Of course you could go for the scientifically unproven higher manifolds of space. That will get you into a big argument as there may be currently only one person looking at it.

Essentially time runs at much faster than perception. Perception being like the random movement of the electron in the wire and subject to loops and vortices. Time runs at the speed the current does and has the ability to rewrite matter for any change made in the past. Access to the past as in before the now of the start of the trip is not possible but the passage of time could be slowed for the crew so that in a near future for them their actions would rewrite the far future for others.

Similarly movement rapidly forward in time makes the crew subject to any changes the rest of society brings about ie they survive and arrive to a dead world. Access to the past as in before now is by crossing through a fold of space in the same way closing a book connects the full page and not just at the crease. Like a bookworm chewing from one end to the other passing through the pages and not reading them.

It assumes an energy universe with matter that is rewritable and memory constant to the now updated not to the past but to the perceived present unless caught in a field of collapsing energy caused by an event occurring at a time prior to the intervention of the observer. It means memory is not accurate but constantly updated as time continually corrects for small defects. And a large correction may cause the cessation of the participant altogether.

But I am just going on the personal experience of the demise of an observer in another iteration of this existence. For what it is worth that is about the best that I can give you and that the rewrite is very rapid, like the capture and closure of all that is within seconds into an entirely alternate existence.

As for FTL, it would not be as necessary as with the right access to the manifolds all times could be accessed but the distances would be problematic. Then there is the mirror symmetry to consider but that only occurs if you travel within the normal time frame and resolves itself when in local space (ie get close enough to the mirror and you do not see yourself).

But it gets weird, reflections, heat shadows and the moment of passing through a physical time turning point in a state of calm unmoving concentration on self. Physicality remains but perception requires time to reorient to the new direction. It is not playing the tape backwards as such but getting to the end or turn point an then playing it at right angles and having to relearn all the basics ... sight, speech, motor skills and experiencing cellular dynamics as parts of the body reverse age until the full adjustment is made. There may be some increase in cognitive ability where mind energy gains over physical ability which does not fall to zero I might add, so the difference may be small or varied for different individuals.

But if you do get that then I can say that makes two.

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"Nature is obliged to let reality determine its laws, whereas mathematics is under no such constraint."