According to relativity, no useful matter can travel faster than light. Suppose that your are a light beam travelling. Now you have a parallel light beam travelling beside you. Suppose you look at the paralle light beam. Since both of your speeds are equal, will it appear stationary to you or ahead of you? If it does not appear stationary, how is it possible when both of your speeds are equal? If it appears stationary, won't it violate maxwells equation?
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We won't be able to observe the light beam because photons don't interact with each other -- there is no way for light to bounce off the other photon so we won't be able to see it!
Even if we imagine a particle travelling parallel to our path, both at the speed of light, if a photon were to bounce off of the particle, it could never reach our position (because we are travelling at the same speed as the reflected photon) and we could therefore never observe the particle travelling parallel with us.
Basically, this means that when we're at light speed, we can never observe another photon in the same reference frame as we are -- we're essentially in our own world until we collide with something. While photon-photon interaction is theoretically possible, interacting photons cannot coexist in the same reference frame due to special relativity.
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Let me put in another way. Suppose I am a human being and I am driving(just for instance) on a light beam. Now I am not a photon.How will the parallel light beam appear to me? – siva phanindra Daggubati Jan 29 '16 at 15:35
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Same answer. You can't look at the light beam that's travelling parallel to you -- and even if a particle were, against all odds, travelling at the speed of light, and a photon bounced off of it in your direction, the photon could never catch up with you because you and the photon (which bounced off the particle at lightspeed) are both travelling at the same speed! – sig_seg_v Jan 30 '16 at 07:33