# hypothetical criteria for non-paradox FTL

Many sci-fi questions here are derailed by complaints that the proposed version of FTL breaks causality. However, relativity-safe FTL concepts do exist. What range of conditions allow FTL (movement, teleportation, or communication) but not time travel?

Time paradoxes I've seen are based on FTL interchange between relativistic reference frames. (edit: see update below) Problems occur when the differential between time frames is larger than the travel time. Is that correct? If so, we can avoid paradox by requiring lower velocities (FTL and/or reference).

Also, those paradoxes use reference frames moving away from each other. If the reference frames are moving towards each other, does paradox still occur?

My goal is to establish parameters for physics-tolerant FTL, so that future answers don't need to nitpick about closed timelike curves.

Here is one example that I think should work:

• vessels can shift to & from "hyperspace", but travel still requires local time (at minimum, hours per light year plus some overhead even if you don't move).
• vessels can't enter or exit hyperspace at high real velocity (>1% c) relative to some local center of mass (e.g. galactic core). Technobabble about nonlinear fluidic space available if needed.
• separate vessels enter separate instances of hyperspace, cannot intercommunicate.

UPDATE:

In the "Sharp Blue" article, the diagrams display Lorentz transformation as a slanting of the space-time axes, and FTL is assumed to be instantaneous. But non-instant FTL would also have a slope, and it seems like paradox could be avoided if the FTL is steeper than the dilation angle.

Mathematically: dilation slope as a function of (relative) frame velocity goes from f(0)=0 to f(c)=1, while the FTL slope as a function of travel velocity goes from f(c)=1 to f(infinity)=0. I'd need to refresh my analytic geometry to make the terms cancel, but such values are determinable. Why is this approach not valid?

CONCLUSION:

Dan Smolinske's answer explains why my thinking is incorrect: even if the endpoints of the FTL don't experience paradox directly, a relativistic observer traveling near an endpoint does.

celtschk's answer provides a solution: require a primary reference frame, such as the ether in Lorentz Ether Theory. Lorentz's math is more complex than Einstein's (Occam's Razor FTW) but their results are indistinguishable for velocities below c. They only differ during FTL; the ether can prevent paradox.

• +1 As a Chief Derailer (really shouldn't put 'FTL' and 'science-based' tags together if derailing needs be avoided), I welcome the question, and look forward to sniping at the answers until they get really really good, or really really scared. :) – Serban Tanasa Feb 17 '15 at 22:50
• Relativity, causality, FTL: pick two. – Mark Feb 18 '15 at 1:09
• I really wish I could answer this question, but I've been stuck on how two reference frames can agree on the speed of light when one of them is going faster. I can't tell if the trend will continue, or if the axes should become inverted. – DaaaahWhoosh Feb 18 '15 at 2:23
• Here was my attempt at a system: worldbuilding.stackexchange.com/questions/9029/… If anyone (@SerbanTanasa) wants to take another crack at breaking it... – AdamHovorka Feb 21 '15 at 0:34

Time travel due to FTL follows directly from the relativity of simultaneity: In different frames, the temporal order of events is different. This is true for all events which are spacelike to each other, which just means that you need FTL to get from one event to the other. So if you want to solve it with delays, then the delays have to be so that you end up not doing FTL travel at all. Note BTW that also the Alcubierre drive is not free from possible time travel paradoxes.

FTL without time travel paradoxes can be achieved in two ways:

• Restrict FTL to a preferred frame so that going to the past in that frame is not possible (which prevents closed timelike loops and thus paradoxes)
• Allow time travel, but invent a mechanism which prevents paradoxes (the main mechanisms are a self-consistent universe and multiple timelines).

As preferred frame, an obvious choice would be the rest frame of the cosmic microwave background (which BTW is also the frame relative to which the age of the universe is measured). Possible explanations for such a preferred frame include

• Relativity might not be fundamental. While for the physics we know it holds, there might be a deeper level where it does not hold, and FTL travel might need that deeper level (e.g Star Trek's subspace might be considered such a deeper level).
• Relativity is fundamental, but the FTL technology depends on pre-existing phenomena (for example, some space-filling fields) which have a preferred frame. That is, while in principle your FTL technology would allow time travel, in practice it doesn't because you depend on existing resources which fix a certain reference frame.
• What does 'restict ftl to a preferred frame' mean? Almost by definition, any ftl object has its own frame... – Serban Tanasa Feb 17 '15 at 23:24
• @SerbanTanasa: It means there is a global preferred frame of reference, relative to which your FTL drive works, and from which you cannot go into past. One example of such a frame would be the aether frame in Lorentz aether theory. – celtschk Feb 17 '15 at 23:27
• But if you're ftl relative to one frame, isn't there always at least one other frame you're also ftl relative to? – Serban Tanasa Feb 17 '15 at 23:31
• The point is that in that specific frame, you're not able to go back into time. You're of course seen as going FTL in other frames (indeed, in all other frames), and in other frame's coordinates you can even be seen to go backwards in time. The important part is that in this specific frame, you cannot go backwards in time, and that means you cannot get into your absolute past. And that's why you need a preferred frame: Because you cannot prevent going back in time in all frames, but in a preferred frame, you can. All paradoxes involve going FTL in two different frames. – celtschk Feb 17 '15 at 23:40
• You are in a different frame. But whatever enables FTL in that scenario still is in the very same frame as before. For example, just because you move relative to earth does not change the way earth moves. So anything dependent on the movement of earth does not care how fast you move. For example, despite relativity, all people will agree whether you are faster than sound, because the atmosphere determines a frame, and for the effects of being faster than sound, the velocity in that reference frame counts, and in none other. Think of the preferred reference frame as "cosmic atmosphere". – celtschk Feb 18 '15 at 7:05

In the "Sharp Blue" article, the diagrams display Lorentz transformation as a slanting of the space-time axes, and FTL is assumed to be instantaneous. But non-instant FTL would also have a slope, and it seems like paradox could be avoided if the FTL is steeper than the dilation angle.

Mathematically: dilation slope as a function of (relative) frame velocity goes from f(0)=0 to f(c)=1, while the FTL slope as a function of travel velocity goes from f(c)=1 to f(infinity)=0. I'd need to refresh my analytic geometry to make the terms cancel, but such values are determinable. Why is this approach not valid?

Consider a situation with three entities. A and B are at rest relative to each other and are extremely far apart (say across a galaxy, thousands of light years). D is moving at a significant fraction of c relative to both, but is much closer to B (within 1 light year).

If your suggestion worked, you can now violate causality by using B as a relay between A and D. A <-> B communication can be instant since they're at rest. Even if B <-> D communication is light bound, the overall result of A <-> B <-> D communication will be faster than your "safe" FTL bound, resulting in paradox.

• Thanks. I wonder if the mere (possibility of) existence of relativistic observers is sufficient to cause paradox, whether or not they're directly involved. – Foo Bar Feb 19 '15 at 13:07
• It's a tricky paradox, I was literally thinking about it yesterday (before this question) which is where I came up with that example. I'd never liked it when explained mathematically, but was finally able to come up with a few scenarios where the logical paradox was obvious to me without it just being the result of odd numbers plugged into a formula. As an aside, I find the thought of relativistic observers causing causality violations to have interesting parallels to the Quantum Observer Effect. – Dan Smolinske Feb 19 '15 at 15:16

Any faster than light travel will create paradoxes.

The article you linked to on relativistic reference frames explicitly states that:

One of the most striking aspects of special relativity is that faster than light travel is equivalent to time travel.

This is for any degree of faster than light travel, it's just that the faster you go the more obvious the problems are.

I don't think that you can avoid this, but for the sake of your story you might have to ignore it, but as long as you ignore it in a consistent way and make sure that you establish your "rules" of FTL before you rely on them as a plot point, you should be OK.

I remember one episode of Star Trek: The Next Generation where they used a micro warp jump to create the illusion that a ship was in two places at the same time - the light from the original location still arriving at the enemy ship for a few seconds after the jump. Because it fitted with the already established parameters of the Star Trek warp drive (or at least didn't wildly contradict it) you felt that it was a logical outcome and one that would really happen, rather than actually highlighting the paradox at the heart of the problem.

My favorite FTL setting has a way around this by literally having the paradox-avoidance built in. Your FTL engine or your FTL message simply won't work, or simply won't send, if moving in that direction or messaging that person can create a time paradox. The paradox-avoidance goes down to the quantum level, so it's not a human or human-device thing.

So you'd be able to jump a trillion light-years away with no problem, as long as you're causally disconnected from the starting point. So waaay out might be ok, while the closer you get (say within the galaxy) the dicier it gets, until it becomes literally impossible.

• which setting is that? – mart May 15 '17 at 13:02

Create a society for your characters to interact with that has dedicated itself to constructing a lifestyle and environment that facilitates time travel. The society spends its time, energy, and resources living in a manner thats easily interchangable throughout time and in an essence terraforms the physical space they occupy for time travel.

Off the top of head one would need an extraordinary amount of clones doing the exact same thing every day as part of a hive. Their consistent hive lives are constantly engineering their physical enviornment over an unconceivably long period of time specifically to eliminate paradoxal contaminates. Essentually using the lives of trillions or more hived clone slaves throughout millenias to pave paradox proof worm hole highways through space/time.

• A bit of formatting and a quick go though the text would help the readability. – Magic-Mouse Mar 15 '15 at 11:47

There is no causality problem with the Alcubierre drive. Like all metrics, all matter stays inside the lightcone, and there are no closed timelike curves involved with it. A modification of that metric does involve closed timelike curves, but it is a different spacetime. A variety of theorems and conjectures probably makes it impossible to go from an Alcubierre spacetime to a version that would violate causality (mostly having to do with blueshifting of incoming fields, divergence of the vacuum energy and non-uniqueness of the spacetime evolution). Those same theorems also apply to wormholes, by the way.

The point is that this kind of FTL isn't actually faster than light. The object inside does not move faster than light. In the case of the Alcubierre drive, it does not move at all. The spaceship just sits at the same spacetime point while the spactime around it does all the work. This is related to the fact that in cosmological expansion for instance, objects can recede from us faster than the speed of light (it was this observation that led to the idea of it).

Not that the Alcubierre drive doesn't have problems, but causality isn't among them.

• Violating causality with the Alcubierre drive is as easy as stopping the FTL flight, turning around (in conventional sub-lightspeed), accelerating (in a normal, non-FTL way), and going into FTL again. It's not the single FTL flight that breaks causality, it's always a sequence of FTL flights. – celtschk Sep 21 '15 at 19:02
• The only causality violation I have seen involving Alcubierre drive involves a direct transformation of the metric. Do you have a reference for this method? – Slereah Sep 21 '15 at 19:14
• A quick internet search turned up this page which describes the issues in detail. Note that these issues are completely independent of the method of FTL travel, as long as it respects the principle of relativity. That's the whole point: It does not matter in which way you obtain FTL travel. The causality problem is not a problem of the specific method, but is caused by the very fact that you are travelling FTL. So even if you invent some type of magic for FTL travel, as long as that magic respects relativity, it allows time travel. – celtschk Sep 21 '15 at 19:30
• I meant an actual science paper. All those kind of problem imply going outside the light cone, which is not at all the case for that kind of FTL. As said, such things actually happen in the expansion of the universe without any causality related problems. – Slereah Sep 21 '15 at 19:35
• I doubt you'll find a science paper for this for the same reason you'll not find a science paper for why some perpetual motion machine doesn't work. Note that outside the "warp bubble" the spacetime is still (approximately) Minkowski, and that's what counts (if you take the inside into account, you'll indeed get aa CTC, but not in the single travel, but in the combination of both travels). Anyway, do you know a scientific paper that covers how to start/stop an Alcubierre journey? Because if you don't do that, you of course won't produce a paradox (but also no useful travel method). – celtschk Sep 23 '15 at 19:59