Can a Pseudo-Special Frame of Reference Eliminate Paradoxes in FTL Travel?

[Asok_Green]

I enjoy a good space opera and have always wanted to write my own, but at the heart of most space operas, even the relatively “hard” sci-fi ones, lurks the FTL drive. Plots just don’t advance well without them. But if relativity is correct, then FTL is the same thing as time travel, which leads to paradoxes and the death of causality.

(There are two main flavors of fictional FTL drives: Those that travel FTL through normal space, and those that jump instantaneously from one place to another. For the purposes of what I'm discussing here, you need only consider the second kind, the "jump drive")

Because I’m unwilling to let go of causality but unable to ignore relativity, I would need a method of FTL travel that couldn't be used to time travel. But as I understand it, there are precious few options for this, and they are: Parallel Universes, Consistency Protection, Restricted Space-Time Areas, and Special Frames. The above link explains each of these better than I can. Of the four, I definitely like Special Frames the best, especially the barely-touched-upon case where the FTL traveler must take on a specific frame of reference as it begins its FTL trip. I understand that this would contradict the relativity concept of all frames being equivalent, but I have a thought on that, which is what brings me here.

My thought is that a pseudo-special frame of reference could be created. If a beacon sent out a constant radio signal at a specific frequency, a ship with knowledge of the frequency should be able to utilize the Relativistic Doppler Effect to determine the frame of reference of the beacon and change velocity to match frames (I have difficulty visualizing this, so it may be the case that multiple beacons and signals would be necessary for it to work on all axes). If instead of a radio signal, the signal sent was a signal “somehow” vital to the FTL drive (not simply for navigation, but for its very function), it should eliminate the potential for paradoxes by forcing all FTL travel to occur in the same frame of reference.

A potential problem I see with this design is that if the frame of reference of the object emitting the signal should change (which would almost certainly happen at some point), relativity demands that the new frame of reference signal allow for FTL travel as well. A ship could then use the new signal to travel FTL to a region of space still receiving the old signal, and use the old signal to travel back, recreating the time travel paradox.

So in addition to the limitation of needing to match frames with the signal origin, the drive must also only be able to connect regions of space currently receiving identical signals (“currently” relative to an object that has matched frames), and without crossing any regions of space receiving signals from different frames of reference.

With all these limitations in place, the FTL system has an interesting dynamic. First of all, ships can’t travel to regions of space that haven’t yet received a signal. If the object emitting the signal gets bumped, changing its frame of reference, a “new” signal is effectively sent out. Ships in a new signal's light cone would be unable to travel into or through the old signal's light cone, though ships in an old cone would still be able to enter the expanding new cone via the progression of time. So if a big ship was preparing to make a historic FTL journey to a distant star system that finally came into range, and terrorists bumped the signal emitter, as soon as the light cone of the new signal passed the ship, it couldn't travel beyond the edge of the new signal. It would create an incentive for a civilization utilizing such a system to continuously expand outward to ensure that the opportunity to travel further didn’t get snatched away from them.

My question is simply, does the above sound right? It's all fictional, of course. But I'd be disappointed to learn that I've missed some glaring design flaw, or worse, the potential for a paradox.

 

[pervect]

If I'm understanding you, time travel in your fictional universe is possible, but you just create a signal to prevent it from happening by accident?

But if something goes wrong (with the transmitter, with the receiver, due to human error or deliberate human action) you'll get time travel and all its plot complications.

 

[Asok_Green]

That's not my intention. I don't want time travel to be possible at all in my fictional universe, because of its implications for causality. But unfortunately, relativity shows FTL travel to be the same thing as time travel. There are a few ways to get around this, but as you'll see, it quickly becomes a game of whack-a-mole dealing with the implications of each "solution".

One of the ways to keep FTL from being the same thing as time travel is the concept of special frames. Basically, if ships can only travel FTL from a certain (special) frame of reference, time travel paradoxes can't occur. The problem with this is that relativity says there are no special frames of reference.

The concept of the signal is (effectively) to create a special frame of reference. But the signal concept comes with strings attached. For one, the signal can't travel faster than light, or it would cause the same headaches it's trying to solve. It takes time, then, for the signal to cross the vast distances between stars. But the bigger problem is that there's nothing in space to bolt a signal emitter to. There's no way to secure it such that it could never change frames of reference. And if it were to get bumped, it would change frames of reference, and would send out a slightly different signal, relative to the old one. Ships receiving this new signal would be matching frames with a slightly different frame of reference. And if a ship could travel FTL away from a place in one frame of reference and return in a different one, the time travel problem would be back.

To prevent this, it must be made impossible (not by rule or regulation, but by author-imposed stardrive limitation) for ships to travel outside whatever signal they are in.

Now, unless I'm mistaken, that is the end of the moles. But I'm concerned I may have missed one, which is why I'm here, asking people more familiar with relativity to spot one.

Either way, the fictional FTL drive created by the above mole-whacking is interesting in its limitations. Suppose you were in a star system sixty light years away from the emitter, and when you tried to jump to a star system close to the emitter, you found you couldn't. Well, now what? Maybe the emitter's been bumped, but then again, maybe it's been destroyed. There's no way to know; neither ships nor information from within the light cone of the new signal (assuming there even is one) can reach you. You could travel to another star system close to the emitter, one that hasn't stopped receiving the old signal, and wait there until the new signal reaches you. But what if there is no new signal? What if the emitter really was destroyed, and for your patience, your reward is isolation, stranded in a single star system? Even if there is a new signal, coming home is still a one-way trip. Once you receive the new signal, it's impossible to travel back to areas of space still receiving the old one. You can't travel there until the new signal reaches them.

 

[Asok_Green]

I didn't realize I was responding to a physics guru. A couple of lines clearing up my design probably would have been enough. Let's pretend I was explaining it to the forum at large, then. At any rate, I hope I haven't offended you. Wasn't trying to.

 

[JesseM]

But the bigger problem is that there's nothing in space to bolt a signal emitter to. There's no way to secure it such that it could never change frames of reference. And if it were to get bumped, it would change frames of reference, and would send out a slightly different signal, relative to the old one. Ships receiving this new signal would be matching frames with a slightly different frame of reference. And if a ship could travel FTL away from a place in one frame of reference and return in a different one, the time travel problem would be back.

To prevent this, it must be made impossible (not by rule or regulation, but by author-imposed stardrive limitation) for ships to travel outside whatever signal they are in.

I don't get what you mean by "outside". Is the signal like a linear tunnel the ship is traveling through? What if you had two such tunnels nearby each other and with their ends (the emitters) in motion relative to one another, and as soon as the ship left the end of one tunnel, it traveled a short distance through normal space and then entered the other tunnel? What prevents time travel using nearby tunnels in motion relative to one another in this way?

 

[Asok_Green]

No, the (invisible) signal moves in all directions at the speed of light, like radio waves. By "outside," I mean beyond the leading edge of the signal. If the signal had only been transmitted for five years, a ship could only travel to star systems five lights years or closer to the object sending the signal.

 

[JesseM]

No, the (invisible) signal moves in all directions at the speed of light, like radio waves. By "outside," I mean beyond the leading edge of the signal. If the signal had only been transmitted for five years, a ship could only travel to star systems five lights years or closer to the object sending the signal.

Would the signal permanently rewrite the area of space it crossed, so that every point in the future light cone of a moment the signal was on would have the same preferred frame for FTL, or would the signal region be more like a thick spherical shell with the outer boundary defined by the moment the emitter was turned on and the inner boundary defined by the moment it was turned off? What would happen if the signal was accelerated as it was transmitting? Would it be necessary to keep its velocity 100% constant in your science fiction world, and if so why wouldn't this violate the uncertainty principle?

 

[Asok_Green]

The signal needs to be continuously broadcast, so your second description is spot-on.

If the emitter had been broadcasting from one frame of reference, and was then accelerated (changed frames of reference), this would be just as disruptive as if it were turned off, because the signal transmitted from the new frame of reference wouldn't match the old one.

I can’t see how the uncertainty principal would be violated by this design, but my understanding of it is limited. I’d be interested in getting your perspective.

In answering this question, another possible scenario popped up. What would happen if the emitter was under constant acceleration? Would the system still work? How would it behave? Might the time travel problem crop back up? Tough questions. From a writing standpoint, it'd be much simpler if the system simply couldn't work with an accelerating emitter. But my intuition is that under the rules given earlier, if a ship could match the constantly changing frame of reference signals, the FTL drive should work. I do think, however, that the potential places to which the ship could travel would be severely limited. Remember that a ship can still only travel to points in space currently receiving a signal identical to the one the ship is receiving. Instead of a "solid" sphere, I think there would be a hollow one with an infinitely thin "shell." I'm pretty sure time travel would still be impossible. This is really difficult for me to visualize, though, and I don’t have the math or physics skills to check it for sure. It'll take someone with a better handle on relativity to say for certain.

 

[Ich]

How would you deal with two emitters covering the same region of spacetime? If a starship could lock to either of them, all the problems will reappear.

 

[Asok_Green]

True, but the stated design already prevents you from crossing areas of space receiving signals from a different frame of reference. If you were at a point in space receiving two signals from different frames of reference, the drive wouldn't be able to take you anywhere.

 

[Ich]

So if you have more than one emitter, the whole scenario breaks down? I mean, how much relative velocity would you allow for the system to first work properly and then break down completely? What mechanism would you invent to justify this strange behaviour?

 

[Asok_Green]

Yes. The entire system wouldn't break down in the same instant, but ships in regions of space receiving one signal couldn't travel to regions of space receiving both signals, and ships in regions of space receiving both signals couldn't travel anywhere. As the light cone of the second signal continued to expand, it would eventually disrupt FTL travel to or from any given star system.

I'm not sure what you mean by how much relative velocity I'd allow for the system to first work properly and then break down completely. As I've said before, my physics knowledge is limited. Could you elaborate on your question?