This is a broad question motivated by philosophical interests. I hope it will not be considered as off topic.
What I am looking for is a technical answer reflecting the standard conception of nowadays physics.
Let me give some details regarding the context.
Traditionnaly, since Hume I think , the distinction betweeen mathematics and natural sciences ( like physics) has been made in the following way:
mathematics deals with "relations of ideas" that are purely logical
natural science deals with truth of facts, involving causal relations ( that cannot be reduced to logoical ones), there is ( said Hume) no logical link betweeen " temperature is below zero" and " water has frozen".
My question is not on the logical status of physical-science truths, but on the role of causality in physics.
I suppose physicists cannot prevent themselves from thinking ( privately) of natural phenomena in terms of causality. But is causality an official concept in physics, a concept having an official theoretical status?
One problem I see is that the language of physics is mathematical, and it seems difficult to translate the ideas of cause and effect in a mathematical languege.
More generally, are physicists interested in problems relating to causality?