I am considering how to implement faster-than-light (FTL) travel in a sci-fi setting without the attendant problems with causality. One of the ways I've been thinking about for this is establishing a preferred frame of reference.
In theoretical physics, a preferred frame or privileged frame is usually a special hypothetical frame of reference in which the laws of physics might appear to be identifiably different (simpler) from those in other frames.
My idea is that going FTL involves a point-to-point jump where both ends of the trip must be at rest in the preferred frame, which itself is approximately at rest relative to the cosmic microwave background (CMB) (that is, in the preferred frame the observed CMB dipole is effectively eliminated). Thus to make an FTL jump from one star system to another, you must first decelerate your ship to rest relative to the CMB (which is approximately 370 km/s relative to Sol), and then after the jump you must accelerate to match velocities with your target star. Importantly, causality is always maintained relative to the preferred rest frame, though there may be other reference frames where it appears to have been violated due to Lorentz transformations. Crucially, even if you contrive a situation where someone observes an apparent causality violation (e.g. they are moving at a high fraction of lightspeed relative to the preferred frame and see a starship arrive at its destination before leaving its origin), they cannot send information about what they have observed in a way that violates causality (e.g. they cannot observe the arrival and then send a message to the starship's origin telling it not to depart in such a way that the message arrives before the departure occurs) because sending anything FTL requires being at rest in the preferred frame (e.g. they have to decelerate, rotating their space and time axes such that their message does not go backwards in time).
My question is: how would our understanding of physics need to be modified to account for such a preferred frame while also fitting the real-life experimental data we have regarding general relativity and special relativity? The theories of relativity specifically say that there is no preferred frame, so in my universe there must be something they're missing. I want it to be something that we could plausibly have missed, for instance something that is only apparent when you get close to being at rest within the preferred frame. I also do want it to be consistent with the experiments we've performed and observations we've made that have so far agreed with relativity.