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It is understood that a way to prevent causality violation and time-travel while still having faster-than-light travel is to introduce a specific reference frame. This is explained in detail in this answer, in Hinson’s Relativity and FTL Travel §9.5.4, and others.

To summarize, all FTL transits occur on a track that can be identified as an x axis of a specific reference frame. All such transit tracks are parallel to each other, regardless of any reference frame of the port of call, the ship’s pilot, etc.

This is easy to draw in an s-t diagram, but the ramifications are not immediately obvious. What does this mean to the logistics and plot elements of my story, or the time-and-motion of elements in a role-playing game?

Not the least of the issues is that even trying to discuss it is perilous, as the very concept of velocity doesn’t make sense, and just what time is it at each port anyway? So how can I describe the transit time of ships, how much time does that take from each point of view, and what other effects do I need to know about?

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  • $\begingroup$ Tangential to all of this, but was there some question/answer/discussion that sparked interest in creating a Q&A for this topic, or did you just want to share your thoughts on the matter? $\endgroup$ – Frostfyre Jul 13 '16 at 20:16
  • $\begingroup$ I've had it on the back burner for some time, thought FTL in hard SF might be a good blog post or something. Coincedently another Q was posted on making FTL free of paradox, and I wrote up my material for that. It followed on a slightly different question that also brought up the question. Then the OP pointed out that he was planning for a game, and filling in details of making use of the concept fit nicely in a practical approach. Due to its length I made it a new QA. That let me set a different tone, and I was able to get it encapsulated nicely. $\endgroup$ – JDługosz Jul 13 '16 at 20:27
  • $\begingroup$ …so I’ve been wanting to share it for some time, just had the excuse and some inspiration on breaking it up to fit this format. $\endgroup$ – JDługosz Jul 13 '16 at 20:28
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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.

drawing 1

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!

drawing 2

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).

drawing 3

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.

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  • $\begingroup$ A lot of interesting points raised about FTL. Shiptime equals distance travelled I knew, but the apparently instantaneous transitions between ports was an eye-opener. A jump-point half a light year away takes nearly a year accelerating close to lightspeed at 1 g. Any preferred reference frame needs to be cosmological (CRF), and the GRF will move relative to it. Velocity should be defined relative to the CRF. Some of paradoxes are akin to ordinary SR paradoxes. If FTL is paradox-free, usually it assumes the causal paradoxes are absent. One-way jump points do help. $\endgroup$ – a4android Jul 14 '16 at 5:51
  • $\begingroup$ “One-way jump points do help.” for the special case of all transits being in the same reference frame, you can jump between any two points in space. For wormholes that stay compatible without being all the same, see Hypnosifl’s comment discussion on my answer and his answer on the earlier question. In this case I think that one-way wormholes are necessary if all wormholes are not in the same reference frame. $\endgroup$ – JDługosz Jul 14 '16 at 15:44
  • $\begingroup$ One-way wormholes are absolutely necessary. I've had fun building toy universes with one-way wormholes or having them separated by enough spacelike distance to negate any causality problems. $\endgroup$ – a4android Jul 15 '16 at 6:55
  • $\begingroup$ I'm not sure about the validity of some of the diagrams, but I have a tenuous grasp of GR diagrams... $\endgroup$ – Serban Tanasa Jul 15 '16 at 18:57
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The ordering of the future and past at FTL velocities may be resolved by a so-called spacelike causality. See this paper by Han & Choi. What they call relativistic causality which applies to sublight inertial frames of reference might be better called timelike causality. This is the causality that knotted and twisted into paradoxes when special relativity and faster-than-light travel collide.

Han & Choi conclude that spacelike causality is a stronger condition for no-signalling than relativistic causality. Now admittedly their paper is about quantum nonlocality, but nonlocality is physicists' code for things happening faster than lightspeed. Strictly speaking, it means events with spacelike separations. The ordering of events involving superluminal velocities may be well behaved and the usual paradoxes may be simply the result of involving the wrong sort of causality.

This suggests that FTL vessels will move forwards in time, always, provided their motion is confined to a preferred frame of reference. The most suitable candidate for a preferred frame of reference is the cosmic microwave background (CMB).

The solar system moves at approximately 627±22 km/s relative to the CMB. Assume a starship with a FTL jump-drive, but because we don't want to multiple impossibilities it only has a plasma fusion sublight propulsion system capable of an acceleration of one cm/sec/sec. This is a realistic plasma drive based on Mallove & Matloff's The Starflight Handbook (1989) where they devised there would be limits on the ratios of mass, power and thrust for interstellar spacecraft.

The starship will first accelerate to the third cosmic velocity or as us lesser mortals refer to it: escape velocity from the solar system. However, it would be reasonable for it to continue accelerating for roughly six months until it is travelling at 150 km/s. Now it aligns itself itself relative to the CMB and commences decelerating until its velocity relative tot he CMB is zero. This will take nearly 720 days (or exactly 719.91 days). The starship realigns itself to its original velocity vector of 150 km/s and decelerates for the next six months. Now it is truly at rest relative to the CMB. By this time it will have travelled twelve light hours from the solar system. It's asafe to assume that this far from the gravitational mass in the solar system local spacetime will be sufficiently that the starship can engage its jump-drive in safety.

The jump-drive is engaged and the starship shifts instantaneously the standard Asimovian jump distance of one hundred light years closer to the galactic centre. Now it sets course for the planetary system that is its destination. Without knowing the relative velocities of this system we can't accurately determine how long getting there will take. But it is safe to assume if it took three years for the starship to get into position to make its FTL jump, it will take another three years to travel there.

"Time to make space pirates eat hard photons," snarled the starship flexing her prosthetic muscles as the starship sets course for the planetary system of Googolplex Minor. "The six years will be well worth the wait."

Yes The Space Pirates of Googolplex Minor can be found in all good book stores.

OK, I admit, there is one big fat fudge in this scenario of the six year trip. That assumption is that if the jump is instantaneous the time inside the starship will be zero. However, if the jump is at a finite velocity but happens very, very, very fast in the rest frame then starship time during this transition will be equal to the light-time distance of 100 years over the 100 light years travelled. This means captain and her crew will be in biosuspension, so they while-away the century without growing old or getting incredibly bored out oft heir brains.

The concept of shiptime being equal to the light-time distance travelled appeared by papers by R T Jones. You can google them but they are either available for sale or not on the net.

Jones RT. 1960. Analysis of accelerated motion in the theory of relativity. Nature 186:790

Jones RT. 1963. Conformal coordinates associated with space-like motions. J. Franklin Inst. 275:1–12

Jones RT. 1982. Relativistic kinematics of motions faster than light. J. Br. Interplanet. Soc. 35:509–14

Of course, starships with high-acceleration, long-duration sublight propulsion systems will spend less time manoeuvring but they still will take time getting to a point, say, 12 light light hours out, where spacetime is flat for jump-drives to operate. Pity that no-one knows how to make high-acceleration, long-duration sublight propulsion systems like this. Lots of non-trivial problems with the physics for starters plus the engineering is insane. If it could be done, this would cut down travel time to only a century in biosuspension.

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  • $\begingroup$ “This suggests that FTL vessels will move forwards in time, always, provided their motion is confined to a preferred frame of reference.” That’s easy to proove without fancy stuff, as the earlier answer shows under multiple FTL trips required. $\endgroup$ – JDługosz Jul 14 '16 at 15:49
  • $\begingroup$ “However, if the jump is at a finite velocity but happens very, very, very fast in the rest frame then starship time during this transition will be equal to the light-time distance of 100 years over the 100 light years travelled” I don't follow. What makes the ship experience 100 years on the inside? And the points are spacelike separated so it's not a lighttime distance (the ship gets there earlier than the light). $\endgroup$ – JDługosz Jul 14 '16 at 15:56
  • $\begingroup$ Time dilates as velocity approaches lightspeed. That's standard special relativity. Above lightspeed time contracts so that effectively if a spacecraft travels any given distance, irrespective of its superluminal velocity, the time inside the ship will equal the light-time distance. This was found by Jones (1963). Astronaut in a FTL ship travels to Sirus, 9 light years away. Nine years pass in the ship during the voyage. The astronaut won't know her velocity until she arrives at Sirius. She could be travelling at 3 c or 3,000,000 c, her shiptime will always be 9 years. Crazy, eh! $\endgroup$ – a4android Jul 15 '16 at 6:41
  • $\begingroup$ Perhaps I misunderstood your query. By light-time distance this means the time it takes light to travel the distance between any two spacelike separated points. Time inside a system moving at superluminal velocity passes at one second per every light second of distance travelled. For a FTL astronaut it appears as if they are travelling at lightspeed. While sublight astronaut at an extreme relativistic velocity seems to travel at FTL speed. $\endgroup$ – a4android Jul 15 '16 at 6:47
  • $\begingroup$ My brain was asleep! What I'm ineptly calling 'light-time distance' is the lightlike separation between any two points. $\endgroup$ – a4android Jul 15 '16 at 8:37
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There are a couple of ways to set up a "Universal Standard Time" usually by using external beacons like Pulsars to mark time, so port time is universal. Planetary calendars may vary wildly depending on rotation and seasons and all of that good stuff, but you can keep a universal clock for trade etc... and you probably need to. Experiments in high velocity time keeping suggest that while the absolute rate of temporal progression, relative to a given frame of reference, may vary experiential time, the time the traveler goes through does not. If that still holds true when going faster than light, ship-time will progress at a normal rate as far as occupants of the ship are concerned so they probably experience the trip in real time which depending on method of transit will either be zero or the trip time at lightspeed, possibly some fraction of it but I'm not sure if is in fact possible. As for what is seen from various viewpoints that again depends on how the ship travels, for example a jump drive of some sort will have (from the perspective of home port) the ship disappears and then reappear at it's destination at a time of T+L where T is the transit time (probably zero) and L is the lag time for light to get back to the ship's home system the conventional way (this is pretty much what you see for any system where the ship goes around normal space, subspace, hyperspace, wormholes, whatever but T will vary depending on exact methodology). A drive that allows for an object to move through real space faster than light is going to show something very different photons from the ship are going to arrive in a strange order, home port sees the ship receding towards the destination at whatever speed, but the destination port sees the ship arrive and then recede towards it's home port at that speed, points passed in transit see the ship appear at closest approach and then two ships disappearing at the ship's speed towards both ports at the same time.

You also need to have a look at time dilation and it's effects on the passage and perception of time. Also red-shift and blue-shift, the effects that the relative velocity of the emission point has on the spectrum of received light.

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