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{{Short description|Physical hypothesis}}
<center>'''This article is under development'''</center>
'''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=] |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=] |volume=13 |pages=333 |bibcode=1971A&A....13..333K }}</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=] |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=] |volume=179 |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=] |volume=95 |issue=1 |pages=188 |bibcode=1981A&A....95..188N }}</ref> is the ] that the ]s of cosmologically distant objects (in particular ] and ]) tend to cluster around multiples of some particular value.


In ], the redshift of cosmological bodies is ascribed to the expansion of the universe, with greater redshift indicating greater ] from the Earth (see ]). This is referred to as ] and is one of the main pieces of evidence for the ]. Quantized redshifts of objects would indicate, under Hubble's law, that astronomical objects are arranged in a quantized pattern around the Earth. It is more widely posited that 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".
'''Redshift quantization,''' '''redshift periodicity''' or '''redshift discretization'''<ref>Karlsson, K. G., "", (1971) ''Astronomy and Astrophysics'', Vol. 13, p. 333</ref> is the ] that the ]s of cosmologically distant objects (in particular ]) tend to cluster around multiples of some particular value. Since there is a correlation of ] and redshift as expressed in ], redshift quantization would either indicate a quantization of the distances of galaxies from the Earth or a problem with the redshift-distance correlation either of which would have serious implications for ]. In particular, many opponents of the ] including ],<ref>Halton Arp, "Quantization of Redshifts" (Ch.8) in (1998) ISBN 0-9683689-0-5. See also "Additional members of the Local Group of galaxies and quantized redshifts within the two nearest groups" (1987) ''Journal of Astrophysics and Astronomy''</ref>, a number of ], and even ] have referred to such observations as reason to reject the standard account of the origin and evolution of the ].<ref>] discusses ]'s advocacy of redshift quantization as evidence against the Big Bang . Additionally, ] ] discusses redshift quantization . Famed ] ] declares that redshift quantization implies that the Earth is at the center of the universe in his book ''Geocentricity'' (Cleveland , 1992).</ref>


In 1973, astronomer ] was the first to report evidence of this pattern. Subsequent discourse focused upon whether ]s of ]s (QSOs) have produced evidence of quantization in excess of what is expected due to ] or ].<ref>{{cite journal |last1=Trimble |first1=V. |last2=Aschwanden |first2=M. J. |last3=Hansen |first3=C. J. |date=2007 |title=Astrophysics in 2006 |journal=] |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=] |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=] |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=]|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 ], 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 ].<ref>For examples, see references by nonstandard cosmology proponents
The first researcher who claimed to observe such a clustering was ]. Recent ]s of ] (QSOs) have found no evidence of quantization,<ref>Tang, Su Min; Zhang, Shuang Nan, "", in ''The Astrophysical Journal'', Volume 633, Issue 1, pp. 41-51 (2005) ]</ref> and consequently most cosmologists dispute the existence of redshift quantization beyond a minimal trace due to ]ing.
*{{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 |url-status=dead |archive-url=https://web.archive.org/web/20061020112037/http://redshift.vif.com/BookBlurbs/SeeingRedBlurb.htm |archive-date=2006-10-20 }}</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>


==Original investigation by William G. Tifft==
==Background==
] (for QSOs, 1971<ref>
"Redshift-magnitude banding correlation" as he first called it, was first investigated in the 1970s by (now Emeritus Professor of astronomy) ] <ref>Tifft, W. G., "", in ''Astrophysical Journal, Part 1'', vol. 236, Feb. 15, 1980, p. 70-74.</ref> 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=]
|volume=30 |pages=51–54
|bibcode=1971AcPhH..30...51P
|doi=10.1007/bf03157173
|s2cid=118710050
}}</ref>) and ] (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=] |volume=236 |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 ] on a single band is presented, which shows a strong redshift periodicity of 220 km s<sup>-1</sup>. An upper limit of 20 km s<sup>-1</sup> is placed on the internal Doppler redshift component of motion in the Coma cluster". <ref>Tifft, W. G., "", ''The Formation and Dynamics of Galaxies: Proceedings from IAU Symposium no. 58 held in Canberra, Australia, August 12-15, 1973''. Edited by John R. Shakeshaft. International Astronomical Union. Symposium no. 58, Dordrecht; Boston: Reidel, p.243</ref> :"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 ] on a single band is presented, which shows a strong redshift periodicity of 220 km s<sup>−1</sup>. An upper limit of 20 km s<sup>−1</sup> 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 |year=1974 }}</ref>


Tifft suggested that this observation conflicted with standard cosmological scenarios. He states in summary:
Tifft's suggestion was 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>Tifft, W. G., "", Astrophysics and Space Science, v. 227, p. 25-39, 1995</ref>
:"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=] |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 ==
===Subsequent work by other researchers===


In 1971 from redshift quantization ] came up with the idea that the ] might have nontrivial ] structure.
In the late 1980s and early 1990s, four studies on redshift quantization were performed:
<ref>
{{cite journal
|last=Paál |first=G.
|date=1971
|title=The global structure of the universe and the distribution of quasi-stellar objects
|journal=]
|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 km/s (Δz=2.4x10<sup>-4</sup>).<ref>Croasdale, Martin R., "", ''Astrophysical Journal'', Part 1, vol. 345, Oct. 1, 1989, p. 72-83.</ref>
#In 1990, B. Guthrie and William Napier were able to find a "possible periodicity" of the same magnitude for a slightly larger data set limited to bright ] and excluding other types<ref>Guthrie, B. N. G.; Napier, W. M., "", Royal Astronomical Society, Monthly Notices (ISSN 0035-8711), vol. 243, April 1, 1990, p. 431-442. </ref>
#In 1992 Guthrie and Napier proposed the observation of a different periodicity in increments of Δz=1.24x10<sup>-4</sup> in a sample of 89 galaxies<ref>Guthrie, B. N. G.; Napier, W. M., "", Royal Astronomical Society, Monthly Notices (ISSN 0035-8711), vol. 253, Dec. 1, 1991, p. 533-544.</ref>
#In 1992, A. Holba, ''et al'' reanalyzed the redshift data from a fairly large sample of galaxies and concluded that there was an unexplained periodicity of redshifts.<ref>Holba, A., Horvath, I., Lukacs, B., & Paal, G, "", ''Astrophysics and Space Science'' (ISSN 0004-640X), vol. 198, no. 1, p. 111-120. 1992. See also reference to Broadhurst ''et al'' ]</ref>


#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>
All of these studies were performed before the tremendous advances in redshift cataloging that would be made at the end of the 1990s. Since that time, the number of galaxies that have measured redshifts has increased by several orders of magnitude.
#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 ] and excluding other types.<ref>{{cite journal |bibcode=1990MNRAS.243..431G| 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==
==Evaluation and criticism==


Most recent discourse has focused upon whether ]s of ] (QSOs) produce evidence of quantization beyond that explainable by ]. This has been assisted by advances in cataloging in the late 1990s that have increased substantially the sample sizes involved in astronomical measurements.
After Tifft made his proposal, discussion of it was generally confined to detractors of standard cosmology<ref>For examples, see references by nonstandard cosmology proponents, Moley B. Bell (1973) , A. Ia Kipper (1979) , Paul Laviolette (1986) , and the Barnothys (1980) as well as a 1977 criticism of the subject by ] </ref>. Nevertheless, it was nearly 20 years before other researchers tried to corroborate his findings. After a brief flurry of interest, the consensus in the astronomical community became that any quantization was either coincidental or due to so-called geometrical effects. Current observations and models of ] trace ] ] and ] that cause most galaxies in a rough statistical sense to have correlated positions, but such groupings would not allow for a strength of periodicity required if it were a hallmark characteristic of the redshifts of galaxies. As such with exceedingly few exceptions, modern cosmology researchers have suggested that redshift quantizations are manifestations of well-understood phenomena, or not present at all.


===Karlsson's formula===
In 1987, E. Sepulveda suggested that a geometric paradigm based on the ] could account for all redshift periodicities, and that:


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 | journal = ] | volume = 154 | 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 | journal = Astron Astrophys | volume = 239| pages = 50 | bibcode=1990A&A...239...50K}}</ref>
:The smallest periodicities (Δz=72, 144 km/s) are due to parallel line segments of galactic clustering. The largest (Δz=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>Sepulveda, E., "" (1987) ''Bulletin of the American Astronomical Society'', Vol. 19, p.689</ref>


:<math>\log_{10}(1 + z) = 0.089n - 0.0632</math>
In 2002, Hawkins et al. found no evidence for a redshift quantization in the 2dF survey and found using Napier's own guidelines for testing redshift periodicity that none, in fact, could be detected in the sample:


where:
: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>E. Hawkins, S.J. Maddox, M.R. Merrifield, ''No Periodicities in 2dF Redshift Survey Data'' Mon.Not.Roy.Astron.Soc. 336 (2002) L13. </ref>
*<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 | 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>
In 2005, Tang and Zhang:
:".. used the publicly available data from the ] and 2dF QSO redshift survey to test the hypothesis that QSOs are ejected from active galaxies with periodic ]. For two different ] models, and find there is no evidence for a periodicity at the predicted frequency in log(1+z), or at any other frequency. "<ref>Tang, Su Min; Zhang, Shuang Nan, "", in ''The Astrophysical Journal'', Volume 633, Issue 1, pp. 41-51 (2005) ]</ref>


===Modern discourse===
They also outlined previous research on the subject, noting that:


A 2001 study by Burbidge and Napier found the pattern of periodicity predicted by Karlsson's formula to be present at a high ] 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 | 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>
:"The above an intrinsic redshift hypothesis, if true, will have far-reaching consequences for cosmology and the nature of QSOs. Most of those previous studies on the Karlsson formula used rather small samples (except for Arp et al. 2005), and have been suspected that the claimed peaks were due to artifacts associated with selection effects (Basu 2005). To avoid such a heterogeneous selection manner as well as personal prejudice, Hawkins et al. (2002) tested the periodicity in log(1 + z<sub>qso</sub>) with 2dF redshift survey data with 67291 nearby galaxies and 10410 QSOs; it was found that there is no periodicity in log(1 + z<sub>qso</sub>). However, Napier & Burbidge (2003) argued that in order to use the 2dF sample to properly test the original hypothesis, it is necessary to establish for each pair that the galaxy is at least a late-type active spiral system. Arp et al. (2005) also re-examined the 2dF sample and claimed that they found that the redshifts of brighter QSOs in the QSO density contours fit very exactly the long standing Karlsson formula and confirm the existence of preferred values in the distribution of quasar redshifts."<ref>Tang ''et al'' (2005) ''op cit''</ref>


In 2002, Hawkins ''et al.'' found no evidence for redshift quantization in a sample of 1647 galaxy-quasar pairs from the ]:
==Footnotes==

<div style="font-size: 95%">
:"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>
<!--See ] for an explanation of how to generate footnotes using the <ref(erences/)> tags-->

<references/>
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>
</div>

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

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|arxiv=astro-ph/0501090 |bibcode = 2005astro.ph..1090A }}</ref>

A 2006 study of 46,400 quasars in the ] 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) reported 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> Bell and Comeau (2010) concur that selection effects give rise to the apparent redshift peaks, but argue that the correction process removes a large fraction of the data. The authors argue that the "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>

A 2006 review by Bajan ''et al.'' discovered weak effects of redshift periodization in data from the ] of galaxies and the ]. 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>

A 2007 ] 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>

==References==
{{Reflist|30em}}


] ]

Latest revision as of 18:14, 22 September 2024

Physical hypothesis

Redshift quantization, also referred to as redshift periodicity, redshift discretization, preferred redshifts and redshift-magnitude bands, is the hypothesis that the redshifts of cosmologically distant objects (in particular galaxies and quasars) tend to cluster around multiples of some particular value.

In standard inflationary cosmological models, the redshift of cosmological bodies is ascribed to the expansion of the universe, with greater redshift indicating greater cosmic distance from the Earth (see Hubble's law). This is referred to as cosmological redshift and is one of the main pieces of evidence for the Big Bang. Quantized redshifts of objects would indicate, under Hubble's law, that astronomical objects are arranged in a quantized pattern around the Earth. It is more widely posited that 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. Subsequent discourse focused upon whether redshift surveys of quasars (QSOs) have produced evidence of quantization in excess of what is expected due to selection effect or galactic clustering. 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 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.

Original investigation by William G. Tifft

György Paál (for QSOs, 1971) and William G. Tifft (for galaxies) were the first to investigate possible redshift quantization, referring to it as "redshift-magnitude banding correlation". 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 galaxies on a single band is presented, which shows a strong redshift periodicity of 220 km s. An upper limit of 20 km s is placed on the internal Doppler redshift component of motion in the Coma cluster".

Tifft 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."

Early research - focused on galaxies rather than quasars

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

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

  1. In 1989, Martin R. Croasdale reported finding a quantization of redshifts using a different sample of galaxies in increments of 72 km/s or Δz = 2.4×10 (where Δz denotes shift in frequency expressed as a proportion of initial frequency).
  2. 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 galaxies and excluding other types.
  3. In 1992, Guthrie and Napier proposed the observation of a different periodicity in increments of Δz = 1.24×10 in a sample of 89 galaxies.
  4. 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.
  5. 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."

Quasar redshifts

Most recent discourse has focused upon whether redshift surveys of quasars (QSOs) produce evidence of quantization beyond that explainable by selection effect. This has been assisted by advances in cataloging in the late 1990s that have increased substantially the sample sizes involved in astronomical measurements.

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

log 10 ⁡ ( 1 + z ) = 0.089 n − 0.0632 {\displaystyle \log _{10}(1+z)=0.089n-0.0632}

where:

  • z {\displaystyle z} refers to the magnitude of redshift (shift in frequency as a proportion of initial frequency);
  • n {\displaystyle n} is an integer with values 1, 2, 3, 4 ...

This predicts periodic redshift peaks at z {\displaystyle z} = 0.061, 0.30, 0.60, 0.96, 1.41, and 1.9, observed originally in a sample of 600 quasars, verified in later early studies.

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.

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."

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.

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.

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."

A 2006 study of 46,400 quasars in the SDSS by Bell and McDiarmid discovered 6 peaks in the redshift distribution consistent with the decreasing intrinsic redshift (DIR) model. However, Schneider et al. (2007) and Richards et al. (2006) reported that the periodicity reported by Bell and McDiarmid disappears after correcting for selection effects. Bell and Comeau (2010) concur that selection effects give rise to the apparent redshift peaks, but argue that the correction process removes a large fraction of the data. The authors argue that the "filter gap footprint" renders it impossible to verify or falsify the presence of a true redshift peak at Δz = 0.60.

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.

A 2007 absorption spectroscopic analysis of quasars by Ryabinkov et al. observed a pattern of statistically significant alternating peaks and dips in the redshift range Δz = 0.0 − 3.7, though they noted no statistical correlation between their findings and Karlsson's formula.

References

  1. Tifft, W. G. (2006). "Redshift periodicities, The Galaxy-Quasar Connection". Astrophysics and Space Science. 285 (2): 429–449. Bibcode:2003Ap&SS.285..429T. doi:10.1023/A:1025457030279. S2CID 120143840.
  2. Karlsson, K. G. (1970). "Possible Discretization of Quasar Redshifts". Astronomy and Astrophysics. 13: 333. Bibcode:1971A&A....13..333K.
  3. Arp, H.; Russel, D. (2001). "A Possible Relationship between Quasars and Clusters of Galaxies". Astrophysical Journal. 549 (2): 802. Bibcode:2001ApJ...549..802A. doi:10.1086/319438. S2CID 120014695. The clusters and the galaxies in them tend to be strong X-ray and radio emitters, and their redshifts occur at preferred redshift values.
  4. Tifft, W. G. (1973). "Properties of the redshift-magnitude bands in the Coma cluster". Astrophysical Journal. 179: 29. Bibcode:1973ApJ...179...29T. doi:10.1086/151844.
  5. Nanni, D.; Pittella, G.; Trevese, D.; Vignato, A. (1981). "An analysis of the redshift-magnitude band phenomenon in the Coma Cluster". Astronomy and Astrophysics. 95 (1): 188. Bibcode:1981A&A....95..188N.
  6. Trimble, V.; Aschwanden, M. J.; Hansen, C. J. (2007). "Astrophysics in 2006". Space Science Reviews. 132 (1): 1–182. arXiv:0705.1730. Bibcode:2007SSRv..132....1T. doi:10.1007/s11214-007-9224-0. S2CID 119570960.
  7. ^ Bell, M. B.; McDiarmid, D. (2006). "Six Peaks Visible in the Redshift Distribution of 46,400 SDSS Quasars Agree with the Preferred Redshifts Predicted by the Decreasing Intrinsic Redshift Model". Astrophysical Journal. 648 (1): 140–147. arXiv:astro-ph/0603169. Bibcode:2006ApJ...648..140B. doi:10.1086/503792. S2CID 17057129.
  8. Godłowski, W.; Bajan, K.; Flin, P. (2006). "Weak redshift discretisation in the Local Group of galaxies?". Astronomische Nachrichten. 387 (1): 103. arXiv:astro-ph/0511260. Bibcode:2006AN....327..103G. doi:10.1002/asna.200510477. S2CID 119388085.
  9. ^ Tang, S. M.; Zhang, S. N. (2005). "Critical Examinations of QSO Redshift Periodicities and Associations with Galaxies in Sloan Digital Sky Survey Data". Astrophysical Journal. 633 (1): 41–51. arXiv:astro-ph/0506366. Bibcode:2005ApJ...633...41T. doi:10.1086/432754. S2CID 119052857.
  10. For examples, see references by nonstandard cosmology proponents
  11. Arp, H. (1998). "Quantization of Redshifts". Seeing Red. C. Roy Keys Incorporated. ISBN 978-0-9683689-0-9. Archived from the original on 2006-10-20.
  12. Arp, H. (1987). "Additional members of the Local Group of galaxies and quantized redshifts within the two nearest groups". Journal of Astrophysics and Astronomy. 8 (3): 241–255. Bibcode:1987JApA....8..241A. doi:10.1007/BF02715046. S2CID 119819755.
  13. Paál, G. (1971). "The global structure of the universe and the distribution of quasi-stellar objects". Acta Physica Academiae Scientiarum Hungaricae. 30: 51–54. Bibcode:1971AcPhH..30...51P. doi:10.1007/bf03157173. S2CID 118710050.
  14. Tifft, W. G. (1980). "Periodicity in the redshift intervals for double galaxies". Astrophysical Journal. 236: 70. Bibcode:1980ApJ...236...70T. doi:10.1086/157719.
  15. Tifft, W. G. (1974). Shakeshaft, J. R (ed.). "Fine Structure Within the Redshift-Magnitude Correlation for Galaxies". Proceedings of the 58th IAU Symposium: The Formation and Dynamics of Galaxies. 58: 255–256. Bibcode:1974IAUS...58..243T.
  16. Tifft, W .G. (1995). "Redshift Quantization - A Review". Astrophysics and Space Science. 227 (1–2): 25–39. Bibcode:1995Ap&SS.227...25T. doi:10.1007/BF00678064. S2CID 189849264.
  17. Paál, G. (1971). "The global structure of the universe and the distribution of quasi-stellar objects". Acta Physica Academiae Scientiarum Hungaricae. 30: 51–54. Bibcode:1971AcPhH..30...51P. doi:10.1007/bf03157173. S2CID 118710050.
  18. Croasdale, Martin R. (1989). "Periodicities in galaxy redshifts". The Astrophysical Journal. 345: 72. Bibcode:1989ApJ...345...72C. doi:10.1086/167882.
  19. Guthrie, B. N. G.; Napier, W. M. (1990). "The Virgo cluster as a test for quantization of extragalactic redshifts". Monthly Notices of the Royal Astronomical Society. 243: 431–442. Bibcode:1990MNRAS.243..431G.
  20. Guthrie, B. N. G.; Napier, W. M. (1991). "Evidence for redshift periodicity in nearby field galaxies". Monthly Notices of the Royal Astronomical Society. 253 (3): 533–544. Bibcode:1991MNRAS.253..533G. doi:10.1093/mnras/253.3.533.
  21. Paal, G. (1992). "Inflation and compactification from Galaxy redshifts?". Astrophysics and Space Science. 191 (1): 107–124. Bibcode:1992Ap&SS.191..107P. doi:10.1007/BF00644200. S2CID 116951785.
  22. Holba, Ágnes (1992). "Cosmological parameters and redshift periodicity". Astrophysics and Space Science. 198 (1): 111–120. Bibcode:1992Ap&SS.198..111H. doi:10.1007/BF00644305. S2CID 118806486. See also reference to Broadhurst, T. J. (1990). "Large-scale distribution of galaxies at the Galactic poles". Nature. 343 (6260): 726–728. Bibcode:1990Natur.343..726B. doi:10.1038/343726a0. S2CID 4356867.
  23. Napier, W. Μ.; B. N. G. Guthrie (1997). "Quantized Redshifts: A Status Report" (PDF). J. Astrophys. Astron. 18 (4): 455–463. Bibcode:1997JApA...18..455N. doi:10.1007/BF02709337. S2CID 73557034.
  24. Burbidge, G (1968). "The Distribution of Redshifts in Quasi-Stellar Objects, N-Systems and Some Radio and Compact Galaxies". Astrophysical Journal. 154: L41–L48. Bibcode:1968ApJ...154L..41B. doi:10.1086/180265.
  25. Karlsson, K. G. (1990). "Quasar redshifts and nearby galaxies". Astron Astrophys. 239: 50. Bibcode:1990A&A...239...50K.
  26. Burbidge, G. (1978). "The line-locking hypothesis, absorption by intervening galaxies, and the Z = 1.95 peak in redshifts". Physica Scripta. 17 (3): 237–241. Bibcode:1978PhyS...17..237B. doi:10.1088/0031-8949/17/3/017. S2CID 250841536.
  27. Holba, Ágnes (1994). "Once more on quasar periodicities". Astrophysics and Space Science. 222 (1–2): 65–83. Bibcode:1994Ap&SS.222...65H. doi:10.1007/BF00627083. S2CID 118379051.
  28. Burbidge, G. (2001). "The Distribution of Redshifts in New Samples of Quasi-stellar Objects". Astronomical Journal. 121 (1): 21–30. arXiv:astro-ph/0008026. Bibcode:2001AJ....121...21B. doi:10.1086/318018. S2CID 15751692.
  29. Hawkins; Maddox; Merrifield (2002). "No Periodicities in 2dF Redshift Survey Data". Monthly Notices of the Royal Astronomical Society. 336 (13): L13–L16. arXiv:astro-ph/0208117. Bibcode:2002MNRAS.336L..13H. doi:10.1046/j.1365-8711.2002.05940.x. S2CID 6832490.
  30. Napier, W. M.; Burbidge, G. R. (2003). "The detection of periodicity in QSO data sets". Monthly Notices of the Royal Astronomical Society. 342 (2): 601–604. Bibcode:2003MNRAS.342..601N. doi:10.1046/j.1365-8711.2003.06567.x.
  31. Arp, H.; Fulton, C.; Roscoe, D. (2005). "Periodicities of Quasar Redshifts in Large Area Surveys". arXiv:astro-ph/0501090. Bibcode:2005astro.ph..1090A. {{cite journal}}: Cite journal requires |journal= (help)
  32. Schneider; et al. (2007). "The Sloan Digital Sky Survey Quasar Catalog. IV. Fifth Data Release". The Astronomical Journal. 134 (1): 102–117. arXiv:0704.0806. Bibcode:2007AJ....134..102S. doi:10.1086/518474. S2CID 14359163.
  33. Richards, G. T.; et al. (2006). "The Sloan Digital Sky Survey Quasar Survey: Quasar Luminosity Function from Data Release 3". The Astronomical Journal. 131 (6): 2766–2787. arXiv:astro-ph/0601434. Bibcode:2006AJ....131.2766R. doi:10.1086/503559. S2CID 55346862.
  34. Bell, M. B.; Comeau, S. P. (2010). "Selection Effects in the SDSS Quasar Sample: The Filter Gap Footprint". Astrophys Space Sci. 326 (1): 11–17. arXiv:0911.5700. Bibcode:2010Ap&SS.326...11B. doi:10.1007/s10509-009-0232-2. S2CID 118655062.
  35. Bajan, K.; Flin, P.; Godlowski, W.; Pervushin, V. N. (2007). "On the Investigations of Galaxy Redshift Periodicity". Physics of Particles and Nuclei Letters. 4 (1): 5–10. arXiv:astro-ph/0606294. Bibcode:2007PPNL....4....5B. doi:10.1134/s1547477107010025. S2CID 15364493.
  36. Ryabinkov, A. I.; Kaminker, A. D.; Varshalovich, D. A. (2007). "The redshift distribution of absorption-line systems in QSO spectra". Mon. Not. R. Astron. Soc. 376 (4): 1838–18481. arXiv:astro-ph/0703277. Bibcode:2007MNRAS.376.1838R. doi:10.1111/j.1365-2966.2007.11567.x. S2CID 16270925.
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