- #1

nomadreid

Gold Member

- 1,586

- 180

- TL;DR Summary
- Is the treatment of the geometry of Minkowski space as in the cited article (angle ϑ between inertial frames ϑ=tanh(v/c) with relative velocity v/c, inner product for timelike vectors as |A|*|B|*cosh(ϑ), etc.) one of the standard treatments?

In "The Geometry of Minkowski Space in Terms of Hyperbolic Angles" by Chung, L'yi, & Chung in the

*Journal of the Korean Physical Society*, Vol. 55, No. 6, December 2009, pp. 2323-2327 , the authors define an angle ϑ between the respective inertial planes of two observers in Minkowski space with a relative velocity of v (with c=1) as arctanh(v), and inner products of vectors denoting events by using this angle : for timelike vectors A and B, denoting |A| and |B| as the corresponding spacetime intervals (+ - - -) , the inner product is |A|*|B|*cosh(ϑ), for spacelike ones the same but negative, and between a spacelike and a timelike vector with a similar expression. (This vaguely reminds me of the discussion of rapidity in https://en.wikipedia.org/wiki/Rapidity, but I'm not sure if that is relevant.) My question is, assuming I have presented it correctly, whether this treatment is one of (albeit not the only) the standard treatments of a geometry in Minkowski space, or whether it is just a curiosity, or whether it is flawed.
Last edited: