Determine the relevance of dynamical symmetries to other forms of emergence

Determine whether dynamical symmetry (equivariance) is relevant to other forms of emergence that focus on enhanced controllability (e.g., causal emergence) and on whole–part relationships, beyond the hierarchical emergence mechanism established via symmetry-induced informational closure.

Background

The paper develops a theoretical framework showing that dynamical symmetries (group equivariance) generate informationally closed macroscopic variables and a hierarchy of emergent levels aligned with subgroup lattices. This provides a symmetry-based account of hierarchical emergence in objective dynamics and Bayesian belief updating.

The authors note that other strands of work investigate different notions of emergence, including those centered on enhanced controllability/causal emergence and whole–part relationships. They explicitly state that it remains an open question whether the symmetry-based mechanism articulated here is relevant to these other kinds of emergence.

References

That said, whether symmetry is relevant for these other kinds of emergence is an interesting open question.

— Symmetries at the origin of hierarchical emergence  (2512.00984 - Rosas, 30 Nov 2025) in Discussion

Whether a strongly nonphysical symmetry must always produce a separation somewhere for a nonclassical theory is their central conjecture, and it is open.

— Restricting the effects hides a nonphysical symmetry from every causal structure  (2609.05322 - Kam, 4 Sep 2026) in Section 1, Introduction; Section 2, subsection “Physical, weakly and strongly nonphysical symmetries”