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I was reading Philip W Anderson's essay "More is Different" (https://www.tkm.kit.edu/downloads/TKM1_2011_more_is_different_PWA.pdf) and at some point he links the isotropy and homogeneity of space and matter with fundamental symmetries of nature:

„By symmetry we mean the existence of different viewpoints from which the system appears the same. It is only slightly overstating the case to say that physics is the study of symmetry. The first demonstration of the power of this idea may have been by Newton, who may have asked himself the question: What if the matter here in my hand obeys the same laws as that up in the sky—that is, what if space and matter are homogeneous and isotropic?“

Therefore, does it mean that if space and matter were anisotropic and non-homogeneous, our local symmetries and laws of physics would be different elsewhere? Are there models or metrics of spacetime (or the universe in general) where this would happen (a model that would imply space and matter anisotropy and non-homogeneity)?

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  • $\begingroup$ See Noether's Theorem: en.wikipedia.org/wiki/…. In essence, if we give up homogeneity, then momentum conservation is gone. If we give up isotropy, then there is no angular momentum conservation. If we give up on time translation symmetry, then energy stops being a locally conserved quantity. None of the above would bode particularly well for the structure of the universe, even though the universe does not conserve energy on the cosmological scale. $\endgroup$
    – FlatterMann
    Commented Apr 1, 2023 at 11:19
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    $\begingroup$ The FLRW metric with these symmetries do not describe local physics anyway. All local 'realistic' matter distributions break these symmetries $\endgroup$
    – Eletie
    Commented Apr 1, 2023 at 14:00
  • $\begingroup$ Didn't go through the pdf. By fundamental symmetries of nature, do you also include internal symmetries? $\endgroup$
    – paul230_x
    Commented Apr 2, 2023 at 1:54
  • $\begingroup$ @KP99 Yes, I would say that $\endgroup$
    – vengaq
    Commented Apr 2, 2023 at 11:13
  • $\begingroup$ @FlatterMann and can other symmetries be affected by giving up homogeneity and isotropy (like Poincaré, Lorentz, diffeomorphism and CPT invariances)? $\endgroup$
    – vengaq
    Commented Apr 2, 2023 at 11:14

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