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consider me sitting on the top of a train which is travelling close to the speed of light, will I be able to see my image on a mirror which I'm holding in my hand??

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marked as duplicate by Alfred Centauri, Waffle's Crazy Peanut, Brandon Enright, Chris White, twistor59 Jun 11 '13 at 16:14

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If an object moves with speed $c$ in one frame of reference, it moves with speed $c$ in all frames of reference, i.e., there is no frame of reference for objects moving with speed $c$, no frame in which the object is at rest. This is one reason it is generally pointless to ask question of the form "will I be able to [whatever] if I'm moving at the speed of light?". Such questions presume that one can move with speed $c$ and have a frame of reference but that's a contradiction. –  Alfred Centauri Jun 11 '13 at 14:05

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Yes, as per the principle of relativity.

This is precisely the sort of thought experiment Albert Einstein started out with. It turns out that yes, you will be able to see your image in the mirror when you move close to the speed of light. You will also not notice anything strange about that image, or anything strange about things that are moving with you in your local reference frame.

This might seem strange in the sense that the rays of light will appear to take a much longer time to reach the mirror, and a much shorter time to be reflected back to the moving observer, when looking at that observer and his mirror from an inertial reference frame "at rest".

This "strangeness" is easily resolved though, if you give up the idea that time is some sort of omnipresent thing which both observers always agree on. This, as special relativity has shown (and general relativity elaborated on), is simply not true for the universe we live in; if you start moving, we will start disagreeing on how time works (but still both be correct).

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The main point is that you cannot travel at exactly the speed of light. You can reach 99%, or even 99.999999% (theoretically, of course; you'd be torn apart in reality). So you will still see your reflection, and it will look the same since the mirror is in your own inertial frame.

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"torn apart"? I do not believe this is generally true; in your little spaceship, you'd still claim that all the laws of physics are the same, and that you are indeed happily at rest (or accelerating at the same rate as you were before you reached $0.9(6)c$). In other words, your speed has nothing to do with the forces you experience. –  Rody Oldenhuis Jun 11 '13 at 14:51
    
@RodyOldenhuis Maybe I was exaggerating a bit. But forces are involved - in order to reach (almost) $c$ at a constant acceleration of, say $5g$ (which is what test subjects could bear for some 10 minutes), you'd have to accelerate for about 70 days (in your own inertial frame, externally it's about 27% longer). And since at $5g$ you'll probably have trouble eating&stuff you cannot accelerate permanently. Unless you increase the acceleration significantly (which would tear you apart), the tension (=suspense) would kill you... –  Tobias Kienzler Jun 12 '13 at 6:45

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