arXiv:2205.00164 · Physical Review A

Indefinite temporal order without gravity

Kacper Dębski, Magdalena Zych, Fabio Costa, Andrzej Dragan

Published Dec 5, 2023• 2 citations

Abstract

According to the general theory of relativity, time can flow at different rates depending on the configuration of massive objects, affecting the temporal order of events. Combined with quantum theory, this gravitational effect can result in events with an indefinite temporal order when a massive object is prepared in a suitable quantum state. This was argued to lead to a theory-independent test of the nonclassical order of events through the violation of Bell-type inequalities for temporal order. Here we show that the theory independence of this protocol is problematic: one of the auxiliary assumptions in the above approach turns out to be essential, while it is explicitly theory dependent. To illustrate this problem, we construct a complete scenario where accelerating particles interacting with optical cavities result in a violation of temporal Bell inequalities. Due to the equivalence principle, the same problem arises when one considers the gravitational case, and thus theory-dependent additional assumptions are needed behind Bell inequalities for temporal order to interpret a violation of the final inequalities as a signature of indefinite temporal order.

DOI: 10.1103/physreva.108.062204

Related papers

Bell’s theorem for temporal order

Magdalena Zych, Fabio Costa, Igor Pikovski +1 more

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.

arXiv:1708.00248Nature CommunicationsAug 21, 2019122 citations

Temporal nonlocality from indefinite causal orders

Laurie Letertre

A temporal counterpart to Bell nonlocality would intuitively refer to the presence of non-classical correlations between timelike-separated events. The hypothesis of temporal nonlocality has received recent support in the literature, and its existence would likely influence the future development of physical theories. This paper shows how Adlam's principle of temporal locality can be violated within a protocol involving indefinite causal orders. While the derivations of Leggett-Garg inequalities or the temporal CHSH inequality are said to involve problematic assumptions preventing a targeted probing of a well-defined notion of temporal nonlocality, the present test is free from such worries. However, it is shown that the test, in its current formulation, fails to be fully model-independent. We provide several considerations regarding the physicality of ICOs that could help alleviate this drawback. In the present work, a specific physical interpretation of ICOs in terms of retrocausal influences would explain the presence of temporally nonlocal correlations. It is argued that, as the physical underpinnings of temporal nonlocality might also account for standard Bell nonlocality, focusing on the former as a consequence of ICOs might support under-explored strategies to make sense of the latter.

arXiv:2501.12870The British Journal for the Philosophy of ScienceJan 22, 20252 citations

Bell’s theorem for temporal order

Magdalena Zych, Fabio Costa, Igor Pikovski +1 more

Abstract 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.

Jan 1, 2019108 citations

Observer-dependent locality of quantum events

Philippe Allard Guérin, Časlav Brukner

In general relativity, the causal structure between events is dynamical, but it is definite and observer-independent; events are point-like and the membership of an event A in the future or past light-cone of an event B is an observer-independent statement. When events are defined with respect to quantum systems however, nothing guarantees that the causal relationship between A and B is definite. We propose to associate a causal reference frame corresponding to each event, which can be interpreted as an observer-dependent time according to which an observer describes the evolution of quantum systems. In the causal reference frame of one event, this particular event is always localised, but other events can be ‘smeared out’ in the future and in the past. We do not impose a predefined causal order between the events, but only require that descriptions from different reference frames obey a global consistency condition. We show that our new formalism is equivalent to the pure process matrix formalism (Araújo et al 2017 Quantum 1 10). The latter is known to predict certain multipartite correlations, which are incompatible with the assumption of a causal ordering of the events—these correlations violate causal inequalities. We show how the causal reference frame description can be used to gain insight into the question of realisability of such strongly non-causal processes in laboratory experiments. As another application, we use causal reference frames to revisit a thought experiment Zych et al (arXiv: 1708.00248 ) where the gravitational time dilation due to a massive object in a quantum superposition of positions leads to a superposition of the causal ordering of two events.

arXiv:1805.12429New Journal of PhysicsOct 10, 201834 citations

Experimental entanglement of temporal order

Giulia Rubino, Lee A. Rozema, Francesco Massa +4 more

The study of causal relations has recently been applied to the quantum realm, leading to the discovery that not all physical processes have a definite causal structure. While indefinite causal processes have previously been experimentally shown, these proofs relied on the quantum description of the experiments. Yet, the same experimental data could also be compatible with definite causal structures within different descriptions. Here, we present the first demonstration of indefinite temporal order outside of quantum formalism. We show that our experimental outcomes are incompatible with a class of generalised probabilistic theories satisfying the assumptions of locality and definite temporal order. To this end, we derive physical constraints (in the form of a Bell-like inequality) on experimental outcomes within such a class of theories. We then experimentally invalidate these theories by violating the inequality using entangled temporal order. This provides experimental evidence that there exist correlations in nature which are incompatible with the assumptions of locality and definite temporal order.

arXiv:1712.06884QuantumJan 11, 202242 citations

Indefinite order in the interface of quantum mechanics and gravity

Bruna Sahdo

Researchers have long been aiming to understand how the characteristics of Quantum Theory and General Relativity combine to account for regimes in their interface. One reason why this is a hard task is how differently the theories approach time and causality. For instance, causal structure in relativity is determined by the distribution of mass in spacetime while, in the quantum formalism, it is supposed to be fixed and given in advance. In this master's thesis, we discuss the notion of indefinite order, which first appears in an abstract generalization of Quantum Theory [...] where the demand for global causal structure is removed, in principle allowing cases for which the order of operations in protocols is not necessarily well defined. One epitomical example of indefinite order is the quantum switch process, which realizes a quantum superposition of orders of two operations on a target system. The quantum switch probabilities have been reproduced in experimental optical setups that are fully described in principle by quantum mechanics. Since these experiments are compatible with spacetime causal structure, this generated uncertainty about the conclusions that can be drawn from obtaining these results depending on the context. Here, we return to the initial motivations and also present how scenarios involving gravity in low energies could lead to indefinite order. This includes the formulation of a quantum switch in a quantum gravity scenario and of a quantum switch in a classical Schwarzschild metric. The switch then provides a common ground to discuss different kinds of setups. The latter proposal of a quantum switch in a classical metric is an original work that, aside from being an example of indefinite order, proposes the realization of the protocol in Earth's gravity as a test of quantum mechanics on curved spacetimes, a regime which has not yet been explored experimentally.

arXiv:2310.02290Oct 3, 20230 citations