Focus issue: Entanglement and quantum gravity (Iopscience)
Recent years have seen a flourishing of interest in the role that entanglement entropy plays in the physics of spacetime. New insights have been obtained into the role of entanglement for the entropy for black hole thermodynamics, and new ideas have been explored connecting entanglement to holography, wormholes, the structure of semiclassical spacetime itself and others. In this special issue, we collect a number of articles on this topic, offering a partial overview of these new developments. The issue includes review articles as well as speculative works on specific ideas.
Eduardo Martín-Martínez and Nicolas Menicucci open the special issue with a review on entanglement in quantum fields, which includes a discussion of flat spacetime phenomena such as the Unruh effect, as well as cosmological spacetimes. They also discuss novel ideas such as echoes of the early universe, entanglement harvesting, and a nascent proposal for quantum seismology.
Robert Myers and Eugenio Bianchi observe the similarity of the role played by entanglement entropy in the context of various approaches to quantum gravity, and propose entanglement entropy as an ingredient of the very semiclassical structure of spacetime in quantum gravity.
In a gauge theory, the definition of the entanglement between two spacetime regions is complicated by the fact that gauge invariant degrees of freedom are not spatially localized. This is a point that can have strong relevance for gravity. William Donnelly reviews the work on the definition of entanglement of quantum gauge theories.
In the context of loop quantum gravity, the role of entanglement entropy in black hole thermodynamics, and its relation to the statistical entropy defined by counting the number of orthogonal quantum states of the hole, has been widely discussed. Norbert Bodendorfer discusses the relation between the two entropies and the extension of the present results to arbitrary spacetime dimensions, which supports the idea of a strict relation between the two entropies.
Sebastian Fischetti and Don Marolf discuss holographic entanglement, presenting arguments supporting the plausibility of the idea that the CFT entropy is controlled by complex extremal surfaces.
Mehdi Saravani, Rafael Sorkin and Yasaman Yazdi study a definition of entropy given by the two-point function of the quantum field in a region, showing that this is global and independent of any choice of spacelike hypersurface.
Finally, John Baez and Jamie Vicary discuss the speculative idea of a relation between entanglement and wormholes in the context of a topological quantum field theory.
We do not yet have a global coherent picture of the relations between quantum field theory, gravity and thermodynamics, and the various developments sampled (or reviewed) in this special issue do not combine into a global coherent picture yet. However, they do converge in pointing out that entanglement entropy plays a central role in this tangle of problems, a role that was probably underestimated, or misinterpreted, for some time. For instance, standard arguments against the possibility of relating black hole entropy with entanglement, such as the ‘species problem’ are now recognized as far less compelling than before.
The relevance of this change of perspective should not be underestimated. Just to make one example, the generalized second law of thermodynamics, according to which the total (non-decreasing) thermodynamic entropy must include the black hole area, is likely to be valid only as a first approximation, if the black hole entropy is dominated by entanglement entropy and if the horizon, because of quantum effects, turns out to be an apparent horizon rather than an event horizon. Thus, a complete evaluation of the role of entanglement entropy in the thermodynamics of spacetime is essential.
Quantum gravity alone is not the only major theoretical open problem in fundamental physics: gravity, quantum theory and thermodynamics form a triple, whose full interconnections we have definitely not yet understood. As soon as quantum effects appear in a curved spacetime, thermal aspects appear to be unavoidable. Therefore, combining thermodynamics and (full) gravity might turn out to be even more crucial than understanding the quantum aspects of the gravitational field alone. In recent years, it has become increasingly clear that entanglement entropy is a central ingredient for the synthesis we are seeking.
The articles listed below are the first accepted contributions to the collection and further additions will appear on an ongoing basis.