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Invariant intervals are fundamental in relativity. But if you make a triangle in space-time from 3 invariant intervals, then it will also have 3 invariant angles, by the cosine law which can easily be proved to still apply in Minkowski space. Yet I have not been able to find any papers on invariant angles. Are there any, and if not, why not?

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  • $\begingroup$ It is a part of a greater property, actually in tensor analysis, by which scalar quantities are invariant under basis transformation. $\endgroup$ – Alexander Aug 15 '15 at 1:24
  • $\begingroup$ Yes, a scalar function of an event is invariant, since, unlike a vector or tensor, it does not depend on direction, and so is unaffected by the rotation of axes which is a Lorentz Transform. But the interval, though a scalar, is a function of the vector from the origin to the event, and so it would change under a more general linear transformation. But rotations do not change lengths, hence the invariance of intervals, so the interval is invariant. Rotations also don't change angles, so Alexander's answer gives a more direct way to show that angles between vectors are invariant. $\endgroup$ – murray denofsky Aug 16 '15 at 22:43

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