A familiar theorem about chords of a circle has an intersting analogue in Minkowskian geometry, the circle being replaced by a null cone. In curved space-time the theorem is not true, and the extent to which it fails provides (with the help of the world-function) a measure of the curvature. The results are interpreted physically in terms of times measured by clooks carried by free particles.
The method of the world-function has been described in detail elsewhere; cf.,J. L. Synge,Relativity: the General Theory, (Amsterdam, North-Holland 1960).
To Enrico Bompiani on his scientific Jubilee.
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Synge, J.L. Intuition, geometry and physics in relativity. Annali di Matematica 54, 275–284 (1961) doi:10.1007/BF02415356
- Free Particle
- Null Cone
- Minkowskian Geometry