A reinforcement-learning agent can reconstruct the causal structure of Minkowski spacetime without being given any direct information about the metric or about causality. In a paper recently posted on arXiv, a team trains a model-based reinforcement-learning agent to maximise the quantum mutual information between localized quantum probes interacting with a quantum field in Minkowski spacetime. In learning to solve this task, the agent builds an internal predictive model whose planner develops the characteristic null structure of spacetime, allowing the causal structure of the metric to be reconstructed with high accuracy.

The work fits into a line of research that seeks to derive geometric and causal concepts from operational and quantum-information considerations, rather than postulating spacetime as a given background. The novelty here is that the geometry is not imposed on the system: it arises from the successful predictions and actions of an agent that is only trying to optimise a quantum-information task. The authors present this result as a first step towards the idea that spacetime concepts emerge from operational quantum experience.

In the concrete task, the agent must maximise the quantum mutual information between localized probes interacting with a quantum field. To do so, the agent's internal model spontaneously develops a planning structure that reproduces the light-cone structure of Minkowski spacetime. From that internal structure, the researchers manage to reconstruct the causal structure of the metric with high accuracy, without the agent ever having been given data on distances, intervals or the shape of the light cone.

The result thus connects quantum field theory, quantum information and machine learning in a single framework, and opens the door to studying how other geometric properties might emerge from information tasks. It remains to be seen to what extent the reconstruction holds in curved or dynamical spacetimes, and whether the emergent structure is unique or depends on the task and the learning algorithm used.