预测未来的经典不确定性
Classical uncertainty in predicting the future
摘要：
在这项工作中，我们仔细检查的确定性性质的全球双曲时空从观察者的角度来看。我们证明了一个时空点$q \in M$位于$p \in M$观测者的未来，它接收到的信号对$p$观测者是不可见的（精确地说）。柯西曲面上的部分初始数据是预测$q$发生的情况所必需的，但在$p$上的观测者也是看不见的。因此，任何观察者都不可能准确地预测未来的事件。当人们试图预测更远的未来时，不确定性就会增加。当且仅当$q \in J^-(p)$时，$p$上的观察者可以访问整个数据，以确定$q$上发生了什么。预言中的经典不确定性不是时空事件的内在特征。它与通常的量子力学不确定性一起限制了我们预测未来的能力。我们还建议一个思想实验来阐明这个问题。
英文摘要：
In this work we scrutinize the deterministic nature of globally hyperbolic space-times from the point of view of an observer. We show that a space-time point $q \in M$ that lies to the future of an observer at $p \in M$, receives signals that are invisible (to be made precise) to the observer at $p$. Part of the initial data on a Cauchy surface, required to predict what happens at $q$, is also invisible to the observer at $p$. Therefore it is not possible for any observer to predict a future event with certainty. The uncertainty increases as one attempts to predict further future. An observer at $p$ can access the entire data to determine what happens at $q$, if and only if $q \in J^-(p)$. Classical uncertainty in prediction is not an intrinsic feature of the events in space-time. It adds up with the usual quantum mechanical uncertainty to limit our ability to predict the future. We also suggest a thought experiment to elucidate the subject.
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