As I understand it Newton's Laws imply that space is relative, as the laws of physics are the same in all inertial frames and as such there is no way, even in principle, to distinguish a frame that is truly at rest (absolute space). Hence the concept is physically meaningless, and the positions of (and distances between) physical objects, events, etc. are relative to the frame in which one is observing them from. Advancing on to Special Relativity, by postulating that the speed of light (in vacuum) is constant in all frames of reference, we are forced to conclude that time is relative also (as if it weren't then different observers would observe a different speed of light (in vacuum)). This leads to the result that the concepts of space and time are no longer completely separate and independent of one another and instead intertwined (as an event that occurs at rest over some time period in one frame, will occur over some spatial interval and a different time interval in another frame). Hence they should be considered as should be considered as a single entity, called spacetime.
Sorry for the waffling so far, just want to check that my understanding is correct up to this point?!
My main question is, given that space and time are (individually) relative quantities, is spacetime itself relative, or can it be considered absolute (as after all, it is the mathematical space of all possible events and exists independently of the physical events that occur within it)?
Best Answer
There is a property of spacetime which is independent of frame of reference.
The geometrical properties of the spacetime are described by the metric tensor, $ \eta _{\alpha \beta} =diag({-1,1,1,1})$ is SR (flat spacetime) or more generally $ g_{\alpha \beta} $ (any spacetime) in GR. This tensor specifies the distance between two infinitesimally close spacetime events, for example $ (t_1,x_1,y_1,z_1) $ and $ (t_1+dt,x_2+dx,y_2+dy,z_2+dz) $ in cartesian coordinates. The representation of this tensor is depending on your your choise of coordinates, but it describes the same physical (more accurate - geometrical) object. With the metric tensor you can calculate proper distances (called lorentz invariants in SR) between any two spacetime coordinates, quantities which are invariant under any coordinate transformation (= independent of frame of reference you're using, not necessarily inertial).