I think some of the people responding to the comment about solving the energy problem are missing the point. There's solving the energy problem in the sense of finding an energy source that can power human civilization (preferably without melting the planet I live on, but that's a discussion for another thread). Then there's solving the energy problem in the sense of accelerating a spaceship to ultrarelativistic speeds. The latter is a very hard problem.

A good rule of thumb to remember is that if you're going fast enough to experience large time dilation, then your kinetic energy is to be large compared to your rest mass. It's the same factor of γ=1/√(1-v²/c²) either way. So if you're traveling 1000 years in 15 years ship time, you've got γ=67 and your kinetic energy is 66 times your rest mass. Ouch! (And here I'm making the incredibly optimistic assumption that you aren't carrying your fuel with you, because if you are then you also have to expend energy to accelerate your fuel, and to accelerate the fuel you use to accelerate your fuel, etc.)

If the rest mass of your ship is about the same as that of an aircraft carrier (the USS Enterprise, CVN-65, seems appropriate), then 66 × 86000000kg × (3×10×⁸ m/s)² = 5×10²⁶J. That's a lot.

Nuclear energy in the ordinary sense is nowhere close to enough. This is thousands of times more energy than we could get with all the U-235 on Earth. Or we could imagine getting this energy from fusion, using the big fusion reactor located a cozy 8.5 light-minutes away from us. Earth gets about 123000TW from the Sun, so another way of looking at this number is that if we captured 100% of that energy, it would take us 130 years to get enough for the ship's kinetic energy.

Accelerating big things to ultrarelativistic speeds isn't easy.