Classical uncertainty in predicting the future

TL;DR

This paper explores how classical uncertainty in predicting future events arises from the causal structure of space-time, showing that observers cannot determine future events with certainty due to inaccessible information, and discusses its relation to quantum uncertainty.

Contribution

It demonstrates that classical uncertainty in predicting the future is due to the causal structure of space-time, not intrinsic to the events themselves, and connects it with quantum uncertainty.

Findings

Observers cannot predict events outside their causal past.

Classical uncertainty accumulates with the attempt to predict further into the future.

The uncertainty is not intrinsic but arises from the causal structure of space-time.

Abstract

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.