Epistemic Horizons From Deterministic Laws: Lessons From a Nomic Toy Theory

Quantum theory has an epistemic horizon, i.e. there are incompatible measurements whose outcomes cannot be simultaneously known. As shown by Spekkens' toy theory, positing an epistemic horizon akin to Heisenberg's uncertainty principle in a classical mechanical setting also leads to a plethora of quantum phenomena. We introduce a deterministic theory - the nomic toy theory - in which information gathering agents are explicitly modelled as physical systems. Our main result shows the presence of an epistemic horizon for such agents. They can only simultaneously learn the values of observables whose Poisson bracket vanishes. Therefore, the nomic toy theory has incompatible measurements and the complete state of a physical system cannot be known. The best description of a system by an agent is possibilistic via an epistemic state of the Spekkens' toy theory. Significantly, the claims follow even though the nomic toy theory is essentially classical. This work invites further investigations of epistemic horizons, such as the one of quantum theory.