Redshift quantization is the hypothesis that the redshifts of cosmologically distant objects (in particular galaxies) tend to cluster around multiples of some particular value. Since there is a correlation of distance and redshift as expressed in Hubble's Law, 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 cosmology. Many scientists who oppose the Big Bang theory, including Halton Arp, have referred to observations claimed to be in favor of redshift quantization as reason to reject the standard account of the origin and evolution of the universe.
In 1973, astronomer William G. Tifft was the first to report evidence of such clustering (before that see György Paál). Recent redshift surveys of quasars (QSOs) have produced no evidence of quantization in excess of what is expected due to galaxy clustering,  and consequently most cosmologists dispute the existence of redshift quantization beyond a minimal trace due to the distribution of galaxies across voids and filaments.
The term refers to any of the theories in which the quantum of action appears in equations describing Hubble redshift's origin and magnitude of redshift with distance.
Most cited authors look for the redshifts of many types of stars, or composite objects such as galaxies. On the contrary, Karlsson, Burbidge  limit their studies to relatively simple objects, isolated quasars or compact galaxies. Their statistic on large numbers of these objects leads to Karlsson's formula for preferred redshifts: most redshifts Z (frequency shifts divided by initial frequency) are close to Z(n) = nK, where K=0,061 and n is an integer having values 3, 4, 6, ... The strange distribution of these integers is explained by the following remark: 3K is close to redshift 0.1852 ≈ 3 ∗ 0.0617 (resp. 0, 25 = 4 ∗ 0.0625) which shifts Lyman beta (resp. Lyman gamma) frequency of H atom to Lyman alpha frequency. Both parameters of Karlsson's formula are explained, but how do these redshifts result from spectroscopy of hydrogen ? J. C. Pecker proposed an incoherent Raman effect, but it could not work, because incoherent Raman adds frequencies, does not shift them. But, in laboratories, using femptosecond laser pulses, coherent Raman shifts the frequencies. This Impulsive Stimulated Raman Scattering (ISRS) works in excited atomic hydrogen, using nanosecond pulses which make time-incoherent light. A cloud of very low pressure relatively cold atomic hydrogen around a quasar is structured by light: If light is absorbed by Lyman alpha of H, produced excited H atoms shift light until an already absorbed line reaches Lyman alpha frequency. All lines of gas are absorbed until a weaker ISRS resulting from high frequency absorptions restarts the redshift. Shifts 3K and 4K connect similar lines in Lyman forests of quasars.
Space cannot be reliably structured around a galaxy which is a too large object. Thus Tifft and followers could not get reliable results. Around extremely powerful supernova, hydrogen is so hot that atoms are excited, Karlsson's formula fails, large local redshifts are interpreted as "voids" in maps of galaxies.
Original investigation by William G. Tifft
- "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".
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."
Subsequent work by other researchers
In the late 1980s and early 1990s, four studies on redshift quantization were performed:
- In 1989, Martin R. Croasdale reported finding a quantization of redshifts using a different sample of galaxies in increments of 72 km/s (Δz = ×10−4). 2.4
- 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
- In 1992, Guthrie and Napier proposed the observation of a different periodicity in increments of Δz = ×10−4 in a sample of 89 galaxies 1.24
- In 1992, G. Paal, et al.  and 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.
- In 1994, A. Holba, et al.  also reanalyzed the redshift data of quasars and concluded that there was unexplained periodicity of redshifts in this sample, too.
- In 1997, W. Μ. Napier and B. N. G. Guthrie 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."
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 for which astronomers have measured redshifts has increased by several orders of magnitude.
Evaluation and criticism
After the discovery of Karlsson's formula, a statistic on a large number of quasars and "compact galaxies" allowed a precise computation of Karlsson's constant, the value of which is found by pure, standard spectroscopy. The spectroscopic computation of Karlsson's formula is founded on the generation of shells in which relatively cold atomic hydrogen is either: -a) pumped to excited states, mainly 2P, whose quadrupolar resonances are able to transfer energy from light to background radiation, using a coherent Impulsive Stimulated Raman Scattering (ISRS). This transfer of energy redshifts light. This redshift requires energy at Lyman alpha frequency, and the redshift renews this energy up to a shift of Lyman beta or an other line written in the spectrum to Ly alpha frequency. -b) in its atomic ground state. There is no redshift because there are no 2P atoms, the 1420 MHz quadrupolar resonance is too high to allow an ISRS. However, atoms pumped by short frequencies to high levels, or 2S, 2P atoms resulting from a decay from these levels provide a small redshift which allows to reach energy at Ly alpha frequency, so that case a may be reached. Thus output from case b to case a requires high frequency light which disappears fast in thermal radiation.
The first case appears where pressure of atomic hydrogen is low enough around the quasar to allow a collisional time longer than the length of light pulses of incoherent light, condition for an ISRS.
These structures of atomic hydrogen cannot be built if many sources are present, as close to a galaxy.
This lack of periodicity for galaxies was demonstrated experimentally:
After Tifft made his proposal, discussion of it was generally confined to detractors of standard cosmology. 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 large-scale structure models trace filamentary superclusters and voids 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.
In 1987, E. Sepulveda suggested that a geometric paradigm based on the polytrope theory could account for all redshift periodicities, and that:
- "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."
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:
- 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 2005, Tang and Zhang:
- ".. used the publicly available data from the Sloan Digital Sky Survey and 2dF QSO redshift survey to test the hypothesis that QSOs are ejected from active galaxies with periodic noncosmological redshifts. For two different intrinsic redshift models, [..] and find there is no evidence for a periodicity at the predicted frequency in log(1+z), or at any other frequency. "
A 2006 historical review of study of the redshift periodicity of galaxies by Bajan, et al., concludes that "in our opinion the existence of redshift periodicity among galaxies is not well established."
In 2006, M. B. Bell and D. McDiarmid, reported: "Six Peaks Visible in the Redshift Distribution of 46,400 SDSS Quasars Agree with the Preferred Redshifts Predicted by the Decreasing Intrinsic Redshift Model". The pair acknowledged that selection effects were already reported to cause the most prominent of the peaks. Nevertheless, these peaks were included in their analysis anyway with Bell and McDiarmid questioning whether selection effects could account for the periodicity, but not including any analysis of this beyond cursory cross-survey comparisons in the discussion section of their paper. There is a brief response to this paper in a comment in section 5 of Schneider et al. (2007)  where they note that all "periodic" structure disappears after the previously known selection effects are accounted for.
- Arp, H. (1998). "Quantization of Redshifts". Seeing Red. ISBN 0-9683689-0-5.
- 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.
- 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.
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- 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/0603169. Bibcode:2006ApJ...648..140B. doi:10.1086/503792.
- 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.
- 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/0506366. Bibcode:2005ApJ...633...41T. doi:10.1086/432754.
- 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.
- Karlsson, K. G. (1970). "Possible Discretization of Quasar Redshifts". Astronomy and Astrophysics 13: 333. Bibcode:1971A&A....13..333K.
- 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.
- 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.
- 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.
- Burbidge, G. The Distribution of Redshifts in Quasi-Stellar Objects, N- Systems and Some Radio and Compact Galaxies. ApJ. 154, L41-L48 (1968)
- Tifft, W. G. (1980). "Periodicity in the redshift intervals for double galaxies". Astrophysical Journal 236: 70. Bibcode:1980ApJ...236...70T. doi:10.1086/157719.
- Tifft, W. G. Shakeshaft, J. R, ed. "Proceedings of the 58th IAU Symposium: The Formation and Dynamics of Galaxies:". International Astronomical Union: 243. Bibcode:1974IAUS...58..243T.
- 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.
- Croasdale, Martin R. (1989). "Periodicities in galaxy redshifts". The Astrophysical Journal 345: 72. Bibcode:1989ApJ...345...72C. doi:10.1086/167882.
- . Bibcode:1990MNRAS.243..431G. Missing or empty
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- Pa�l, 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. replacement character in
|last=at position 3 (help)
- Holba, �gnes (1992). "Cosmological parameters and redshift periodicity". Astrophysics and Space Science 198 (1): 111–120. Bibcode:1992Ap&SS.198..111H. doi:10.1007/BF00644305. replacement character in
|first=at position 1 (help) 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.
- Holba, �gnes (1994). "Once more on quasar periodicities". Astrophysics and Space Science 222 (1-2): 65–83. Bibcode:1994Ap&SS.222...65H. doi:10.1007/BF00627083. replacement character in
|first=at position 1 (help)
- Napier, W. Μ.; B. N. G. Guthrie (1997). "Quantized Redshifts: A Status Report" (PDF). J. Astrophys. Astr.
- For examples, see references by nonstandard cosmology proponents
- Bell, Moley B. (1973). "A Quantitative Alternative to the Cosmological Hypothesis for Quasars". The Astrophysical Journal 186: 1. Bibcode:1973ApJ...186....1B. doi:10.1086/152474.
- . Bibcode:1979AZh....56..232K. Missing or empty
- Laviolette, P. A. (1986). "Is the universe really expanding?". The Astrophysical Journal 301: 544. Bibcode:1986ApJ...301..544L. doi:10.1086/163922.
- . Bibcode:1980BAAS...12..852B. Missing or empty
- Sepulveda, E. (1987). "Geometric Paradigm Accounts for All Redshift Periodicities". Bulletin of the American Astronomical Society 19: 689. Bibcode:1987BAAS...19Q.689S.
- 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.
- On the Investigations of Galaxy Redshift Periodicity, Bajan, K.; Flin, P.; Godlowski, W.; Pervushin, V. N.,. arXiv:astro-ph/0606294. Bibcode:2006astro.ph..6294B. Missing or empty
- Schneider; et al. (2007). "The Sloan Digital Sky Survey Quasar Catalog. IV. Fifth Data Release". The Astrophysical Journal 134 (1): 102–117. arXiv:0704.0806. Bibcode:2007AJ....134..102S. doi:10.1086/518474.