Chapter

Special relativity: The geometric formulation

Ta-Pei Cheng

in Relativity, Gravitation and Cosmology

Second edition

Published in print November 2009 | ISBN: 9780199573639
Published online February 2010 | e-ISBN: 9780191722448 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199573639.003.0003

Series: Oxford Master Series in Physics

                      Special relativity: The geometric formulation

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Constancy of light speed allows us to interpret geometrically the relativistic invariant interval s as a length in the 4D manifold, called Minkowski spacetime, with a metric equal to diag(-1,1,1,1). Physics of SR follows directly from the Lorentz transformation, which is a rotation in the Minkowski spacetime. We introduce 4-vectors as the simplest example of tensors in Minkowski space, and construct their scalar products. Besides the 4-position vector, we also introduce the 4-velocity and 4-momentum. The principal features of a spacetime diagram and its representation of Lorentz transformations are presented. In particular, the causal structure of SR is clarified in terms of lightcones in a spacetime diagram.

Keywords: geometric formulation of relativity; light speed; invariant interval; Minkowski spacetime; 4-velocity; relativistic energy and momentum; spacetime diagram; lightcone

Chapter.  12094 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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