According to general relativity there is no privileged frame of reference, and faster than light travel leads to time travel paradoxes.

Now imagine a handwavium "FTL field generator" that creates a privileged frame of reference at its focus (F) with the following property for any point (P) within the effective region of influence of the field: If under GR, a photon emitted at point P at time Tp in the appropriate direction would arrive at point F at time Tf, then Tp and Tf are truly simultaneous, and in fact a craft can travel from point F at time Tf and arrive at point P at time Tp. For another point Q and time Tq, Tp=Tf=Tq, so Tp=Tq.

I think that this setup avoids time travel paradoxes. Suppose you have two systems, P and Q both in the same FTL field F. A traveller can go from P to Q via F and arrive much sooner than light from P would arrive at Q, allowing the traveller to win bets with non-travelers about radio signals sent from P. But the traveller can't push the paradox any further into the past of P or Q: if she travels back to P via FTL, she still arrives strictly after she departed; if she transmits a radio signal from Q to P, that signal arrives still later.

Perhaps when the field turns on, its volume of effect spreads out slower than the speed of light; even if it propagates at light speed, the whole universe is not opened for travel at once. If we turned on FTL today, we'd have around 4 years before any extrasolar destinations became available.

There might be multiple FTL field generators in the universe, but any point can lie in just one FTL field. Where fields meet, they form a boundary (invisible?), and the universe would eventually become divided into a voronoi-like partition. Perhaps the contest is won by whatever was there first (so you can't build an FTL drive if you're already in an FTL field), perhaps the closest FTL generator wins, or maybe fields come in different strengths so that you can "take" territory simply by pumping more power into your FTL. Or "mine" a region of space with a large number of low-power FTL emitters that wouldn't own much space by volume but could still be a hazard to a FTL ship in the area that is travelling on a different field.

Do craft literally have to travel via F, severely limiting the quantity of craft that can travel and giving F's owners a huge degree of control over travel and commerce?

Maybe present-day scientists discover and build the FTL generator, or maybe present-day earth is already bathed in an ancient FTL field. Is the field hard to measure if you don't know its direction?

Is the field the explanation for some observation, like CMB polarization (in the news this week :-P), galaxy rotation curves, or maybe the Fermi paradox? I'm sure it is.