Say you have flat (Minkowski) spacetime. Suppose you could talk about a chunk of space/spacetime in such a way. Take some frame, and in that reference, pick a region of space. Where is it a bit later? Ok. So, you consider it to have not moved? Now consider the system again but in a different reference frame, where things at rest in the first frame are in motion in the second. So, where is the chunk a bit later in the second frame?
Things that are Lorentz invariant are unlike fluids.
Your example fails at Galilean relativity: the water you claim is static from your frame on an anchored boat is moving from my frame on an airplane above it — and so isn’t a counter example. We don’t need Lorentz invariance at all. (Though, your example of non-moving water fails Einstein relativity too.)
So you’ve failed to show a difference between spacetime and a fluid.
And to address your point directly:
Gravitational waves leave a wake that perturbs the medium.
Sorry, I was unclear. The contradiction was that if you could take chunks like that it would be moving in the other frame, but Lorentz invariance says that flat spacetime has the same structure in different frames, and so wouldn’t be moving.
You say that “if the spacetime is moving, there’s local curvature”?
Then, in flat spacetime, as there is no curvature, then (by the contrapositive) there is no “movement of spacetime”?
But if some stuff is not moving in one inertial frame, then in another inertial frame it is moving.
But that implies that, if spacetime is stuff and such that, if it is moving then there is local curvature, it follows that in a different inertial frame, the spacetime is not flat.
But, whether spacetime is flat doesn’t depend on the choice of an inertial reference frame.
As for how to describe those things without talking about spacetime moving,
How spacetime works has the general coordinate invariance or covariance or whatever.
You have a manifold with a pseudo-Riemannian metric tensor. You can talk about like, geodesics and such.
For a warp bubble (suppose a sub-luminal one) you could talk about a non-accelerating time-like path that remains within the bubble, and talk about how the spacetime interval along it relates to the spacetime interval of some time-like path that starts in the bubble, leaves it, “travels besides it”, and finally re-joins the original path.
(Of course, in some reference frame, the bubble would not move.)
I don’t think it really makes sense to talk about spacetime moving, even in the case of a warp bubble. A position doesn’t have a position, or a time a time, but rather a position is a position, and a time is a time.
You can talk about how, in some particular coordinate system, with some particular foliation into space-like slices, some aspects/pattern of the metric tensor at some position and time coordinate values, correspond to those at a later time coordinate at a different position coordinate value, but this is relative to a choice of coordinate system.
We can talk about how a region moves in relation to other regions.
I’m still not following your objection based on relativity:
We have one frame where I’m on Earth; we have another where I’m in a rocket traveling away at a fixed velocity. In one case we see the rocket traveling away; in the other, we see Earth traveling away. But neither one tells us that the spacetime itself is moving — they’re both just local coordinates.
In the case we see the spacetime itself move, eg with a gravitational wave, both the frame from the rocket and the earth agree that the manifold has been changed in a way that left a wake — moving relative to its local, original shape.
As a side note, “inertial reference frames” are a useful fiction: we’re always being accelerated, eg, by the galactic center, fellow galaxies, dark matter filaments, etc. Conclusions based on such a fiction may be practical, but cannot be used to derive conclusions about physical reality — as they don’t exist.
1) coordinate acceleration from gravity doesn’t make one not in an inertial reference frame?
2) Why would something have to be in an inertial reference frame in order for inertial reference frames to “exist”? Doesn’t make sense to me.
In any case, that seems like just an excuse to ignore Lorentz boosts. One should address SR before addressing GR.
3) If spacetime were stuff, then it would be stuff always, not just when there are ripples or whatnot. But, in flat spacetime, you cannot describe it as a stuff in a way that is compatible with Lorentz symmetry, because the velocity of stuff changes under boosts, and so stuff can’t be stationary both when one doesn’t and when one does apply a boost. Therefore, it isn’t stuff.
Things that are Lorentz invariant are unlike fluids.