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I may be wrong, but this is just what I've heard.

People often talk about what would happen if we, humans, were able to make a spaceship travel at the speed of light. If I'm not mistaken, then we should not be able to make it out of our own galaxy, since it's millions of light years wide. But, I've heard, that due to the contraction effect, at the speed of light, the distance traveled will actually be much less than what is actually the width of the galaxy, so we should be able to reach the end of the galaxy, and even beyond in a much smaller time span than you would think. Is this right ?

And, if that is actually true, does this hold for light as well ? We've heard that light is about 8 minutes to travel from the sun to the earth, but that is not when taking contraction into consideration, is it ? Or is it different with photons that with ordinary objects at the speed of light ?

Yeah, a lot of questions, and I might just have misread everything I've ever heard. In that case, sorry :)

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    $\begingroup$ People often talk about what would happen if we, humans, were able to make a spaceship travel at the speed of light. Don't listen to them, speed of light observers are meaningless in Physics. $\endgroup$ – jinawee Jan 5 '14 at 21:57
  • $\begingroup$ Then close to speed of light observers. Relativity, time dilation and contraction is still valid for close-to-speed-of-light objects if I'm not mistaken ? $\endgroup$ – Denver Dang Jan 5 '14 at 22:01
  • $\begingroup$ In that case look up the length of our galaxy and divide by the speed, that"s the time taken. $\endgroup$ – jinawee Jan 5 '14 at 22:04
  • $\begingroup$ Indeed, travelling fast enough, we should be able to make it out of our galaxy. In fact, we can do it in an arbitrarily short time providing we go fast enough. It's impossible to travel at the speed of light, but the effects of time dilation and length contraction become so pronounced when we are close to it that in principle we could go from here to the edge of the galaxy in seconds. $\endgroup$ – gj255 Jan 5 '14 at 23:51
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The most important lesson to take away from the special theory of relativity is that the laws of nature behave the same in all reference frames; however, coming in at a close second is the idea that the details of what you observe are highly dependent on reference frame.

To answer your specific questions: from the reference frame of the galaxy, the galaxy is many, many light years wide, but from the perspective of our fast-moving spaceship, the galaxy is contracted (along the direction of the ships motion) by an appropriate amount.

This contraction is "nature's way" of making all the laws work out the same. In the ship's reference frame the galaxy contracts, but in the galaxy-frame, time aboard the ship dilates. The result is that an observer in either reference frame sees that for the people on the ship it only takes a small amount of time to cross the galaxy (as compared to the amount of time it takes as measured by an observer at rest with respect to the galaxy).

It doesn't really make sense to talk about a reference frame moving at the speed of light, but you might think of it as time standing completely still for a photon from our perspective. So while it takes however many millions of years for light to traverse our galaxy, to the photon it is instantaneous (whatever that means).

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If you travel at the speed of light, time will not have passed at all to you. You'll be completely frozen in time. But for any observer, time will have passed.

So if you travel from Earth to the Sun, it'll take 0 seconds to you but 8 minutes to me. If you travel across the milky way it'll take 0 seconds to you and millions of years to me and my grand-children.

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    $\begingroup$ This is the limiting case. There are no observers traveling at the speed of light. $\endgroup$ – Brandon Enright Jan 5 '14 at 22:45
  • $\begingroup$ Well, wouldn't be right to do this thought experiment since, by the special law of relativity, the further you are close to the speed of light the slower time passes? $\endgroup$ – Digger Jan 5 '14 at 23:35

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