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Poincare' group

  1. Nov 30, 2011 #1
    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?
     
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  3. Nov 30, 2011 #2

    tom.stoer

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    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.
     
  4. Nov 30, 2011 #3

    dextercioby

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    Poincare symmetry connects observers on different worldlines in a flat space-time, irrespective whether the worldlines are geodesics or not. One observer describes physics through one system of space-time coordinates x, another has x' for that. x and x' are linked through Poincare transformations. Observer's motion needn't be along a geodesic.
     
  5. Dec 1, 2011 #4

    Matterwave

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    Geodesics...don't form a group, they are just curves in the space-time. I don't believe there is a natural group operation that would make geodesics into a group....
     
  6. Dec 1, 2011 #5

    robphy

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    Maybe the OP is asking about characterizing the Poincare transformations as [determinant 1] symmetries that preserve the set of geodesics of Minkowski space.
     
    Last edited: Dec 1, 2011
  7. Dec 2, 2011 #6
    Very nice. This does it.
     
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