Kinematical Groups

Intuitive

Explanations in this section should contain no formulas, but instead colloquial things like you would hear them during a coffee break or at a cocktail party.

Concrete

  • For a nice introduction, see Section 3.4.5 "Kinematical groups and their mutual contractions" in the book Symmetries in Fundamental Physics by Sundermeier.
  • See also Section 4 in Missed opportunities by Freeman J. Dyson

Abstract

The motto in this section is: the higher the level of abstraction, the better.

Why is it interesting?

A proper understanding of possible kinematical groups helps us to understand why spacetime symmetry groups are possible.

Suppose that somebody had been bold enough in 1908 to take [the kinematical groups] seriously. He would have correctly predicted the expansion of the universe twenty years before it was discovered observationally by Hubble. More importantly, he would have been led to postulate the curvature of space-time, and so he would have considerably eased the path which led to general relativity. Missed opportunities by Freeman J. Dyson