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##??
A space-like hypersurface is a mathematical concept used in the study of relativity and space-time. It refers to a three-dimensional surface in space that is perpendicular to the time axis and marks a distinct moment in time. This means that any two events that occur on this surface are considered to have happened simultaneously.
A time-like hypersurface is also a three-dimensional surface in space, but it is perpendicular to the space axis and marks a distinct point in space. This means that events that occur on this surface are considered to have happened at the same location, but at different times. In contrast, events on a space-like hypersurface are considered to have happened at the same time, but at different locations.
The concept of simultaneous events on a space-like hypersurface is important in understanding the relativity of time and space. It helps us to understand that the perception of time and space can vary depending on an observer's frame of reference. It also plays a crucial role in the study of causality and the relationship between cause and effect.
In physics, space-like hypersurfaces are used to describe the geometry of space-time in the theory of relativity. They are also used in the study of black holes, gravitational waves, and other phenomena that involve the curvature of space-time. In addition, they are used in cosmology to study the evolution of the universe and the Big Bang theory.
While space-like hypersurfaces are a mathematical concept, they can also be used to describe real-world events and phenomena. For example, the surface of a table can be considered a space-like hypersurface, as events that occur on different parts of the table can be considered to have happened simultaneously. However, it is important to note that the concept of space-like hypersurfaces is a theoretical construct and may not exist in the physical world as a tangible entity.