Special Relativity and Geometry
C. E. Harle, R. Bianconi

Einstein's synchronization principle:
light rays are red, observers are blue and magenta (these work as a sort of mirrors).

This will be a book on the foundations of Special Relativity from a synthetic viewpoint. This means that we start from a few postulates on how to represent light rays and the principle of inertia and using Einstein's idea of light clocks we define the notion of measure of time and distance (and simultaneity) and introduce coordinates a posteriori.

The book has a strong visual appeal, modelling with affine geometry. As a subproduct we develop several geometric algorithms which allow us to write programs to visualize relativistic motions.

Download a preliminary version (The two and three dimensional spacetimes) in gzipped postscript format. NEW (May, 2001: Beware of the typographic (and, I am afraid, other) errors. Sorry, not yet fully proofread ;-)

Things to come:

  1. Some odds and ends in the three dimensional model (hyperboloid of synchronization, etc).
  2. The four dimensional model: how to do four dimensional descriptive geometry!
  3. The geometry of the visual effects in special relativity (apparent shape and, I hope, colour).

Light cone intersecting two simultaneity spaces

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LAST UPDATE: December 6, 1999.