Giovanni Amelino-Camelia

University of Naples Federico II
Philip Hoehn
IQOQI
Agency-dependent spacetime and spacetime-dependent agency

Most of the current usages of the notion of agent in Science rely on a convenient idealization: like someone playing a videogame, the agent can influence, with her decisions, the physical world, without being directly influenced by it in return. This is true in general relativity as well as in quantum theory, although in different ways. We intend to investigate a situation in which this idealization becomes problematic: when quantum and gravitational effects are both relevant, and the familiar geometric picture of space and time makes room for a novel entity endowed with quantum properties.
Recent progress in quantum information theory allowed researchers to deduce the structure of the flat, classical spacetime of special relativity purely from assumptions on how agents can or cannot communicate by means of quantum systems. This result shows that in quantum theory what one assumes about agents, their knowledge and their communications has implications for the structure of the spacetime those agents live in – and vice-versa. This enables us to ask a fascinating question: what are the implications of a quantum spacetime for agents and, conversely, how do agents’ choices determine how spacetime reveals itself to them?

Recent results in quantum information theory uncovered a connection between abstract quantum theory and properties of spacetime. Simple assumptions on the quantum communication of two agents in a protocol for reference-frame synchronization suffice to prove that their reference frames are related by a Lorentz transformation – without assuming spatiotemporal particulars. Our project aims at extending this remarkable result in various ways: first, by establishing precisely which assumptions about communication among agents lead to Poincaré or (Anti-)de Sitter group transformations. Second, by studying the consequences of deforming these groups to quantum groups, which are candidates for the description of symmetries of quantum spacetimes. This operational language will enable us to ask deep and unexplored questions about how agency could be affected by quantum gravity. In particular, quantum gravity is expected to disallow the idealization of agents as being external to the observed systems. We will study how `internalizing’ agents renders their frames `fuzzy’ through quantum deformations, leading to an uncertainty principle for frame transformations. The way spacetime properties reveal themselves through reference frame relations will thereby depend on agents’ choices. Conversely, we shall also exhibit how deformed symmetries of spacetime affect agency by necessitating modifications of standard quantum information protocols.

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