In a Minkowski space diagram of ct vs x, with 2 stationary events in the same plane of spacetime (1 event located along a worldline, 1 not on a worldline) is this still considered euclidean space?
The definition of euclidean space is a space in any finite number of dimensions, in which points are designated by coordinates (one for each dimension) and the distance between two points is given by a distance formula. (Given by Encyclopedia Britannica)
In our proposed Minkowski diagram above, there are a finite number of dimensions, and a defined distance in spacetime between them, given by: $$ (\Delta s)^2 =(\Delta x)^2 -(\Delta ct)^2$$
The book I am following (J. Hartle, Gravity: An Introduction to Einstein’s General Relativity), states that, in Euclidean space, for the distance between two points we will always have $\Delta s >0$. It cannot be negative, or even 0, unless $\Delta x =0$.
Does this mean if I'm finding the distance in spacetime between 2 points like the ones stated in the scenario at the beginning, the events can never be time-like $(\Delta s < 0)$? Or does the fact that one event is not located along a wordline mean that this distance can be located outside the light cone?
