Justification of Bohmian quantum equilibrium uncertainty

Determine why it is in principle impossible in Bohmian mechanics to reduce epistemic uncertainty about the initial particle configuration below the Born-rule distribution given by \(\lvert\psi(x)\rvert^2\), including for a short time or in a single non-typical experiment.

Background

The paper examines whether Bohmian mechanics genuinely provides an ontology independent of epistemology. Although Bohmian mechanics is deterministic and assigns definite positions to particles, the quantum equilibrium hypothesis limits the predictive information available about their initial conditions to the Born-rule distribution ∣ψ(x)∣2\lvert\psi(x)\rvert^2.

The paper notes that existing arguments establish convergence toward quantum equilibrium but do not explain why greater predictive accuracy is impossible in principle. This unresolved issue bears directly on whether the uncertainty in Bohmian mechanics can properly be regarded as epistemic rather than as an additional constraint imposed by fiat.

References

Moreover, although have shown that the uncertainty tends to converge to the QEH, it remains unclear why it is in principle impossible to reduce one's epistemic uncertainty by more than \lvert \psi(x) \rvert2, be it for a short time, be it in a single non-typical experiment.

— An interpretation-independent formulation of the measurement problem  (2609.03409 - Soulas, 3 Sep 2026) in Remark \ref{rk:BM}, subsection “Comparing the main interpretations,” Section \ref{sec:interpretations}