If we are travelling with the speed of light, can we see whats behind us(like if we are moving away from earth can we able see the earth)? And how we see the things that we are approaching with speed of light? Does the things look like fast forwarding because we are moving and the source also sending photons with the same light speed.
closed as not a real question by Waffle's Crazy Peanut, Manishearth♦ Feb 6 '13 at 15:28
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Remember that there are no preferred frames in special relativity, so your question "If we are travelling with the speed of light, can we see whats behind us?" is exactly equivalent to asking "If something is travelling away from us at the speed of light can we see it?".
We know the answer to this because Nature has kindly done the experiment for us. You probably know that the universe is expanding so galaxies distant from us are moving away, and the speed they move away is dependent on their distance from us. This means there is a distance at which the galaxies are moving away from us at the speed of light. Subject to a few assumptions about the universe, the red shift of light from those galaxies will be infinite and this means we can't see them.
So the answer to your question is no!
I know you don't realize it, but you're actually asking the wrong question. You're making an assumption (massive objects can go at the speed of light) that is unphysical. Still, thinking about this very question (and why it is wrong) is how Einstein came up with his Theory of Special Relativity, so it is worth thinking about.
One way to think about this is to imagine that you send out two photons, say one second apart. They're separated by a distance of one light-second, and assuming they never bounce off of something, they will never collide in the history of the universe.
However, photons don't experience time the way that massive objects do. Their creation and destruction occur at the same instant (as they would experience it); for things traveling at slightly below the speed of light, their creation & destruction occur rapidly (relative to the at-rest reference frame we're using to define their speed), but never quite instantly (as they never go quite at the speed of light).
In short, in order to think about how this works, you want to think about Special Relativity. I recommend reading Mr. Tompkins in Paperback. It does a lot better than I will, at helping you to get a sense of how things work when dealing with special relativity and things that move close to the speed of light. The book imagines that the speed of light were relatively slow, a few tens of miles per hour, and what happens when you take a train trip. It's a fun read.