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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?

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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).

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  • $\begingroup$ It had been my impression that closed timelike curves simply express a potential for repetition, which may be essential for unitarity (the idea that all probabilities for a physically-possible event occurring must add up to 1). That's why they're a part of the description of rotating black holes (which may itself equate to "all black holes", inasmuch as their rotation may only approach zero asymptotically, as stars generally rotate, although that rotation may eventually be slowed nearly to zero by gravitational effects of other astrophysical bodies). Correct me if I'm wrong. $\endgroup$ – Edouard May 13 '19 at 20:11

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