Redshift quantization

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Redshift quantization, also referred to as redshift periodicity,[1] redshift discretization,[2] preferred redshifts[3] and redshift-magnitude bands,[4][5] 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 doppler effect caused by 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. Ruling out errors in measurement or analysis, quantized redshift of cosmological objects would either indicate that they are physically arranged in a quantized pattern around the Earth, or that there is an unknown mechanism for redshift unrelated to cosmic expansion, 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[6]). Recent discourse has 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.[7][8][9][10]

Many 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.[11][12][13]

Redshift quantization is a fringe topic with no support from mainstream astronomers in recent times. Although there are a handful of published articles in the last decade in support of quantization, those views are rejected by the rest of the field.

Original investigation by William G. Tifft[edit]

William G. Tifft was the first to investigate possible redshift quantization, referring to it as "redshift-magnitude banding correlation".[14] 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−1. An upper limit of 20 km s−1 is placed on the internal Doppler redshift component of motion in the Coma cluster".[15]

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."[16]

Early research[edit]

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 = 2.4×10−4 (where Δz denotes shift in frequency expressed as a proportion of initial frequency).[17]
  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.[18]
  3. In 1992, Guthrie and Napier proposed the observation of a different periodicity in increments of Δz = 1.24×10−4 in a sample of 89 galaxies.[19]
  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.[20][21]
  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."[22]

Quasar Redshifts[edit]

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[edit]

Historically, K. G. Karlsson and G. R. Burbidge were first to note that quasar redshifts were quantized in accordance with the empirical formula:[23][24]


  1. refers to the magnitude of redshift (shift in frequency as a proportion of initial frequency).
  2. is an integer with values 1, 2, 3, 4 ...

This predicts periodic redshift peaks at = 0.061, 0.30, 0.60, 0.96, 1.41, and 1.9, observed originally in a sample of 600 quasars,[25] verified in later early studies.[26]

Modern discourse[edit]

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.[27]

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."[28]

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.[29]

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.[10]

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."[30]

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. They conclude that this correlation is unlikely to be a selection effect, given the method used to determine intrinsic redshift relations.[8]

Schneider et al. (2007) and Richards et al. (2006) report that the periodicity reported by Bell and McDiarmid disappears after correcting for selection effects.[31][32] 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 Δz = 0.60.[33]

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", though the evidence is not well established pending study of larger databases.[34]

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.[35]

Explanatory Theories[edit]

Galactic clustering[edit]

Some have proposed that quantization is caused by the geometry of filamentary superclusters and voids observed in 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 theory:

Rendering of the 2dF Galaxy Redshift Survey data. The galaxy filaments visible here can appear as weak redshift quantization by some statistical measures.
"The smallest periodicities (Δz = 72 km/s and 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."[36]

Hydrogen spectroscopy[edit]

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.[37]

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 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 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.


  1. ^ Tifft, W. G. (2006). "Redshift periodicities, The Galaxy-Quasar Connection". Astrophysics and Space Science. 285 (2): 429. Bibcode:2003Ap&SS.285..429T. doi:10.1023/A:1025457030279. 
  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. 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. ^ Paal, G. (1970). "The global structure of the universe and the distribution of quasi-stellar objects". Acta Physica Academiae Scientarium Hungaricae. 30 (1): 51. Bibcode:1971AcPhH..30...51P. doi:10.1007/bf03157173. 
  7. ^ Trimble, V.; Aschwanden, M. J.; Hansen, C. J. (2007). "Astrophysics in 2006". Space Science Reviews. 132 (1): 1. arXiv:0705.1730Freely accessible. Bibcode:2007SSRv..132....1T. doi:10.1007/s11214-007-9224-0. 
  8. ^ a b 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. arXiv:astro-ph/0603169Freely accessible. Bibcode:2006ApJ...648..140B. doi:10.1086/503792. 
  9. ^ Godłowski, W.; Bajan, K.; Flin, P. (2006). "Weak redshift discretisation in the Local Group of galaxies?". Astronomische Nachrichten. 387 (1): 103. arXiv:astro-ph/0511260Freely accessible. Bibcode:2006AN....327..103G. doi:10.1002/asna.200510477. 
  10. ^ a b 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. arXiv:astro-ph/0506366Freely accessible. Bibcode:2005ApJ...633...41T. doi:10.1086/432754. 
  11. ^ For examples, see references by nonstandard cosmology proponents
    • Ratcliffe, Hilton (2009). "A Review of Anomalous Redshift Data". 2nd Crisis in Cosmology Conference, CCC-2 ASP Conference Series. 413: 109. 
    • Bell, Moley B. (1973). "A Quantitative Alternative to the Cosmological Hypothesis for Quasars". The Astrophysical Journal. 186: 1–21. Bibcode:1973ApJ...186....1B. doi:10.1086/152474. 
    • Kipper, A. Ia. (1979). "periodicity of quasar redshifts ln /1 + z/". Astronomicheskii Zhurnal. 56: 232–236. Bibcode:1979AZh....56..232K. 
    • Laviolette, P. A. (1986). "Is the universe really expanding?". The Astrophysical Journal. 301: 544. Bibcode:1986ApJ...301..544L. doi:10.1086/163922. 
    • Barnothy, J. M.; Barnothy, M. F. (1980). "The Redshift Periodicity of QSO's and the Origin of Cosmic Radiation". Bulletin of the American Astronomical Society. 12: 852. Bibcode:1980BAAS...12..852B. 
  12. ^ Arp, H. (1998). "Quantization of Redshifts". Seeing Red. ISBN 0-9683689-0-5. 
  13. ^ 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. Bibcode:1987JApA....8..241A. doi:10.1007/BF02715046. 
  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. 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. International Astronomical Union: 255–256. Bibcode:1974IAUS...58..243T. 
  16. ^ Tifft, W .G. (1995). "Redshift Quantization - A Review". Astrophysics and Space Science. 227 (1–2): 25. Bibcode:1995Ap&SS.227...25T. doi:10.1007/BF00678064. 
  17. ^ Croasdale, Martin R. (1989). "Periodicities in galaxy redshifts". The Astrophysical Journal. 345: 72. Bibcode:1989ApJ...345...72C. doi:10.1086/167882. 
  18. ^ 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. 
  19. ^ Guthrie, B. N. G.; Napier, W. M. (1991). "Evidence for redshift periodicity in nearby field galaxies". Monthly Notices of the Royal Astronomical Society. 253: 533–544. Bibcode:1991MNRAS.253..533G. doi:10.1093/mnras/253.3.533. 
  20. ^ 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. 
  21. ^ 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.  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. 
  22. ^ Napier, W. Μ.; B. N. G. Guthrie (1997). "Quantized Redshifts: A Status Report" (PDF). J. Astrophys. Astr. 
  23. ^ 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. 
  24. ^ Karlsson, K. G. (1990). "Quasar redshifts and nearby galaxies". Astron Astrophys. 239: 50. Bibcode:1990A&A...239...50K. 
  25. ^ Burbidge, G. (1978). "The line-locking hypothesis, absorption by intervening galaxies, and the Z = 1.95 peak in redshifts". Physica Scripta. 17: 237. 
  26. ^ 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. 
  27. ^ Burbidge, G. (2001). "The Distribution of Redshifts in New Samples of Quasi-stellar Objects". Astronomical Journal. 121: 21–30. arXiv:astro-ph/0008026Freely accessible. 
  28. ^ 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/0208117Freely accessible. Bibcode:2002MNRAS.336L..13H. doi:10.1046/j.1365-8711.2002.05940.x. 
  29. ^ Napier, W. M.; Burbidge, G. R. (2003). "The detection of periodicity in QSO data sets". Monthly Notices of the Royal Astronomical Society. 343: 601–604. 
  30. ^ Arp, H.; Fulton, C.; Roscoe, D. (2005). "Periodicities of Quasar Redshifts in Large Area Surveys". arXiv:astro-ph/0501090v1Freely accessible. 
  31. ^ Schneider; et al. (2007). "The Sloan Digital Sky Survey Quasar Catalog. IV. Fifth Data Release". The Astronomical Journal. 134 (1): 102–117. arXiv:0704.0806Freely accessible. Bibcode:2007AJ....134..102S. doi:10.1086/518474. 
  32. ^ Richards, G. T.; et al. (2006). "The Sloan Digital Sky Survey Quasar Survey: Quasar Luminosity Function from Data Release 3". The Astronomical Journal. 131: 2766–2787. arXiv:astro-ph/0601434v2Freely accessible. doi:10.1086/503559. 
  33. ^ 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:0911.5700v1Freely accessible. doi:10.1007/s10509-009-0232-2. 
  34. ^ 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/0606294Freely accessible. 
  35. ^ 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: 1838–18481. 
  36. ^ Sepulveda, E. (1987). "Geometric Paradigm Accounts for All Redshift Periodicities". Bulletin of the American Astronomical Society. 19: 689. Bibcode:1987BAAS...19Q.689S. 
  37. ^ Moret-Bailly, J. (2015). "Absorption spectrum of very low pressure atomic hydrogen" (PDF). Instrumentation and Methods for Astrophysics.