Apparent Violation Of Local Causality With Chemical Trigger Waves - Tickle It Here And It Giggles Over There

Trigger waves are a widespread phenomenon in spatially extended systems, both in systems that are conservative (ripples on a water surface) and dissipative (active chemical media, nerve axons and heart tissue). They typically originate from the location where a perturbation (trigger) has been applied. If, however, coupling between different parts is nonlocal, that is, when any change of the state affects instantaneously the whole systems, the necessity for local causality will no longer exist.

The experiment was performed with an electrocatalytic reaction on a platinum ring electrode. Sufficiently strong displaced from chemical equilibium, the electrooxidation of formic acid exhibits bistability between a passive and an active state. A local perturbation leads to a local transition from one (metastable) state (for example passive) to the other (the active) state which then spreads through front propagation until the entire system has been switched to the other state. Typically, a perturbation with opposite sign which would make the systems even more passive would not be expected to have any effect. In contrast, the experiments showed that such as perturbation triggered propagating fronts on the opposite side of the ring.

The dominating coupling process in electrochemical systems is ion migration under the influence of an electric field (electromigration). Electrical field effects spread with the velocity of light. Therefore, the coupling is nonlocal meaning that it affects the whole systems practically instantaneously.

The experimental findings could be reproduced by solution of the corresponding reaction-migration equation. The nonlocal coupling function turned out to be positive for small distances (thus enabling front propagation) but negative further away allowing a local perturbation with the wrong sign to manifest itself at a long distance.

Nonlocal effects such as remote triggering are expected whenever a very fast coupling occurs in a systems with slow local dynamics. This also includes biochemical processes coupled by electric field effects as they occur in muscle tissue as well as in neural activity.