Well, if you were traveling at light speed you could move anywhere in the universe instantly. If you are an observer on earth, watching an object move away from you at the speed of light, then it will take a very long time to traverse the tiniest regions of the universe.
even in a vaccum, light speed travel from the travelers POV still takes time, and said traveler would perceive time passing exactly as occurring in that local space.
But yes you're totally correct, the observer on earth would in this time see only the briefest part of my journey's trail due to light from my journey taking "exponentially" longer to travel back to the observer.
Actually, in special relativity, if you could somehow travel at light speed, your own proper time wouldn’t pass at all. The journey would be instant from your perspective. You’d experience zero time between departure and arrival.
That’s not just "relativistically instant", that’s literally instant in your frame. The time dilation becomes total at light speed, and length contraction collapses the entire distance in the direction of travel to zero.
Now, it’s true we can’t really assign a rest frame to a photon, so this is a thought experiment. But if you extrapolate the math, the conclusion holds: no time passes for something traveling at light speed.
