Would We See the Same Light After Travelling Back to Earth at Double the Speed of Light?

[markterry]

TL;DR Summary

Not Sure

Just joined because I have been unable to find an explanation: please avoid comments about FTL speed since they don't pertain to the question. The question:

A planet is 30 light years away, so when viewing it from earth we are seeing it from "30" years previous. Now, we travel 30 years at light speed and should basically arrive when that light (reflection) left. The question is: if we traveled back to earth at double the speed of light would we not see the same light as it was before we left earth? Where is the time dilation?

 

[PeterDonis]

please avoid comments about FTL speed since they don't pertain to the question.

Yes, they do, since it is pointless to ask what the laws of physics say about a thought experiment that violates the laws of physics.

A planet is 30 light years away, so when viewing it from earth we are seeing it from "30" years previous.

If we assume that the planet is at rest relative to the Earth, and we choose the common rest frame of the Earth and the planet, yes.

Now, we travel 30 years at light speed and should basically arrive when that light (reflection) left.

No, we don't. To arrive when the light left the planet that we saw on Earth before we left, we would have to travel backwards in time. If we travel at light speed (or, to avoid complications, at a speed very, very close to light speed, so the difference in travel time in the common rest frame of Earth and planet is negligible), we will arrive at the planet 30 years after we leave Earth, in the common rest frame of Earth and planet.

The question is: if we traveled back to earth at double the speed of light

We would be violating the laws of physics. But if we traveled back to Earth at a speed very, very close to the speed of light, as above, we would arrive back at Earth 60 years Earth time after we left.

would we not see the same light as it was before we left earth?

Certainly not. See above.

Where is the time dilation?

So far you haven't talked about anything that is even relevant to time dilation. Time dilation comes into play when you ask how much time has elapsed on our clock, the clock that travels with us as we go to the planet and back. The answer to that question is that we can make that time as short as we like by making the speed we travel closer and closer to the speed of light (again, in the common rest frame of Earth and planet). So when we get back to Earth, while 60 years will have elapsed on Earth clocks, only a very short time will have elapsed on our clocks. That is time dilation. (Actually a more precise term would be "differential aging".)

 

[Dale]

please avoid comments about FTL … we traveled back to earth at double the speed of light

That makes it impossible to answer. You ask us not to make comments about something and then the question explicitly states that thing. So we cannot talk about the topic of the question in the answer.

You will need to make a choice. Either you can remove the unmentionable topic from your question or you can remove the prohibition against mentioning it.