Redshift quantization, also referred to as redshift periodicity, redshift discretization, preferred redshifts and redshift-magnitude bands, is the

hypothesis A hypothesis (plural hypotheses) is a proposed explanation for a phenomenon. For a hypothesis to be a scientific hypothesis, the scientific method requires that one can test it. Scientists generally base scientific hypotheses on previous obse ...

that the

redshift In physics, a redshift is an increase in the wavelength, and corresponding decrease in the frequency and photon energy, of electromagnetic radiation (such as light). The opposite change, a decrease in wavelength and simultaneous increase in f ...

s of cosmologically distant objects (in particular

galaxies A galaxy is a system of stars, stellar remnants, interstellar gas, dust, dark matter, bound together by gravity. The word is derived from the Greek ' (), literally 'milky', a reference to the Milky Way galaxy that contains the Solar System. ...

and

quasars A quasar is an extremely luminous active galactic nucleus (AGN). It is pronounced , and sometimes known as a quasi-stellar object, abbreviated QSO. This emission from a galaxy nucleus is powered by a supermassive black hole with a mass ranging ...

) 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 Hubble's law, also known as the Hubble–Lemaître law, is the observation in physical cosmology that galaxies are moving away from Earth at speeds proportional to their distance. In other words, the farther they are, the faster they are moving a ...

). This is referred to as

cosmological redshift Hubble's law, also known as the Hubble–Lemaître law, is the observation in physical cosmology that galaxies are moving away from Earth at speeds proportional to their distance. In other words, the farther they are, the faster they are moving ...

. 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. Subsequent discourse focused upon whether

redshift survey In astronomy, a redshift survey is a survey of a section of the sky to measure the redshift of astronomical objects: usually galaxies, but sometimes other objects such as galaxy clusters or quasars. Using Hubble's law, the redshift can be used ...

s of

quasar A quasar is an extremely Luminosity, luminous active galactic nucleus (AGN). It is pronounced , and sometimes known as a quasi-stellar object, abbreviated QSO. This emission from a galaxy nucleus is powered by a supermassive black hole with a m ...

s (QSOs) have produced evidence of quantization in excess of what is expected due to

selection effect Selection bias is the bias introduced by the selection of individuals, groups, or data for analysis in such a way that proper randomization is not achieved, thereby failing to ensure that the sample obtained is representative of the population int ...

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 The Big Bang event is a physical theory that describes how the universe expanded from an initial state of high density and temperature. Various cosmological models of the Big Bang explain the evolution of the observable universe from the ...

theory, have referred to evidence of redshift quantization as reason to reject conventional accounts of the origin and evolution of the

universe The universe is all of space and time and their contents, including planets, stars, galaxies, and all other forms of matter and energy. The Big Bang theory is the prevailing cosmological description of the development of the universe. Acc ...

Original investigation by William G. Tifft

György Paál György Paál (Budapest, 1934 – Budapest, 1992) was a Hungarian astronomer and cosmologist. Work In the late 1950s Paál studied the quasar and galaxy cluster distributions. In 1970 from redshift quantization he came up with the idea that t ...

(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⁻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 The University of Arizona (Arizona, U of A, UArizona, or UA) is a public land-grant research university in Tucson, Arizona. Founded in 1885 by the 13th Arizona Territorial Legislature, it was the first university in the Arizona Territory. T ...

, 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 The universe is all of space and time and their contents, including planets, stars, galaxies, and all other forms of matter and energy. The Big Bang theory is the prevailing cosmological description of the development of the universe. Acc ...

might have nontrivial

topological In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing ...

structure. 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 or Δ''z'' = (where Δ''z'' denotes shift in frequency expressed as a proportion of initial frequency). #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 Spiral galaxies form a class of galaxy originally described by Edwin Hubble in his 1936 work ''The Realm of the Nebulae''

Quasar redshifts

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.

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_(1 + z) = 0.089n - 0.0632

where: *

z

refers to the magnitude of redshift (shift in frequency as a proportion of initial frequency); *

n

is an integer with values 1, 2, 3, 4 ... This predicts periodic redshift peaks at

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 frequentist statistics, a confidence interval (CI) is a range of estimates for an unknown parameter. A confidence interval is computed at a designated ''confidence level''; the 95% confidence level is most common, but other levels, such as 9 ...

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 The Sloan Digital Sky Survey or SDSS is a major multi-spectral imaging and spectroscopic redshift survey using a dedicated 2.5-m wide-angle optical telescope at Apache Point Observatory in New Mexico, United States. The project began in 2000 a ...

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. They conclude that this correlation is unlikely to be a

, given the method used to determine intrinsic redshift relations. Schneider ''et al.'' (2007) and Richards ''et al.'' (2006) report that the periodicity reported by Bell and McDiarmid disappears after correcting for selection effects. 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. A 2006 review by Bajan ''et al.'' discovered weak effects of redshift periodization in data from the

Local Group The Local Group is the galaxy group that includes the Milky Way. It has a total diameter of roughly , and a total mass of the order of . It consists of two collections of galaxies in a "dumbbell" shape: the Milky Way and its satellites form ...

of galaxies and the

Hercules Supercluster The Hercules Superclusters (SCl 160) refers to a set of two nearby superclusters of galaxies. Relative to other local superclusters, Hercules is considered particularly large, being approximately 330 Mly in diameter. The Northern Local Supervoid ...

. 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 Δ''z'' = 0.0 − 3.7, though they noted no statistical correlation between their findings and Karlsson's formula.

References

{{Reflist, 30em Physical cosmology