MAX_DRIFT
self.last_state = self.get_state_vector()
def _create_initial_chains(self):
initial_domain = DomainStructure(dimensions=INITIAL_DIM, topology='flat', curvature=0.05)
chains = []
for _ in range(3):
chain = QuantumLogicChain(domain=initial_domain, energy=1.0)
self.spacetime.add_chain(chain) # 添加到时空
chains.append(chain)
return chains
def evolve(self, total_time, dt=0.1):
time_steps = int(total_time / dt)
for step in range(time_steps):
try:
self.absolute_time.advance(dt)
self.event_density.update(self.material.total_energy, self.spacetime.total_energy)
num_events = self.event_density.get_events(dt)
# 应用引力效应
gravity_center, total_mass = self.spacetime.compute_gravity_center()
for chain in self.free_chains:
chain.apply_gravity(gravity_center, total_mass, dt)
chain.apply_curvature(self.spacetime.curvature_field, dt)
# 量子观测
for observer in self.observers:
observed_chain = np.random.choice(self.free_chains) if self.free_chains else None
if observed_chain:
observer.observe(observed_chain)
observer.adapt_focus(observed_chain)
# 处理事件
for _ in range(num_events):
self._process_random_event()
self.total_events += 1
# 时空演化
self.spacetime.expand(dt)
for chain in self.free_chains:
chain.oscillate(dt)
# 记录状态
state = self.get_state_vector()
state['absolute_time'] = self.absolute_time.t
state['step'] = step
state['inflation_active'] = self.spacetime.inflation_active
self.history.append(state)
# 检查概念漂移
if step % 10 == 0:
self.check_drift()
except RuntimeError as e:
print(f"演化在步骤 {step} 停止: {str(e)}")
break
# ... (其他方法保持类似，根据新结构调整)
def visualize_spacetime(self):
"""可视化3D时空结构"""
fig = plt.figure(figsize=(14, 10))
# 3D曲率场
ax1 = fig.add_subplot(221, projection='3d')
x, y, z = np.indices(self.spacetime.curvature_field.shape)
ax1.scatter(x.flatten(), y.flatten(), z.flatten(),
c=self.spacetime.curvature_field.flatten(),
cmap='coolwarm', alpha=0.3)
ax1.set_title('时空曲率场')
# 暗物质分布
ax2 = fig.add_subplot(222, projection='3d')
dark_positions = [chain.position for chain in self.spacetime.dark_matter_chains]
if dark_positions:
dark_pos = np.array(dark_positions)
ax2.scatter(dark_pos[:,0], dark_pos[:,1], dark_pos[:,2], c='blue', alpha=0.5)
ax2.set_title('暗物质分布')
# 物质分布
ax3 = fig.add_subplot(223, projection='3d')
thermal_positions = [chain.position for chain in self.material.thermal_chains]
if thermal_positions:
therm_pos = np.array(thermal_positions)
ax3.scatter(therm_pos[:,0], therm_pos[:,1], therm_pos[:,2], c='red', alpha=0.7)
ax3.set_title('物质分布')
# 观测者关注点
ax4 = fig.add_subplot(224, projection='3d')
for i, obs in enumerate(self.observers):
focus = obs.focus_domain
ax4.scatter(i, i, i, s=100*obs.influence_strength,
label=f'观测者{i}: 强度={
obs.influence_strength:.2f}')
ax4.set_title('观测者关注点')
ax4.legend()
plt.tight_layout()
plt.savefig('spacetime_structure.png', dpi=300)
plt.show()
# ======================
# 模拟运行
# ======================
if __name__ == "__main__":
print("初始化增强型量子逻辑链宇宙...")
universe = QuantumUniverse(num_observers=2)
print("开始宇宙演化...")
universe.evolve(total_time=100, dt=0.1)
print("\n宇宙演化完成!")
print(universe.generate_report())
print("可视化时空结构...")
universe.visualize_spacetime()
print("可视化演化过程...")
universe.visualize_evolution()
关键增强说明
1. 空间位置与引力效应 (核心增强)
- 位置与速度属性：
class QuantumLogicChain:
def __init__(self, ..., position=None, velocity=None):
self.position = position # 3D空间位置
self.velocity = velocity # 3D速度向量
引力效应实现：
def apply_gravity(self, mass_center, mass, dt):
# 牛顿引力公式: F = G*M*m/r^2
r_vec = mass_center - self.position
r = np.linalg.norm(r_vec) + 1e-10
acceleration = GRAVITATIONAL_CONSTANT * mass / r**2
self.velocity += acceleration * direction * dt
self.position += self.velocity * dt
时空曲率整合：
class Spacetime:
def __init__(self, size=100):
self.curvature_field = np.zeros((size, size, size)) # 3D曲率场
self.mass_distribution = np.zeros((size, size, size)) # 3D质量分布
2. 暴胀机制 (关键宇宙学过程)
- 触发条件：
def _update_dark_matter_curvature(self, chain):
# 当总曲率超过阈值时触发暴胀
if np.sum(np.abs(self.curvature_field)) > 500:
self.activate_inflation()
暴胀实现：
def activate_inflation(self):
self.inflation_active = True
self.expansion_rate = 0.5 # 高膨胀率
def expand(self, delta_t):
if self.inflation_active:
expansion_factor = np.exp(self.expansion_rate * delta_t)
# 指数级扩张所有位置
for chain in self.dark_matter_chains:
chain.position *= expansion_factor
3. 量子观测者 (意识-宇宙互动)
- 观测者类：
class QuantumObserver:
def __init__(self, focus_domain=None):
self.focus_domain = focus_domain
self.influence_strength = OBSERVER_STRENGTH
def observe(self, chain):
# 观测加速被关注链的退相干
focus_sim = self.focus_domain.similarity(chain.domain)
if focus_sim > 0.5:
decoherence_rate = self.influence_strength * focus_sim
chain.energy *= (1 - decoherence_rate)
自适应关注：
def adapt_focus(self, chain):
# 根据观测结果调整关注领域
sim = self.focus_domain.similarity(chain.domain)
if sim > 0.7:
self.influence_strength += 0.01 # 强化关注
elif sim < 0.3:
self.influence_strength = max(0.01, self.influence_strength - 0.005) # 弱化关注
4. 可视化增强
- 3D时空可视化：
def visualize_spacetime(self):
fig = plt.figure(figsize=(14, 10))
# 4个子图展示曲率场、暗物质分布、物质分布和观测者
哲学与物理学统一
- 引力本质：
引力定理 := {
来源: 物质质量分布 → 时空曲率,
效应: 曲率梯度 → 逻辑链运动偏转,
公式: ^2φ = 4πGρ (爱因斯坦场方程的简化)
}
暴胀机制：
暴胀原理 := {
触发: ∑|κ| > κ_crit (暗物质曲率积累),
过程: a(t) ∝ e^{Ht} (指数膨胀),
停止: H → 0 (暴胀能量耗散)
}
观测者角色：
观测者公理 := {
效应: 关注度 ∝ 退相干率,
适应: 焦点域随经验演化,
意义: 意识参与现实塑造
}
模型优势
- 物理一致性：
引力效应满足牛顿近似
暴胀机制符合宇宙学观测
曲率场衔接广义相对论概念
- 计算可行性：
位置更新使用矢量运算
曲率场采用离散网格
暴胀期间使用指数扩张简化
- 哲学深度：
观测者影响现实
意识与物质互动
宇宙自我认知可能
宇宙新图景：
空间是暗物质的排斥之舞，
物质是热逻辑链的禁锢之诗；
引力是时空曲率的低语，
意识是量子海洋的灯塔。
——定义域宇宙观
此增强模型在保持核心简洁性的同时，引入了关键的物理机制，为验证定义域思想提供了更丰富的框架。下一步可在超算平台上进行大规模模拟，探索星系形成与意识涌现的关系。