Gell-Mann and Hartle (GMH) have recently considered time-neutral cosmological models in which the initial and final conditions are independently specified, and several authors have investigated experimental tests of such models. We point out here that GMH time-neutral models can allow superluminal signaling, in the sense that it can be possible for observers in those cosmologies, by detecting and exploiting regularities in the final state, to construct devices which send and receive signals between space-like separated points. In suitable cosmologies, any single superluminal message can be transmitted with probability arbitrarily close to one by the use of redundant signals. However, the outcome probabilities of quantum measurements generally depend on precisely which past and future measurements take place. As the transmission of any signal relies on quantum measurements, its transmission probability is similarly context dependent. As a result, the standard superluminal signaling paradoxes do not apply. Despite their unusual features, the models are internally consistent. These results illustrate an interesting conceptual point. The standard view of Minkowski causality is not an absolutely indispensable part of the mathematical formalism of relativistic quantum theory. It is contingent on the empirical observation that naturally occurring ensembles can be naturally pre-selected but not post-selected.
Gell-Mann and Hartle (GMH) have recently considered time-neutral cosmological models in which the initial and final conditions are independently specified, and several authors have investigated experimental tests of such models. We point out here that GMH time-neutral models can allow superluminal signaling, in the sense that it can be possible for observers in those cosmologies, by detecting and exploiting regularities in the final state, to construct devices which send and receive signals between space-like separated points. In suitable cosmologies, any single superluminal message can be transmitted with probability arbitrarily close to one by the use of redundant signals. However, the outcome probabilities of quantum measurements generally depend on precisely which past and future measurements take place. As the transmission of any signal relies on quantum measurements, its transmission probability is similarly context dependent. As a result, the standard superluminal signaling paradoxes do not apply. Despite their unusual features, the models are internally consistent. These results illustrate an interesting conceptual point. The standard view of Minkowski causality is not an absolutely indispensable part of the mathematical formalism of relativistic quantum theory. It is contingent on the empirical observation that naturally occurring ensembles can be naturally pre-selected but not post-selected.
Causality is fundamental to science, but it appears in several different forms. One is relativistic causality, which is tied to a spacetime structure and forbids signaling outside the future. A second is an operational notion of causation that considers the flow of information between physical systems and interventions on them. In [V. Vilasini and R. Colbeck, General framework for cyclic and fine-tuned causal models and their compatibility with space-time, Phys. Rev. A 106, 032204 (2022).PLRAAN2469-992610.1103/PhysRevA.106.032204], we propose a framework for characterizing when a causal model can coexist with relativistic principles such as no superluminal signaling, while allowing for cyclic and nonclassical causal influences and the possibility of causation without signaling. In a theory without superluminal causation, both superluminal signaling and causal loops are not possible in Minkowski spacetime. Here we demonstrate that if we only forbid superluminal signaling, superluminal causation remains possible and show the mathematical possibility of causal loops that can be embedded in a Minkowski spacetime without leading to superluminal signaling. The existence of such loops in the given spacetime could in principle be operationally verified using interventions. This establishes that the physical principle of no superluminal signaling is not by itself sufficient to rule out causal loops between Minkowski spacetime events. Interestingly, the conditions required to rule out causal loops in a spacetime depend on the dimension. Whether such loops are possible in three spatial dimensions remains an important open question.
A central goal in the foundations of physics is to understand the structure of physical theories, such as quantum theory, from physical principles. This is often explored by considering various information-theoretic principles. Here, we initiate a similar approach considering relativistic causality principles. No superluminal causation (NSC) and no superluminal signaling (NSS) are distinct relativistic principles, requiring respectively that causal influence/the ability of agents to signal are within the future lightcone. After formalizing their distinction, we investigate how well theories constrained by NSC and NSS perform in a task that involves generating nonclassical correlations. We find a spacetime configuration in which this task cannot be achieved in any theory (classical, quantum, or postquantum) satisfying NSC. However, we show that theories violating NSC but satisfying NSS can perfectly achieve the task. We give a protocol that would, in a world allowing superluminal causation, enable its operational certification without violating NSS, in general spacetimes. In the case of (1 + 1)-dimensional Minkowski spacetime, the task remains achievable in a configuration where measurement outcomes occur arbitrarily earlier in time than the settings, allowing a form of certifiable retrocausality without violating NSS. We illustrate our results by linking two different types of nonclassical postquantum resources: PR boxes and jamming. Our work offers insights into the role of different relativistic causality principles in fundamental physics and paves the way for characterizing the information-theoretic structure of theories obeying such principles.
Quantum theory is compatible with special relativity. In particular, though measurements on entangled systems are correlated in a way that cannot be reproduced by local hidden variables, they cannot be used for superluminal signaling. As Czachor, Gisin, and Polchinski pointed out, this is not generally true of general nonlinear modifications of the Schr\"odinger equation. Excluding superluminal signaling has thus been taken to rule out most nonlinear versions of quantum theory. The no-superluminal-signaling constraint has also been used for alternative derivations of the optimal fidelities attainable for imperfect quantum cloning and other operations. These results apply to theories satisfying the rule that their predictions for widely separated and slowly moving entangled systems can be approximated by nonrelativistic equations of motion with respect to a preferred time coordinate. This paper describes a natural way in which this rule might fail to hold. In particular, it is shown that quantum readout devices which display the values of localized pure states need not allow superluminal signaling, provided that the devices display the values of the states of entangled subsystems as defined in a nonstandard, although natural, way. It follows that any locally defined nonlinear evolution of pure states can be made consistent with Minkowski causality.
Philosophers of science have not paid much attention to recent developments in quantum cosmology. This fact is surprising, since quantum cosmology is replete with conceptual issues involving (e.g.) the fundamental nature of time and space, the interpretation of quantum mechanics, and the ultimate meaning of probability. One notable exception, Quentin Smith, has recently examined the Hartle-Hawking (1983) proposal. Trying to make sense of the view, he resorts to an instrumentalist picture, which treats the proposal as merely a heuristic device for the algorithm responsible for predictions. While we do not examine Smith's account here, we would like to contrast it with the model presented in this note, in which a fully realistic interpretation of quantum cosmology is developed. Recently there has been a resurgence of interest in the de Broglie-Bohm causal interpretation of quantum mechanics.
Abstract Causality is pivotal to our understanding of the world, presenting itself in different forms: information-theoretic and relativistic, the former linked to the flow of information, and the latter to the structure of space-time. Leveraging a framework introduced in PRA, 106, 032204 (2022), which formally connects these two notions in general physical theories, we study their interplay. The framework defines information-theoretic causality through a causal modelling approach, which enables the inference of causal connections through agents’ interventions and correlations. First, we improve the characterization of information-theoretic signalling as defined through so-called affects relations. Specifically, we provide conditions for identifying redundancies in different parts of such a relation, introducing techniques for causal inference in unfaithful causal models (where the observable data does not ‘faithfully’ reflect the causal dependences). In particular, this demonstrates the possibility of causal inference using the absence of signalling between certain nodes. Second, we define an order-theoretic property called conicality, showing that it is satisfied for light cones in Minkowski space-times with d > 1 spatial dimensions but violated for d = 1. Finally, we study the embedding of information-theoretic causal models in space-time without violating relativistic principles such as no superluminal signalling (NSS). In general, we observe that constraints imposed by NSS in a space-time and those imposed by purely information-theoretic causal inference behave differently. We then prove a correspondence between conical space-times and faithful causal models: in both cases, there emerges a parallel between these two types of constraints. This indicates a connection between informational and geometric notions of causality, and offers new insights and tools for studying the relations between the principles of NSS and no causal loops in different space-time geometries and theories of information processing.
Quantum theory is compatible with special relativity. In particular, though measurements on entangled systems are correlated in a way that cannot be reproduced by local hidden variables, they cannot be used for superluminal signalling. As Czachor, Gisin and Polchinski pointed out, this is not true for general nonlinear modifications of the Schroedinger equation. Excluding superluminal signalling has thus been taken to rule out most nonlinear versions of quantum theory. The no superluminal signalling constraint has also been used for alternative derivations of the optimal fidelities attainable for imperfect quantum cloning and other operations. These results apply to theories satisfying the rule that their predictions for widely separated and slowly moving entangled systems can be approximated by non-relativistic equations of motion with respect to a preferred time coordinate. This paper describes a natural way in which this rule might fail to hold. In particular, it is shown that quantum readout devices which display the values of localised pure states need not allow superluminal signalling, provided that the devices display the values of the states of entangled subsystems as defined in a non-standard, but natural, way. It follows that any locally defined nonlinear evolution of pure states can be made consistent with Minkowski causality.