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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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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The linked question referenced as duplicate is gone. Is there another link that is a duplicate question? – Kyle Weller Oct 17 '17 at 22:03
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Voting to reopen since the duplicate-source is deleted... – Tobias Kienzler Oct 21 '19 at 20:34
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Probably would be better to just request the other question be undeleted than reopen this one, @TobiasKienzler – Kyle Kanos Oct 21 '19 at 22:57
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@KyleKanos How so? I don't know why the other one even got deleted nor can I check its quality (lacking 10k rep). But either way I'm fine – Tobias Kienzler Oct 23 '19 at 06:52
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@Tobias use a custom moderator flag on this one indicating the deleted link dupe. I already flagged the other one as to be undeleted, but haven't checked on results – Kyle Kanos Oct 23 '19 at 11:05
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@KyleKanos Good point, done now – Tobias Kienzler Oct 23 '19 at 15:27
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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).
Rody Oldenhuis
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By the way, Einstein never thought of such a thing, at least not on record. He did think of a similar experiment, as follows:
"If I pursue a beam of light with the velocity c (velocity of light in a vacuum), I should observe such a beam of light as a spatially oscillatory electromagnetic field at rest. But there seems to be no such thing, whether on the basis of experience or according to Maxwell's equations."
– yungwean Jun 25 '20 at 11:32 -
By the way, why are you talking about "close to the speed of light" when the question is asking "at the speed of light"? I would say that this question is nonsensical, as you cannot travel at the speed of light. Who knows what the model predicts with a hypothetical? – yungwean Jun 25 '20 at 12:00
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@yungwean Well, that's why I said "...the sort of thought experiment..." and not "the exact thought experiment...". And like you say, "close to " is physical, while "at " is nonsense (for sentient observers, that is). Also, I thought that explaining things like that the observer's time dilation would be infinite and they'd need an infinite amount of energy to reach that speed etc. would be mere distractions and a missed learning opportunity. – Rody Oldenhuis Jun 25 '20 at 22:30
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@yungwean Granted, I could have written this answer more elaborately to include all of it, building up to a more exact and complete answer to the question, but I feel that textbooks are simply a better format for that... – Rody Oldenhuis Jun 25 '20 at 22:30
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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.
Tobias Kienzler
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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
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@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 06:45