Colóquio Jorge André Swieca (IF-IME)
Dia 06/04/2015 (segunda-feira), Auditório Novo I (IF), às 13h30.
Título: "Causality implies the Lorentz Group" Redux
Palestrante: Prof. Pedro Lauridsen (UFABC)
Abstract: A landmark mathematical result in Special Relativity is the celebrated theorem proved in 1964 by E. C. Zeeman about the structure of causality-preserving transformations of Minkowski space-time, almost sixty years after Einsteins work. More precisely, Zeeman showed that any such transformation is the composition of a space-time translation, a Lorentz boost, a spatial rotation and a dilation. This theorem received a fair amount of attention after its inception, receiving alternative proofs under slightly different hypotheses by Borchers, Hegerfeldt and others, and being extended to general, strongly causal space-times by Hawking, King and McCarthy. In this mostly pedagogical talk, we revisit this result, presenting a streamlined, self-contained proof with very few prerequisites under the same hypotheses originally employed by Einstein, that is, assuming only that the transformations preserve the speed of light. Our proof, closely related to Zeemans original one, can b!
e understood as a strengthening of the fundamental theorem of affine geometry, which is the natural arena for Special Relativity.
