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Conservation of three-momentum

  1. Mar 8, 2014 #1
    I'm blanking on this at the moment, but a quick application of Noether's theorem would imply that, aside from the momentum-four vector, [itex] p_{\mu} = (E/c,-\vec{p}) [/itex] being conserved, that each component of [itex] \vec{p} [/itex] is also conserved due to invariance of the Lagrangian under translations - this is certaintly true in classical mechanics, but it also applies to special relativity, correct?
  2. jcsd
  3. Mar 9, 2014 #2

    Ben Niehoff

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    A vector being preserved is the same as all of its components being preserved.
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