Causal reasoning and motion

A clash of paradigms?

The scientific theory of causality in its current form was born through the efforts of Pearl and others, who aimed to get artificial intelligence to reason like humans do. The original context of these efforts was robotics, for which the theory of Bayesian networks was developed.

Whether these efforts have ultimately proven successful at capturing most human intuitions about causality is beyond the scope of this post. It is clear, though, that any mathematical formalization of causality able to capture our intuition to a sufficient degree will also end up capturing aspects that may clash with established physical theory, given that the latter is largely at odds with our intuition.

This clash is perhaps absent in biology, economics, sociology, and other disciplines where the machinery of causal graphs is either rapidly taking hold or being opposed solely on philosophical grounds. Interestingly, these disciplines all developed their own precursors to causal inference theory, however limited in scope: the Book of Why spends several pages on Wright (biology), Haavelmo (economics), and Baron & Kenny (psychology/sociology).

Not physics though. Note that I am not referring here to quantum physics, but to good old classical mechanics. It seems that causal reasoning à la Pearl is representing reality in a way that is more in line with pre-Galilean notions than with the body of received classical mechanics.

Take the little propeller plane cartoon below as an example: does it feel more natural to say that A: the plane is moving or that B: the plane is stationary and the rest of the world is moving? Note that the rest of the world includes the air and clouds and most importantly -though not shown- the Earth, the Sun, our Galaxy and even the faraway quasars and the cosmic microwave background.

Galilean relativity tells us that the two pictures A and B are equivalent in all respects (at least if the plane is in uniform rectilinear motion), but no matter how much physics training you received, the first option will always sound more natural: the plane is intuitively in motion against a stationary background.

There may be several reasons for this intuition, and I suspect most of them have no relation to the motion in question being either uniform or accelerated: in fact here we are staring at a picture of a plane, not at a video. The reasons that we may be able to dig up via introspection may even end up differing between individuals, but one reason should be universal and it happens to be the most interesting for our discussion because it is causal: the cause of the plane's motion, the red propeller, is firmly attached to the plane, while it is not part of the rest of the world.

This idea that a causal argument can be used as a criterion for distinguishing between absolute and relative motion dates back to Leibniz (fifth letter to Clarke):

I will here show how men come to form the notion of space to themselves. They consider that many things exist at once, and they observe in them a certain order of coexistence, according to which the relation of one thing to another is more or less simple. This order is their situation or distance. When it happens that one of those coexistent things changes its relation to a multitude of others which do not change their relation among themselves, and that another thing, newly come, acquires the same relation to the others as the former had, we then say that it is come into the place of the former; and this change we call a motion in that body in which is the immediate cause of the change.

Leibniz would agree that the plane is really moving because it has a propeller. The rest of the world does not have a propeller. Yet post-Galilean physics assures us that we will be able to write perfectly good equations, that is equations that make perfectly good predictions, even if we assume that the plane is stationary and the rest of the world is moving, as long as the relative motion is unaccelerated. What gives?

I have been able to find surprisingly little discussion of this tension between Pearl and Galileo in the computer science literature. The closest I could get is this exchange on Pearl's blog, deep down in the comments. ChatGPT's deep research helped a little, but this topic surely seems under-explored compared to its importance.

Now it could be that the tension is only apparent. Perhaps our intuitive causal notions may find a meaningful connection with the established body of physics knowledge in a limited context. Compare this with people who have an intuitive understanding of mechanical advantage in levers. Their intuition may be off in contexts where kinetic energy is important, but in the quasi-static limit of Archimedean mechanics everything would check out. We just need to understand how to define the limits of applicability of causality theory within the broader scope of physics.

Perhaps we can find a meaningful way to say that the propeller is causing the plane to move only when it is accelerating it and not afterwards, when equilibrium with drag has been reached? This would align our ability to tell that the plane is accelerating by detecting inertial forces --which are absolute in classical mechanics as well as in special relativity-- with the notion that the plane is in absolute motion because its motion has a cause.

To play the devil's advocate here one could point out that the forces between the propeller and the air are equal and opposite to the forces between the air and the propeller. So while it is true that the plane has a propeller, it is also true that the rest of the world "has" a pocket of air that is in contact with the propeller. Could we see that as the cause of the motion of the rest of the world in the frame of reference where the plane is at rest?

Maybe we should be making the meaning of "has" precise: we could say that the plane has a propeller because it is rigidly connected to it. The rest of the world does not really "have" the pocket of air that is touching the propeller: any signal emitted from it will take a prohibitively long time to travel all the way to the stars, even if we let it propagate at the speed of light. Are relativistic limits to rigidity (together with the fact that our plane is small and the rest of the world is big) making it possible to break the apparent symmetry of physical law?