It is my understanding that time dilation slows down perceived time relative to the outside of a given vessel as it approaches the speed of light. Does that not mean that the inhabitants of said vessel would experience a journey, while traveling close to the speed of light, as taking proportionally less time the closer the vessel gets to light speed?
Assuming time dilation is linear, if I'm traveling at 99% the speed of light, for every 1 year that I see go by, the outside of my ship sees 100. That would mean, to me, in 1 year I traveled 99 light years, and to the resting universe, that same distance took me 100 years, which doesn't break any laws.
Lets say the speed was 99.9% the speed of light. Now 999 light years only took me a year. What about 99.99%, 9999 light years in a year? That's the average thickness of the Milky Way! You see the trend. Would it not be more feasible to develop technology to approach the speed of light and take advantage of time dilation than to develop technology to break the laws of physics as we know them?
Apologies, I should have phrased the last part differently. The theoretical "breaking the speed of light" technologies I'm referring to are the ones that "warp" space-time to allow the user to "take shortcuts" through space-time. My question is, why develop space-time warping technologies which at the moment, we have no or very few theoretical designs for, when we can push our efforts to developing faster and faster means of travel, taking advantage of time dilation. I've heard that an implementation of the Orion project (the propulsion of vessels with explosives and a bumper plate to absorb the energy, pushing it through space) could take us to a reasonable percentage of the speed of light.
Also, I realized that time dilation is not linear. I didn't feel the exact mathematics were important in posing my question; I wanted a simple example in my explanation of the question. Here's a good link for the correct mathematics: http://dilation.1e5b.de/
Finally, though it would be great if interstellar travel were possible in our lifetimes, I doubt it will be seeing the space program (NASA's space program, that is) hasn't been given the funding it used to. Then again, one of the Wright brothers stated that a trans-Atlantic flight would be impossible for the next 1000 years, and you see how quickly he was proven wrong. Either way, I doubt anybody is really working on this technology in the present or will be in the near future. I could be wrong, though.