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The introduction of FTL travel/communication in a relativistic universe may effectively be equal to having a time-machine with all the problems that may entail for causality.

I would like to avoid that in my setting and I think I have managed. But I'm not a 100% sure of that. So please, look at my setup and tell me if I got it right or wrong.

The non-FTL bits:
Ships can do up to 0.35C and accelerating to such speeds from 0 takes about 24 hours. There is some handwaving technology like "artificial gravity" and "acceleration compensators" to keep the people inside the ships comfortable.

All inhabited star-systems make use of "Terran Standard Time" which is a sort of NTP system on steroids that provides a single consistent time-source everywhere. It makes use of signals from pulsars and quasars to synchronize across star-systems. Local clocks and clocks on-board ships that are subject to time-dilation can be calibrated against this time-system.

This also provides an "independent frame of reference" which is often important in discussing relativistic speeds and FTL.

The FTL part:
Ships go FTL by means of a Hyper-drive. This drive makes jumps varying between 0.5 and 10 light-years. (The maximum/minimum distances are determined by several technical limitations of the drive.)

After a jump the Hyper-drive needs to cool down and requires some re-calibration. This takes between 1 and 2 hours depending on the exact type of ship.

You can't install 2 drives and use them in turns to minimize the down-time between jumps. (You can't even have a spare drive as cargo.) The unused drive will resonate with the active one and the result is spectacular, but unfortunately such a mini-supernova is rather fatal for anything within several light-seconds.

Furthermore Hyper-drives are sensitive to gravity. You can't start a jump or end one too deep inside the gravity well of a large mass like a star or a planet. If you try anyway you will cause the same mini-supernova as you would get by having 2 drives on-board.

This unsafe zone is called the gravity shadow and for our Sun the gravity shadow has a radius of 3.5 light-days. For a star 4x as massive the radius is 2x as large. For most planets the shadow normally falls within the much larger shadow of its star (e.g Jupiter has a shadow just over 2.5 light-hours) so you normally just ignore the planets.

It makes no sense for a FTL ship to travel for weeks inside the shadow to deliver the groceries to an inner world, while meanwhile it could have traveled to several other star-systems. So FTL ships typically stay clear of the shadow altogether and will transfer cargo and passengers to in-system ships for further distribution.

The ship must travel at a minimum velocity of 0.23C before a jump can be initiated. When the Hyper-drive kicks in the ship simply vanishes from normal space and re-appears some time later at the endpoint of the jump. The ship will exit the jump traveling at the same velocity and in the same direction as before the jump started.

For an outside observer the ship will have covered the distance in jump with an apparent speed of approximately 2 light-years per hour.

The people on board will notice nothing strange except that the view out of the windows will go completely black. Time progresses normally for the people on board at the same rate as it as doing before and after the jump. So for them the time in-jump will be slightly less than for the outside observer due to the time-dilation in effect when the jump was initiated while traveling at a minimum of 0.23C.

(Why this happens is a question that has been driving the astrophysicists nuts for centuries ever since the FTL drive was discovered. Every theory insists that on-board the jump would appear to be instantaneous, but that is just not the case.)

Ships in-jump are completely isolated from normal space and each other if they happen to be in-jump simultaneously.

There is no FTL communication in my setup. Communication relays throughout a star-system forward messages to FTL ships about to leave the system. The ships will offload these messages to the comms-relays in the destination systems upon arrival.

For routes where there is a lot of communication traffic small drone-ships jump back and forth at regular intervals just to carry messages. These drones are called "ponies" after the Pony Express.

These "ponies" are also used to get a replacement Hyper-drive to a ship with a broken drive. After all, due to the resonance effect, you can't transport a spare drive on a FTL ship. So a pony is send to the ship and the ship's engineering staff will remove its drive and put it in their own ship.

That was a long story but I wanted to give you a good feel for the setup.

Now for the big question: Is there some way to exploit this setup for time-machine shenanigans?

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    $\begingroup$ You're not in a relativistic universe, because you can't have a speed limit like 0.23c in such a universe, since there's no such thing as an absolute speed. $\endgroup$ – Mike Scott Mar 26 '17 at 19:02
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    $\begingroup$ up to 0.35C compared to what? In what reference frame? $\endgroup$ – Mołot Mar 26 '17 at 19:13
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    $\begingroup$ I think we can assume that he means 0.35c Delta-V $\endgroup$ – Douglas Mar 27 '17 at 1:23
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    $\begingroup$ See this answer under “time travel happens”, and other linked content. $\endgroup$ – JDługosz Mar 27 '17 at 6:34
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    $\begingroup$ I think the two drives thing is a very good weapon: two ships travel to enemy territory. Ship A gives drive to Ship B. Activate drive on Ship B (perhaps after Ship A can retreat). $\endgroup$ – Mathmagician Aug 13 '17 at 4:07
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In short: Yes, as others answerers have shown, a system like that which you describe could be used for potentially-paradox-inducing time travel, if the universe doesn't provide some deep, fundamental way to forbid it.

What makes FTL time travel possible is the ability to perform FTL jumps in different frames of reference moving at different speeds relative to each other. This video, for instance, shows how an FTL ship can go back in time by performing two FTL jumps- one at 2x lightspeed relative to Earth, and one at 2x lightspeed relative to some random reference frame moving at nearly the speed of light away from Earth.

In order to prevent time travel, you could find a way to prevent FTL jumps being made in different reference frames. In other words, you could decree that all FTL jumps must be made relative to some agreed-upon universal frame of reference. All FTL travelers would be moving forward in time relative to this frame, and so there wouldn't be any serious causality issues. In terms of the spacetime diagrams in that video, hyperdrives could have nearly-horizontal world lines in the universal reference frame, but they could never dip downward, into the past (which would allow time paradoxes); and in other sub-lightspeed reference frames, the hyperdrive's world line could never drop into the 45° region at the bottom (and doing so would be a time paradox).

However, this raises the question of what this universal reference frame is and why FTL travel only works relative to it. It can't be centered on Earth, or the Sun, or indeed the Milky Way- because if aliens from, say, the Andromeda galaxy have technology that works in a similar manner, but relative to their home system, that's all the ingredients needed for a serious temporal conundrum.

It's tempting to say that these FTL drives operate relative to the fabric of spacetime itself, but any physicist will tell you that spacetime has no such universal reference frame. The universe does, however, offer something close: all the matter within it. If you zoom out far enough and account for the uniform expansion of space, everything seems to be pretty much stationary. This seems like an ideal reference frame to lock the FTL drives to- but "the average motion of all the galaxies in the universe" is a bit nebulous. Especially since the universe is expanding.

Enter the Cosmic Microwave Background. It's the closest thing we have to a universal frame of reference- essentially representing the motion of all the matter in a particular spherical shell at the time of photon decoupling- that is, when the opaque plasma that filled the early universe cooled to the point that electrons could bind to protons, creating transparent neutrally-charged hydrogen gas. The Local Group (consisting of the Milky Way, Andromeda, and a few other galaxies) is, by the way, moving somewhere around 630 km/s relative to the CMB, according to the "Data reduction and analysis" section in that Wikipedia page. So although you might be able to use a CMB-locked FTL drive to visit the Crab Nebula sometime before the light from its star's supernova reached Earth (but long after the star went nova and the nebula formed), returning to Earth would take you forward in time by exactly the same amount. You'd return home after you left, with no chance of paradoxes.

As for why the FTL drives are locked to the CMB... That's up to you, really. Maybe they rely on some intrinsic property of the universe that modern science has yet to discover. Or maybe they work by shifting over into a parallel universe ("hyperspace") in which the speed of light is infinite and relativity doesn't really happen, and which just happens to be stationary relative to the CMB. Whatever; just make up something that sounds good and/or would make a good story.

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    $\begingroup$ I agree the key is to have a physically preferred reference frame, but the OP may not have been clear on that since the idea of "Terran standard time" sounded more like a convention, like Greenwich mean time, rather than a frame that was preferred by the laws of physics. But the OP may not realize that velocity is relative in real-world physics, so it would make no sense to say some physical phenomenon can only happen "at a minimum of 0.23C", unless you modify physics to include a preferred frame and "absolute velocity". $\endgroup$ – Hypnosifl Mar 27 '17 at 16:46
  • $\begingroup$ That video also clearly states that you can't actually make the jump from two reference frames that it proposes as necessary for time travel to occur. $\endgroup$ – Ash Aug 2 '17 at 16:01
  • $\begingroup$ Pretty sure we are moving at a speed of c ( aprox 300,000 km/s, not 630km/s), relative to ALL em-radiation (cosmic background, or otherwise). $\endgroup$ – Glurth May 13 '18 at 2:16
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    $\begingroup$ @Glurth We're moving at the speed of light relative to any photon in a vacuum, yes. But that's not what I meant. If you look at the CMB, you'll see that it's warmer on one side of the sky than the other, because the Earth is moving, causing a Doppler shift. However, there is one reference frame in which this Doppler shift of the CMB does not occur, because it's at rest relative to the average motion of the plasma filling the early universe at the time when the CMB was created, and that's the frame I'm proposing as the absolute universal reference frame of the universe. $\endgroup$ – Someone Else 37 May 14 '18 at 3:27
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Leaving aside the issue that I mentioned in my comment, this can easily be used for time travel.

  • We'll do this in empty space to avoid your "unsafe" zones.
  • We assume you start at a space station that doesn't move, which will be our "static" frame of reference.
  • Accelerate to 0.341175c (that number makes the numbers easier later) relative to the station, and consider the point 100 light years away (from the ship's frame of reference) in its direction of travel. That point is only 94 light years away as seen from the space station's frame of reference.
  • If it's the 1st of January 2000 on the space station and on your ship (they're the same because they start in the same place, although at different speeds) then the time at the point 100 light years away that the ship sees as the 1st of January 2000 is seen by the space station as 1st of January 1994.
  • So take the ship there, which will take two days.
  • It will arrive on 3rd of January 2000 by its own clock, but on 3rd January 1994 as seen by the space station (which of course won't actually see the arrival until 3rd January 2088).
  • Now decelerate the ship until it's at rest relative to the space station. Let's assume this takes a week. It's now 10 January 1994 (as seen by the space station).
  • Jump back to the space station, taking another two days, and you arrive on the 12th of January 1994, almost six years before you left.

I might have got the maths wrong for my Lorentz transformations of the time coordinate, which means the six year time difference could be some other amount, but it will certainly exist and be more than the 10 days that you can afford it to be if you don't want time travel.

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  • $\begingroup$ You interpreted “apparent speed” as in the reference frame of the ship, while it's said that the ship is travelling at a conventional speed of at least 0.23C, so speed is not being noted in the ship’s own frame. At the beginning he defines a standard reference frame, so speeds are being noted in that, right? $\endgroup$ – JDługosz Mar 27 '17 at 7:04
  • $\begingroup$ @JDługosz His question says explicitly that it refers to a relativistic universe, so we must regard his apparent choice of a standard reference frame as misleading phrasing, not an actual explicit rejection of special relativity. $\endgroup$ – Mike Scott Mar 27 '17 at 7:06
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    $\begingroup$ Either he's referring to speeds using the frame defined atbthe beginning (or why else mention it?) or he’s sloppy, incomplete and inconsistent in expressing relativistic velocities, as if he forgot about relativity. $\endgroup$ – JDługosz Mar 27 '17 at 7:09
  • $\begingroup$ You might look here researchgate.net/post/… for an interesting discussion of preferred frames of reference. $\endgroup$ – a4android Mar 27 '17 at 7:14
  • $\begingroup$ "It will arrive on 3rd of January 2000 by its own clock, but on 3rd January 1994 as seen by the space station (which of course won't actually see the arrival until 3rd January 2088)." This step lost me. Why can't/won't it appear at the star on Jan 3 2000, as seen by the space station (which won't actually "see" it's arrival till 94 years after THAT.) $\endgroup$ – Glurth May 15 '18 at 16:57
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Yours is a science-fiction universe. To it simply if you decide causality isn't violated with FTL travel, then it isn't and you don't need to worry about time travel effects.

Specifically your fictional universe has established a preferred frame of reference based on pulsars and quasars. All FTL jumps will take inside that preferred frame of reference. This means one of the principal assumptions of special relativity does not apply. This is the assumption that there are no preferred frames of reference.

What you describe is a perfectly acceptable model for FTL travel in a science-fiction universe. It is irrelevant whether this obeys all the principles of special relativity. Fiction often traffics in entities that do not have a basis in reality. Vide vampires, zombies and shrinking rays among many other fictions. Science-fiction invariably deal in conceptual entities that are both fantastic and scientific. FTL travel is commonly accepted trope of science-fiction. The majority of science-fiction employing FTL travel will flatly ignore time travel problems as normal practice. Your fictional model of FTL travel sets out a plausible set of rules within which it operates. Just go with it.

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  • $\begingroup$ The question refers specifically to a relativistic universe. If there is a preferred frame of reference, then it's not relativistic. And in any case, you can't get a preferred frame of reference from quasars or pulsars, because they're very far away from all being in the same frame of reference themselves (especially quasars). $\endgroup$ – Mike Scott Mar 27 '17 at 5:15
  • $\begingroup$ @MikeScott see comoving frame. $\endgroup$ – JDługosz Mar 27 '17 at 7:05
  • $\begingroup$ @MikeScott If a relativistic universe permits FTL jumps as this fictional one does, then this can be considered to be a relativistic universe approximation of a more complete universe which has special relativity and FTL travel. This is not different from Newtonian gravitation being an approximation to general relativity. A preferred reference frame based on pulsars & quasars may not be the best. The cosmic microwave background (CMB) would have been a better choice. Some latitude can be allowed as this is science-fiction universe not a science-based one, with quasi-scientific accessories. $\endgroup$ – a4android Mar 27 '17 at 7:21
  • $\begingroup$ @JDługosz If he's referring to the comoving frame, then relative to the Earth his speed limit is 0.351c in one direction and 0.349c in the opposite direction. Because the Earth itself is not at rest relative to the comoving frame. $\endgroup$ – Mike Scott Mar 27 '17 at 8:30
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First, see this answer and others for all the detail.

You need to draw s-t diagrams.

In your case,

an outside observer the ship will have covered the distance in jump with an apparent speed of approximately 2 light-years per hour.

you can draw a FTL transit track with this slope.

Ah, but which outside observer? You probably mean to use the standard time you describe earlier, so OK it's not ambiguous.

However, your FTL transit track seems to vary based on the direction of travel. In your sample diagram which only shows one dimension of space) just draw a round trip, and you’ll see they slope different ways.

Since all FTL transit tracks are not all parallel, we suspect this can be used to violate causality. It might still be OK though: if you model it as an instantaneous transit in the standard reference frame followed by a delay based on the length of transit, then you are fine!

The big deal is: is your “independent frame of reference” a construct used for standardized timekeeping, or is it a real preferred frame that defines all FTL transit tracks?

Your statement of “speed” might be stated in this preferred frame, or you might be sloppy and didn’t realize it was an issue.

Likewise, the ship’s minimum velocity: relative to what? In this post I use the terms SRF and GRF; if you are attempting to indicate that SRF=GRF, you are fine, you just didn’t make clear that FTL transit is based on a specific reference frame.

The only other issue is whether your gravity shadows are properly sized. “For a star 4x as massive the radius (of the exclusion zone) is 2x as large.” That doesn’t make sense physically. Since the strength of gravity at the edge of the zone will increase with the mass, for massive enough objects you will still have strongly curved spacetime.

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  • $\begingroup$ I think the OP's exclusion zones are proportional to mass (despite being called 'gravity shadows'). A one solar mass object has an exclusion zone of 3.5 light days. Presumably a four solar mass star will have an exclusion zone of seven light days. The strength of gravity at the edge of the exclusion zone seems to have little to do with it. The radius of exclusion zones scales with mass. As gravity decreases with the square of the difference the outer edge of the exclusion zones seems to be at a critical value for gravitation. Kind of nifty. $\endgroup$ – a4android Mar 27 '17 at 7:41
  • $\begingroup$ He indicated they are proportional to the square root of mass. As does your example here, 1->3.5, 4->7.0. «the outer edge of the exclusion zones seems to be at a critical value for gravitation» ah, you’re right, the acceleration towards the mass at the exclusion distance is a constant. $\endgroup$ – JDługosz Mar 27 '17 at 8:40
  • $\begingroup$ @a4android in my head I was picturing the scaling of the parabola “dents”. The greater slope corresponds to tidal shears. Having the safe radius computed in a simple manner and breaks down in extreme cases is good fodder for plots. $\endgroup$ – JDługosz Mar 27 '17 at 8:54
  • $\begingroup$ i wrote "As gravity decreases with the square of the difference " when I meant to write "As gravity decreases with the square of the distance ". Yes @JDługosz the phrase "scales with mass" meant proportional to the square root of mass, implicitly, because I didn't feel I needed to explain that to you. You can figure these things out for yourself. Also, I prefer keeping things simple and easy to compute, makes the plotting easier too. $\endgroup$ – a4android Mar 27 '17 at 10:25
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FTL is about the worst flavour of ice cream in the science fiction universe. Now, I love LeGuin's fiction, and Shevak is a great man, and the invention of the Ansible was fun. But it totally failed to reconcile the fact that different stars have totally different frames of reference to each other, meaning that living around one star happens slower (or faster) than living somewhere else. So, if the ansible were to work then 'the voice' at the other end would sound slow or fast. Now, that's just communications (which you barred in your question). But everything else that you asked is merely because you haven't really 'got' special relativity sorted out in your head yet.

If you want to write space opera, then just 'star trek' it and accept some sort of means of preserving causality with FTL. Otherwise, if you want your universe to live in a relativistic universe, don't even get close to that, and go for far more believable, and thereby more engaging, fiction.

People use FTL in order to write SciFi as an analogy for international travels, with countries being replaced by planets. It is, frankly, disappointing. I've said it elsewhere - and I'll say it again: Planets are HUGE, and solar systems are GIGANTIC. Every single thought that every culture has had has happened within a tiny envelope of space.

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    $\begingroup$ This is an editorial on the same subject the OP's question was in, but does not contain anything like an Answer to the OP’s question. Note that there is already a comment attached to the OP pointing to a blog post with the same thesis as your post. $\endgroup$ – JDługosz Mar 28 '17 at 7:12
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Everyone who suggests that FTL can violate causality is ignoring "Time's Arrow", macro-system temporal asymmetry, it prevents actual physical time travel and until it's solved as a [mathematical] problem in physical systems it always will (and probably even once we understand it well enough to solve for it still will until we can nullify the effects of entropy), it excludes 3 dimensional beings, or objects, from realising time-space travel curves that would violate causality. Everything I've read or seen on the physics of time travel agrees on this point, as such any form of FTL must conform to this limitation meaning that if you want FTL it must be locked against some frame of reference in which it, by definition, cannot then violate causality. What the hell that frame of reference actually is is a mystery to me but that's not my problem.

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