FTL is one of those things which is acceptable even in fully hard science fiction, because our stories don't work without it.
So, what are our chances of cracking it in reality, by the laws of our presumably non-fictional universe (presumably, because we can't actually prove we aren't all living in a computer simulation...)?
The very short answer is: Probably not.
The longer answer is, well...we don't actually know yet. The more we learn, the more the loopholes (wormholes?) seem to close.
The big problem with faster-than-light is that as you approach it, you need ever more energy to increase speed. Theoretically, going faster than light speed (a bit under 300,000km/s in a vacuum) requires infinite energy.
The most promising idea is the Alcubierre warp drive, which works pretty much...like the warp drive in Star Trek. It creates a space-time bubble that squashes in front of the spacecraft to pull it, and then one which expands behind. The problem is that to start the process you would need to...
...convert the entire mass of Jupiter into energy. Maybe if we had a dyson sphere...
And then you would have to keep producing that much energy. In other words, the warp drive is not impossible, merely impractical.
There's also the possibility of wormholes, but they just aren't big enough to drive a spaceship through. We have no idea what it would take to build a stargate (a controlled wormhole large enough to fly through).
The system I use in Araña is even less likely, but more fun. The idea of crossing into a layer of space in which the light speed barrier is higher and then back is pure science fiction. I mean, it's what they use in Star Wars, which probably crosses the line into fantasy.
But it's the only trick that allows for some of the events in the plot to happen. Sometimes the science just has to bow to the plot...
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