Math of GR
part 7

In the Minkowski Space formulation of SR, you have not 3 set of axes XYZ but four, XYZT, the last one for "time." You might say that right there, it can't be "real" space, because time is not a place where an object can be positioned geometrically, and I would agree. But for now, let's ignore this objection and see another better objection .... I think.

In Minkowski Space (MS), which we will call MS4 since it is in 4D, you have your XYZ rods at right angles to each other, as usual, but you also construct mathematically a 4th rod at right angles to all the other three. I know, I know, you cannot picture it, but that in no way hampers the math you can do. Trust me. You can have 37 dimensions and do math with it.

Let out first coordinate system in MS4 likewise be called XYZT-1, and then we set up another one called XYZT-2. Also at time T equals zero, each respective axis is against the other one: X1 against X2, etc.