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[Phys-l] homogeneity and isotropy



In the context of:

>> homogeneous == same everywhere
>> isotropic == same in all directions

Anthony Lapinski wrote:
This seems to imply that these words are synonyms. Are they? I know they
are used differently in cosmology.

They're not the same.

Note: By way of background: nothing is homogeneous or isotropic
on an atomic scale. These are macroscopic concepts.

1) It is easy to be homogenous but not isotropic if there is a
texture, like the grain of wood. You can imagine an ideal piece
of wood that has grain, but the graininess is the same everywhere.

An ideal bar magnet is anisotropic (magnetized in one direction
and not the other) but ideally it would be homogeneous.

Ditto for a piece of "polaroid" polarizing plastic. Also in
my experience cellophane tape is homogeneous but anisotropic.
Also Mylar ... apparently the polymer molecules have some
preferential orientation. I hypothesize the material underwent
uniaxial stretching during manufacture. In contrast Kapton is
isotropic:
http://www.lgarde.com/people/papers/spacestructs.html



2) A starburst pattern of outgoing rays is isotropic (if viewed
from the center) but not homogeneous.

In general, if it looks isotropic, that implies it's also homogeneous,
unless you are a very lucky observer, situated at just the right spot.


====================

These terms certainly don't cover all the possibilities. A
crystal is the same in some directions but not all, and is
symmetric with respect to some displacements but not all.