system
Given the following post, respond as if you're commenting on Reddit:
human
What would the ramifications of a lack of causality be?

People say you can have two of three: causality, relativity, and FTL communication. The convention is to discard FTL communication. But what are the consequences of an acausal universe?
gpt
Unpredictability. The equations of motion lose existence and uniqueness. Given a certain initial condition at time t, there might not exist a solution to later time, or there might be infinite equally valid. Essentially the Universe doesn't know what to do with itself, and even if it does, there is no way of predicting anything even having knowledge of the equations of motion and initial condition. Physics is dead.

That loss of existence and uniqueness actually occurs has been studied for various cases, including the motion of a rigid ball in a spacetime with a wormhole allowing timetravel (see e.g. the works of Novikov & Thorne), or classical field theories in the presence of CTCs.

The exceptions are free theories, but these are boring, no actual physics can happen in them. As soon as you add interactions of any kind it's over.

Another sort of consideration comes from thermodynamics. We have a second law because our Universe has two temporal extremities with different entropies. So entropy increases when moving from one to the other; we call the low-entropy one the Big Bang and the direction of increasing entropy gives the arrow of time, and interesting stuff happens following the Universe in this direction.

If you have a region with CTCs where, say, you can think of time as a circle, there is no way of course for entropy to always increase in one direction. The most probable situation is to always have constant maximum entropy, that is thermal equilibrium.