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

TL;DR

This paper introduces a deterministic 'nomic toy theory' that models agents as physical systems, demonstrating an epistemic horizon similar to quantum uncertainty, and showing that classical systems can exhibit quantum-like measurement limitations.

Contribution

It presents a new deterministic framework where agents experience epistemic horizons, bridging classical and quantum measurement concepts.

Findings

Agents can only learn compatible observables simultaneously.

Nomic toy theory exhibits incompatible measurements despite being classical.

Measurement uncertainty arises from the inseparability of subjects and objects.

Abstract

Quantum theory has an epistemic horizon, i.e. exact values cannot be assigned simultaneously to incompatible physical quantities. 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 - 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, 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 via an epistemic state of Spekkens' toy theory. Our result reconciles us to measurement uncertainty as an aspect of the inseparability of subjects and objects. Significantly, the claims follow even though nomic toy theory is essentially classical. This work invites further investigations of epistemic horizons, such as the one of (full) quantum theory.