If by seeing you mean looking through a ship window, then Earth would appear to move faster or slower based on direction of travel.
Since "seeing" is nothing more than light transmission being translated by our eyeballs, as you leave Earth it would redshift and appear at a standstill (no new information is reaching you). However, as you return to Earth it would blueshift and appear to be spinning really fast. (Information reaching you at the speed of light which you are receiving near the speed of light)
Factor in Earths orbit/rotation and the traveler wouldn't likely be able to see Earth while in approach due to the doppler effect since at blueshift it would visually appear to move so fast that it would be either a blur or invisible.
Yeah, fair point. When I spoke about what an observer "sees", it was ambiguous whether I meant "what they see with their eyeballs/camera" (which is affected by the Lorentz transforms and the Doppler effect) or "what's happening in their reference frame, after accounting for the speed-of-light delay" (which is just affected by the Lorentz transforms). In this case I meant the latter.
This ambiguity is pretty common when discussing special relativity. People normally assume you're going to subtract away the speed-of-light delay to get to the "true" picture.
As you say, the Doppler effect means that as you approach Earth you'll really see it blueshifted and sped-up, but only because the speed-of-light delay is decreasing as you get closer.
I don't think Earth would ever be invisible though: the infrared light would be blueshifted into visible, and if anything I would expect it to appear brighter due to relativistic beaming.
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u/mjones8004 Nov 28 '24
If by seeing you mean looking through a ship window, then Earth would appear to move faster or slower based on direction of travel.
Since "seeing" is nothing more than light transmission being translated by our eyeballs, as you leave Earth it would redshift and appear at a standstill (no new information is reaching you). However, as you return to Earth it would blueshift and appear to be spinning really fast. (Information reaching you at the speed of light which you are receiving near the speed of light)
Factor in Earths orbit/rotation and the traveler wouldn't likely be able to see Earth while in approach due to the doppler effect since at blueshift it would visually appear to move so fast that it would be either a blur or invisible.