Okay, I'm not a fan of "hard science", but I don't think a propulsion system to reach FTL speeds is feasible?
Short answer: No.
Long answer:
e=mc
2 which means energy needed to even reach light speed will become prohibitive.
So, to accelerate 1000 tones of people and equipment (we can assume a spaceship will weight in that neighborhood) to the speed of light, you will need 90,000,000,000,000,000,000,000 Joule of energy. That is about 21,510,516,252,390 megatons.
Castle/Bravo the biggest US atomic detonation was 15 megatons (63,000,000,000,000,000 J) and the Tsar Bomb tested by Russia was 50 megatons (210,000,000,000,000,000 J).
By comparison:
90,000,000 PJ needed to travel by light speed
210 PJ Tsar Bomb = 428,571 bombs
63 PJ Castle/Bravo bomb = 1,428,571 bombs
Tsar bomb weight 27 tons which means you need a total of 11,571,417 tons of fuel to accelerate a spaceship of 1000 tons to the speed of light and that is ideal case where the energy is 100% converted in velocity.
P.S. I hope my calculation are correct, just picked numbers from internet.
P.P.S. Relativity theory is our best work case. When a new theory is going to be developed and proven viable, those numbers might become obsolete and maybe made FTL possible.