What is the difference between homogeneity and isotropy?
This is a question more of semantics than cosmology. It is said that our universe is "homogeneous and isotropic" (on large enough scales). Doesn't the word 'homogeneous' imply or include 'isotropic' by default?
Neither word implies the other must be true; it is possible to have something that is homogeneous but not isotropic (eg. equally spaced stripes which definately have a prefered direction) and it is also possible to have something isotropic but not homogeneous (eg. concentric rings which look very different depending on where you are, but are isotropic if you are in the middle).
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