Quantized Redshifts. I. Introduction

In the previous post, I examined the claim that the SDSS galaxy survey visibly exhibits symmetry that places the Earth in a favored position.  The claim did not hold up very well to some very simple visual tests (see Delusions of Geocentric Quantization...).

This is the first of a series of posts dealing with claims of 'quantized' redshifts of extragalactic objects (galaxies and quasars) using the power spectral density (PSD), a popular tool for searching for frequencies in data.  Redshift quantization is often claimed as a means for dismissing the Big Bang as a cosmological model and is commonly invoked by supporters of Plasma Cosmology and/or Electric Universe as well as various flavors of creationism (CreationWiki). Not all creationists support claims of redshift quantization, most notably Reasons To Believe is an Old-Earth Creationism (OEC) group that accepts much of Big Bang cosmology.  See also RationalWiki & Wikipedia

The power spectral density (PSD, Wikipedia) is a popular analysis tool for temporal (time series) and spatial datasets.  At one time it was performed in analog circuits with wide frequency bins using band-pass filters for such applications as audio signal analysis.  While once a very computationally-intensive technique for digital signals, the development of the Fast Fourier Transform (FFT) combined with the speed and memory of modern computing hardware, has made the PSD relatively easy to compute.  Unfortunately, many who have access to the PSD make the mistake of assuming that it blindly 'finds frequencies' in datasets.  They don't take the time to understand what the PSD actually does with a dataset.

It would be nice if there were a comprehensive tutorial with detailed demonstrations of what types of datasets work well with the PSD as well as what types of artifacts are created by poorly chosen sampling and other misuses, but I have yet to find one.  Most researchers working with this tool, myself included, have had to discover these problems for themselves, by generating test datasets of known content and processing them through the PSD.  Then one discovers just how easy non-periodic processes can create peaks in the PSD that can be misinterpreted as real frequencies. 
The PSD has had popular use in time-series and one-dimensional spatial analysis.  There is a well-defined extension for computing the PSD in 3-D space.  It is tempting to reduce 3-D spatial datasets to 1-D for their simplicity, but if done, one must be careful to transform the coordinates correctly, lest errors and artifacts be introduced.

For most of those researchers reporting redshift periodicities with the radial technique, you find many of them do most of their work in areas other than cosmology - so they don't take the time to learn the nuances of the technique on the data they are using. They often seem to have a MatLab or IDL toolbox that generates an FFT and they use it without experimenting with what their process does to signals of KNOWN content.

Now for some quick overview questions.

Would 'quantized redshifts' be evidence against the Big Bang?

Possibly, but not definitively.

If the quantized redshifts were a property of the light as it propagated over cosmological distances, there are scenarios where it would not impact actual cosmological structure. 

The serious impact for Big Bang cosmology would be if the quantization represented the actual distribution of galaxies in concentric shells around the Milky Way galaxy.  Such structure formation would be very difficult to reconcile with current known physics.

Are 'periodicities' the same thing as 'quantization'?

No.

The action of gravity is expected to create large scale structures in Big Bang cosmology, with density enhancements and voids created by gravity attracting material from one region to collect it to form structure.  This can create create regions with preferred size scales just as water waves have preferred scales in bodies of water.  We have actually observed the enhancement predicted by Big Bang cosmology as it has propagated from the cool spots of the cosmic microwave background into the large galaxy collections we observe today.  See Baryon Acoustic Oscillations are NOT 'Redshift Quantization'

Most of those who try to deny Big Bang cosmology evidence have been attempting to hijack the terminology, trying to claim that the periodicities actually observed are the same as quantization.  In this way, they can cite mainstream cosmology references as evidence for their claims.  From a Christian perspective, such willful distortion of the professional use of the term could be considered equivalent to bearing false witness (Wikipedia: Ten Commandments).

Do Periodicities imply geocentrism or galacto-centrism?

No.

Structure formation limits homogeneity (the uniformity or smoothness of the distribution of matter in the cosmos) to particular size scales.  When compared to the large scale, these inhomogeneities are so small that they do not significantly violate the conditions of homogeneity for Big Bang cosmology any more than the existence of mountains is a killer for the 'round earth' theory (see Wikipedia: Flat Earth Society,  The Flat-out Truth).  See also Testing the Homogeneity of Large-scale Structure with the SDSS Data and The scale of homogeneity of the galaxy distribution in SDSS DR6)

In cosmology, homogeneity is defined at a cosmic scale value, often designated by the variable, a, defined over all space, which increases with cosmic time, which I will represent with the Greek letter, tau. When we do observations, we see a galaxy at distance, d, we are sampling the cosmos at time tau-d/c (due to the curvature of space, this relationship is not strictly true and as a result, there are several different measures of distance in cosmology - wikipedia). Therefore the density distribution and structure will appear to change with distance due to this sampling effect.

In addition, one of the beauties of the power spectrum technique used for identifying structure in these datasets is that while it can identify periodicities in a system, it does so without regard to any 'center' for those periodicities.  Note that even the periodicity of the baryon acoustic oscillations identified in the SDSS data (see Baryon Acoustic Oscillations are NOT 'Redshift Quantization') of about 500 million light years is not obviously visible in the SDSS data.  In the SDSS sample from the previous post (Delusions of Geocentric Quantization...), the graphic is about 500 million light years in radius and should contain about two oscillations across its diameter.  Can you visibly identify it?  If so, where is it's center?  Use the methods outlined in the previous post.

My Goals for this series of posts

The basic topics I plan to cover in this series of posts (and some of these will require more than one post) are

• An introduction to Fourier Series and its extension to the Fourier Transform, the FFT, and the PSD
• Explore the PSD produced with ideal data as input
• Explore what happens to the PSD when noise is introduced into the data
• Discuss some common misuses of the PSD
• Problems created in the PSD by radially sampling a 3-D dataset
• More experiments with the PSD, demonstrating some specific claims found in creationist literature

I've scheduled these at about one post per week, with perhaps a short digression in between some posts.  I think I've got these split out in just about reasonable chunks suitable for blog posts, but I will no doubt miss some nuances.  There are a substantial number of graphs and equations that need to be installed via the Blogger interface, which is not really ideal for these types of communications.  Let's see how it goes...

Next: The Fourier Series and its Applications