Special relativity is about reconciling mechanics, electromagnetism, and the null result of the Michelson-Morley experiment. Prior to that experiment, the preferred reconciliation was "luminiferous aether", which was a form of distinguished reference frame.

@Mark: Yes, I should say that...

Problem with the preferred reference frame method for FTL is that while in theory it might work, it's impossible in practice. You can slow down your ship relative to the preferred frame as much as you want, but you'll never quite match with it. Even a tiny difference millions of times smaller than what's detectable will technically put it in a different frame. not to mention your ship is not one solid object, but containing more atoms than there are kilograms in the Sun! Each atom vibrating at their own velocities depending on temperature... yeah... no.

@Hanhan658 What is wrong with a ship being in a slightly different frame than the preferred one? We call that "moving slowly". Water has a preferred frame and tiny differences are resolved just fine by things like "oars" and "propellers" and "ropes"

@user253751 if a tiny difference from the special frame of reference is allowed for the FTL jump to work, then where goes the limit for when it stops to work? That only reason a special frame of reference is needed for FTL is because you need to make simultaneity as absolute as possible. The only reason why FTL leads to paradoxes is because different frames of reference has different "simultaneities", and jumping between them at FTL speeds allows you to make a route to jump back in time.

@user253751 an "absolute" simultaneity eliminates this problem, that's why a special frame is required. However, if you allow even a tiny deviance from the special frame, you'll break the "absoluteness" of the simultaneity required for the FTL jump, thus allowing you to break causality. That's why a ship CAN'T be in a different frame than the special frame if it wants to FTL, not even slightly.

@Hanhan658 probably you lock onto the FTL frame the moment you warm up the FTL engines, just like a boat locks onto the water frame when we lower it into the water.

@user253751 sure, but what about all the individual atoms, people, air and everything inside the ship, moving at their own independent velocities?

@Hanhan658: You don't have to be at rest with respect to the distinguished frame of reference. All that is needed is that the motion be relative to it. That is, when your fantastic engines accelerate you to 15 c, they accelerate you to 15 c with respect to that frame of reference. As long as all FTL motion has a well-defined velocity with respect to a fixed distinguished frame of reference all bad metaphysical consequences disappear. (The essential property is that if you have a distinguished frame of reference you have a well defined time coordinate, avoiding the time travel problem.)

@AlexP but then when it comes to FTL signals, suppose a ship is sending a signal to another ship moving in a vastly different frame of reference than the special frame. The signal travels at 15 c relative to the special frame (could be the CMB for instance), but what velocity would it be arriving at relative to the receiving ship? Woudln't it, if the receiving ship was moving in certain reference frames, see the signal travel back in time to reach it?

@AlexP what if, for instance, I was travelling at 0.99 c relative to the CMB, then decide to use the warp to boost up to 15 c relative to the CMB. I would imagine that if I were to warp in a certain direction, the warp engine has to behave like a time machine, i.e. go back in time relative to my reference frame (of 0.99 c) in order to get to 15 c relative to the CMB. Even if the trip itself can't be used to go back to your absolute past, the existence of the time machine engine implies it can be used in ordinary circumstances to go back into your absolute past and violate causality.

@Hanhan658: We don't care about the velocity of the signal with respect to the ship. If we introduce a special frame so that FTL signals have a well-defined velocity with repect to that frame, that is, as long as all FTL travel is done with respect to that one distinguished frame of reference you cannot travel back in time, because in any given frame of reference time can only move forward. (And in your own reference frame your velocity is always zero, so that I don't understand the point.)

@AlexP I know, but the reason why FTL without a special frame breaks causality is because if you were travelling at 15 c from Earth to a moving planet and then back with 15 c relative to the planet, that 15 c relative to the planet might as well be going backwards in time relative to Earth. The opposite is then true. If you establish an absolute frame of reference for FTL travel, but don't requre your ship to match it in order to fire up your FTL engine, then you could activate it in any reference frame. If you were moving really fast relative to the special frame then activate the FTL

@AlexP you could still go 15 c relative to the special frame no problem, but relative to the frame your ship was in when you activated your FTL, you're now potentially going back in time. This is just an observation from someone at that frame, so the point isn't saying this will make you go back in time. Point is, unless you fire up the FTL at absolute rest with the special frame, your FTL engine has to have time machine like properties in order to work. And that time machine like property could then be used to engineer an actual time machine to travel back in time with.

Note that a distinguished frame of reference introduces huge problems of it's own. Most importantly it means that physics does not work the same in every frame of reference, but rather is always qualified by the one distinguished frame of reference. We live on a planet that rotates every 24 hours and revolves around our sun which orbits within a galaxy which is moving wrt other galaxies. Which means that our qualified frame of reference is changing constantly and different from even other stars in our same galaxy.

@RBarryYoung: Quite obviously, if there is a distinguished frame of reference then there is a distinguished frame of reference. We know that in physics-as-we-know-it there is no such thing. That is why I said that the distinguished frame of reference must be introduced by whatever new physics we discover.

@Hanhan658: "But relative to the frame your ship was in when you activated your FTL, you're now potentially going back in time": No you are not. That's the entire point of requiring the existence of one distinguished frame of reference. Note that in physics-as-we-know-it a frame of reference is a local thing. If a global frame of reference exists, then this is enough to guarantee no time travel.

@Hanhan658 In special relativity, there is the future, the past, and everything else. This FTL drive allows you to move in and out of the everything else, but it doesn't allow you to move from the past to the future.

How much could we change $\epsilon_0$ or $\mu_0$ while still permitting molecules of similar sizes to form? If it's a lot, it opens the question up to a frame challenge by way of increasing the speed of light by a few orders of magnitude.

@KRyan: OK, changed to "Anglicized Latin".