Bell’s theorem for temporal order

• Published in: Nature communications Vol. 10; no. 1; pp. 3772 - 10
• Main Authors: Zych, Magdalena, Costa, Fabio, Pikovski, Igor, Brukner, Časlav
• Format: Journal Article
• Language: English
• Published: London Nature Publishing Group UK 21-08-2019; Nature Publishing Group; Nature Portfolio
• Subjects: 639/766/483/1139; 639/766/483/481; 639/766/483/640; Bell's inequality; Humanities and Social Sciences; multidisciplinary; Quantum entanglement; Quantum mechanics; Quantum physics; Quantum theory; Relativity; Science; Science (multidisciplinary); Superposition (mathematics); Temporal variations; Theory of relativity
• ISSN: 2041-1723; 2041-1723
• DOI: 10.1038/s41467-019-11579-x

Time has a fundamentally different character in quantum mechanics and in general relativity. In quantum theory events unfold in a fixed order while in general relativity temporal order is influenced by the distribution of matter. When 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 thought experiment with a massive body in a spatial superposition and show how it leads to entanglement of temporal orders between time-like events. This entanglement enables accomplishing a task, violation of a Bell inequality, that is impossible under local classical temporal order; it means that temporal order cannot be described by any pre-defined local variables. A classical notion of a causal structure is therefore untenable in any framework compatible with the basic principles of quantum mechanics and classical general relativity.
Time has a fundamentally different character in quantum mechanics and in general relativity. Here, the authors consider a thought experiment where a massive body in a spatial superposition leads to entanglement of temporal orders between time-like events, resulting in a violation of a Bell-type inequality.