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You can't travel faster than the speed of light, so the question doesn't have an answer.
Based off of empirical evidence the question can have one of three answers: yes, no, or maybe. I'm wondering if you could supply a source for your information, or why you bothered to answer the topic if you had no real information to provide.
Say you are in a space ship moving away from the planet, for all purposes in a straight vector, at or faster than light speed, how about 1ly/h. For example, if you travel for one hour and you turn around, will you be able to see (through a telescope/viewer) events on earth that occurred a year before you left?
Now back to your question: Since it is more SF than science, let's fantasize (for argument only) that Star Trek Enterprise ship will give you 1 hour free FTL ride taking you 1 ly away from Earth. Also, let's assume that the ship' sensors observing the Earth are based on capturing photons that Earth emits. Let's fantasize that somehow those sensors can capture photons even when traveling FTL.Your question was: how and at what time will you see the Earth? My guess is that there are 3 situations:i) while traveling FTL away from Earth: - probably you will see Earth going backward in time. ii) the ship stop (i.e. it is no longer FTL) at a distance of 1 ly from Earth. - while the ship is stopped, you will see yourself on Earth 1 year before leavingiii) the ship returns at FTL - you should see fast forwarding during 1 hour of FTL travel back to Terra, the 1 year of history starting from the time you left minus 1 year to the time you arrived + 2 hour. However, the most likely scenario is that there is no Star Trek Enterprise ship to give free FTL rides
I know that you have warned that this is more SF than science, but, even speculating, I can't understand on which basis you are speculating: aproaching light speed you would see nothing from where you are coming and infinite light from where you are going.
The problem is that there is no known way of accelerating a camera to FTL speeds then stopping it suddenly to do this. I'm all for though experiments, but when you start breaking laws of physics to do them, the results don't tell you anything about physical reality.
Made me think a little that one. Assuming we look at a astronomical picture, each photon on it might represent a different age, thinking that way. Normally we define a time and a 'now' from the moment the picture was taken, but using 'c' each photo should consist of 'photons/waves' of a different time mix (sources).
will you be able to see (through a telescope/viewer) events on earth that occurred a year before you left?
If you really want to see the past, why not take a "selfie" on your smartphone?
... fortunately however if you could travel that speed then you could see earth in the past by traveling far enough away (1 light year per year) and looking through a telescope, the image you see would be from the past. you could even tailor the distance to look back to the required time.theoretically if you can travel faster than light you could set of and catch up the light that left earth from whenever you wanted to see it and observe through a telescope and see the romans/greeks/egypt or however else tickled your fancy
To me that almost sounds doable, even if it's at a smaller scale (say we place a mirror the equivalent of 1 light day away) we'd be able to see 2 days into the past. What do people more educated than me think? Does this sound like a more feasible way of looking into the past rather than trying to "beat the light" to a location?