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Homogeneity and isotropy

  1. Nov 30, 2007 #1
    If the assumptions of homogeneity and isotropy lead to the conservation laws of linear momentum, angular momentum, and energy, would a cosmology that drops either of those assumptions lead to violations of those conservation laws which in turn could be observed? My first guess would be yes, but from what little I understand it becomes very difficult if not impossible to define and measure those quantities on a global scale. Thoughts?
  2. jcsd
  3. Nov 30, 2007 #2


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    Sort of. One still has local conservation laws of linear momentum and energy in a small section of empty space, but if the overall cosmology lacks (for instance) time translation symmetry, there won't necessarily be a globally conserved energy.

    Note that in spite of homogeneity and isotropy, the FRW metric does NOT have time translation symmetry, which implies there isn't any global notion of the mass/energy of the universe.

    See for instance the sci.physics.faq Is energy conserved in General Relativity?, which I will quote in part. For copyright and other reasons I am only quoting a "fair use" portion of the FAQ, so I encourage the OP and other interested people to read the entire original.

    You might also look at the wikipedia article for a more advanced discussion about the various sorts of mass, energy, and momentum defined in GR.
    Last edited: Nov 30, 2007
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