Recently an interesting paper came out that starts by accepting all solutions to special relativity (usually the faster-than-light solutions are ignored) and goes on to derive the axioms of quantum mechanics from just that. It turns out what you need to prevent timetravel paradoxes is exactly quantum mechanics.

https://www.eurekalert.org/news-releases/540753

https://arxiv.org/abs/1910.02780

I don't understand the whole derivation (especially the way they move from 1+1 to 3+1 spacetime), but it feels quite elegant. It could be interpreted as universe having a separate family of particles going backward in time synchronizing entangled particles over distance.