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Nuovo cimento della Società italiana di fisica. A, Nuclei, particles and fields

Causality in indefinite metric theories

Henry Pierce Stapp

Published Sep 1, 1974• 0 citations
Publisher
DOI
10.1007/bf02739490

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Classically, the causal order of two timelike separated events A and B is fixed-either A before B or B before A. This is no longer true in quantum theory, where it is possible to encounter superpositions of causal orders. The quantum switch is one of the most prominent processes with indefinite causal order. Optical realizations of the quantum switch have been successfully implemented in experiments, but some argue that this merely simulates a process with indefinite causal order and that a superposition of spacetime metrics is required for a true realization. Here, we provide a relativistic definition of causal order between operationally defined events that defines a meaningful observable in both the general relativistic and quantum mechanical sense. Importantly, this observable does not distinguish between the indefinite causal order implemented on an optical bench and the gravitational quantum switch, a gedanken experiment where the indefinite causal order is achieved by a quantum superposition of gravitational fields. Therefore, our results support the thesis that the optical quantum switch is just as much a realization of indefinite causal order as its gravitational counterpart, which makes use of the quantum mechanical behavior of spacetime.

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Quantum clocks and the temporal localisability of events in the presence of gravitating quantum systems

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The standard formulation of quantum theory relies on a fixed space-time metric determining the localisation and causal order of events. In general relativity, the metric is influenced by matter, and is expected to become indefinite when matter behaves quantum mechanically. Here, we develop a framework to operationally define events and their localisation with respect to a quantum clock reference frame, also in the presence of gravitating quantum systems. We find that, when clocks interact gravitationally, the time localisability of events becomes relative, depending on the reference frame. This relativity ia a signature of an indefinite metric, where events can occur in an indefinite causal order. Even if the metric is indefinite, for any event we can find a reference frame where local quantum operations take their standard unitary dilation form. This form is preserved when changing clock reference frames, yielding physics covariant with respect to quantum reference frame transformations.

arXiv:1908.10165•Nature Communications•May 29, 2020•143 citations
Classically, the causal order of two timelike separated events A and B is fixed-either A before B or B before A. This is no longer true in quantum theory, where it is possible to encounter superpositions of causal orders. The quantum switch is one of the most prominent processes with indefinite causal order. Optical realizations of the quantum switch have been successfully implemented in experiments, but some argue that this merely simulates a process with indefinite causal order and that a superposition of spacetime metrics is required for a true realization. Here, we provide a relativistic definition of causal order between operationally defined events that defines a meaningful observable in both the general relativistic and quantum mechanical sense. Importantly, this observable does not distinguish between the indefinite causal order implemented on an optical bench and the gravitational quantum switch, a gedanken experiment where the indefinite causal order is achieved by a quantum superposition of gravitational fields. Therefore, our results support the thesis that the optical quantum switch is just as much a realization of indefinite causal order as its gravitational counterpart, which makes use of the quantum mechanical behavior of spacetime.
The standard formulation of quantum theory relies on a fixed space-time metric determining the localisation and causal order of events. In general relativity, the metric is influenced by matter, and is expected to become indefinite when matter behaves quantum mechanically. Here, we develop a framework to operationally define events and their localisation with respect to a quantum clock reference frame, also in the presence of gravitating quantum systems. We find that, when clocks interact gravitationally, the time localisability of events becomes relative, depending on the reference frame. This relativity ia a signature of an indefinite metric, where events can occur in an indefinite causal order. Even if the metric is indefinite, for any event we can find a reference frame where local quantum operations take their standard unitary dilation form. This form is preserved when changing clock reference frames, yielding physics covariant with respect to quantum reference frame transformations.