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You (and pretty much everbody else) are forgetting that relativity treats space and time as one, and how it does so... the gif is also completely wrong in how to describe it.
For starters: You are always moving through spacetime at the speed of light,as expressed by a simple formula:
v(time) + v(space) = c
As "c", the speed of light, is known to be a constant, as v(space) increases, you have to reduce v(time) and vice versa.
v(time) is the "velocity" you move through time with.
v(space) is what you would regularily know as velocity. This variable cannot be negative, as simply reversing your ship still implies a positive velocity, just in another direction.
if v(space) > c, time would only go backwards locally on your ship (since c is constant, and v(time) would nescessarily need to be negative), not to external observers, as their v(time) and v(space) remains normal.
However with this normal, "unprotected" FTL travel in our spacetime frame, would also dangerously violate local and universal causality:
Imagine you are the pilot, and you lauched the ship when you were 20 years old (for simplicity, on your 20th birthday)... you engage your "normal spacetime frame" FTL drive after travelling a few years (say on your 25th birthday.). This will quickly hit a wall, as the time frame inside the ship quickly moves to the point where you pressed the button for your FTL drive and the ship hit light speed... with the end effect being that when you press the FTL button, nothing will happen, short of you accelerating to c and never passing the barrier.
IF it WAS to work, you would end up at a point where the local timeframe of your ship would be at the point where you launched the ship... There would NOT be 2 of you, as time for everybody else passes normally, and outside it's still the day of your 25th birthday. But local (ship) causality dictates that you and the ship should be on the launchpad... That travel would end up with you ripping causality apart when you leave FTL, as you have created your own time frame and causality that is completely disjointed from the rest of the universe and any consequences thereof.... or with pre-fetal you and a bunch of rocks travelling at FTL speeds, yet with everything else progressing as normal... until those bits hit the local causal and temporal point of the Big Bang :-O
In order to travel at FTL speeds in the first place, you will have to do one of the following:
>change "c" by moving into another domain where "c" is differentthis is the core concept of most fictional hyperspace mechanics, especially Babylon 5 hyperspace or Star Control hyperspace/metaspace
>change v(time) by moving into another domain where v(time) is also rendered negative or 0 for the rest of the universeyou WILL need to have a positive v(time) inside the ship or you will violate local causality or never be able to leave (because if v(time) = 0 you will be frozen in time and never be able to leave the domain
>disjoint space and timewhich cannot happen in our spacetime frame,as you cannot exist without space to inhabit your body, or time to enable your travel
>teleport (essentially ignoring the space part)theoretically teleporting can solve the problem, however it's very hard and energy expensive to do so... plus, you would logically die while your "copy" reached its target due to the rules of quantum teleportation.
>exploit space itselfby moving space around your ship instead of moving the ship itself... the core concept of the Alcubierre/warp drive, so far the only viable method of FTL travel. It does not violate any of the above. Space in itself is nothing and contains nothing.. it does not have a definable "age" and it does not perform any actions on itself or surrounding matter, in essence. even if space is a part of spacetime it is not affected by time, just as time does not affect space itself (only its contents).
As space itself is also not an "object", by creating a pocket of spacetime to store the ship in (and moving the pocket itself), you can exploit a very important property of space, that it can EXPAND and CONTRACT at FTL speeds (as it provably did during the Big Bang).
Another way of exploiting space would be to punch a hole through its very fabric (a wormhole) and create a shortcut through spacetime... however whether this is possible is still unknown, as we don't have any idea yet of what or where this shortcut should pass through.
this should put a suffieciently large nail in that coffin... either nothing happens or you (very unlikely) destroy the Universe by creating a new Big Bang, take your pick...