when light travels away from earth, are we not travelling away from that light at the speed of light?what implications does this have?
Light travels AWAY from a physical source at the speed of light. The physical source does not travel AWAY from the light at the speed of light.
Special relativity says two objects with rest mass cannot move at the speed of light relative to one another. Light has no rest mass, so a photon is not a valid frame of reference. If you did take a photon as a frame of reference, the universe would be contracted to zero thickness and time would cease to exist. So the source of the photon would have velocity equal to zero divided by zero in that reference frame.
No, the speed of Earth relative to the light ray is an immeasurable quantity. It's not even a quantity. No observer can ride the light ray to measure it. No inertial reference frame exists where that light ray is at rest in which such a measurement might be made.
Speed is relative. If we were the only two things in the universe and approcahed each other at 1,000 mph there would be no way to tell which of us was moving. It is as correct to say you are moving at 1,000 mph and I am standing still or vice versa or any combination. However, light (indeed any massless thing) *must* move at light speed. It cannot go slower (yes you can slow light down by making travel through a medium such as glass and other things but that is just the speed of light in that medium...it is still a speed limit). As such there is no reference frame to pretend you are moving and the light particle is standing still. You *know* the light particle is the thing that is moving. ETA: If we extend my example of you and me in space (just above) but make you a photon then to be the same there is a frame of reference where I am standing still and the photon is moving at light speed. So, can the flip side be true where the photon is standing still and I am moving at light speed? No, because nothing with mass can move that fast so what worked for you and me falls apart with me and a photon. There is no reference frame other that the photon moving at light speed which it must always do.
I think you are describing the twin paradox of special relativity, the short answer is no there are no real implications, first off photons are photons, they don't know they are traveling at the speed of light, time is irrelevant to a photon. The twin paradox is that you have 2 twins, one goes off in a space ship for a long time (traveling close to the speed of light), then comes back. What happens? If you look at it from the perspective of the twin in the space ship, then it would appear that he stood still, while the other twin (left on the Earth) hurtled off into space at great speed, so he should predict that the other twin aged less (since it was the OTHER twin that was traveling fast). On the other hand, the twin left on Earth sees the exact opposite, that the one in the space ship flew off at great speed was gone for a long time, then came back. He will predict that the twin in the space ship should not have aged for very much and will say that the time was less. OK, so who is right, since obviously it's impossible for them both to be right. The answer is the twin in the spaceship will age less. This is because we are ignoring one MAJOR aspect of the experiment...one that we didn't even mention earlier. That is that although it may appear that the twin in the space ship sees the earth twin hurtling off, the truth is that it IS the space ship twin that is accelerating, he would know (feel) this acceleration and thus know that he was the one that was traveling faster and thus would realize that he will experience less time. It's this time in the non-inertial frame from when he accelerates to near light speed and then when he turns around that distinguishes the two twins and thus this is not a paradox at all.
