Euclidean and Affine Spaces: A Hidden Complementarity
Michael H. Brill
Keywords: metrics, line elements, space-time physics, general relativity, invariance, covariance, color science
A structure that can be interpreted as either affine or Euclidean is identified. That structure was invented to describe the manifold of colors, which has an undisputed affine symmetry (based on color matches) but a debated line element (based on color discrimination). The affine/Euclidean structure is reviewed here as a way to tune our notions of "invariance" and "covariance" in space-time physics. In particular, the structure displays a kind of manifest covariance that is rare in space-time physics, despite common invocations of the Principle of General Covariance in that field.
