Bell's Theorem for Temporal Order

TL;DR

This paper demonstrates that quantum superpositions of massive bodies can entangle temporal orders of events, leading to violations of Bell inequalities and revealing non-classical aspects of space-time.

Contribution

It introduces a novel framework for analyzing quantum superpositions of space-time and shows how they can produce non-classical temporal correlations.

Findings

Entanglement of temporal orders in superposed space-times

Violation of Bell inequalities for temporal order

Quantum superpositions affect space-time structure

Abstract

Time has a fundamentally different character in quantum mechanics and in general relativity. In quantum theory events unfold in a fixed time order while in general relativity temporal order is influenced by the distribution of matter. When the distribution of matter requires a quantum description, temporal order is expected to become non-classical -- a scenario beyond the scope of current theories. Here we provide a direct description of such a scenario. We consider a massive body in a spatial superposition and show how it leads to "entanglement" of temporal orders between time-like events in the resulting space-time. This entanglement enables accomplishing a task, violation of a Bell inequality, that is impossible under classical temporal order. Violation of the inequality means that temporal order becomes non-classical -- it cannot be described by locally defined classical variables. Our approach provides a quantitative method for investigating quantum aspects of space-time and gravity.