Some things will remain impossible, but some will not.
As for a form of entertainment or a unit in a staff canteen that produces objects with physical form, less than likely at the moment or the foreseeable future but, as with most things, I refuse to dismiss the possibility they could exist in the distant future.
I've found two things drive technology:
Solid cash
War (or cold war)
The former will look after entertainment, convenience items, and normal transport, the latter will be driven by political idiots but still produce its one useful outcome - a massive technological leap forward (assuming the human race survives politicians)
The indications from mathematical models are that a warp drive would require literally astronomical amounts of energy to operate. We're talking about amounts equal to the mass-energy of Jupiter here. That's more mass-energy than 300 Earths. This is a separate issue from generating the required amounts of negative energy, by the way. So even if turns out that these currently-understood energy requirements are an over-estimate, they would have to be reduced to at least 1/300th of current estimates, likely much more than that, if we are to be able to operate a warp drive without first growing to become a Kardashev 2 civilisation.
Note that even if the warp drive mass-energy requirement can be lowered to the point where it
equals the Voyager probe, the only fuel with the energy density necessary is antimatter,
according to physicist Sean Carrol. Which has its
own production issues, costing as it currently does about $100 trillion per gram to synthesise. And unlike with STL starships, we don't have the option of leaving the power plant behind and pushing the ship using lasers or particle beams.
The implications of all this are that even if warp drives are physically possible, and even if they don't require astronomical quantities of mass-energy to operate, then by the time we can seriously consider actually building one of these things, we'll have already been in space for centuries, or more likely millennia. We would have to have control of stellar quanties of energy, which under current understandings of physics would require a Dyson swarm.
But if you've built a Dyson swarm*, then even without having warp drives or antimatter, you're already in a position where the energy required to push a starship at relativistic velocities is trivial compared to the total output of the star you're collecting. So it's not like we even
need warp drives to travel to the stars.
*(Which can be done in the Solar system without dismantling any the planets. There's more than enough material within the Sun itself, which can be mined using
starlifting techniques. As a bonus, we could use starlifting technology to prolong the life of the Sun, preventing it from getting too bright as it ages and progressing to the red giant phase.)
