@SpacemanSR For your question on ang. mom: The angular momentum tensor is conserved but just the spatial angular momentum is not.
Remember boosts just relate coordinates in diff. inertial frames. It is a mathematical description and does not “impart” anything physical.
@SpacemanSR Yes, in special relativity, transformations are linear, but are best described using tensor notation. Quantities are vector-like, but have four components (since we are in a 4D vector space). For example, four-velocity and four-momentum.
@SpacemanSR Yes, hyperbolic in the sense that sin and cos in SO(3) can be replaced with sinh and cosh with a suitable angle (known as rapidity). These special rotations, known as Lorentz boosts, preserve ds^2, and time dilation and length contraction is a direct consequence.
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