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I was recently reading about NASA Faster than Light proposed spaceship, it supposedly will bend spacetime behind the spacecraft, so technically instead of bringing the ship to the destination, "it will bring the destination to you." now, I have an understanding of calculus-based physics, and a basic understanding of relativity.

From my lackluster knowledge of relativity, by conventional means achieving the speed of light is nearly impossible if not impossible, according to Special Relativity. if I am not mistaken if we try using a spaceship, as we approach the speed of light because of relativity, wouldn't the mass of the spaceship go to infinity? and if we have infinite mass doesn't it mean we need an infinite amount of energy to push it?

Even so, if we travel to say alpha centauri, which is 4.4 light-years away it will probably take around a month to go there at the speed of light, which is not bad. It will take a month for the traveler to go there, what about those outside?

to put it simpler, if someone goes to Alpha Centauri at the speed of light and he comes back, how much time would have passed in Earth?

(I would have used, calculations to illustrate better, but I do not know how to use equations in Stack-Exchange yet.)

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Well here's an easier way to see it: as the universe is a fabric of space and time, the fabric can be rolled up and spread according to our needs. The problem: large amounts of energy is necessary for this to happen. In the starting, the Big Bang provided the energy necessary to do it. The speed of light limit is on actual objects, not on expansion of space, as observed during the period just after Big Bang. Thus we can bend space behind us and expand it in front of us at speeds faster than light, appearing as if we are travelling faster than light.

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