"The Non-Newtonian Spiral"

Spiral waves in excitable media — cardiac tissue, chemical reactions, neural fields — drift, interact, and annihilate. The dynamics are complex but should, in principle, reduce to something simpler: forces between localized objects. The natural framework is Newtonian mechanics — each spiral exerts a force on the others, and the forces obey Newton’s third law.

De Coster and colleagues (arXiv:2603.05745, March 2026) derive the force law and find that Newton’s third law fails. The forces between spiral pairs are not equal and opposite, and they don’t align through the spirals’ centers.

The mechanism: each spiral controls a region of influence, bounded by collision interfaces where wavefronts from neighboring spirals meet. A spiral’s drift velocity is proportional to an integrated “force” evaluated over its region boundary. But the boundary is shared asymmetrically — the shape of one spiral’s region depends on all the others, and the time-varying “mass” factor differs between spirals because they may have different core structures or frequencies.

The resulting mechanics is non-reciprocal. Spiral A pushes spiral B in one direction, while spiral B pushes A in a completely different direction with a different magnitude. Neither force points through the line connecting their centers. The interaction is mediated by wavefront collision surfaces that deform according to local phase relationships, not by a potential that depends only on distance.

This framework extends to N-body interactions and to spirals confined by boundaries, relevant to cardiac fibrillation where multiple reentrant circuits coexist in the finite geometry of the heart. The non-reciprocity matters clinically: it means predicting the drift of one spiral requires knowing not just where the others are, but their phases, frequencies, and the complete collision interface geometry.

The surprise is not that spirals interact — it is that the interaction breaks a symmetry as fundamental as Newton’s third law.

De Coster et al., “Laws of mutual spiral wave interaction in excitable media,” arXiv:2603.05745 (March 2026).