Discord for Discordant Redshifts. II.

In the first post on this topic (Discord for Discordant Redshifts. I.), I demonstrated algebraically that the cosmological model produces the high-probability associations of high-redshift objects with low-redshift foreground objects.  I also pointed out that this was recognized in 1975, still the early days of this redshift controversy (Noerdlinger, 1975).

In this part,  I present a more concrete, visual example.  We can write a simulation using the simple cosmology simulator that I wrote for the quantized redshift analyses (see Quantized Redshifts. IX. Testing the Null Hypothesis, Quantized Redshifts. X. Testing Our "Designer Universe", Quantized Redshifts XI. My Designer Universe Meets Some Data and What's Next...).

For the simulation, we generate a volume filled with a random, but uniform, distribution of points in 3-dimensional space.  We'll build this set of points in Cartesian space (we'll ignore spatial distortions created by General Relativity for now) around the observer, which, for convenience, we'll place at (0,0,0).  Each point represents a galaxy.

For the observer at (0,0,0), we'll select a field-of-view of a few degrees.  This represents the region of the sky we see.

Next, for the observer at (0,0,0), we compute the distance between the observer and each of the galaxies in the model and mark each position with a dot, giving them a color based on the distance proportional to their redshift.  In this case, we'll make blue close and red furthest away.  If we make a slice through the field of view, it would look something like this:

Click to enlarge

The observer is positioned on the left.  The two lines making the wedge represents a fixed angular size on the sky representing the observer's field of view.  We see that the further away the galaxies are, the more there are in the field of view.  This is just perspective.

Next, we look at how these points would be projected on the sky.  Run the simulation and concentrate on a bright, low-Z objects (large and blue), then examine region around it.  We see many more objects with higher z (small and red) in background. 

Click to enlarge for a better view

Note some of the features we can see in this 'image.

• high redshift objects (orange and red) very close to low redshift objects (blue and aqua)?
• How many objects in a line of three or more do you see? 
• What about high-redshift objects lined up with low-redshift objects?

Here's a couple more sample runs to view:

 

Click to enlarge for a better view

Click to enlarge for a better view

A large number of characteristics of  the 'evidence' for quasar-galaxy discordant redshift associations can be created via random number generator!

Effects that I have not included in this analysis:

1. Orientation effects for quasars in the Unified model of AGN (Pierre Auger Observatory).  This means the number of dots above that represent high-redshift quasars is actually a fraction of those in the graphic above.  However, if our telescope is sufficiently sensitive, we would see these high-redshift objects as regular galaxies.
2. Evolutionary effects on quasars.  There might be a different density of quasars formed in the early universe.
3. Don't include grouping or voids of galaxies or quasars.   This would create regions of high and low alignment probabilities.
4. Don't include changing size of co-moving volumes in relativistic cosmology.  This is a reasonable approximation for redshifts significantly less than one.

Consider point 1.  Even if we weren't just interested in quasars, what it implies is we should generally see a large number of galaxies in the background for any reasonable sized field-of view with a nearby galaxy.

Do we see this?

Yes!

Consider these older survey images, created from the Palomar Observatory Sky Survey (POSS) (wikipedia) imagery of the Tadpole galaxy from Aladin.

I've rotated the image above for easier comparison to the Hubble image below.  Now look at  Hubble image which not only exhibits higher resolution, but penetrates to deeper (higher) magnitudes.

In addition to the foreground Tadpole galaxy, we see many more distant galaxies in the background.  To see more galaxies, check the image at full resolution at the Hubble website.

I remember the first time I saw this image, shortly after the ACS camera was installed on Hubble.  I was astonished, not so much by the incredible foreground 'Tadpole galaxy', but by all the galaxies which we could see beyond it!  If any of those galaxies were turned near face-on to us, it would very possibly appear as a quasar!

You can explore many of the images from the newer cameras on HST of bright foreground galaxies and see many fainter, more distant galaxies in larger numbers.  Here are links to the stories and full-resolution images at the Space Telescope Science Institute:

• Hubble's Largest Galaxy Portrait Offers a New High-Definition View
• Hubble Snaps Images of a Pinwheel-Shaped Galaxy
• A Poster-Size Image of the Beautiful Barred Spiral Galaxy NGC 1300
• Celestial Composition
• Hubble Photographs Grand Design Spiral Galaxy M81
• Galaxy on Edge
• NASA's Hubble Rules Out One Alternative to Dark Energy
• NASA's Hubble Celebrates 21st Anniversary with "Rose" of Galaxies
• Chance Alignment Between Galaxies Mimics a Cosmic Collision

Food for thought…
Now one of the key assumptions in this model is that the universe is fairly uniform on large scale and BIG.  So big that even our most powerful telescopes must really work to see further and further.  And when they do, we see more and more stuff…

If we want to rescue Arp's probablility calculations, we would not only have to make the Universe smaller (to reduce the probability of chance alignments), but we would kinda have to be center of it.  This is probably why Creationists and Biblical Geocentrists often invoke Arp's claims to support their notion that the Universe is small and centered on us.

Who the frak do I think I am...
to challenge someone of Arp's reputation?  If you're defending discordant redshift claims, you're probably thinking exactly that.  We'll ignore the fact that this is the fallacy of Argument from Authority (Wikipedia).

But note that in this post I'm not presenting my original work.  I had figured this out independently, but I wasn't willing to assemble the posts on this topic until I was able to determine if anyone before me had this same realization, as it was so simple.  It turned out that others had, but the discordant redshift supporters avoided these issues for over thirty years to keep their fantasy alive!