Spacetime and Euclidean Geometry

Details Spacetime and Euclidean Geometry Spacetime and Euclidean Geometry

2004-07-06

arxiv.org/abs/gr-qc/0407022v2

Gen.Rel.Grav. 38 (2006) 643-651

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

11 pages, 9 figures; for a festschrift honoring Michael P. Ryan; v.2: References to related work added

Scientific paper

10.1007/s10714-006-0254-9

Using only the principle of relativity and Euclidean geometry we show in this
pedagogical article that the square of proper time or length in a
two-dimensional spacetime diagram is proportional to the Euclidean area of the
corresponding causal domain. We use this relation to derive the Minkowski line
element by two geometric proofs of the "spacetime Pythagoras theorem".

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