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What convervation law is required by the Lorentz Transformations

  1. Jul 9, 2005 #1
    Time invariance implies conservation of energy. Space invariance implies momentum convervation. What convervation law does the Lorentz invariance imply?
     
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  3. Jul 9, 2005 #2

    dextercioby

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    Angular momentum. Immediate by Noether's theorem for classical fields.

    Daniel.
     
  4. Jul 9, 2005 #3

    selfAdjoint

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    The Lorentz transformations by definition preserve the four-interval [tex]c^2t^2 - x^2 - y^2 - z^2[/tex].
     
  5. Jul 9, 2005 #4

    pervect

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    Conservation of angular momentum is generated by spatatial rotation invariance. Space rotation invariance is indeed part of the Lorentz group. But I suspect the original poster was interested in the symmetries related to the Lorentz boost, not by the spatial rotation part of the Lorentz group.

    I seem to recall that this question was discussed before, but I don't recall the conclusion that we came to.
     
  6. Jul 9, 2005 #5
    I was thinking the same thing but there are many 4-vector invariants in SR. Energy-momentum, space-time. The classical conservation laws have one specific quantity conservered not a variety.
     
  7. Jul 9, 2005 #6

    George Jones

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    Read the stuff here.

    Regards,
    George
     
  8. Jul 9, 2005 #7
    Thinking by analogy, shouldn't it imply conservation of the stress-energy tensor?
     
  9. Jul 9, 2005 #8

    dextercioby

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    Nope, stress- energy tensor is linked to space-time translations.

    Daniel.
     
  10. Jul 19, 2005 #9
    This should be a straightforward question with an obvious answer - but authors seem to skirt the issue
    spatial displacement symmetry - conservation of momentum
    temporal displacement symmetry - conservation of energy
    isotropic symmetry - conservation of angular momentum

    When gauge symmetry is applied to Maxwells's em equations, one consequence is conservation of charge - isn't conservation (invariance) of the spacetime interval also consequent to gauge symmetry?
     
    Last edited: Jul 19, 2005
  11. Nov 1, 2007 #10

    arivero

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    It is a funny answer... the position of the center of mass? Ok, in absence of external forces, the center of mass is a preserved quantity, so it makes sense, or sort of.
     
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