Earlier quoted context omitted.
Ok, so if that's the case, why can't objects be relative to spacetime rather than other objects, as discussed in the article?
Short answer: because tachyons don't exist (i.e. haven't been found) Slightly longer answer: To be relative to spacetime would (most likely) mean having a means of transmitting information faster than the speed of light, but information cannot travel faster than the speed of light. * "The world line (or worldline) of an object is the path of that object in 4-dimensional spacetime, tracing the history of its location…
You can describe the manifold using a coordinate system corotating with the gyroscope, the worldlines will still have a non-zero acceleration. There is absolutely no need for any matter field satisfying hyperbolic PDE's with faster than light characteristics.