Causality

My friend Seth asks, via gchat away message, "How is it that there are phenomena which are independant of all but a very small set of conditions?" In essence, he is asking about the concept of causality, and how it is that this concept can even make sense.

One of the first abstract ideas we are asked to understand as kids is the idea that some actions cause others. It fell because I dropped it. She's crying because I kicked her. But as we grow older, we see that causality is rarely so simple. Most events depend on a great many past events, none of which can be identified as a single cause. Yet we still use the language of causality ("Today's earnings report caused stocks to close lower") and, at least sometimes, this usage seems appropriate. So how can we tell when causality makes sense and when it doesn't?

In my conversations with Seth on this idea, I was reminded of a principle from special relativity: causality can't travel faster than light. For example, nothing you do today can affect events on Alpha Centauri tomorrow, because not even light can get from here to there that quickly.

This leads to the idea of a "causal cone" in spacetime. Consider the following picture:



The blue "cone" coming out of point A shows all the points in spacetime that light could possibly reach from point A. So points B and C can be affected by something that happens at point A, but Point D cannot because, like Alpha Centauri tomorrow, it is too far away in space and not far enough in the future.

In most everyday situations, causality travels at a speed much slower than light. The specific speed depends on the medium through which causality is travelling. For example, if an underwater earthquake causes a tidal wave, causality travels at the speed by which waves move through water. A rumor travels at the speed it takes people to hear the rumor and repeat it. The point is that, in all cases, causality moves at a finite speed. You can't affect something that is too close to the present (timewise) and too far away in a spatial sense or an information-sharing network sense (i.e. too many degrees removed from you.)

Now consider a situation where we have three potentially causal events:



Suppose we know that events D, E, and F could only have been caused by A, B, or C. Clearly D was caused by B, since A and C are too far away to have influenced D. E, on the other hand, could have been caused by A, B, or both, and F could have been caused by any combination of the three.

In real life, there are millions of events happening all the time, all of which have the potential to cause or influence other events. In the immediate aftermath of an event, the causal cone is undiluted by other cones (as in event B above). But as we get further away (spatially and temporally) from the event, other cones intersect and complicate the effects caused by the original event. This leads to our conclusion:

The statement "A causes B" is most likely to make sense if B happens immediately following and in close proximity to A. Otherwise, there are too many other effects that could dilute the influence of A.

Visually, this would probably look like a "causal flame" coming out of event A, representing the points in spacetime over which A the the most direct influence.



In short, you could reasonably say that dropping the urn caused it to break. But you'd have a much harder time arguing that this event caused your relationship to break up two years later.