If I and a group of friends are travelling at or just below the speed of light - can I see myself, can I see them, or they me? Would we see anything at all?
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5$\begingroup$ You can't travel at the speed of light - that's been discussed to death around here. As for just below, there is, for example, this pretty simulation from the MIT. $\endgroup$– ACuriousMind ♦Commented Oct 22, 2014 at 17:37
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$\begingroup$ You'll die almost instantly due to microscopic small dust particles colliding with your spacecraft at extremely relativistic speeds, releasing energies larger than that of exploding nuclear devices. Also, the microwave background will be blue shifted to become hard gamma rays. So, you'll be vaporized before you can experience anything at all. $\endgroup$– Count IblisCommented Oct 22, 2014 at 19:19
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$\begingroup$ First of all, according to you and your friends, you are at rest - everything else is moving with respect to you. That's the essence of the relativity of motion. Second, regardless of how fast other stuff is moving with respect to you, you will measure the speed of light to be $c$. Third, no material objects moving with respect to you will have speed $c$ or greater, only speed less than $c$. $\endgroup$– Alfred CentauriCommented Oct 23, 2014 at 0:11
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Unless you have zero mass, you cannot reach the exact speed of light. But lets work with the hipothesis that you are just below light speed. Two things would happens:
Doppler effect: light coming towards you would get blue shifted. That means you would be unable to see a blue object coming towards you, since you would see it as UV radiation or, depending on how fast you are, even as a X-Ray or gamma radiation. But you would be able to see the infrared radiation of a oven flying towards you, or even the radiowaves of a cellphone tower (your cellphone would not work, although). In the other hand, light coming from behind you would get red shifted. You would not be able to see a red object behind you because, for you, it would be infrared light. And if someone fired an X-Ray machine behind you, perhaps you could see it as a blue flash.
The other effect is a geometrical one and is caused due to a combination of the time dilatation and spatial contraction. It is called Terrel rotation and basically states that if someone at large relativistic speeds sees a cube, it would appear rotated. Wikipedia points to some references about this http://en.wikipedia.org/wiki/Terrell_rotation
