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You are standing still in a vacuum, and you throw a ball that moves 10 m/s away from you. Now you start moving in one direction at 5 m/s, and throw the ball in the other direction, away from the direction you are moving. The ball, relative to you, is going 10 m/s, but relative to an unmoving body, it is traveling 5 m/s.

My question is: is this same concept applied to light? If a light source is traveling away from you at a speed greater than that of light, would you be unable to see it? Or would light just keep going the same speed relative to an unmoving body?

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    $\begingroup$ You'll see the Doppler effect for accelerated sources, but the light always has the speed of light (duh!). Note that your title question is wholly unrelated to the question asked in the post, and that no source can move with the speed of light (or even faster). $\endgroup$ – ACuriousMind Jan 19 '15 at 16:48
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    $\begingroup$ There are probably many duplicates of this type of question. $\endgroup$ – ProfRob Jan 19 '15 at 16:52
  • $\begingroup$ possible duplicate of Does a photon instantaneously gain $c$ speed when emitted from an electron? $\endgroup$ – Kyle Kanos Jan 19 '15 at 17:34
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Special relativity deals with high velocities.

In special relativity, the relative speed of light is constant it always moves at $c$. Nothing can move faster than the speed of light relative to you.

Also velocities are not additive in special relativity.

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    $\begingroup$ That's not exactly true. Nothing can move through space faster than the speed of light relative to you, but space can do whatever it wants. Given a universe with accelerating expansion, a light source can be receding from you at greater than the speed of light without violating any cosmic speed limit. Since the intervening space itself is expanding faster than light can travel, the light will never reach you. $\endgroup$ – Stan Rogers Jan 19 '15 at 20:17
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If a light source is traveling away from you at a speed greater than that of light, would you be unable to see it?

You'd be unable to see it because it would not exist. Speed of light's a limit. A light source moving away from you faster than that doesn't even make sense.

If it were moving away from you at the speed of light (well, really really close to it) then you would be unable to see the light that arrived from it because it would be red-shifted down below human vision.

Or would light just keep going the same speed relative to an unmoving body?

If there's a detector fixed to the light source, one on your planet, and one on a craft moving towards that light source at half the speed of light, the photon would pass through ALL THREE detectors at the speed of light, even though they are moving, respectively, at 0, 0.5, and almost-1 $c$ away from the light source.

But the three of them would not be able to agree on what time it was.

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