We present a simple toy model of a rat moving in a box, where the rat’s motion follows a quantum-inspired rule. At each time step, the rat selects its next position from a probability distribution that evolves under a fixed Hamiltonian. This defines the objective probability —the distribution that actually governs the rat’s movement.

An outside observer, however, does not know this objective distribution. Instead, the observer forms a subjective probability — a belief about the rat’s possible location — by updating based on indirect evidence (the rat’s observed positions over time) and prior knowledge (initial position and evolution rule).

This setup highlights the distinction between objective and subjective probabilities, a central issue in quantum foundations (e.g., QBism and related interpretations). Our model shows how the same physical system can yield two distinct yet meaningful probability distributions: one tied to the system’s internal dynamics and the other to the observer’s knowledge. The gap between them may be viewed as mismodelling.

While the model itself is simple, its main contribution is interpretational. It connects to contexts where real-world systems must be monitored or inferred under uncertainty or incomplete information.

The second part of the talk introduces ongoing work (Quantum Rat Vol.3: Learning Dynamics from Measurements) exploring how the dynamics governing the rat’s evolution can be learned from partial measurement records.

Speaker: Aleksej Gaj