It's well known that, in relativity, if you can go faster than light, you can go backwards in time and create a paradox.
Also, attempts to create "warp-drive" space-times in which something moves faster than light (the best known is the Alcubierre drive) usually require lots of "negative energy", something which in reality may only be available under rather special quantum-mechanical conditions (e.g. Casimir effect).
So one might suppose that the universe obeys an "energy condition" which provides a physical (and not just logical) barrier to paradox.
But lately there's a news story about an American physicist (Erik Lentz) who claims to have constructed a superluminal soliton using only positive-energy sources. The preprint was released last year and has now been published.
I have yet to find a technical analysis of the paper. The closest thing so far is a comment to a journalist by relativist Ken Olum, who proved one version of a relationship between faster-than-light travel and energy condition violation, and who thinks his theorem must apply to Lentz's soliton too.
At his blog, Lentz also mentions a recent review of warp-drive space-times that talks about slower-than-light positive-energy warp-drives, and faster-than-light warp-drives that violate energy conditions, but says they didn't analyze his own construction (which, to repeat, is meant to be a faster-than-light warp-drive that doesn't violate energy conditions).
So what's the story? What exactly is Lentz's new idea? Is there a reason why a sufficiently advanced civilization can't build a Lentz drive and change the past?
(Thanks to T.L. for bringing these works to my attention.)