[codethief]

> Extending that logic, if the observer can also move at superluminal speeds, he could prevent the cause of the event after seeing the event happen, leading to a paradox

This is a guess, i.e. one possible outcome physicists are considering.

People have proposed alternative outcomes of FTL like the (in my opinion much more sensible) Novikov consistency principle, which roughly proposes that spacetime and the entities it contains (e.g. an observer's wordline) should be looked upon as a whole, in the sense that they need to be self-consistent. Spacetime is not time-dependent and does not evolve, so it does not make much sense to say "something something leads to a [spacetime] paradox".

[codethief]

Addendum: Self-consistency basically amounts to periodic boundary conditions – not really surprising when you have (almost) closed time-like curves.

[zachf]

Periodicity in time is unusual to think about in physics, partly because you start to get wacky results. If you could establish a CTC in nature, it would allow for computers that can efficiently (i.e. in polynomial time) solve not just NP problems but actually even all of PSPACE [0]. You can interpret this in two ways. There’s the hopeful way: “we should spend a boatload of money trying to find CTCs in our universe since they’ll let us create super-ultra computers”. And then there’s the pessimistic way, that nature probably isn’t going to give us a free lunch like that. Sadly, I’m in the pessimist camp on this one!

[0] https://www.scottaaronson.com/papers/ctc.pdf