If we do space travel between stars it would not be this century or even the next. I think star trek might have it right with the 23rd century, but it could also be never ever.
Faster than light travel is theoretically possible, maintaining respect for relativity. The problem is the energy-density required.
Near-light speed is pretty fast and is attainable likely in a few generation’s time. The problem is slowing down will take just as much energy as it took to accelerate - and carrying that mass with the craft will create an exponents paradox.... but this doesn’t even begin to describe the bigger problem - just how bloody big space is.
Proxima Centuri is our closest celestial neighbor at 4.2 light years (or 270,000 times the distance of Earth to the sun).
There’s a slight chance that Proxima B (around 4.5 light years away) is a Class M planet with it being in the “sweet spot”.
so there’s a chance. But it’s a one way ticket. Much like the explorers and settlers of the past three hundred years.... the next generation will be colonizing other planets. Those who survive any way.