Redshift quantization: Difference between revisions

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{{Short description|Physical hypothesis}}

'''Redshift quantization''', also referred to as '''redshift periodicity''',<ref>

{{cite journal |last=Tifft |first=W. G. |date=2006 |title=Redshift periodicities, The Galaxy-Quasar Connection |journal=[[Astrophysics and Space Science]] |volume=285 |issue=2 |pages=429–449 |bibcode=2003Ap&SS.285..429T |doi=10.1023/A:1025457030279|s2cid=120143840 }}</ref> '''redshift discretization''',<ref name=Karlsson>{{cite journal |last=Karlsson |first=K. G. |date=1970 |title=Possible Discretization of Quasar Redshifts |journal=[[Astronomy and Astrophysics]] |volume=13 |issue= |pages=333 |bibcode=1971A&A....13..333K |doi=}}</ref> '''preferred redshifts'''<ref>{{cite journal |last1=Arp |first1=H. |last2=Russel |first2=D. |date=2001 |title=A Possible Relationship between Quasars and Clusters of Galaxies |journal=[[Astrophysical Journal]] |volume=549 |issue=2 |pages=802 |bibcode=2001ApJ...549..802A |doi=10.1086/319438|s2cid=120014695 |quote=The clusters and the galaxies in them tend to be strong X-ray and radio emitters, and their redshifts occur at preferred redshift values.|doi-access=free }}</ref> and '''redshift-magnitude bands''',<ref>{{cite journal |last=Tifft |first=W. G. |date=1973 |title=Properties of the redshift-magnitude bands in the Coma cluster |journal=[[Astrophysical Journal]] |volume=179 |issue= |pages=29 |bibcode=1973ApJ...179...29T |doi=10.1086/151844}}</ref><ref>{{cite journal |last1=Nanni |first1=D. |last2=Pittella |first2=G. |last3=Trevese |first3=D. |last4=Vignato |first4=A. |date=1981 |title=An analysis of the redshift-magnitude band phenomenon in the Coma Cluster |journal=[[Astronomy and Astrophysics]] |volume=95 |issue=1 |pages=188 |bibcode=1981A&A....95..188N |doi=}}</ref> is the [[hypothesis]] that the [[redshift]]s of cosmologically distant objects (in particular [[galaxies]] and [[quasars]]) tend to cluster around multiples of some particular value.

In [[inflation (cosmology)|standard inflationary cosmological models]], the redshift of cosmological bodies is ascribed to the expansion of the universe, with greater redshift indicating greater [[cosmic distance ladder|cosmic distance]] from the Earth (see [[Hubble's Lawlaw]]). This is referred to as [[cosmological redshift]]. Rulingand outis errorsone inof measurementthe ormain analysis,pieces quantizedof redshiftevidence offor cosmologicalthe [[Big Bang]]. Quantized redshifts of objects would either indicate, under Hubble's law, that theyastronomical areobjects physicallyare arranged in a quantized pattern around the Earth, or that. thereIt is anmore unknownwidely mechanismposited forthat the redshift is unrelated to cosmic expansion and is the outcome of some other physical mechanism, referred to as "intrinsic redshift" or "non-cosmological redshift".

In 1973, astronomer [[William G. Tifft]] was the first to report evidence of this pattern (note also: [[György Paál]]<ref>{{cite journal |last=Paal |first=G. |date=1970 |title=The global structure of the universe and the distribution of quasi-stellar objects |journal=Acta Physica Academiae Scientarium Hungaricae |volume=30 |issue= 1|pages=51–54|bibcode=1971AcPhH..30...51P |doi=10.1007/bf03157173}}</ref>). RecentSubsequent discourse has focused upon whether [[redshift survey]]s of [[quasarsquasar]]s (QSOs) have produced evidence of quantization in excess of what is expected due to [[selection effect]] or [[galaxy cluster|galactic clustering]].<ref>{{cite journal |last1=Trimble |first1=V. |last2=Aschwanden |first2=M. J. |last3=Hansen |first3=C. J. |date=2007 |title=Astrophysics in 2006 |journal=[[Space Science Reviews]] |volume=132 |issue=1 |pages=1–182 |doi=10.1007/s11214-007-9224-0 |arxiv=0705.1730|bibcode = 2007SSRv..132....1T |s2cid=119570960 }}</ref><ref name="adsabs.harvard.edu">{{cite journal |last1= Bell |first1=M. B. |last2=McDiarmid |first2=D. |date=2006 |title=Six Peaks Visible in the Redshift Distribution of 46,400 SDSS Quasars Agree with the Preferred Redshifts Predicted by the Decreasing Intrinsic Redshift Model|journal=[[Astrophysical Journal]] |volume=648 |issue=1 |pages=140–147 |bibcode=2006ApJ...648..140B |doi=10.1086/503792|arxiv = astro-ph/0603169 |s2cid=17057129 }}</ref><ref>{{cite journal |last1=Godłowski |first1=W. |last2=Bajan |first2=K. |last3=Flin |first3=P.|date=2006 |title=Weak redshift discretisation in the Local Group of galaxies? |journal=[[Astronomische Nachrichten]] |volume=387 |issue=1 |pages=103 |bibcode=2006AN....327..103G |doi=10.1002/asna.200510477|arxiv = astro-ph/0511260 |s2cid=119388085 }}</ref><ref name=Tang>{{cite journal |last1=Tang |first1=S. M. |last2=Zhang |first2=S. N. |date=2005 |title=Critical Examinations of QSO Redshift Periodicities and Associations with Galaxies in Sloan Digital Sky Survey Data |journal=[[Astrophysical Journal]]|volume=633 |issue=1 |pages=41–51 |bibcode=2005ApJ...633...41T |doi=10.1086/432754 |arxiv=astro-ph/0506366|s2cid=119052857 }}</ref> The idea has been on the fringes of astronomy since the mid-1990s and is now discounted by the vast majority of astronomers, but a few scientists who espouse [[nonstandard cosmology|nonstandard cosmological models]], including those who reject the Big Bang theory, have referred to evidence of redshift quantization as reason to reject conventional accounts of the origin and evolution of the [[universe]].<ref>For examples, see references by nonstandard cosmology proponents

Many scientists who espouse [[nonstandard cosmology|nonstandard cosmological models]], including those who reject the [[Big Bang]] theory, have referred to evidence of redshift quantization as reason to reject conventional accounts of the origin and evolution of the [[universe]].<ref>For examples, see references by nonstandard cosmology proponents

*{{cite journal | last1 = Ratcliffe| first1 = Hilton| date=2009| title = A Review of Anomalous Redshift Data| journal = 2nd Crisis in Cosmology Conference, CCC-2 ASP Conference Series | volume = 413| pages = 109| bibcode = 2009ASPC..413..109R}}

*{{cite journal|bibcode=1973ApJ...186....1B|doi = 10.1086/152474 | title=A Quantitative Alternative to the Cosmological Hypothesis for Quasars | journal=The Astrophysical Journal|date=1973|volume=186|pages=1–21|first=Moley B.|last=Bell|doi-access=free}}

*{{cite journal|bibcode=1979AZh....56..232K| title=periodicity of quasar redshifts ln /1 + z/ | journal=Astronomicheskii Zhurnal|date=1979|volume=56|pages=232–236|first=A. Ia.|last=Kipper}}

*{{cite journal|bibcode=1986ApJ...301..544L|doi = 10.1086/163922 | title=Is the universe really expanding? | journal=The Astrophysical Journal|date=1986|volume=301|pages=544|first=P. A.|last=Laviolette}}

*{{cite journal|bibcode=1980BAAS...12..852B| title=The Redshift Periodicity of QSO's and the Origin of Cosmic Radiation | journal=Bulletin of the American Astronomical Society|date=1980|volume=12|pages=852|first1=J. M.|last1=Barnothy|first2=M. F.|last2=Barnothy |author-link2=Madeleine Barnothy Forro}}</ref><ref>{{cite book |last1=Arp |first1=H. |date=1998 |chapter=Quantization of Redshifts |chapter-url=http://redshift.vif.com/BookBlurbs/SeeingRedBlurb.htm |title=Seeing Red |publisher=C. Roy Keys Incorporated |isbn=978-0-9683689-0-9 |deadurlurl-status=yesdead |archiveurlarchive-url=https://web.archive.org/web/20061020112037/http://redshift.vif.com/BookBlurbs/SeeingRedBlurb.htm |archivedatearchive-date=2006-10-20 |df= }}</ref><ref>{{cite journal |last1=Arp |first1=H. |date=1987 |title=Additional members of the Local Group of galaxies and quantized redshifts within the two nearest groups |journal=Journal of Astrophysics and Astronomy |volume=8 |issue= 3|pages=241–255 |bibcode=1987JApA....8..241A

|doi=10.1007/BF02715046|s2cid=119819755 }}</ref>

Redshift quantization is a controversial topic considered to be in the fringes of modern astronomy. Though the idea is generally discounted by the large majority of astronomers, peer-reviewed publications and discourse on the topic still continue to the present day.<ref>{{cite book |last1= Babu |first= G. Jogesh |last2=Feigelson |first2= Eric D. |year= 1996 |title= Astrostatistics |page= 183 |isbn= 978-0412983917}}</ref>

==Original investigation by William G. Tifft==

[[György Paál]] (for QSOs, 1971<ref>

[[William G. Tifft]] was the first to investigate possible redshift quantization, referring to it as "redshift-magnitude banding correlation".<ref>{{cite journal |last=Tifft |first=W. G. |date=1980 |title=Periodicity in the redshift intervals for double galaxies |journal=[[Astrophysical Journal]] |volume=236 |issue= |pages=70 |bibcode=1980ApJ...236...70T |doi=10.1086/157719}}</ref> In 1973, he wrote:

{{cite journal

|last=Paál |first=G.

|date=1971

|title=The global structure of the universe and the distribution of quasi-stellar objects

|journal=[[Acta Physica Academiae Scientiarum Hungaricae]]

|volume=30 |pages=51–54

|bibcode=1971AcPhH..30...51P

|doi=10.1007/bf03157173

|s2cid=118710050

}}</ref>) and [[William G. Tifft]] was(for galaxies) were the first to investigate possible redshift quantization, referring to it as "redshift-magnitude banding correlation".<ref>{{cite journal |last=Tifft |first=W. G. |date=1980 |title=Periodicity in the redshift intervals for double galaxies |journal=[[Astrophysical Journal]] |volume=236 |issue= |pages=70 |bibcode=1980ApJ...236...70T |doi=10.1086/157719}}</ref> In 1973, he wrote:

:"Using more than 200 redshifts in Coma, Perseus, and A2199, the presence of a distinct band-related periodicity in redshifts is indicated. Finally, a new sample of accurate redshifts of bright [[Coma cluster of galaxies|Coma galaxies]] on a single band is presented, which shows a strong redshift periodicity of 220 km s⁻¹. An upper limit of 20 km s⁻¹ is placed on the internal Doppler redshift component of motion in the Coma cluster".<ref>{{cite journal |last=Tifft |first=W. G. |title=Fine Structure Within the Redshift-Magnitude Correlation for Galaxies |editor-last=Shakeshaft |editor-first=J. R |journal=Proceedings of the 58th IAU Symposium: The Formation and Dynamics of Galaxies |volume=58 |pages=255–256 |bibcode=1974IAUS...58..243T |doi=|year=1974 }}</ref>

Tifft, now Professor Emeritus at the [[University of Arizona]], suggested that this observation conflicted with standard cosmological scenarios. He states in summary:

:"Throughout the development of the program it has seemed increasingly clear that the redshift has properties inconsistent with a simple velocity and/or cosmic scale change interpretation. Various implications have been pointed out from time to time, but basically the work is observationally driven."<ref>{{cite journal |last=Tifft |first=W .G. |date=1995 |title=Redshift Quantization - A Review |journal=[[Astrophysics and Space Science]] |volume=227 |issue=1–2 |pages=25–39 |bibcode=1995Ap&SS.227...25T |doi=10.1007/BF00678064|s2cid=189849264 }}</ref>

== Early research - focused on galaxies rather than quasars ==

In 1971 from redshift quantization [[György Paál|G. Paál]] came up with the idea that the [[Universe]] might have nontrivial [[topological]] structure.

<ref>

{{cite journal

|last=Paál |first=G.

|date=1971

|title=The global structure of the universe and the distribution of quasi-stellar objects

|journal=[[Acta Physica Academiae Scientiarum Hungaricae]]

|volume=30 |pages=51–54

|bibcode=1971AcPhH..30...51P

|doi=10.1007/bf03157173

|s2cid=118710050

}}</ref>

Studies performed in the 1980s and early 1990s produced confirmatory results:

#In 1989, Martin R. Croasdale reported finding a quantization of redshifts using a different sample of galaxies in increments of 72&nbsp;km/s or Δ''z'' = {{val|2.4|e=-4}} (where Δ''z'' denotes shift in frequency expressed as a proportion of initial frequency).<ref>{{cite journal |bibcode=1989ApJ...345...72C|doi = 10.1086/167882 | title=Periodicities in galaxy redshifts | journal=The Astrophysical Journal |date=1989 |volume=345 |pages=72 |first=Martin R. |last=Croasdale|doi-access=free }}</ref>

#In 1990, Bruce Guthrie and William Napier reported finding a "possible periodicity" of the same magnitude for a slightly larger data set limited to bright [[spiral galaxy|spiral galaxies]] and excluding other types.<ref>{{cite journal |bibcode=1990MNRAS.243..431G|doi = | title=The Virgo cluster as a test for quantization of extragalactic redshifts | journal=Monthly Notices of the Royal Astronomical Society |date=1990 |volume=243 |pages=431–442 |first1=B. N. G.|last1=Guthrie|first2=W. M.|last2=Napier}}</ref>

#In 1992, Guthrie and Napier proposed the observation of a different periodicity in increments of Δ''z'' = {{val|1.24|e=-4}} in a sample of 89 galaxies.<ref>{{cite journal |bibcode=1991MNRAS.253..533G|doi = 10.1093/mnras/253.3.533| title=Evidence for redshift periodicity in nearby field galaxies | journal=Monthly Notices of the Royal Astronomical Society |date=1991 |volume=253 |issue = 3|pages=533–544 |first1=B. N. G.|last1=Guthrie|first2=W. M.|last2=Napier|doi-access=free}}</ref>

#In 1992, Paal ''et al.'' and Holba ''et al.'' concluded that there was an unexplained periodicity of redshifts in a reanalysis of a large sample of galaxies.<ref>{{cite journal|bibcode=1992Ap&SS.191..107P|doi = 10.1007/BF00644200 | title=Inflation and compactification from Galaxy redshifts? | journal=Astrophysics and Space Science|date=1992|volume=191|issue=1|pages=107–124|first=G.|last=Paal|s2cid = 116951785 }}</ref><ref>{{cite journal |bibcode=1992Ap&SS.198..111H|doi = 10.1007/BF00644305 | title=Cosmological parameters and redshift periodicity | journal=Astrophysics and Space Science |date=1992 |volume=198 |issue=1 |pages=111–120 |first=Ágnes |last=Holba|s2cid = 118806486 }} See also reference to {{cite journal|bibcode=1990Natur.343..726B|doi = 10.1038/343726a0 | volume=343 | issue=6260|title=Large-scale distribution of galaxies at the Galactic poles|journal=Nature|date=1990|pages=726–728|first=T. J.|last=Broadhurst|s2cid = 4356867 }}</ref>

#In 1997, Guthrie and Napier concluded the same:

::"So far the redshifts of over 250 galaxies with high-precision HI profiles have been used in the study. In consistently selected sub-samples of the datasets of sufficient precision examined so far, the redshift distribution has been found to be strongly quantized in the galactocentric frame of reference. ... The formal confidence levels associated with these results are extremely high."<ref>{{cite journal|last=Napier|first=W. Μ.|author2=B. N. G. Guthrie |title=Quantized Redshifts: A Status Report|journal=J. Astrophys. Astron.|volume=18|issue=4|pages=455–463|date=1997|url=http://www.ias.ac.in/jarch/jaa/18/455-463.pdf|bibcode=1997JApA...18..455N|doi=10.1007/BF02709337|s2cid=73557034}}</ref>

==Quasar redshifts==

Line 41 ⟶ 61:

===Karlsson's formula===

Historically, K. G. Karlsson and G. R. Burbidge were first to note that quasar redshifts were quantized in accordance with the empirical formula:<ref>{{cite journal | last1 = Burbidge | first1 = G | year = 1968 | title = The Distribution of Redshifts in Quasi-Stellar Objects, N-Systems and Some Radio and Compact Galaxies | url = | journal = [[Astrophysical Journal]] | volume = 154 | issue = | pages = L41–L48 | doi = 10.1086/180265 | bibcode=1968ApJ...154L..41B| doi-access = free }}</ref><ref>{{cite journal | last1 = Karlsson | first1 = K. G. | year = 1990 | title=Quasar redshifts and nearby galaxies | url = | journal = Astron Astrophys | volume = 239| issue = | pages = 50 | doi = | bibcode=1990A&A...239...50K}}</ref>

:<math>\log_{10}(1 + z) = 0.089n - 0.0632</math>

where:

Where:

#*<math>z</math> refers to the magnitude of redshift (shift in frequency as a proportion of initial frequency).;

#*<math>n</math> is an integer with values 1, 2, 3, 4 ...

This predicts periodic redshift peaks at <math>z</math> = 0.061, 0.30, 0.60, 0.96, 1.41, and 1.9, observed originally in a sample of 600 quasars,<ref>{{cite journal | last1 = Burbidge| first1 = G. | year = 1978 | title=The line-locking hypothesis, absorption by intervening galaxies, and the Z = 1.95 peak in redshifts | url = | journal = Physica Scripta | volume = 17| issue = 3| pages = 237–241 | doi = 10.1088/0031-8949/17/3/017| bibcode= 1978PhyS...17..237B| s2cid = 250841536 }}</ref> verified in later early studies.<ref>{{cite journal|bibcode=1994Ap&SS.222...65H|doi = 10.1007/BF00627083 | title=Once more on quasar periodicities | journal=Astrophysics and Space Science|date=1994|volume=222|issue=1–2|pages=65–83|first=Ágnes|last=Holba|s2cid = 118379051 }}</ref>

===Modern discourse===

A 2001 study by Burbidge and Napier found the pattern of periodicity predicted by Karlsson's formula to be present at a high [[confidence level]] in three new samples of quasars, concluding that their findings are inexplicable by spectroscopic or similar selection effects.<ref>{{cite journal | last1 = Burbidge| first1 = G. | year = 2001| title=The Distribution of Redshifts in New Samples of Quasi-stellar Objects | url = | journal = Astronomical Journal | volume = 121| issue = 1| pages = 21–30| arxiv=astro-ph/0008026 | bibcode= 2001AJ....121...21B| doi=10.1086/318018| s2cid = 15751692 }}</ref>

In 2002, Hawkins ''et al.'' found no evidence for redshift quantization in a sample of 1647 galaxy-quasar pairs from the [[2dF Galaxy Redshift Survey]]:

:"Given that there are almost eight times as many data points in this sample as in the previous analysis by Burbidge & Napier (2001), we must conclude that the previous detection of a periodic signal arose from the combination of noise and the effects of the window function."<ref>{{cite journal|author1=Hawkins|author2=Maddox|author3=Merrifield|title=No Periodicities in 2dF Redshift Survey Data|doi=10.1046/j.1365-8711.2002.05940.x|date=2002|journal=Monthly Notices of the Royal Astronomical Society|volume=336|pages=L13–L16|issue=13|doi-access=free |arxiv=astro-ph/0208117|bibcode = 2002MNRAS.336L..13H |s2cid=6832490}}</ref>

In response, Napier and Burbidge (2003) argue that the methods employed by Hawkins ''et al.'' to remove noise from their samples amount to "excessive data smoothing" which could hide a true periodicity. They publish an alternate methodology for this that preserves the periodicity observed in earlier studies.<ref>{{cite journal|last1=Napier|first1=W. M.|last2=Burbidge|first2=G. R.|title=The detection of periodicity in QSO data sets|date=2003|journal=Monthly Notices of the Royal Astronomical Society|volume=342|pages=601–604|issue= 2|doi=10.1046/j.1365-8711.2003.06567.x |bibcode = 2003MNRAS.342..601N |doi-access=free}}</ref>

In 2005, Tang and Zhang found no evidence for redshift quantization of quasars in samples from the [[Sloan Digital Sky Survey]] and 2dF redshift survey.<ref name="Tang"/>

Line 65 ⟶ 85:

Arp ''et al.'' (2005) examined sample areas in the 2dF and SDSS surveys in detail, noting that quasar redshifts:

:"... fit very closely the long standing Karlsson formula and strongly suggest the existence of preferred values in the distribution of quasar redshifts."<ref>{{cite journal| last1=Arp| first1=H.| last2=Fulton| first2=C.| last3=Roscoe| first3=D.| title=Periodicities of Quasar Redshifts in Large Area Surveys|date=2005|journal=|volume=|pages=|issue=|arxiv=astro-ph/0501090 |bibcode = 2005astro.ph..1090A }}</ref>

A 2006 study of 46,400 quasars in the [[Sloan Digital Sky Survey|SDSS]] by Bell and McDiarmid discovered 6 peaks in the redshift distribution consistent with the decreasing intrinsic redshift (DIR) model. They conclude that this correlation is unlikely to be a [[selection effect]], given the method used to determine intrinsic redshift relations.<ref name="adsabs.harvard.edu"/>

Schneider ''et al.'' (2007) and Richards ''et al.'' (2006) report that the periodicity reported by Bell and McDiarmid disappears after correcting for selection effects.<ref>{{cite journal | last1 = Schneider | display-authors =etal | date=2007| title = The Sloan Digital Sky Survey Quasar Catalog. IV. Fifth Data Release| bibcode=2007AJ....134..102S | journal = The Astronomical Journal | volume = 134 | issue = 1| pages = 102–117 |doi = 10.1086/518474 |arxiv = 0704.0806 }}</ref><ref>{{cite journal | last1 = Richards | first1 = G. T. | display-authors =etal | date=2006| title = The Sloan Digital Sky Survey Quasar Survey: Quasar Luminosity Function from Data Release 3| journal = The Astronomical Journal | volume = 131 | issue = 6 | pages = 2766–2787 |doi = 10.1086/503559 |arxiv = astro-ph/0601434 | bibcode=2006AJ....131.2766R}}</ref> However, Bell and Comeau (2010) have since argued that this correction removes nearly half of the sample and does not explain how selection effects give rise to redshift peaks. The same study also concludes that a "filter gap footprint" renders it impossible to verify or falsify the presence of a true redshift peak at Δ''z'' = 0.60.<ref>{{cite journal | last1 = Bell| first1 = M. B. | last2 = Comeau | first2 = S. P. | date=2010| title = Selection Effects in the SDSS Quasar Sample: The Filter Gap Footprint| journal = Astrophys Space Sci | volume = 326 | issue = 1| pages = 11–17 |doi = 10.1007/s10509-009-0232-2 |arxiv = 0911.5700 |bibcode = 2010Ap&SS.326...11B }}</ref>

A 2006 review by Bajan ''et al.'' discovered weak effects of redshift periodization in data from the [[Local Group]] of galaxies and the [[Hercules Supercluster]]. They conclude that "galaxy redshift periodization is an effect which can really exist", but that the evidence is not well established pending study of larger databases.<ref>{{cite journal |bibcode=2007PPNL....4....5B|arxiv=astro-ph/0606294 | title=On the Investigations of Galaxy Redshift Periodicity | journal=Physics of Particles and Nuclei Letters |date=2007 |volume=4 |issue=1 |pages=5–10 |first1=K. |last1=Bajan |first2=P. |last2=Flin |first3=W. |last3=Godlowski |first4=V. N. |last4=Pervushin |doi=10.1134/s1547477107010025}}</ref>

A 2007 [[absorption spectroscopy|absorption spectroscopic]] analysis of quasars by Ryabinkov ''et al.'' observed a pattern of statistically significant alternating peaks and dips in the redshift range Δ''z'' = 0.0 − 3.7, though they noted no statistical correlation between their findings and Karlsson's formula.<ref>{{cite journal | last1 = Ryabinkov| first1 = A. I. | last2 = Kaminker| first2 = A. D. | last3 = Varshalovich| first3 = D. A. | date=2007| title = The redshift distribution of absorption-line systems in QSO spectra| journal = Mon. Not. R. Astron. Soc. | volume = 376| issue = 4 | pages = 1838–18481 | doi=10.1111/j.1365-2966.2007.11567.x | bibcode=2007MNRAS.376.1838R|arxiv = astro-ph/0703277 }}</ref>

==Explanatory theories==

===Galactic clustering===

Some have proposed that quantization is caused by the geometry of [[Galaxy filament|filamentary]] [[superclusters]] and [[void (astronomy)|voids]] observed in [[Large-scale structure of the cosmos|large-scale structure models]] of the cosmos.

In 1987, E. Sepulveda suggested that galactic clustering could account for all redshift periodicities, using a geometric model based on [[polytrope|polytrope theory]]:

[[Image:2dfgrs.png|right|thumb|300px|Rendering of the [[2dF Galaxy Redshift Survey]] data. The [[galaxy filament]]s visible here can appear as weak redshift quantization by some statistical measures.]]

:"The smallest periodicities (Δ''z'' = 72 km/s and 144 km/s) are due to parallel line segments of galactic clustering. The largest (Δ''z'' = 0.15) are due to circumferential circuits around the universe. Intermediate periodicities are due to other geometric irregularities. These periodicities or apparent quantizations are relics or faithful fossils of a real quantization that occurred in the primordial atom."<ref>{{cite journal | last1 = Sepulveda | first1 = E. |date=1987| title = Geometric Paradigm Accounts for All Redshift Periodicities |bibcode=1987BAAS...19Q.689S | journal = Bulletin of the American Astronomical Society | volume = 19 | issue = | page = 689 }}</ref>

===Hydrogen spectroscopy===

A 2006 study of 46,400 quasars in the [[Sloan Digital Sky Survey|SDSS]] by Bell and McDiarmid discovered 6 peaks in the redshift distribution consistent with the decreasing intrinsic redshift (DIR) model.<ref name="adsabs.harvard.edu"/> However, Schneider ''et al.'' (2007) and Richards ''et al.'' (2006) reportreported that the periodicity reported by Bell and McDiarmid disappears after correcting for selection effects.<ref>{{cite journal | last1 = Schneider | display-authors =etal | date=2007| title = The Sloan Digital Sky Survey Quasar Catalog. IV. Fifth Data Release| bibcode=2007AJ....134..102S | journal = The Astronomical Journal | volume = 134 | issue = 1| pages = 102–117 |doi = 10.1086/518474 |arxiv = 0704.0806 | s2cid =14359163 }}</ref><ref>{{cite journal | last1 = Richards | first1 = G. T. | display-authors =etal | date=2006| title = The Sloan Digital Sky Survey Quasar Survey: Quasar Luminosity Function from Data Release 3| journal = The Astronomical Journal | volume = 131 | issue = 6 | pages = 2766–2787 |doi = 10.1086/503559 |arxiv = astro-ph/0601434 | bibcode=2006AJ....131.2766R| s2cid = 55346862 }}</ref> However, Bell and Comeau (2010) haveconcur sincethat arguedselection thateffects thisgive correctionrise removesto nearlythe halfapparent ofredshift thepeaks, samplebut andargue doesthat notthe explaincorrection howprocess selectionremoves effectsa givelarge risefraction toof redshiftthe peaksdata. The sameauthors study also concludesargue that athe "filter gap footprint" renders it impossible to verify or falsify the presence of a true redshift peak at Δ''z'' = 0.60.<ref>{{cite journal | last1 = Bell| first1 = M. B. | last2 = Comeau | first2 = S. P. | date=2010| title = Selection Effects in the SDSS Quasar Sample: The Filter Gap Footprint| journal = Astrophys Space Sci | volume = 326 | issue = 1| pages = 11–17 |doi = 10.1007/s10509-009-0232-2 |arxiv = 0911.5700 |bibcode = 2010Ap&SS.326...11B | s2cid = 118655062 }}</ref>

Various models propose that the quantization predicted by Karlsson's formula is related to the [[emission spectrum]] signature of hydrogen, described by the [[Lyman series]].<ref>{{cite journal | last1 = Moret-Bailly| first1 = J. | year = 2015 | title=Absorption spectrum of very low pressure atomic hydrogen | journal = Instrumentation and Methods for Astrophysics | volume = | issue = | pages = | doi = | bibcode=2015arXiv151208516M| arxiv = 1512.08516 }}</ref>

A 2006 review by Bajan ''et al.'' discovered weak effects of redshift periodization in data from the [[Local Group]] of galaxies and the [[Hercules Supercluster]]. They conclude that "galaxy redshift periodization is an effect which can really exist", but that the evidence is not well established pending study of larger databases.<ref>{{cite journal |bibcode=2007PPNL....4....5B|arxiv=astro-ph/0606294 | title=On the Investigations of Galaxy Redshift Periodicity | journal=Physics of Particles and Nuclei Letters |date=2007 |volume=4 |issue=1 |pages=5–10 |first1=K. |last1=Bajan |first2=P. |last2=Flin |first3=W. |last3=Godlowski |first4=V. N. |last4=Pervushin |doi=10.1134/s1547477107010025|s2cid=15364493 }}</ref>

According to this explanation, redshift periodicity arises from the interaction between cosmic atomic hydrogen and [[electromagnetic radiation]] in the spectrum of visible light. As atomic hydrogen absorbs and emits energy in the form of electromagnetic radiation, it oscillates between higher and lower [[excited state|states of excitation]]. This transfer of energy redshifts the radiation it emits. Because the states of excitation are quantized in accordance with the Lyman series, the redshift is also quantized.

A 2007 [[absorption spectroscopy|absorption spectroscopic]] analysis of quasars by Ryabinkov ''et al.'' observed a pattern of statistically significant alternating peaks and dips in the redshift range Δ''z'' = 0.0 − 3.7, though they noted no statistical correlation between their findings and Karlsson's formula.<ref>{{cite journal | last1 = Ryabinkov| first1 = A. I. | last2 = Kaminker| first2 = A. D. | last3 = Varshalovich| first3 = D. A. | date=2007| title = The redshift distribution of absorption-line systems in QSO spectra| journal = Mon. Not. R. Astron. Soc. | volume = 376| issue = 4 | pages = 1838–18481 | doi=10.1111/j.1365-2966.2007.11567.x | doi-access = free | bibcode=2007MNRAS.376.1838R|arxiv = astro-ph/0703277 | s2cid = 16270925 }}</ref>

A limitation of this model is that the phenomenon described above can only arise in conditions where atomic hydrogen is within stringent parameters of low pressure and excitation, away from massive or highly radiant cosmological bodies such as galaxies and [[supernovae]].

==References==