Would one-way FTL travel be safe from a causality standpoint? Any demonstration I've seen of using FTL signals to violate causality seemed to involve an exchange of FTL signals.  Would FTL travel be consistent with causality if it always involved motion in one general direction?
For example, call the direction toward the Andromeda Galaxy from here (and continuing beyond in the same direction, of course) "universal west."  You could go as fast as you want to if you're going west, northwest, or southwest, but not an inch east.
I think this gives up "Lorentz invariance," but that's OK.  I can't remember getting any Christmas cards or birthday gifts from Lorentz invariance in, like, ever.
EDIT: I'm not worried about things appearing out-of-order to an external observer, but really only worried about preventing FTL signals from being able to directly or (as in every case I've seen) indirectly send a signal into one's own past.  The "universal west" direction is arbitrary but would be the same for all observers.
 A: I've been playing around with a concept for this for a while now.  I call it Paradox Shadow.  One-way FTL would be a subset of this, and I think you're correct that it should work without causing time travel.
FTL violates causality due to relativistic time dilation.  In other words - FTL would be fine if everything in the universe was at rest to everything else (obviously impossible).  It's only when you start moving that things get wonky.
The idea behind Paradox Shadow is that whenever you do FTL (whether travel or communication) it creates a 3-dimensional, non-contingent area behind you, which I'm going to call the shadow (which is my terminology, I just think it's fitting when compared to light cones).  This is defined as the area that if you used FTL travel to go back into, you would violate causality, and every single object in the universe would create it's own shadow relative to you.  The size and expansion of the shadow would be an equation defined by the relative speed between you and the object.
Now, I don't have the math or physics to put this into actual equations - I've been debating opening a question here for that - but my intuition of the physics is that the following would happen:


*

*Shadows of objects that were close to you in relative speed would be extremely small.

*Shadows would slowly evaporate, even as the propagate outward - the total area would reduce over time.  The rate of evaporation would be a function of the relative speed between you and the object, and c.


So you might not even need to restrict it to one-way, it might be that you'd just need to keep a map of objects in the area you're travelling, and track/avoid shadows.  So it might work out (for example) that if you travel a light year, you might just need to wait a few days or a week before you could travel back.
