Emmy Noether Workshop: Quantum Space Time

Many researchers in quantum gravity favour the notion of a quantum foam, coined by Wheeler 70 years ago to capture "whatever becomes of spacetime at the Planck scale". The underlying idea is that the quantum fluctuations of spacetime are so large that a description based on smooth metrics is no longer adequate. Equally popular is the notion that spacetime as we know it should "emerge" from this primordial quantum foam, alongside interesting quantum-gravitational effects. These ideas are enticing, but remain speculative unless backed up by quantitative analysis and modelling within a coherent, nonperturbative formulation of quantum gravity. Fully nonperturbative computational tools are available in the form of 'lattice quantum gravity 2.0', based on causal dynamical triangulations. The power and beauty of this methodology lies in its use of curved, dynamical lattices, incorporating the principles of quantum field theory and general relativity from the outset. This has produced quantitative blueprints of both quantum foam and spacetime emergence, and a concrete perspective on what it means to “solve" quantum gravity. [arXiv:2501.17972]

While a complete theory of quantum gravity remains elusive, several alternative approaches are being explored. Which ones are the most promising, and whether they are connected or fundamentally distinct, remain outstanding open questions. I will argue that looking at quantum gravity through the lens of effective field theory offers a promising path to test the internal consistency of different theories and systematically compare their low-energy manifestations. I will illustrate this perspective using asymptotically safe quantum gravity as a case study, discussing its interface with positivity bounds and swampland conjectures. Finally, I will outline how a similar strategy can be utilized to chart the landscape of quantum spacetimes stemming from an asymptotically safe ultraviolet completion.

The Planck scale is generally believed to mark the onset of quantum gravity effects. In this talk, I will illustrate some of the most relevant features of models where the Planck scale governs deformations of relativistic symmetries and discuss opportunities for experimental tests of such models arising in physical frameworks much below the Planck scale. This concerns astrophysical observations, sensitive to tiny residual signatures at low energies thanks to amplification mechanisms, and table-top experiments, whose extremely high-precision might soon allow us to test the interplay between (quantum) gravity and quantum systems at ultra-low energies.

I will discuss aspects of  the path sum of causal set theory, in which the continuum is replaced by a sample space of locally finite partially ordered sets.  This sample space not only contains continuumlike causals of different dimensions, but an entire zoo of non-continuumlike ones.  An open question is whether this path sum can be treated as a UV regularisation of the continuum path integral, as  the number of elements increases. I will discuss some results as well as  challenges in answering this question.

Observers in a typical gravitational or cosmological setting only have access to part of the spacetime and the degrees of freedom in it. The observer sees an open quantum system, and the complete dynamics of all degrees of freedom can be reconstructed by gluing together the (possibly overlapping) open systems associated with each observer. I will discuss what can be learned from treating familiar laboratory closed systems as ensembles of open systems, and how we can begin to extrapolate from there to systems relevant for cosmology.

Gravitational waves are generally a classical GR phenomenon, carrying the imprint of compact merger sources with strong curvature and dynamic interactions. I will give an overview of current and future gravitational-wave observations, and discuss some areas where gravitational waves astronomy makes contact with the quantum regime.

The swampland is the space of those effective field theories that cannot be ultraviolet completed in quantum gravity. Understanding the swampland is relevant for phenomenological model-building and for observational tests of quantum gravity. This talk will have three parts: First, I will introduce the notion relative swamplands, to distinguish the swamplands of different quantum-gravity approaches. Their intersection forms the absolute swampland. Second, I will discuss a subset of swampland conjectures in the light of asymptotically safe gravity. Third, I will explain how asymptotic safety can provide a mechanism to generate universality, when it is realized within an intermediate regime between a non-quantum-field-theoretic quantum regime of gravity and the standard effective field theory regime below the Planck scale.

Within the AdS/CFT correspondence, two manifestations of the black hole information paradox are given by the nonisometric nature of the bulk-boundary map and by the factorisation puzzle. By considering timeshifted microstates of the eternal black hole, we demonstrate that both these puzzles may be simultaneously resolved by taking into account non-local quantum corrections that correspond to wormholes arising from state averaging. This is achieved by showing, using a resolvent technique, that the resulting Hilbert space for an eternal black hole in Anti-de Sitter space is finite-dimensional with a discrete energy spectrum. The latter gives rise to a transition to a type I von Neumann algebra. Talk based on 2411.09616.

Causal set theory is an approach to quantum gravity where the underlying spacetime is a locally finite poset. Glaser gave a formula for the causal set theory analogue of the d'Alembertian in general dimension (growing out of previous work of Sorkin, Benincasa and Dowker, and Dowker and Glaser). The formula contains rational coefficients. Who can resist trying to find something that these coefficients count -- not me! -- so I will tell you about such a something.