I actually spent some time sketching out the math for an aborted science fiction world in which I had FTL that was prevented from time travel by a cosmic censor. You don't really have to "work it out" because the numbers are quite plain as day.

It turns out that if you use any remotely sane numbers on the speed of an FTL craft, it is extremely difficult to travel in time. To get time travel, you have to accelerate on the other end to very significant fractions of the speed of light, which itself takes so much time that it's hard to recover it via the FTL drive again. You have to put in absurd numbers for the speed of the drive and your ability to accelerate (and your ability to carry energy for conventional acceleration!) before you can get time travel out of most FTL drives, because bending your light cone enough to put the past into your FTL drive's path takes a lot of energy.

The only fictional drives that have serious time travel possibilities are the ones in universes where accelerating to significant fractions of the speed of light is easy-peasy, and the FTL drive is very, very fast (some are instantaneous) and can be arbitrarily steered. It's actually not that long of a list; a lot of FTL drives can hypothetically be used for time travel but the engineering in the universe still doesn't practically permit it. Just adding a cosmic censor post facto would preserve the story just fine. Many of the universes that meet those criteria are already so fantastical that they do in fact have time travel, so... those work out too.

(There's also several video universes where it's nominally possible, but the video wildly contracts the documentation. Both Star Wars and Star Trek have documentation that their ships can get to pretty significant fractions of the speed of light in small amounts of time, with ludicrous amounts of acceleration available to them, but on screen we only see them moving with absurd levels of acceleration like 50 or 100G, but which still takes a long time to get to light speed as a result, and with refueling being necessary often enough that it's hard to believe they could actually make it.)

> Both Star Wars and Star Trek have documentation that their ships can get to pretty significant fractions of the speed of light in small amounts of time, with ludicrous amounts of acceleration available to them, but on screen we only see them moving with absurd levels of acceleration like 50 or 100G, but which still takes a long time to get to light speed as a result, , and with refueling being necessary often enough that it's hard to believe they could actually make it.)

I don't know about Wars, but Trek strongly implies that impulse drive reaches significant fractions of light speed with near-zero acceleration time; there is certainly nothing to indicate that the on-screen non-warp acceleration is limited to 50-100G, and there is little on-screen indication that refueling (as opposed to drive system maintenance, and replacing non-fuel consumables used onboard) is regularly needed.

In both Star Trek and Star Wars, the ship accelerates very fast and then "blinks" away. Maybe it just needs a running start, like the turbocharger in car engine.

I thought the Bussard ramscoops on the warp nacelles were explicitly mentioned on-screen, not just in the show’s technical manuals?

"there is certainly nothing to indicate that the on-screen non-warp acceleration is limited to 50-100G,"

The indication I refer to is that when you see a ship moving on screen from the perspective of another ship, it never suddenly blinks to "near lightspeed", because what that would look like is that in one frame the ship is there, and the next it isn't. That is never what happens. What happens is that the ship lumbers off, and slowly turns over the course of a couple of seconds, and can be seen to visibly accelerate in a way that the ship doesn't even cover its own length in less than five or six seconds. If you work the math it comes out on the order of 50-100G. Accelerating to near-lightspeed in a couple of seconds is several orders of magnitude larger than that.

Of course the ships don't blink around at near lightspeed; it wouldn't be photogenic. So all ships on all shows in all screens move within roughly a single order of magnitude of screen speed, no matter what the tech manuals say. Similarly, no matter what the claimed ranges of the weapons are, all engagements take place within a range where the two ships can clearly see each other, meaning no more than a handful of kilometers at most. No matter how far the ships are nominally apart from each other, a bolt of energy fired from one ship to another will take on the order of half a second to arrive. Almost no matter how zoomed in we are or are not, the energy bolts will subtend roughly the same amount of our eyes. If the ship is, say, firing on a planet, the bolts will perspective shrink maybe by a factor of two or three, if they shrink at all, rather than doing what they should do which is disappear entirely (except for perhaps one lit pixel if the bolt is sufficiently emissive). There's this one ST:TNG episode where the Enterprise uses phasers to quickly mine holes in the ground and when you start to see this sort of thing it's hard not to see the Enterprise as firing on a roughly 5-mile-diameter ball sitting right next to it, because if you follow the perspective of the "beam" that's what it implies about the size of the target.

Space isn't photogenic. Even today on earth, real combat takes place at ranges where you don't have a direct visual on the target a lot of the time. Any even vaguely realistic space combat will take place across ranges where you can't see a mile-sized ship with the naked eye. But that's not what they want to show. Consequently there's a massive, massive mismatch between the numeric claims of performance and what we actually see on the screen. So you might say something like "oh, the screen is maybe being symbolic", but then they routinely do things that imply what's on the screen is the real truth, such as in the one TNG movie where Data leaps between two ships. That's just one example, there's plenty of other situations like that.

It’s a cool idea, and admittedly would be a sort of loophole, but it might just mean that such a drive would require an arbitrarily high amount to work. Maybe Stephen Hawking was right and as soon as you build a machine capable of time travel, turning it on blows it up, because of QM effects. It does seem a little neat if how we intend to use the machine is the deciding factor in how it works.

Back in his collection All the Myriad Ways, Larry Niven wrote a brief essay called "The Theory and Practice of Time Travel" that explored ideas like these. One excerpt:

> GIVEN: That the universe of discourse permits both time travel and the changing of the past.

> THEN: A time machine will not be invented in that universe.

> For, if a time machine is invented in that universe, somebody will change the past of that universe. There is just too much future subsequent to the invention of a time machine: too many people with too many good motives for meddling with too many events occurring in too much of the past.

thus

> Niven's Law: If the universe of discourse permits the possibility of time travel and of changing the past, then no time machine will be invented in that universe.

It also could blow up if it accidentally causes time travel...

Any progress on that idea (Alcubierre drive)? Always seems the most interesting. I do a Google Scholar search, but I don't know the physics journals, so its hard for me to know legit from crank abuse, without laboriously checking each result for journal impact factors.

The debate continues. E.g.

https://www.hindawi.com/journals/isrn/2013/482734/

I suspect using GR to design a warp drive is like using a spoon to build a freeway. Without a theory of quantum gravity - which appears to mean not just a theory of quantised space time, but also of the non-locality and complex distributed relationships that haunt QM - you're probably not going to get very far.