# FTL Gravity Waves?

• B
On the one hand, gravity waves travel at c, but on the other hand, spatial expansion has no speed limit; ie, it can happen at FTL speeds. At first one might think, "So what? Gravity waves are gravity waves and spatial expansion is spatial expansion." But what is a gravity wave other than the cyclical expanding and contracting of a region of space for some duration? Seems to me like they shouldn't have a speed limit either. But if they can't propagate faster than c, then doesn't that mean Alcubierre drives are impossible? Since a vessel using an Alcubierre drive is really just a surfboard riding a gravity wave of it's own design and creation?

mfb
Mentor
You probably mean gravitational waves. Gravity waves are something different (e. g. surface water waves).
spatial expansion has no speed limit
Spatial expansion does not even have a well-defined speed. You can measure how the distance changes, but this is not a relative speed of objects anywhere.
But if they can't propagate faster than c, then doesn't that mean Alcubierre drives are impossible? Since a vessel using an Alcubierre drive is really just a surfboard riding a gravity wave of it's own design and creation?
No, and the argument does not make sense.

pervect
Staff Emeritus
On the one hand, gravity waves travel at c, but on the other hand, spatial expansion has no speed limit; ie, it can happen at FTL speeds. At first one might think, "So what? Gravity waves are gravity waves and spatial expansion is spatial expansion." But what is a gravity wave other than the cyclical expanding and contracting of a region of space for some duration? Seems to me like they shouldn't have a speed limit either. But if they can't propagate faster than c, then doesn't that mean Alcubierre drives are impossible? Since a vessel using an Alcubierre drive is really just a surfboard riding a gravity wave of it's own design and creation?

Spatial expansion just doesn't propagate. You may think it "should" propagate, , but it turns out it doesn't. Another thing that doesn't propagate is the direction of the gravitational pull (or, for that matter, the direction of an electrostatic pull). The apparent position of the sun as observed visually (by light waves) changes due to the Earth's velocity, a phenomenon known as "aberration". Star positions change due to aberration too, a phenomenon known as "stellar aberration" that has to be routinely taken into account in astronomy. However, the actual direction of Newtonian gravity is well known NOT to aberrate in such a fashion. Note that this matches the behavior of the electrostatic force, which also do not aberrate.

The main point I'm trying to make is that the presence or absence of aberration can serve as an experimental distinction between things which we consider to propagate, and things which we do not consider to propagate. The second point I'm making is that using this experimental distinction, we can say that waves propagate (because they do aberrate), while other gravitational effects (such as the direction of the Newtonian gravitational pull) do NOT propagate because they do not aberrate.

I don't have any references for the non-aberration of spatial expansion, but there are some references on the non-aberration (and hence non-propagation) of the direction of gravitational pull. See for instance Steve Carlip's paper, "aberration and the speed of gravity", https://arxiv.org/abs/gr-qc/9909087.

PeterDonis
Mentor
2020 Award
what is a gravity wave other than the cyclical expanding and contracting of a region of space for some duration?

You are assuming that "spatial expansion" is one thing. It isn't. The "spatial expansion" of the whole universe is different from the "expanding and contracting of space" in a gravitational wave. They are different spacetime geometries with different properties, and the implied analogy you are making between them by using the words "spatial expansion" to refer to both is not a valid analogy.