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Do physicists need the idea of 'cause' or 'causation' to do physics?
Does it appear in physics, either in theory, answered here, or in experiment? In a way analogous to how names and mathematics do.
If not, then it seems like a folk concept which exists only to help us learn physics or be inspired by it.
It turns out that this is a very, very deep question, and I don't think there is a final authoritative answer on this. What we can say with certainty is that, contrary to what some of the comments to the original question imply, physics as a whole is absolutely not "all about finding causes". Indeed, a strong argument can be made that mature physical theories do not need nor use the concept of causes.
For example, in one of his Messenger Lectures at Cornell on "The Character of Physical Law" (Lecture 2 on "The Relation of Mathematics to Physics", worth watching no matter what...) Feynman discusses the example of Newton's theory of gravitation, and how it can be formulated in radically different ways: In Newtonian Mechanics we have a somewhat mysterious "action at a distance", with forces causing the specific motion of planets, whereas in modern formulations of classical mechanics we end up with an integral variational principle that does not (easily) map on any concept of causation (and almost looks teleological). And finally in general relativity, the picture changes again.
For some food for thought I would recommend John Norton's paper on Causation as a Folk Science. I will state for the record that I do not necessarily agree with everything Norton says on that topic, but his thoughts are certainly well worth considering.
Other than that, this question clearly veers quite far into the area of (legitimate) philosophy. Not that it's not also a good question to ask in this forum, but philosophers may have something to offer on this question as well.
Well, I will try an answer. I will try without worrying too much about 'deep philosophy', but just something about how it is used in physics. And without saying that you have to go read something. I may misstate a couple things, but will try to be as accurate as I can.
But I will stay away from philosophy or pure interpretation.
I think this below is not too different than what Countto10 is saying and possibly also JMLCarter
First various examples on how causality is so deeply embedded in the physics we know, and the physics we are investigating. Actually the summ of all examples is the main point.
1) in the Large Scale Structure of Spacetime, a book by Hawking, he laid out the way General Relativity (GR) is causal. It is really about the causal structure of Spacetime. It's a hard topic because GR allows you to do physics in any coordinate system, and the time sequence of things are not obvious sometimes. Penrose and others found coordinate systems, for example for Black Holes and other geometries, where one could see the causal structure. It involved creating coordinate systems where light rays travel at 45 degree angles, like in Minkowski spacetime. Those then define light cones, and GR, as well as Special Relativity (SR), say that an event can be causally connected to another if it is in the future light cone of it. Doesn't mean it is the cause, but it could be. If it isn't inside the light cone they are causally disconnected. The book is https://www.amazon.com/Structure-Space-Time-Cambridge-Monographs-Mathematical/dp/0521099064, but there's plenty of the topic in Wikipedia and accessible articles. In this fashion we can get also event horizons, such as the Black Hole horizon, or the Universe's event horizon, where anything beyond those can't affect (cannot possibly be a cause for) anything that happens on this side (yes, watch out what side you're on) of the horizon.
2) Those kinds of causality constraints started with SR imposing, and over time having it be accepted in physics, that matter/energy cannot go faster than light, and by the way, also information as is now also accepted. And all experiments and observations done are consistent with that.
3) So in Quantum Field Theory (QFT) the same holds, but in the language of quantum theory. When QFT was developed having causality be embedded in it was an important criteria. For instance, the expected value of a propagator of a QF is 0 for two states at two spacetime points which are outside their respective light cones. So two states that have a space like separation have a zero transition probability (now, I do remember on Tongs QFT course that in some cases it is not zero but approaches zero exponentially quickly, so there some fine points to account for, due to quantum's probabilistic nature). But it does not change the main fact of causal QFT.
4) certainly Quantum Electrodynamics follows that, as you'd expect since photons travel at c. But the theories fo electroweak forces and strong forces were done also with those causality constraints imposed.
5) So do physicists worry about what causes what? We do expect everything we study and everything we see to have an explanation - if it didn't it'd be magic. Physics officially does not believe in magic per say, but it does believe it doesn't know everything, and likes to find and explain magical things.
6) An example of one of those is entanglement. It's been explained, it's cause, and why two particles separated by spacelike distances can still be correlated. But there's still some doubt and some thinking on some of the entanglement effects that have been observed. Still, physics keeps looking for the description and use of it. Going further is the who,e set of work being done in the AdS/CFT correspondence, where there is a holographic relationship that look non-local, and still obeys some kinds of laws. There is more investigations in those areas, for quantum gravity and for information theory. Maybe cause and effect is too Linear A relationship, but still the thinking is that there would be a physics law that relates them. I'd call that, in simplistic terms, cause and effect.
7) So finally, yes, all physics looks for explanations and have them explain new observations, and only when you get consistent enough on it is it a physical law. And it may change as we learn more, it m turn I it a more complex law that reduces to the earlier one in the right limits. Thus in QFT and really all physics there is what is called 'effective field theory', where as one goes to higher energy or smaller scales a new theory is needed, which reduces to the earlier one at lower energies.
So, is that an answer to cause and effect? It is where we are in physics, and it is close enough to some idea of cause effect that only philosophy can find better terms
Most definitions of cause involve some form of "arrow" of time. By "arrow" I mean that time is assumed to be unidirectional: causes are in the past and consequences in the future (I am not talking about the thermodynamical arrow of time). For our universe, however, it seems that most fundamental physics theories have a time reversible interpretation, in which causes can become effects and effects can become causes. This kind of arrow of time also appear in formal systems: theorems follows from axioms. However, you can use aesthetics to decide which principle is an axiom and which one is a theorem (theorems can become axioms and vice versa). In the same way, in physics you can chose what is in the past and what is the future (by this I mean the direction of the "arrow of time"). Viewed in this way, causality in its standard meaning no longer exists.
Causality is not apparent from the reversible theory, but is still important implicitly. But this sense of causality comes after the facts. By this I mean that the "reversible=non-causal" theory appears first and then some problems (mostly paradoxes) appear which need to be explained using additional assumptions. One example is Norton's dome, which seems to show that Newtonian mechanics has solutions in which effects are non-causal (like the bigbang, they happen spontaneously). Another example is the grandfather paradox, which some proposed it is solved by adding the principle of "cosmic censorship". In both examples you can eliminate those paradoxes if you add some constraints that were not initially part of the theory.
There are other possibilities too. Some macroscopic theories (for instance classical thermodynamics), or physics of alternative universes (for instance some cellular automata) are not time reversible. This introduces a non ambiguous arrow of time, in the sense that in one direction the past predicts the future, but in the other direction it does not.
You could also ask, like in quantum mechanics, that your theory be only predictive probabilistically. So, the effect can happen by chance, among a set of possibilities. But I do not want to discuss quantum mechanics. It has so many issues!
