I Line Element in Minkowski Space: Geometric Meaning

Joe Cool
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Hello,
how can you imagine the geometrically meaning of the minus sign in ds2=-dx02+dx12+dx22+dx32, maybe similar to ds2=x12+dx22 is the length in a triangle with the Pythagoras theorem?
 
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Joe Cool said:
Hello,
how can you imagine the geometrically meaning of the minus sign in ds2=-dx02+dx12+dx22+dx32, maybe similar to ds2=x12+dx22 is the length in a triangle with the Pythagoras theorem?
Geometrically it means that surfaces of constant spacetime interval form hyperboloids instead of spheres. This is important because it clearly distinguishes spacelike intervals which form hyperboloids of one sheet from timelike intervals which form hyperboloids of two sheets (future and past)
 
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@bcrowell's GR book, downloadable from http://www.lightandmatter.com/, includes some postulates (in the manner of the postulates of Euclidean geometry) for Minkowski geometry.
 
Thanks a lot for your answers!
 
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