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Spacetime and Euclidean geometry

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Abstract

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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References

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Authors and Affiliations

  1. University of Maryland, College Park, MD, 20742-4111, USA

    Dieter Brill & Ted Jacobson

Authors
  1. Dieter Brill
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  2. Ted Jacobson
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Corresponding author

Correspondence to Ted Jacobson.

Additional information

This article is dedicated to Michael P. Ryan on the occasion of his sixtieth birthday. Mike's passion for, and deft practice of, both geometry and pedagogy is legendary at Maryland. We are pleased with this opportunity to present our pedagogical effort to elucidate the geometry of Minkowski spacetime, the most homogeneous of cosmologies.

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Brill, D., Jacobson, T. Spacetime and Euclidean geometry. Gen Relativ Gravit 38, 643–651 (2006). https://doi.org/10.1007/s10714-006-0254-9

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  • DOI: https://doi.org/10.1007/s10714-006-0254-9

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