Thinking About Large-Scale Structure

Consider a hollow sphere of inert material moving inertially in
interstellar space. The volume of the sphere is on the order of 10^6
cubic centimeters , and inside we have enough helium atoms to yield an
average density of on the order of 500 atoms per cc. We let the system
equilibrate and observe the distribution of He atoms periodically. I
envision that the distribution would be something I would unreservedly
call homogeneous virtually every time the distribution was observed
and recorded. Note: since this is a thought experiment we can do
miraculous things like observe, with our educated imaginations, the
distribution of atoms with high resolution.

Now consider an analogy to the observable universe representing the
hollow sphere and galaxies as the He atoms. Here our technical
challenges of determining distributions are easier in some ways and
harder in others. In this case we observe that there is a hierarchical
clustering of galaxies, groups, clusters of groups, and superclusters.
Most importantly we observe the Cosmic Web/Void structure that appears
to dominate the large-scale structure within the observable universe.

I have a hard time seeing the observed galactic distribution as even
remotely "homogeneous", especially compared to our distribution of He
atoms in the little toy model.

However, astrophysicists routinely argue that the large-scale
distribution of matter is statistically homogeneous, apparently like
the distribution of He atoms. This confuses me.

To me the two distributions are highly different and must be
distinguished in any rigorous scientific description. I assume others
might vigorously argue otherwise. So I present this thread as an
opportunity to air ideas related to the inhomogeneity/homogeneity
controversy. I would be most interested to hear why the galactic
distribution deserves the term homogeneous, relative to the He atom
distribution archetype.

RLO
Fractal Cosmology

On Friday, March 11, 2016 at 1:16:28 AM UTC-7, Robert L. Oldershaw wrote:
Consider a hollow sphere of inert material moving inertially in
interstellar space. [Mod. note: rest of quoted article snipped -- mjh]

For one thing, the He model really isn't homogeneous if you look at a
small enough scale. There are individual knots of matter called atoms
and then there are clouds of electrons and then there are really, really
tiny knots of matter called nuclei and then there are protons and
neutrons and then there are quarks and gluons. So one might ask the same
question of a sphere with helium inside, yes?

Gary

On 3/11/2016 9:16 AM, Robert L. Oldershaw wrote:
Consider a hollow sphere of inert material moving inertially in
interstellar space. The volume of the sphere is on the order of 10^6
cubic centimeters , and inside we have enough helium atoms to yield an
average density of on the order of 500 atoms per cc. We let the system
equilibrate and observe the distribution of He atoms periodically.

Why don't you use H or Li atoms? Perhaps He would just not
liquify at 2.73K cosmic background temperature, but many other
atoms would cluster in droplets or condense at the sphere's wall.

..
Now consider an analogy to the observable universe representing the
hollow sphere and galaxies as the He atoms.

Again, why He atoms? Galaxies look much more complicated. You
could use some complex kind of molecule, perhaps!

...
However, astrophysicists routinely argue that the large-scale
distribution of matter is statistically homogeneous, apparently like
the distribution of He atoms.

I don't think they argue that, they say it is like a distribution
of filaments. You really should use some more complex material than
He to have a good analogy! Perhaps some molecules that form an
aerogel, or proteins forming fibers, would somewhat better resemble
the structure of the universe (but then agian, perhaps no molecules
exists that would really do the job..)

To me the two distributions are highly different and must be
distinguished in any rigorous scientific description.

Yes, the He atom distribution is very different from that of
other types of atoms or molecules. (He is a rather special
element, of course.)

--
Jos

In article , "Robert L.
Oldershaw" writes:

Consider a hollow sphere of inert material moving inertially in
interstellar space.

Now consider an analogy to the observable universe representing the
hollow sphere and galaxies as the He atoms.

I have a hard time seeing the observed galactic distribution as even
remotely "homogeneous", especially compared to our distribution of He
atoms in the little toy model.

However, astrophysicists routinely argue that the large-scale
distribution of matter is statistically homogeneous, apparently like
the distribution of He atoms. This confuses me.

To me the two distributions are highly different and must be
distinguished in any rigorous scientific description. I assume others
might vigorously argue otherwise. So I present this thread as an
opportunity to air ideas related to the inhomogeneity/homogeneity
controversy. I would be most interested to hear why the galactic
distribution deserves the term homogeneous, relative to the He atom
distribution archetype.

Assuming (and that's a big assumption, considering quote-mining and
other such devices in recent posts, but I'm willing to give you a
chance) that this is an honest question: I think you really don't
understand what is meant by "statistical homogeneity". Your admission
that you have spent little time on statistics underpins this assessment.
As George McVittie said, "The essence of cosmology is statistics.". If
you read up on the history of statistics, you will see that many
contributions were made by astronomers.

I think a meaningful discussion is not possible unless it can be assumed
that all parties understand basics statistics.

On Friday, March 11, 2016 at 3:16:28 AM UTC-5, Robert L. Oldershaw wrote:
Consider a hollow sphere of inert material moving inertially in
interstellar space. The volume of the sphere is on the order of 10^6
.....

A better way to think about it is a metal foam:
https://en.wikipedia.org/wiki/Metal_foam

On the size scale of the foam cell and cell wall, obviously there are
major inhomogeneities in the density. The density of metal in the
walls is much higher than the air in the voids.

However, on the size scale much larger than the cell size, the foam is
actually quite uniform. One can weigh different large chunks and get
very nearly the same density.

Pretty much the same for the observable universe. At the small scale,
walls and voids with extremes in density variations. At the large
scale, measureably uniform. Note I said measureably uniform. It's
possible to measure the clumpiness of galaxies on different
observational lenghth scales, and beyond a few hundred Mpc, there is
very little detectable clumpiness.

CM

On 3/13/2016 10:26 AM, Craig Markwardt wrote:
On Friday, March 11, 2016 at 3:16:28 AM UTC-5, Robert L. Oldershaw wrote:
Consider a hollow sphere of inert material moving inertially in
interstellar space. The volume of the sphere is on the order of 10^6
....

A better way to think about it is a metal foam:
https://en.wikipedia.org/wiki/Metal_foam

On the size scale of the foam cell and cell wall, obviously there are
major inhomogeneities in the density. The density of metal in the
walls is much higher than the air in the voids.

However, on the size scale much larger than the cell size, the foam is
actually quite uniform. One can weigh different large chunks and get
very nearly the same density.

Pretty much the same for the observable universe. At the small scale,
walls and voids with extremes in density variations. At the large
scale, measureably uniform. Note I said measureably uniform. It's
possible to measure the clumpiness of galaxies on different
observational lenghth scales, and beyond a few hundred Mpc, there is
very little detectable clumpiness.

If this Atlas of The Universe is accurate:
http://www.atlasoftheuniverse.com/universe.html

then there's a nice resemblance with 3D graphene foam:
http://acsmaterial.com/product.asp?cid=99&id=126

And on the "Atlas" you can nicely zoom in, After two
zoom levels you just see the Virgo supercluster and the
homogeneity is clearly gone.

--
Jos

On Sunday, March 13, 2016 at 5:16:44 AM UTC-4, Gary Harnagel wrote:


For one thing, the He model really isn't homogeneous if you look at a
small enough scale. There are individual knots of matter called atoms
and then there are clouds of electrons and then there are really, really
tiny knots of matter called nuclei and then there are protons and
neutrons and then there are quarks and gluons. So one might ask the same
question of a sphere with helium inside, yes?


Thanks, Gary, but in the intended analogy the He atoms are analogous
to the galaxies, and galaxies have nuclei and central supermassive
black holes. Also galaxies are surrounded by large halos which we
could say are analogous to electron "clouds.

I am NOT saying that the analogy is an exact one, OR EVEN CLOSE, but
it is reasonably useful for discussion purposes.

We are not talking primarily about the internal physics of the
fundamental "particles" on the two radically different scales, but
rather their DISTRIBUTIONS. The analogy does not involve sub-nuclear
phenomena. It is an unimportant of off-topic matter, but quarks and
gluons have never been observed to my satisfaction.

RLO http://www3.amherst.edu/~rloldershaw

On Sunday, March 13, 2016 at 5:18:36 AM UTC-4, Jos Bergervoet wrote:

To me the two distributions are highly different and must be
distinguished in any rigorous scientific description.

Yes, the He atom distribution is very different from that of
other types of atoms or molecules. (He is a rather special
element, of course.)


I know this is a subtle difference for some to grasp, but I am not
trying to reproduce galactic scale structure with the He analogy. I am
specifically choosing an atomic scale system that *avoids* most of the
complexities you mention because I want to compare the *distributions*
of the particles and *only* the spatial distributions of them.

I want to compare what I think of as an archetypal homogeneous
distribution with what I think of as an archetypal inhomogeneous
distribution.

Hope this helps.

On Sunday, March 13, 2016 at 5:19:16 AM UTC-4, Phillip Helbig (undress to reply) wrote:

Assuming (and that's a big assumption, considering quote-mining and
other such devices in recent posts, but I'm willing to give you a
chance) that this is an honest question: I think you really don't
understand what is meant by "statistical homogeneity". Your admission
that you have spent little time on statistics underpins this assessment.
As George McVittie said, "The essence of cosmology is statistics.". If
you read up on the history of statistics, you will see that many
contributions were made by astronomers.

I think a meaningful discussion is not possible unless it can be assumed
that all parties understand basics statistics.

Your condescension is truly princely. However, I was not encouraging
you to avoid substantive discussion but to speak plainly on a simple
question.

And here is the question once again for all to see: Given these two
very different distributions, are we allowed to say they are the same,
or are we scientifically required to distinguish the physical
characteristics of the two distributions?

Can you offer us a direct answer?

RLO http//www3.amherst.edu/~rloldershaw

On Sunday, March 13, 2016 at 5:26:47 AM UTC-4, Craig Markwardt wrote:

Pretty much the same for the observable universe. At the small scale,
walls and voids with extremes in density variations. At the large
scale, measureably uniform. Note I said measureably uniform. It's
possible to measure the clumpiness of galaxies on different
observational lenghth scales, and beyond a few hundred Mpc, there is
very little detectable clumpiness.


I would direct you to the newest paper,
http://arxiv.org/abs/1603.03260 , on this issue that I have cited in
my 3/13/16 post to the thread entitled something like "Largest
Structure...".

Are we really confident that we can claim that "there is very little
detectable clumpiness"..."beyond a few hundred Mpc"? Is this due to
the fact that the lumpiness is not there, or is it due to the fact
that we have trouble seeing it? Can we *confidently* decide which is
the case with existing data, or are we engaging in wishful thinking?

RLO http://www3.amherst.edu/~rloldershaw