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For this question assume that.

We found a way to go faster than light.

I build a ship that could go faster than light and go to another planet with this ship in the span of mere hours. The ship was built in a year time.

If I travel to another planet one light year from Earth, and I would look back.

Would I see the ship being built?

Since the light that comes from earth is 1 year old when it reaches me you would assume that I can see the ship being built 1 year back(with a powerful telescope)

So my question is : If FTL travel is possible, can I look back in time to a younger earth?

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    $\begingroup$ Hang on, let me try to reach Prof. Einstein on my tachyonic antitelephone... $\endgroup$
    – Mike G
    Mar 18, 2019 at 16:07
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    $\begingroup$ I'm voting to close this question as off-topic because it seems to fall into the "purely hypothetical" category mentioned in the Help Center, and the principles already have an answer on Physics SE physics.stackexchange.com/questions/52249/… $\endgroup$
    – user24157
    Mar 18, 2019 at 19:06
  • $\begingroup$ If FTL travel is possible, you can even send a message to your past self back. Google for "tachyonic antitelephone". $\endgroup$
    – peterh
    Dec 23, 2020 at 22:55

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"Yes, but no."

If you could jump through space faster than light can travel, and you went 1 light year away to 'look back at earth', then you would observe the light emissions that began 1 year ago, and continue to observe them as they arrive. [And if you start moving towards or away from the emission source, then 'neat things' happen due to blue/red shift. Or red/blue shift, I'm waiting on coffee and forget which direction the shift is in.]

(Whether you could have the optical resolution to actually SEE something like a ship being built from that far away is another matter. At that distance the dominating signal would be the star's output as a whole, and digging other information out of it would get tricky. And if we handwave how exactly we punch a hole through space-time to actually make the FTL jump, then resolving details from that distance might actually be the harder part of the question here...)

This is however not strictly speaking looking back 'through time', but merely observing a signal delay between the event's actual time and the point where you can detect the signal.

If you watch someone driving a fence post from a distance you'll be able to see the hammer strike, but the sound will be slightly delayed - We don't normally consider this as "hearing through time", but it is ultimately the same effect: Observing a signal after it was emitted due to the time required for the signal to travel from its origin to the observer's location.

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You could do better than that. You could walk around on a younger earth. This Physics.SE Q&A addresses why. The short of the matter being that things are moving with respect to each other, and so have different inertial reference frames. Your ability to travel faster than light lets you exploit the differing reference frames to conduct a round trip that arrives before it departs. It doesn't matter how it is you manage to go faster than light. Any FTL travel implies time travel.

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If you have the technology to build a faster than light ship then you will probably have the technology to build equipment capable of receiving any signal ever transmitted on earth. Why stop one light year away. Go for a hundred or so. Get the first broadcast by Marconi, the first I love Lucy or the first text message ever sent.

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