论文标题
因果关系在大地运动中的混乱
Causality bounds chaos in geodesic motions
论文作者
论文摘要
因果关系可以确保可预测性，而在混乱中迷失方向。为了调和这两个流行的概念，我们研究了具有外部电势的通用弯曲空间中的地球运动中的混乱，其中因果关系受标量潜力控制。我们开发了一种依赖性的方法，以分析估计粒子运动的lyapunov指数$λ$。我们表明，因果关系给出了通用的上限$λ\ propto e \（e \ rightarrow \ infty）$，它与穆拉塔（Murata），塔纳哈西（Tanahashi），沃特那比（Watanabe）和作者之一（K.H.）所提出的混乱能量相吻合。我们还发现，即使有因果关系，也可能会侵犯Maldacena，Shenker和Stanford发现的混乱。我们的估计虽然等待数值确认，但揭示了物理理论的隐藏性质：因果关系界定混乱。
Predictability is ensured by causality while lost in chaos. To reconcile these two popular notions, we study chaos in geodesic motions in generic curved spacetimes with external potentials, where causality is controlled by a scalar potential. We develop a reparametrization-independent method to analytically estimate the Lyapunov exponent $λ$ of a particle motion. We show that causality gives the universal upper bound $λ\propto E\ (E\rightarrow\infty)$, which coincides with the chaos energy bound proposed by Murata, Tanahashi, Watanabe, and one of the authors (K.H.). We also find that the chaos bound discovered by Maldacena, Shenker, and Stanford can be violated in particular potentials, even with causality. Our estimates, although waiting for numerical confirmation, reveal the hidden nature of physical theories: causality bounds chaos.
