Will This Violate Causality?

Okay, so I have a sci-fi setting in which there is a form of FTL travel.

Imagine the universe(all three/four dimensions of it) was stretched out onto the surface of a sphere.

Now assume that there is no way of traveling through space FTL but it is possible to rotate towards the centre of the "sphere" and skip parts of space. Thereby, allowing STL ships that can acheive significant STL speeds to take a shortcut by cutting across the spere.

For the sake of easy calculation, assume that the trip to Alpha Centauri is halfed in distance by taking the shortcut. (I know that if the universe was that curved then it would have been noticed by now. This is just for illustration.)

Would it be possible for a ship that could travel at 75% the speed of light through space, taking the shortcut which halfs the distance (Resulting in an effective speed of 1.5c), to violate causality?

EDIT:

If anyone can tell me the math I'd have to do to figure it out myself, that would also be appreciated.

• Depends on your own rules really, nobody can say for sure in the real world. – Callum Bradbury Mar 22 '17 at 16:44
• It's an idea I'm looking to stress test. I'm certain isn't the case in reality but if it were the case could someone come up with a way of time traveling. Or at least a closed time-like curve. – Douglas Mar 22 '17 at 17:12
• Ah ok, I suspect you'd be ok, as you wouldn't be going back in time, or actually travelling faster than light, but I'll give the matter some thought, it's a good question to ponder I think – Callum Bradbury Mar 22 '17 at 17:22
• I like the system because 1, no pissing off Einstein, 2, the further away you go, the better the shortcut becomes. – Douglas Mar 22 '17 at 17:27
• Isn't this the standard wormhole thing? – Willk Mar 22 '17 at 18:00

The mechanism does not matter. The description in Time Travel Happens applies to hyperspace jumps, wormholes, folding space, or whatever. In fact, some kind of out-of-universe motion is presumed because FTL velocities in our spacetime simply don’t compute.

Here is the relevant illustration from that answer:

It is possible to avoid causality violations as given in detail on that Answer, and the underlying “jump” mechanism does not matter. In general, not following the constrains but jumping willy-nilly does lead to causality issues.

• Compare also particularly one of the answers to Does the Alcubierre drive have a theoretical upper speed limit? on Physics. Full disclosure: My own question. – a CVn Mar 23 '17 at 8:46
• As an addition, perhaps this video is of interest: PBS Spacetime on Superluminal Time Travel – Doomed Mind Mar 23 '17 at 16:00
• Those light cone diagrams show instantaneous transit. The question talks about travel time at < c. Are those light cones relevant to the question? – Schwern Mar 23 '17 at 18:09
• @Schwern@sc “taking a shortcut” beats light, with an effective speed of 1.5c: how is that <c? A FTL transit track is instantaneous in some reference frame, and this is explored in detail in my linked posts. Light cones are always relevant as they are equivalent to an axis on a normal graph. – JDługosz Mar 24 '17 at 3:36

Apparent FTL between two warped points in space is fine, so long as it's not actual FTL through space. The speed of light only applies to movement through space.

What you've described is effectively a wormhole or warp drive: something that changes the topology of space to shorten the spacial distance between two points. A wormhole is like a tunnel, warping is like taking the Great Circle Route. Both are faster than going in a "straight line" over the surface of the sphere.

Note that such warping requires mind-boggling amounts of energy: optimistic calculations for the Alcubierre Drive require the mass-energy of 700 kg, roughly 6e19 J. That's all the electricity in the world for a year.

This does not violate causality. The speed of light/causality only applies to traveling through space. Curving space, and forming a tunnel is still curving space, does not count. So long as your ship is traveling through that curved space at less than $c$ you're fine.

Apparent FTL due to the warping of space is happening right now due to the expansion of the universe. The distance between two galaxies can increase faster than light. This is fine because space itself is expanding between them. The two galaxies don't violate relativity or causality because their own reference frames are different.

If the expansion continues to accelerate, eventually there will be distant galaxies we can never see because they are receding faster than light: the Future Horizon. Their light will never reach us.

• The energy requirement is not an issue. In my setting they discover that space is already curved and they can leave space without building wormholes. They just need to rotate their ship in the new direction and fire the engines as normal. – Douglas Mar 22 '17 at 20:40
• «The speed of light/causality only applies to traveling through space. Curving space, and forming a tunnel is still curving space, does not count.» That is wrong. – JDługosz Mar 23 '17 at 7:01
• How a transit takes place — some variation on a hyperspace jump or wormhole — does not matter. Just getting there faster than light is the problem. You don’t travel through space in this model. – JDługosz Mar 23 '17 at 7:13
• Gotta agree with @JDługosz . While apparent FTL doesn't break any laws of physics it absolutely will create a causality violation. – Joe Bloggs Mar 23 '17 at 8:53

If you want some reasonably plausible handwaving to prevent the possibility of causality violation from an ftl drive that is in principle capable of it, just say that if your drive is actually used to create a closed timelike curve then that will create a feedback loop as more and more virtual particles traverse the loop until the ship (and any information contained within it) is destroyed.