what time is it in port?
First of all, the idea of simultaneous is relative. Given events plotted in space-time, which events occur at the same time is not an absolute thing. So synchronizing clocks in different places is a matter of convention, not absolute truth. That is true in our normal universe, so don’t panic. Interstellar commerce will bring this issue to mind, but it is not a new thing due to FTL travel.
Besides the idea of same-time being different between observers in different reference frames, we have the worse problem in that the relative ordering of events is not a universal truth! In normal physics everything you do stays in your light cone and although the rates of ticking of clocks will vary, the ordering of the time value of different events will be the same for all observers.
With space-like separation though even that goes out the window! What is past and what is future, even in principle? For two events that are space-like separated, the relative ordering of the times are one way or the other depending on the observer’s reference frame.
Now since we introduced a single FTL transit reference frame as a solution to preserving causality, we are confidant that we won’t have any loops, but we still have the concept of past and future being fluid in ways we are not used to.
Look at diagram 1 below. Planets A, B, and C have approximately the same reference frame and their world lines are drawn as vertical lines. If you review the Andromeda paradox you’ll understand that this is only an approximation. But we will suppose that the difference in reference frames are small compared to the distance between the planets, so the difference in time is small compared to the scale of events we care about.
So one reference frame of interest is the shared (approximate) frame of the planets. Rather, we will use the reference frame of the average motion of the center of mass of our galaxy, and ignore the (non-relativistic) motion of the planets within this Galactic Rest Frame (GRF).
Horizontal lines on the graph are lines of “same time” in GRF.
Meanwhile, the green lines show the transit track of FTL travel. In principle this can be anything that lies outside the light cone, and the specific value chosen based on your desired plot details, or mostly ignored if you know what to avoid. On the graph the green lines are “same time” in the Subspace Reference Frame (SRF). (As explained in this answer, the FTL transit tracks are all parallel and this defines an axis on the diagram.)
So, Charlie gets on a ship and goes from point A1 to B1. In SRF these points are simultaneous. In GRF he traveled into the past! Don’t panic. Deal with it. The idea of what time is it is not a universal truth but a convention for synchronizing the clocks.
It will make sense for the SRF to define an Empire Time (ET), as that is what will matter for shipping schedules and commerce. The civilization will use SRF = ET, not GRF, for timekeeping.
When GRF ≠ ET
In the general case, GRF is not the same as ET (which is taken as SRF). This only matters when you look at events that take place in normal space across the same distances. This re-introduces the confusion about what is past and what is future, and gives an asymmetry in the real-space effective distance between planets.
In figure 2, below, we see planets A and B. They are separated by 5 light years according to conventional measurements (made in GRF). But people using SRF will measure that a light pulse (such as an old-fashioned messaging laser) will take 2 years to go from B to A, but 8 years to go from A to B!
More dramatically, look at the case of star B which is between A and C. Suppose something dramatic happens that is visible through normal space, like, say, a nova. The light from the nova reaches reaches planet A, and then a ship leaves A shortly after the nova is seen, passes B while the nova is farther along than it was when they saw it at A, and arrives at C shortly before the nova takes place (in GRF). As expected from FTL travel, they have time to set up observation to watch the nova’s light arrive at C and study the precursor star before it blew up. Thinking about SRF only, as that is their ET, that makes sense. That it is actually in the past and the nova has not occurred yet is an artifact of relativity as there is no absolute past or future (although the existence of SRF puts some constraints on it).
In general, people in this setting will use ET. Having a significant difference between ET and GRF can be interesting in a novel, where the above effects are carefully worked out and put to good use as plot elements. But it can be confusing in game play. In a role-playing game, the game should work in ET, and either set SRF to be the same as GRF, or avoid making it matter at all. Having SRF=GRF avoids the mind-bending deal of past and future at different ports of call. But just using ET and avoiding any need to use SRF in the game means that the point is moot.
How fast is the ship?
The idea of velocity is rather slippery. Even in normal space, an object’s velocity is relative to the observer. But we are specifically interested in the velocity as it affects the various ports of call and the ship itself.
time inside the ship
First of all, the passage of time inside the ship is completely decoupled from the passage of time in normal space. Look at one of the green transit tracks. In the SRF it is departing A and arriving at B simultaneously. In other reference frames it departs and arrives at different times, or even arrives earlier than it departs! But to the people and goods on board the ship, there must be a single unique answer.
You get to choose the result. Depending on the detail of the technology you use to explain FTL travel, it may make sense to say that it is instantaneous with respect to the ship’s time. That is, a jump. But if the ship drops into subspace and drives through it, time will pass on the ship and it makes sense to scale that based on the length of the transit. So, draw a scale on the green track line.
Define it to be anything you want. Naturally you might say that it takes a few days ship-time to cover 5 light years between A and B. But does it have to be that way? It might be an interesting way to distinguish your plot from common SF by saying that the time on the ship is longer than a light-speed journey. Maybe the transit is instantaneous (in ET) from the point of view of the civilization trading goods between A and B, but those on board the ship have to spend 10 years in cryosleep!
In any case, once you choose your scale you need to know how to apply it. The ship time will be proportional to the distance between the endpoints, as expressed in the SRF. If SRF is different from GRF, the distance between stars will be changed based on relativistic distance foreshortening.
Realize that the SRF reference frame is a vector quantity: it has a direction. So foreshortening occurs in that direction only and not perpendicular to it. (The same issue applies to calculating the offset between time in GRF and SRF.)
So a journey twice as far will take twice as long, but some directions are "slower" than others, relative to the normal maps of stars presented in GRF.
In a role-playing game, you can have time tables made in advance or a program at hand to do it, so the calculation is no worse than figuring out the 3-D distance between arbitrary ports anyway.
The time spent aboard ship will affect the provisioning for the crew and the perishability of goods. Having time pass differently on board ship will complicate game-play if play take place on board ships and in port. As we will see in the next section, if you try to set the scale so the ship’s elapsed time matches the port’s elapsed time, you end up with transit being instantaneous.
But, a ship’s journey might consist of more than a subspace jump. If jumps must take place far from the star, and perhaps at different locations around the star rather than some arbitrary point, then a significant amount of the journey will be made traveling from the inner planets out to the jump point, and from the arrival jump point back to the inner system planet. So events can take place abort the ship during time time period, even if the jump is instantaneous (in ET). If the ship is traveling at relativistic speeds between jump points and ports, you have to deal with the time slowing down on the ship. If the jump point is, say, half a light year from the sun, then even at relativistic speeds you are going to spend a significant amount of ship time in this leg of the voyage.
time at the port of call
Regardless of how time passes on board the ship while it is in the FTL transit, the round trip voyage appears instantaneous from the point of view of the port of call. The outbound and return transit tracks are parallel in the s-t diagram, which is different from how normal motion works. So, if a ship leaves planet A and goes to B, spends a day at B, and returns to A, it will arrive a day after it left. The time spent in normal space is the only time that passed, in the outside universe.
Note that this does not consider the legs of the voyage that move between jump points through normal space, or other things introduced for the purpose of making time pass to reduce turn-around time. For example, maybe a jump takes some hours to engage the field and this is spent in the real-space side. Maybe jump points (places where FTL is accessed) are fixed around the star and each one is one way, so the ship must travel between jump points through normal space in order to make a round trip.
so how fast is the FTL flight, anyway?
The question is ill-defined. We have seen above that in ET the transit is instantaneous. In other reference frames we have different times, positive and negative. Due to the difference in synchronization between clocks on different planets explained earlier, there is a big offset to adjusting between SRF and GRF time, and as with the example of the nova, expressing the speed of the ship in GRF will give different answers or even negative numbers depending on the specific endpoints.
The idea of a “warp factor” being some multiple of the speed of light just doesn’t work.