Time Travel, CTC and Causal Loop

Question

What is the difference between a closed timelike curve and a causal loop?

If someone is travelling in a closed timelike curve, are they also in a causal loop?

Answer 1

A causal loop is, as far as I'm aware (it's not 100% a standard term), a sequence of events that form a loop. It is not quite a physical concept (it's more likely to pop up in the philosophy of physics, like in the books of Reichenbach or Earman), but it does apply to a variety of physical theories. For instance, a basic one would be that given two events $A$ and $B$, you have that $A$ causes $B$ and $B$ causes $A$, which is considered pathological in causal chains. In our experience, an event cannot be ultimately caused by itself.

There's a variety of physical theories that can cause causal loops. Tachyon point particles, charged Rarita-Schwinger fields, advanced fields and yes, closed timelike curves, as well as plenty of way stupider models that were mostly concocted for the point of discussing causal loops. The basic difference between causal loops and closed timelike curves, if we consider the curve involved, is that the curve described by a closed timelike curve is everywhere timelike (and doesn't contain any nonsense like timelike curves switching time orientation on a dime).

In other words, a causal loop isn't necessarily from a closed timelike curve, nor does a closed timelike curve necessarily cause a causal loop (it's entirely fine if no matter actually travels along that curve).