FTL in a relativistic universe: can my scheme be exploited to make a time-machine?

Question

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?

Answer 1

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.

Answer 2

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.

Answer 3

If you are going for science-fiction, don't fret too much about realism. You are allowed some considerable degree of fantastic elements - that's what sci-fi is about! If you wish to be 100% accurate, you will never get a novel written (or a tabletop RPG session done, or a videogame developed...).

Two of my favorite sci-fi books are The Forever War by Joe Haldeman and Old Man's War by John Scalzi. The former even won a Hugo, a Nebula and a Locus awards! Those books feature FTL and at no moment the authors attempt to science it out; In Old Man's War there is a part where a more science-inclined character tries to explain the FTL mechanism to the protagonist, but it stays at a metaphoric level.

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That said, if you wish to be really correct, you are out of luck. To understand why, you must familiarise yourself with the concept of light cones.

Because signals and other causal influences cannot travel faster than light (...), the light cone plays an essential role in defining the concept of causality: for a given event E, the set of events that lie on or inside the past light cone of E would also be the set of all events that could send a signal that would have time to reach E and influence it in some way. For example, at a time ten years before E, if we consider the set of all events in the past light cone of E which occur at that time, the result would be a sphere (2D: disk) with a radius of ten light-years centered on the position where E will occur. So, any point on or inside the sphere could send a signal moving at the speed of light or slower that would have time to influence the event E, while points outside the sphere at that moment would not be able to have any causal influence on E. Likewise, the set of events that lie on or inside the future light cone of E would also be the set of events that could receive a signal sent out from the position and time of E, so the future light cone contains all the events that could potentially be causally influenced by E. Events which lie neither in the past or future light cone of E cannot influence or be influenced by E in relativity.

If you travel faster than light, you can travel to outside a light cone. That allows you to break causality.

Suppose you have friends in Proxima Centauri and you wish to pay them a visit. You hop into a ship, take the hyper-drive and boom, you're there!

From your point of view, you first entered the ship, travelled to the hyper-drive, then unboarded in Proxima Centauri.

From your friends' point of view though, first you unboarded the ship, and then, four years and a couple months later, they will see the ship preparing to pass through the hyper-drive headed their direction. Effect precedes cause.

This can lead to a load of fun, because you can add relativity to it. Let's say I am in a ship travelling at close to the speed of light, say 0.9987c relative to Earth - but not accelerating. Why that speed? Because from your point of view, clocks in my ship tick at about half normal speed. But from my point of view, my clocks are fine, it's yours that are slowed down. You can double check with this calculator.

It is time t₀. You know where I will be in two minutes (relative to you), so you spend a minute and a half writing a message in a bottle. Then you send it through the hyper-drive at your t_1m30s. From your point of view, I would have received the message in about two minutes your time, but my watch should say one minute has passed. But in my watch, two minutes would have passed, and through my magical super-telescope I would see one minute has passed on your watch.

Relativity works like that. There is no simultaneity for people travelling relativistic to each other.

So I pick the message at what I believe is my t_1m, and because I type fast I take 20 seconds to write "don't send me that message I just saw you write or we will all die!" and send it to you via hyper-drive. You will receive my reply at your t_40s, which is 50 seconds before you send me your message! I have sent you a message from the future!

Ergo, FTL + relativity allows for one to receive messages, goods and other things from the future, so it does allow for time travel.

Answer 4

The max 1 jump drive per ship seems like a strange limitation. I would not be satisfied with that in a movie, it makes no sense.

Since you have no FTL communication or other ways of observing light that hasn't reached you, you can easily make a much more sensible explanation to why you can't have 2 drives:

It's not the drive itself that's the limitation, it's your computers. It can only calculate a jump trajectory based on light it's able to see. If it jumps 10 lightyears, the light received will show your destination as it were 10 years ago, and your computer needs a lot of time calibrating your engine to a correct jump by extrapolating that data 10 years into the future to predict a good jump path through spacetime. You can't calculate the next jump until you have completed the previous one, since you need to observe the data, hence two jump drives would not get you faster going.

Failure to calculate a proper jump could have a very high risk of jumping into planets, suns or black holes. You could argue that the jump path must be carefully planned since the trajectory will tend to draw towards gravity wells on the way and fall into their center if not correctly compensated by the computer. Which you need the data to do.

Answer 5

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.

Answer 6

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.

Answer 7

There's really no way around it: if you have relativity, then FTL equals time travel and time travel equals FTL.

The best solution to the issue that I've seen in published fiction is this: A powerful entity from the future arrives and makes it known that it will not tolerate time travel shenanigans in its past, which is your present.

And, that's all it does. It just sits there in the solar system that it claimed, being all mysterious and keeping to itself, but anyone who decides to try time travel suffers a very dramatic and high-energy accident.

This gets you a world where time travel is possible and everyone knows it, but--after a few examples were made--no one does it.

Answer 8

No, because FTL doesn't equal time travel. I know, I'm a heretic, but hear me out.

Given any inertial frame of reference an object can travel at any arbitrary velocity to a point in that reference frame. Let's make it near-instantaneous, just to get the most absurd results we can. At T₀ you hit the button and at T₀ plus a few seconds you have transitioned from Earth orbit to a point a hundred light years away. Congratulations, you are now a hundred light years from Earth, and your time is the same as the time on Earth. You mess about out there for a few weeks, taking measurements and so on and then you hit the return button and return to Earth, where the same period of time has elapsed.

If as part of your messing about you took extremely accurate observations of Earth and recorded a radio transmission made 100 years ago, that doesn't mean that you've traveled back in time. Your time and Earth's time were in sync during the entire journey. It's just that radio waves from Earth take 100 years to get that far.

And that's the key here. You don't get time travel by moving in space, no matter how fast you go. What you get is historical photons that have been in transit for a long time.

And it doesn't matter how many extra frames of reference you throw into the mix. In any frame of reference the trip will have the exact same consequences. It's only when you start fooling around with irrelevancies like mapping one part of the trip to reference frame A and another part of the trip to reference frame B that things like time differentials start to pop up. And when they do it should be a clear indication that you just screwed up the math. It's like adding 20 degrees Centigrade then subtracting 20 degrees Fahrenheit and being surprised that the temperature is different.

So don't worry about time travel. It's not involved if you don't make an effort to do it... unless there's something about the drive you're using that makes it happen. That's up to you.

And yes, I know that there are a lot of people out there who disagree. Often stridently. And there are a lot of very smart minds among them. Just as soon as they solve the problem presented by the privileged position of the present (my, how alliterative that was) I'll reconsider.

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Let me explain a little more, since from the comments it appears that a few people don't understand.

In any single inertial frame of reference no amount of spacial translation can result in temporal translation. Ever. The only way you can make time travel happen is by a bait-and-switch where you do half of the math in one inertial reference frame and the other half in a different inertial reference frame. Regardless of which inertial reference frame you choose, if you do the math in that frame alone you get zero time travel. Time dilation due to acceleration (if any) yes, time travel no.

What people get most wrong however is thinking that seeing photons from a ship arriving before you see the photons from it leaving means that the ship has traveled in time. It has not. It might look like it has done so, but if you know - as we all should - that the speed of light is not infinite then you can figure out what happened. You can even work out how fast the ship was travelling in your reference frame.

And this is where the Relativity of Simultaneity comes from. Given two events A and B that can be perceived, observers in different locations in space relative to the events will perceive those events happening in different sequence. Whether A happens before B, B happens before A or they two happen together will be perceived differently by observers at different locations.

But if the observers know the distance, relative motion and other pertinent factors all of them could calculate the actual origination time of the events in their own inertial reference frames, because they're not primitive knuckleheads.

Answer 9

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.