The discussion centers on the nature of simultaneity in spacetime, particularly within a space-like hypersurface. It is established that two events can appear simultaneous from a frame moving at a velocity less than the speed of light (##v < c##), but this simultaneity is not universal across all frames. In flat spacetime, simultaneity is straightforward, while in curved spacetime, the absence of global frames complicates the definition. Events in curved spacetime must be analyzed with respect to their tangent vectors, which are always spacelike.
PREREQUISITESThis discussion is beneficial for physicists, students of relativity, and anyone interested in the complexities of spacetime and simultaneity in both flat and curved geometries.
In flat spacetime, yes. In curved spacetime there are no global frames, and you have to be a bit more careful with your definition. It would be better to say something like that they lie in a plane whose tangent vectors are everywhere spacelike.Apashanka said:If two events are occurring in a space like hypersurface...is it that the two events will appear to be simultaneous from a frame moving with velocity ##v\lt c##
You cannot consistently describe such a thing.Apashanka said:a frame with velocity ##v\gt c##??