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Physics, Astronomy & Cosmology / Re: Does the cosmological principle dictate isotropy?
« on: 01/07/2021 23:34:19 »
Hi again.
It looks like there are plenty of good replies and answers here already. I've read through most of this discussion again and it still seems that a few things might still have been left unanswered or unclear. I'm going to break this post into smaller chunks because otherwise it will become a monologue and may not be useful to you (ChiralSPO) anyway.
Your (ChiralSPO) first post said the following:
Are you (ChiralSPO) now able to see why people tended to think that isotropy (on a large scale in the universe) follows from the idea that no point in space is special?
We may hit a similar upper size limit for scale: If the universe has positive curvature then it has finite extent. Once we are averaging over the whole of space and considering structures of that size, there is no larger scale we can go to.
Ignoring these limitations and trying to answer in the spirit in which the question was asked - Well possibly. If the universe is infinite and the distribution of matter in it was random then somewhere within it there is a structure (a region of above average density) that has a size exceeding any fixed number you want to set. We then only need to consider a point in space that is close to the boundary of that structure and take averages over lengths comparable to the size of that structure.
It looks like there are plenty of good replies and answers here already. I've read through most of this discussion again and it still seems that a few things might still have been left unanswered or unclear. I'm going to break this post into smaller chunks because otherwise it will become a monologue and may not be useful to you (ChiralSPO) anyway.
Your (ChiralSPO) first post said the following:
As I understand it, the main idea underlying the cosmological principle is that no part of the universe is "special"..and I'm not sure that we (previous contributors) have really explained why isotropy is generally implied.
That seems a reasonable axiom, but where I have difficulty is that this appears to be widely interpreted as implying that the universe must be isotropic on some grand scale.
Are you (ChiralSPO) now able to see why people tended to think that isotropy (on a large scale in the universe) follows from the idea that no point in space is special?
I think what my question down to is this: does the definition of "local anisotropy" scale with the scale that is being considered?This is very difficult to answer. If we go to small scales, then we are in the territory of quantum mechanics and most reasonable ideas go out of the window. If there is a fundamental Planck length then we cannot meaningfully divide space into smaller regions and calculate average densities or consider structures below this scale.
We may hit a similar upper size limit for scale: If the universe has positive curvature then it has finite extent. Once we are averaging over the whole of space and considering structures of that size, there is no larger scale we can go to.
Ignoring these limitations and trying to answer in the spirit in which the question was asked - Well possibly. If the universe is infinite and the distribution of matter in it was random then somewhere within it there is a structure (a region of above average density) that has a size exceeding any fixed number you want to set. We then only need to consider a point in space that is close to the boundary of that structure and take averages over lengths comparable to the size of that structure.
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