Delusions of Geocentric Quantization...

In a couple of comments sections of this blog (links), Mr. Rick DeLano claims that, despite evidence to the contrary, he SEES periodicities in some of the skymaps produced by such groups as the Sloan Digital Sky Survey (SDSS).  In particular, he mentions skymaps such as those available at the SDSS at links like the one reproduced here.

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I suggested Mr. DeLano conduct an exercise with this graphic to test his statement but I find no evidence that he has actually done so.  A LOT of bad science is driven by researchers claiming they 'see' something in a dataset that can't be objectively identified (see Pathological Science, Pareidolia).  Persistence in pursuit of these claims has destroyed more than a few careers.

Since Mr. DeLano is unwilling or unable to make any actual effort to validate his claim in an objective way, I will examine the claim in detail here, performed the test which I described to him.

Let's examine the issues in several steps to make sure we have a reasonably complete understanding of the data we are examining.

What does the SDSS plot represent in its projection from a 3-dimensional space? 

I have taught several astronomy classes and occasionally found that students unfamiliar with the ways in which 3-D datasets are sometimes projected into a 2-dimensional page genuinely do not understand what they are seeing.

The SDSS  plot is a 'slice' of the sky 1.25 degrees above and below the celestial equator.  In this case, the two-dimensional plot of galaxies on the sphere of the sky is projected in to the third dimension with the value of the redshift, z, which is a proxy for the distance of the galaxy from the observer.  Once extended into three dimensions, a slice is cut through the sphere, creating a circular plane on which we will project a small amount of data above and below the slice.

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In this construction, the Earth is in the center of the sphere is represented by the blue dot in the center of the plot.  The pie-slice shaped regions marked in yellow are areas where data could not be collected because the Milky Way obstructs too many of the more distant objects.  This map represents a very small section of the entire sky visible from Earth, so one needs to exercise caution when extending anything 'seen' in this dataset to the entire sky.

What is meant by 'quantization' in the rigorous scientific sense? 

Historically, describing a physical quantity as 'quantized' has meant that it has discrete measured values.   In atomic physics, the energy levels of atoms are described as quantized because they would correspond to a fixed energy in each state.  In the case of a hydrogen atom, the electron energy levels were proportional to 1/n^2, where n is an integer, 1,2,3,4,...  Intermediate values, such as energies corresponding to n=1.2 or 5.7, are never observed.

For redshifts to be 'quantized', they would have to only occur at certain discrete values.  For example, if redshifts were quantized in steps of z = 0.02, we would expect to only see galaxies with redshifts that were integral multiples of this value.  For a quantized redshift of z=0.02, we would only find galaxies on the green circles surrounding the Earth in the graphic below.

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In the plot above, there is not even the suggestion of alignment of galaxies along these curved lines.  Note that Hartnett & Hirano, using power spectral analysis (Galaxy redshift abundance periodicity from Fourier analysis of number counts N(z) using SDSS and 2dF GRS galaxy surveys) reported redshift periodicities at z = 0.0102, 0.0246, and 0.0448.  All of these values, and their integral harmonics, should be visible in this graphic as well-defined walls of galaxies confined between the green circles.  As I will illustrate in the coming posts, many different things can create peaks in power spectra.

Yet we see many of these 'walls' of galaxies cutting across the green circles, in violation of the claim that the distribution is spherically symmetric around the Earth. 

Here's some structures I've identified in the SDSS map.  None of them exhibit an Earth-centered symmetry.

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What is meant by 'periodicity' in the rigorous scientific sense?

Substances that support wave-type motions, such as gases and fluids, can support various periodic behaviors, both in time and space.  In fact, Fourier analysis was developed to mathematically handle just these types of physics problems.  The superposition of these wave motions will create density enhancements in otherwise uniform gases and fluids.

Is there structure in the SDSS survey?

Absolutely!  Modern cosmological simulations predict a pattern of clumping under gravity (including some energy loss by radiative processes in the plasma, which forms due to the energy release of the collapse).  Here is a snapshot from one of the modern simulations (see more at Simulating the joint evolution of quasars, galaxies and their large-scale distribution) which exhibit some similarity to a collection of soap bubbles, where the bubbles enclose 'empty' voids with membranes and filaments of soap and water.

It is possible to identify a number of apparent cross-sections of 'bubbles' in the structure.  I mark just a few in the graphic with light-blue ovals, but many more, with overlaps can clearly be identified.  These are like the slices through many of the cosmological simulations

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This is a slice through the data incorporating distances inferred from the galaxy's redshift value.

What happens when you look through the data in directions perpendicular to this, if you were to see these galaxies projected on the sky at night?  Does it retain a similar bubble-like structure?  Here's a sample from the NYU value-added catalog.

This is how the SDSS galaxy distribution would look if we could see it projected on a section of the sky about 100 degrees x 60 degrees in area.  The animated gif steps through the data at different values of redshift, z.  We see structures, very similar to the filaments and bubbles in the SDSS projection in z,  out to about z = 0.2, suggesting that the structures we observe look the same from at least two very different directions.   Beyond z = 0.2, the galaxies become too sparse to identify any structure.

Astronomy Picture of the Day also recently posted a release of the 2MASS survey that plotted one million galaxies on the sky.  I leave it as an exercise to the reader to identify structures (walls & bubbles) in this map.  The structures revealed in this map resemble those in the SDSS survey in angle and z plotted above, consistent with the idea that the universe is homogeneous.

Does the structure in the SDSS surface exhibit a high degree of symmetry around the Milky Way Galaxy?   

There is a selection effect created by the fact that observers look outward from the Earth radially and this places us in the center of the data, with everything else scattered beyond that.  These plots only go out to z = 0.14 (or about 0.14*(3e5 km/s)/(72 km/s/Mly) = 580 million light years).  You can obtain a more accurate distance using the cosmology calculator at Ned Wright's Cosmology Tutorial site.  The SDSS survey extends far beyond this.  To use this aspect of the geometry to claim the Earth is the center of the Universe is as bizarre as standing on a mountaintop, noticing that your view extended equally in all directions around you, and then declaring YOU are the center of the universe.

So I've tried to identify the 'concentric/geocentric structures' claimed by Mr. DeLano and others, but no objective tests seem to support the claim.  This suggests that the 'concentric structures' are a form of pareidolia and only exist in the mind of the observer who wishes them to exist.

As I have demonstrated above, this was a very simple set of tests, which I performed with very simple, and freely available, graphics tools.  Yet Mr. DeLano was unable, or unwilling, to do it himself.  Why?  
Annotations installed in SDSS graphics using Inkscape.