论文标题
部分可观测时空混沌系统的无模型预测
Breakdown of quantum mechanics in gravitational holography
论文作者
论文摘要
储层计算是预测湍流的有力工具，其简单的架构具有处理大型系统的计算效率。然而，其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间，然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用，该系统模拟了湍流的若干特征。我们表明，使用径向基函数作为非线性投影器，即使只有部分观测并且不知道控制方程，也能稳健地捕捉复杂的系统非线性。最后，我们表明，当测量稀疏、不完整且带有噪声，甚至控制方程变得不准确时，我们的网络仍然可以产生相当准确的预测，从而为实际湍流系统的无模型预测铺平了道路。
According to the holographic principle, the information content assigned to a gravitational region is processed by its lower dimensional boundary. As an example setup compatible with this principle, the AdS/CFT correspondence relies on the existence of D-branes in superstring theory. Black hole complementarity is inevitably linked to holography and states that information associated with the collapsed pure state is reflected in the near horizon region. Yet, if this is so, it is indispensable to understand the mechanism that makes black holes viewed from the outside evolve unitarily. We here argue that the information preserving quantum atmosphere of the black hole emerges from hidden variables on its horizon which would necessitate going beyond a probabilistic description within standard quantum theory. In AdS/CFT, this would mean that the completion of the semiclassical subalgebra to the complete boundary algebra has to be traced back to the emergent near horizon Hilbert space structure. The present investigations suggest that spacetime horizons, in general, may play a crucial role in restoring a long speculated ontology in quantum mechanics.
