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When you look at the stars, the light that you see is probably hundreds of years old. Which means that you don't know if they still exist.

Does all this mean, that if you fly in a speed faster than the light, more far and far away from something, you can see how it looked back in time?

Qmechanic
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    If you could travel faster than light you could go back in time, not just see back in time. Luckily for causality you can't. – John Rennie Nov 10 '14 at 17:35
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    Murplyx, you might be interested in Googling for the answer to that. One place to start would be Why can't we accelerate objects past the speed of light?. – John Rennie Nov 10 '14 at 17:38
  • To answer the question in the title as it is currently posed though, yes, you can see back in time. As described in the first paragraph, any time you look into the night sky you are seeing objects as they were when the light left it, not as they are. When you look at the Pillars of Creation in the Eagle Nebula, you are seeing them as they were 7000 years ago. In fact, those structures likely don't exist anymore, but it will take observers on Earth up to 7000 years to see their destruction – Sean Nov 10 '14 at 17:48

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This is a reasonable enough question. Imagine that you are looking at the object and behind you, you have a very large mass of clear, but very high index of refraction material (with index of refraction $n$). Then you could easily say "I wonder how this looked 100 years ago", and then very quickly run behind your large block of material at some speed $c/n < v < c$, and look through the material at the object you are viewing. You would see it at a time prior to what you originally saw it at, and this doesn't violate special relativity or anything. You should make sure not to stand directly behind where you were, because then you would be blocking your own view.

Brian Moths
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But the theory of relativity tells us that you need a lot of energy to reach the speed of light and when you won't be able to travel at the speed of light no question arises of looking back in time

sayan chattopadhyay
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    "...you need a lot of energy to reach the speed of light." Well that's an understatement. You would need an infinite amount of energy, which is precisely why an object with rest mass can only ever asymptotically approach the speed of light – Sean Nov 10 '14 at 17:42