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+ | ====== Kinematical Groups ====== | ||
+ | |||
+ | <tabbox Intuitive> | ||
+ | |||
+ | <note tip> | ||
+ | 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. | ||
+ | </note> | ||
+ | | ||
+ | <tabbox 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 [[https://projecteuclid.org/euclid.bams/1183533964|Missed opportunities]] by Freeman J. Dyson | ||
+ | |||
+ | <tabbox Abstract> | ||
+ | |||
+ | <note tip> | ||
+ | The motto in this section is: //the higher the level of abstraction, the better//. | ||
+ | </note> | ||
+ | |||
+ | <tabbox Why is it interesting?> | ||
+ | |||
+ | A proper understanding of possible kinematical groups helps us to understand why spacetime symmetry groups are possible. | ||
+ | |||
+ | <blockquote>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. <cite>[[https://projecteuclid.org/euclid.bams/1183533964|Missed opportunities]] by Freeman J. Dyson</cite></blockquote> | ||
+ | |||
+ | /*<tabbox FAQ>*/ | ||
+ | |||
+ | /*<tabbox History>*/ | ||
+ | |||
+ | </tabbox> | ||
+ | |||