# Why does an Alcubierre drive, travelling FTL, violate causality, if the universe expanding FTL doesn't?

An Alcubierre drive seems to be plausible as a means to travel faster than light, because

• it doesn't move the object itself, but the space around it.
• it's said that matter and information can't move through space faster than light, but space itself can.

However, it turns out that an Alcubierre drive still can't achieve superluminal speed without violating causality, because:

• the limit of speed of light doesn't apply only to matter and information, but to anything that moves from one point to another in space.
• anything that moves faster than light also makes information that comes out of it travel back in time, which violates causality.
• since the warp bubble itself moves faster than light within the rest of the universe, an Alcubierre drive will violate causality as it moves faster than light.

But if this is true, why can the universe expand faster than light, without time travel and therefore violation of causality happening? What makes it different to a warp bubble?

• but space itself can "Space itself" isn't moving through space (or some kind of meta-space). Space isn't going anywhere, it's just expanding. The expansion rate isn't a speed, it's a speed divided by distance, so it has units of 1/time. Apr 24, 2022 at 20:35
• I've had a lot of arguments, on physics forums, about the difference between expansion & relative motion, but it's great to see it so clearly related to time. (I don't understand why people think nothingness, rather than objects bounding it, could be moved relative to anything else.) The gist of that difference was explicitly described by Einstein in the 1916 edition (the first "pop sci" version) of 1915's General Relativity, somewhere near the middle of the book, which was printed in several different languages! Even so, some half-arsed impression managed, magically, to leak out...! Apr 27, 2022 at 4:54
• I guess it was a collective spelling error: "No thing" should never have been contracted into "nothing". Apr 27, 2022 at 5:04

In any curved spacetime we can still talk about local reference frames that are small enough scale we can ignore the curvature. We also can ask if there are closed timelike curves (CTC) which basically is asking whether we can time-travel to our past selves. CTCs are strongly thought to be impossible in reality.

The universe is thought to be spatially flat, but the spacetime as a whole is curved. CTC's are impossible: at each point in spacetime you have an "age of the universe". To be precise, this is maximum path-length (proper time) a geodesic could have between the big-bang singularity and said point. Any time-like or light-like curve is moving in the direction of increasing age of the universe; this is just as strong a concept of "future" and "past" as in flat spacetime.

With a single warp-drive you don't have CTC's. But you can still get CTC's with multiple warp-drives. Suppose you build a warp-drive on Earth and send it out into space. You start with an (almost) flat initial-condition and then generate a strongly curved spacetime (your warp bubble). Starting from a flat spacetime (or for very large scales from the spacetime of the universe), is much more physically realistic than starting from any other spacetime. You have to make your weird and wonderful curvature from an "empty canvas" !

With a warp-bubble, the highly curved spacetime is on a small scale. This allows us to glue two bubble spacetimes together so long as the ships don't get very close to each-other. If we consider two Earths, moving relative to each-other, that each make a warp-drive, we can set up the system to generate CTCs. This is one reason we suspect this to be impossible.

There is another reason to suspect making warp drives is impossible: Geodesics would have to diverge in some region, which is an anti-gravity effect. Neither matter nor light can make anti-gravity (antimatter has positive mass just like matter). The "attractive gravity only" rule is more precisely defined as an energy condition and at least one of these is violated by warp drives. Violating certain energy conditions would make the speed of sound faster than light which also allows for time-travel paradoxes.

In general, no known solution with CTC's is physically realistic. They either involve infinitely large systems that cannot be setup from an "empty canvas" or violations of energy conditions. For example, the Kerr metric concentrates it's energy condition violation in it's singularity. Real black holes are thought to lack this feature and be much deadlier instead.

• Unfortunately the strict "no negative energies" has been punched out. The space inside a non-vacuum dielectric capacitor has a negative energy component proportional to the energy stored on the capacitor plates, and this energy is the same energy required to pull the dielectric out of the capacitor while it is charged. So far, all known dielectrics have a breakdown voltage too low to make an absolute negative energy region but there's no proof this must be the case. Apr 25, 2022 at 4:13
• Incidentally I beg to differ about cannot get CTCs with a single warp bubble. Use a supermassive black hole. I am reasonably convinced that such a drive would enable climbing back out of one. Apr 25, 2022 at 4:22
• @joshua: there is positive energy in the electric field also, which always exceeds the energy it takes to pull away the dielectric. But your "negative energy" exists when particles bind together. However, the mass defect is always less than the mass of the particles, so the energy conditions hold. You are right there is no proof. Apr 25, 2022 at 5:44
• I know this comes a little late but I think opening a new question would get dinged, so - if there were a single preferred reference frame in which all warp drives in principle had to operate - let's call it subspace - that would prevent CTCs right? Jan 6, 2023 at 0:10
• @PeterMoore: There is nice, unique "zero velocity" frame you can define in the early universe. Run all of these geodesics forward in time and use their proper time as your universal time. When there are caustics (multiple geodesics that pass through the same point; not to be confused with singularities), choose the largest proper time. Allow FTL but all paths must strictly increase in universal time. These FTL rules aren't Lorentz-invariant, of course. How physics would work inside the engine nacelles of your jump drives is left as an exercise for Worldbuilding stack exchange. Oct 16, 2023 at 0:54

There are two fundamental differences between these two cases.

First, an Alcubierre warp tube is supposed to be something that you make. The problem is that if you can make one of them, and the laws of physics are Poincaré (Lorentz+translation) invariant, then you can make two of them in a configuration that violates causality, as Kevin Kostlan said.

This is a nonissue for the large-scale structure of spacetime, because you can't make two universes, or even one universe. Its shape is (by assumption) out of your control, and it has, as a matter of fact, no closed timelike curves.

Second, the expansion of the universe is, in a certain sense, faster than $$c\triangleq 299{,}792{,}458\text{ m/s}$$, but it isn't faster than light. A galaxy distant enough to have a recession speed larger than $$c$$ won't outrun a receding beam of light at the same distance, because the light's recession speed is even larger. $$c$$ is only the speed of light in inertial coordinates, and the standard cosmological coordinates aren't inertial.

If you go through an Alcubierre tube – even a unique one made by God so there are no causality issues – then you do outpace light that travels between the endpoints outside the tube. Nothing analogous to that ever happens in cosmology.

• To clarify: the reverse of an Alcubierre tube is OK: A light-ray passing through the center of earth will take ~nanoseconds longer to get to it's destination than a light-ray geodesic that is (very-slightly) bent around Earth's gravity well. But no localized physically-possible spacetime curvature (such as spinning black holes, etc) could end up making light take less time than flat spacetime. Apr 25, 2022 at 0:38