The discussion centers on the relationship between the Poincaré group and geodesics in Minkowski spacetime. Participants explore the definitions and implications of these concepts within the context of flat spacetime and Riemannian geometry.
Participants express differing views on the nature of geodesics and their relationship to the Poincaré group, indicating that multiple competing perspectives remain without consensus.
Some statements rely on specific definitions of geodesics and the Poincaré group, which may not be universally accepted. The discussion does not resolve the implications of these definitions or their application across different geometrical contexts.
A geodesic is a curve in an arbitrary curved Riemann manifold generalizing the "straight line" in flat space. A geodesic in a Riemann manifold is both the straightest curve and the shortest curve connecting two points A and B. Poincare symmetry is not a symmetry of arbitrary Riemann manifolds but a symmetry of flat Minkowski spacetime space only.matumich26 said:The poincare' group is the group of isometries of Minkowski spacetime, in a nutshell. In terms of an actual physical definition it is the group of all distance preserving maps between metric-spaces in Minkowski spacetime. What is the difference between this and geodesics?
tom.stoer said:A geodesic is a curve in an arbitrary curved Riemann manifold generalizing the "straight line" in flat space. A geodesic in a Riemann manifold is both the straightest curve and the shortest curve connecting two points A and B. Poincare symmetry is not a symmetry of arbitrary Riemann manifolds but a symmetry of flat Minkowski spacetime space only.