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According to Einstein's theory of Special Relativity, one's speed in relation to a relatively stationary object would 'slow down' time on the moving object.

With this in mind, would it be possible to travel in a straight line away from Earth (stationary object) in a space craft able to travel at +90% the speed of light for 2 years and return with significant time dilation?

What technologies have we generated that could reach speeds for significant time dilation (+10 years)?

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For the fist question it is theoretically possible, and it is explained in the popular Twin Paradox example.

For the second one I'm not sure if there are some advances but as far as I know there is an important problem about relativistic speeds: the mass of the object traveling at such speed increases dramatically to the point it would weight so much it would collapse(It wouldn't collapse actually).

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    $\begingroup$ Fast moving objects do not collapse, as explained for example here: physics.stackexchange.com/questions/29632/… The relativistic mass is not invariant, so there exists a reference frame in which I (sitting in my chair) am moving at 99.9999% of the speed of light. But yet I am not collapsing. Gravitational collapse depends on other things (namely the stress-energy temsor) than relativistic mass. $\endgroup$ – mpv May 22 '14 at 13:32
  • $\begingroup$ Thanks @mpv , I shall removoe de collapsing part from my answer. $\endgroup$ – Joan.bdm May 22 '14 at 13:55
  • $\begingroup$ Additionally, the claim "the mass of the object traveling at such speed increases dramatically" is mistaken, or at best engenders a conceptual confusion better left to the dustbin of history. $\endgroup$ – Stan Liou May 22 '14 at 14:26
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    $\begingroup$ Why do you say it is a mistake? The inertia of the object does actually increase. $\endgroup$ – Py-ser May 23 '14 at 5:13
  • $\begingroup$ @Py-ser: In what sense are you using 'inertia' in your statement? If you're transplanting the Newtonian 'resistance to acceleration', then yes, it is greater, but then it is not a scalar and depends on direction of applied force, from $\gamma m$ to $\gamma^3 m$, and so is not actually the relativistic mass. The relativistic mass is just another name for total energy anyway. $\endgroup$ – Stan Liou May 23 '14 at 9:49

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