Intervening on time derivatives

Interventionism analyses causal influence in terms of correlations of changes under a distribution of interventions. But the correspondence between correlated changes and causal influence is not obvious. I probe its plausibility with a problem-case involving variables related as time derivative (velocity) to integral (position), such that the latter variable must change given an intervention on the former unless dependencies are introduced among the testing and controlling interventions. Under the orthodox criteria such interventions will fail to be appropriate for causal analysis. I consider various alternatives, including permitting control interventions to be chancy, restricting the available models and mitigating variation of off-path variables. None of these work. I then present a fourth suggestion which modifies the interventionist criteria in order to permit interventions which can influence other variables than just their own targets. The correspondence between correlated changes and causal influence can thereby saved when dependencies are introduced among such interventions. This modification and the required dependencies, I argue, are perfectly in line with practice and may also assist in a wider class of cases.