Aliens who might have evolved ages before us are not doing it so why do you think humans will?
They aren't?
Really?
I'm curious how one could claim to have both a rational mindset and claim what you have.
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As to the original question:
We already have the technology and the ability to travel to other star systems.
The unfortunate reality is that it would be the great great grandchildren of the crews that launched who would actually arrive in the target star system - and it's quite possible that they would find out that this other hyper-advanced humanoid species beat them to it... because they are our own descendants who made a breakthrough in near-light or FTL travel a hundred and fifty years after the first crew left.
But that does introduce some interesting moral quandaries.
People tend to get upset about abortion being an involuntary end to a life given no chance at a future. What is to be said of the generations aboard a generational ship whose purpose is decided at birth? They are to live, produce a couple offspring, raise them to continue the mission, and die.
I think any practical generational ship idea would have to include a means for cryogenic preservation and revival. Basically - the successive generations would be able to be frozen and revived when they reach the destination - so all generations would effectively be able to reach the destination while maintenance on the ship could be continued (of course, this begs the question of why not just freeze everyone to begin with, if we have the ability to do it and return people to life?).
Anyway -
I also believe that it is possible for a form of Faster Than Light travel to exist. I do not believe, however, that it will involve wormholes, 'warp bubbles' or other contrived nonsense. I think it will be as simple as "It was in this place, now it is in that place." The world of QM is much more tolerant of such behavior from objects than contrived warp bubbles and fields that have no precedent.
Of course... if we knew how something like this might be done - then we'd have some solid experimental data to hammer out a theory of how to do this on a larger scale. Right now, the speed of light seems fairly impenetrable.
Even so, propulsion technology is improving quite quickly. VASIMR drives are looking to be the drive system of choice. Scaling the drive system up for higher thrust ratings is possible, and I posit that the magnetic field can be strengthened to the point that fusion can be induced as a sort of 'afterburn' for even greater thrust (but reduced efficiency) values.
There are some other interesting developments in plasma-related propulsion (such as the double-layer drive) - all of which have their potential applications.
I think we will get much farther than we believe possible, currently.
But I don't know how quickly we will get there.
Consider history for a bit.
Imagine you were living in Europe during the 1200s. You're surrounded by the echoes of an empire that you know was great - that historians talk about and culture still reveres.... but you look at its relics and you can't even begin to maintain them, much less recreate them.
Yet, here we are, today with the ability to do things the Romans could only dream of.
Sure - they did some clever things that we will probably never know, for sure, how they pulled them off... as with the Egyptians before them. Every great culture has left its share of accomplishments and mysteries... but we've moved forward.
Even during the dark ages, we were refining the process of forging and tempering steel. Chemistry was coming to light. Concepts of health were becoming more common as plagues wrought destruction.
Perhaps our own civilization will decline for a time. When a forest becomes too cluttered with the old, dead things - a fire will surely cleanse the ground to make way for the new.
Imagine that our grandchildren grow up without being able to mass-produce cars, but still have computers and automated production concepts like CNC machines and 3d printing. The world they'll create will be completely different from ours with different solutions to some of the problems that we solved a century ago and haven't revisited.
Perhaps they will only rarely recreate our massive factories, preferring to have a "replicator" in every basement - even if their power is only on for 6 hours of the day.
It's hard to say what direction everything would go.
But, eventually, we would look to expand to the stars, and we would begin solving that problem once again, no matter how hard of a blow we are dealt.