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Take our universe as a 3d chart with 2 space dimensions and one time dimension (ignoring the other space dimension for simplicity). You chart it using some "god's eye view" reference frame, or just any single reference frame. So you end up with simultaneous events perpendicular to the time axis for any point in time. Each time slice is just a rectangle showing that moment in time (for the 'god-like' observer).

Now when you apply lorentz transformations for another observer, can you use that same chart? Is it true that the new observer just has a slightly angled time slice (due to the transformation) but still uses the same chart? So their time slices are stretched rectangles compared to the god-like observer?

Or do lorentz transformations change things so much that it would be impossible to represent the universe using a single 4d block (i.e. you'd need a different 4d block for each observer)?