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So if I understand right, the warping does not affect the "internal" speed of the spaceship in relation of the universe outside of the warp bubble.

Maybe someone much better with maths and physics can answer this: will the 0.1c speed have a noticable relativistic age-slowing effect for the travelers compared to their Earth-bound friends?

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1.005 seconds vs the observer at rest [1] So 157 days on the ship (.43 years) would be 158 days back at home.

[1] http://www.wolframalpha.com/input/?i=time+dialation+at+.1c

The time dilation effects don't become large enough to have significant affects on aging until speeds significantly higher than .1C. For example, to age at 1/2 normal rate, you would need to be going ~0.86C. This site has a calculator to play with: http://www.1728.org/reltivty.htm?b0=0.1

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