Thats interesting but not the effect I was talking about.
Imagine for a second that a species is observing us right at this moment. Now whatever distance they are away measured in lightyears, that is how far back in time they see. So does that mean that both events are simultaneous. The intuitive answer is no. Light takes time to travel and while it is traveling, other events are occuring. However imagine for a second that you could somehow beat the light. For the sake of this experiment, it doesn't matter how you beat the light. Warp drive, hyper drive. Inter dimensional travel. W/E.
So now you are lightyears away and the light you created before you left has not left yet. Now if for whatever reason you were able to transmit just as instantaneously back to the point of origin could you read your own message? Or stop yourself from going in the first place. What would you see? Like I said this is a time travel question, not a light speed question.
I ask because when we look at the stars we are looking back in time. Everyone agrees with that. But an Einstein-Rosen Bridge travels faster. So what does it mean to be able to see the light you made. What effect does that have on reality?
I see what you're saying now. Basically you would have to throw out time as we understand it normally. Time is inseparable from space. The Alcubierre (I think) Drive which is the most realistic idea for FTL travel gets by the paradox that you are describing by compressing and expanding space-time.
To answer your question yes in theory if you could accelerate to relative speeds of FTL you would be able to see and even intercept your transmission. This creates a paradox however which is why it is not possible in practice with our current understanding of the universe.
I think this answers your question. You cannot depart and arrive back before you departed which is what the latter half of your second paragraph seemed to imply. If you instantaneously traveled back to your point of origin you would have just missed yourself depart.
Okay that isn't very clear. I'm not an expert I just read about this stuff and don't work with it enough to communicate it well I guess.