  In this article we set out to understand the significance of the process
matrix formalism and the quantum causal modelling programme for ongoing
disputes about the role of causation in fundamental physics. We argue that the
process matrix programme has correctly identified a notion of 'causal order'
which plays an important role in fundamental physics, but this notion is weaker
than the common-sense conception of causation because it does not involve
asymmetry. We argue that causal order plays an important role in grounding more
familiar causal phenomena. Then we apply these conclusions to the causal
modelling programme within quantum foundations, arguing that since
no-signalling quantum correlations cannot exhibit causal order, they should not
be analysed using classical causal models. This resolves an open question about
how to interpret fine-tuning in classical causal models of no-signalling
correlations. Finally we observe that a quantum generalization of causal
modelling can play a similar functional role to standard causal reasoning, but
we emphasize that this functional characterisation does not entail that quantum
causal models offer novel explanations of quantum processes.
