I've been spending quite some time trying to understand why an FTL-drive would also imply time-travel, but every answer I can find seems to mainly be about semantics and perception. I will break it down to a very simple question:
I have a watch. Jean-Luc Picard leaves on the Enterprise from my position at my current time (10:05, 2021-09-13), his mission is to go to [place] and then return to my position. No matter how fast or slow his FTL-drive is, I am going to claim that there is no way he will ever achieve time-travel and thus violate causality according to my time at my current position, i.e he will never arrive to me before he left in a way where it's not just the perception of light-lag to my retina, and thus he will never be able to interact with himself in any way (meaning: no time travel). Can anyone refute this?
On John Donnes request I will clarify a few things. What spurred me to write my own (according to me) simpler question was reading through the answer given here: How does faster than light travel violate causality?.
This answer is basically "plug x numbers into equation y and then you have time travel", but it allows zero intuitive understanding, and I can still not see how it would allow Jean-Luc to arrive at my position before he left. Erudaki exemplifies my confusion in his comment to that answer, where he calculates that the ship in that question would return to earth at year 23204, not year 2796 as the answer claims.
Here's the specific part of that answer which irks me:
- In the futuristic Earth year of 3000, Tralfamadore is 98,000 light years away, and receding at 20% of $c$. I leave Earth at 1000% of $c$, relative to Earth.
- In Earth year 13000 Tralfamadore is 100,000 light years away, and I catch up to it. I turn around and leave Tralfamadore at 1000% of $c$, relative to Tralfamadore.
- In Earth year 2796, I arrive home.
I do not understand why in this example the traveller would arrive at 2796 (earth calendar), rather than 13000 + x (where x is travel time from Tralfamadore).