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This article is about the physical phenomenon. For the photochemical usage, see bathochromic shift. For other uses of the phrase "red shift" or "redshift", see red shift.

In physics and astronomy, redshift occurs when the visible light from an object is shifted towards the red end of the spectrum. Redshift is therefore an observed increase in the wavelength, which corresponds to a decrease in the frequency of electromagnetic radiation, received by a detector compared to that emitted by the source. The corresponding shift to shorter wavelengths is called blueshift.

The phenomenon goes by the same name even if it occurs at non-optical wavelengths (e.g. gamma rays, x-rays and ultraviolet). At wavelengths longer than red (e.g. infrared, microwaves, and radio waves) redshifts shift the radiation away from the red.

Redshift typically occurs when a light source moves away from an observer, analogous to the Doppler shift which changes the frequency of sound waves. While observing this redshift has a number of terrestrial uses (e.g. Doppler radar and Radar guns), it is famously employed in astronomy where it is used as a diagnostic in spectroscopic astrophysics to determine information about the dynamics and kinematics (i.e. movement) of distant objects. This redshift phenomenon was first predicted and observed in the nineteenth century as scientists began to consider the dynamical implications of the wave-nature of light. There is also a gravitational redshift which happens due to the time dilation that occurs in general relativity near massive objects, also known as the Einstein effect. Most famously, redshifts are observed in the spectra from distant galaxies, quasars, and intergalactic gas clouds to increase proportionally with the distance to the object. This is generally considered to be one of the major forms of evidence that the universe is expanding, as predicted by the Big Bang model.

History

The Doppler effect is named after Christian Andreas Doppler who proposed the effect in 1842. The hypothesis was tested and confirmed for sound waves by the Dutch scientist Christoph Hendrik Diederik Buys Ballot in 1845. Doppler correctly predicted that the phenomenon should apply to all waves, and in particular suggested that the varying colors of stars could be attributed to their motion with respect to the Earth. While this idea turned out to be incorrect (stellar colors are indicators of a star's temperature, not motion), Doppler would later be vindicated by verified redshift observations.

The first Doppler redshift was described by French physicist Armand-Hippolyte-Louis Fizeau in 1848 who pointed to the shift in spectral lines seen in stars as being due to the Doppler effect. The effect is sometimes called the "Doppler-Fizeau effect". In 1868, British astronomer William Huggins was the first to determine the velocity of a star moving away from the Earth by this method.

The earliest occurrence of the term "red-shift" in print (in this hyphenated form), appears to be by American astronomer Walter S. Adams in 1908, where he mentions "Two methods of investigating that nature of the nebular red-shift". The word doesn't appear unhyphenated, perhaps indicating a more common usage or its German equivalent, Rotverschiebung, until about 1934 by Willem de Sitter.

Beginning with observations in 1912, Vesto Slipher discovered that most spiral nebulae had considerable redshifts. Subsequently, Edwin Hubble discovered an approximate relationship between the redshift of such "nebulae" (now known to be galaxies in their own right) and the distance to them with the formulation of his eponymous Hubble's law. These observations are today considered strong evidence for an expanding universe and the Big Bang theory.

Measurement, characterization, and interpretation

A redshift can be measured by looking at the spectrum of light that comes from a single source (see idealized spectrum illustration top-right). If there are features in this spectrum such as absorption lines, emission lines, or other variations in light intensity, then a redshift can in principle be calculated. This requires comparing the observed spectrum to a known spectrum with similar features. For example, the atomic element hydrogen, when exposed to light, has a definite signature spectrum that shows features at regular intervals. If the same pattern of intervals is seen in an observed spectrum occurring at shifted wavelengths, then a redshift can be measured for the object. Determining the redshift of an object therefore requires a frequency- or wavelength-range. Redshifts cannot be calculated by looking at isolated features or with a spectrum that is featureless or white noise (random fluctuations in a spectrum).

Redshift (and blueshift) may be characterized by the relative difference between the observed and emitted wavelengths (or frequency) of an object. In astronomy it is customary to refer to this change using a dimensionless quantity called z. If λ represents wavelength and f represents frequency (note, λf = c where c is the speed of light), then z is defined by the equations:

Measurement of redshift, ${\displaystyle z}$

Based on wavelength	Based on frequency
${\displaystyle z={\frac {\lambda _{\mathrm {observed} }-\lambda _{\mathrm {emitted} }}{\lambda _{\mathrm {emitted} }}}}$	${\displaystyle z={\frac {f_{\mathrm {emitted} }-f_{\mathrm {observed} }}{f_{\mathrm {observed} }}}}$
${\displaystyle 1+z={\frac {\lambda _{\mathrm {observed} }}{\lambda _{\mathrm {emitted} }}}}$	${\displaystyle 1+z={\frac {f_{\mathrm {emitted} }}{f_{\mathrm {observed} }}}}$

After z is measured, the distinction between redshift and blueshift is simply a matter of whether z is positive or negative. According to the mechanisms section below, there are some basic interpretations that follow when either a redshift or blueshift is observed. For example, Doppler effect blueshifts (z < 0) are associated with objects approaching (moving closer) to the observer with the light shifting to greater energies. Conversely, Doppler effect redshifts (z > 0) are associated with objects receding (moving away) from the observer with the light shifting to lower energies. Likewise, Einstein effect blueshifts are associated with light entering a strong gravitational field while Einstein effect redshifts imply light is leaving the field.

Mechanisms

A single photon propagated through a vacuum can redshift in several distinct ways. Each of these mechanisms produces a Doppler-like redshift, meaning that z is independent of wavelength. These mechanisms are described with Galilean, Lorentz, or general relativistic transformations between one frame of reference and another.

Redshift Summary

Redshift type	Transformation frame	Metric	Definition
Doppler redshift	Galilean transformation	Euclidean metric	${\displaystyle z\approx {\frac {v}{c}}}$
Relativistic Doppler	Lorentz transformation	Minkowski metric	${\displaystyle z=\left(1+{\frac {v}{c}}\right)\gamma -1}$
Cosmological redshift	General relativistic tr.	FRW metric	${\displaystyle z={\frac {a_{\mathrm {now} }}{a_{\mathrm {then} }}}-1}$
Gravitational redshift	General relativistic tr.	Schwarzschild metric	${\displaystyle z={\frac {1}{\sqrt {1-\left({\frac {2GM}{rc^{2}}}\right)}}}-1}$

Doppler effect

If a source of the light is moving away from an observer, then redshift (z > 0) occurs; if the source moves towards the observer, then blueshift (z < 0) occurs. This is true for all electromagnetic waves and is explained by the Doppler effect. Consequently, this type of redshift is also called the Doppler redshift. If the source moves away from the observer with velocity v, then, ignoring relativistic effects, the redshift is given by

${\displaystyle z\approx {\frac {v}{c}}}$     (Since ${\displaystyle \gamma \approx 1}$, see below)

where c is the speed of light. In the classical Doppler effect, the frequency of the source is not modified, but the recessional motion causes the illusion of a lower frequency.

Relativistic Doppler effect

A more complete treatment of the Doppler redshift requires considering relativistic effects associated with motion of sources close to the speed of light. A complete derivation of the effect can be found in the article on the relativistic Doppler effect. In brief, objects moving close to the speed of light will experience deviations from the above formula due to the time dilation of special relativity which can be corrected for by introducing the Lorentz factor γ into the classical Doppler formula as follows:

${\displaystyle 1+z=\left(1+{\frac {v}{c}}\right)\gamma }$

This phenomenon was first observed in a 1938 experiment performed by Herbert E. Ives and G.R. Stilwell, called the Ives-Stilwell experiment.

Since the Lorentz factor is dependent only on the magnitude of the velocity, this causes the redshift associated with the relativistic correction to be independent of the orientation of the source movement. In contrast, the classical part of the formula is dependent on the projection of the movement of the source into the line of sight which yields different results for different orientations. Consequently, for an object moving at an angle θ to the observer (zero angle is directly away from the observer), the full form for the relativistic Doppler effect becomes:

${\displaystyle 1+z={\frac {1+v\cos(\theta )/c}{\sqrt {1-v^{2}/c^{2}}}}}$

For the special case that the source is moving at right angles (θ = 90°) to the detector, the relativistic redshift is known as the transverse redshift, and a redshift is measured, even though the object is not moving away from the observer. Even if the source is moving towards the observer, if there is a transverse component to the motion then there is some speed at which the dilation just cancels the expected blueshift and at higher speed the approaching source will be redshifted.

Expansion of space

The current models of cosmology derived from general relativity show that space is (currently) expanding. As a result, objects within the universe are moving relative to one another, creating the cosmological redshift. For z < 0.1 the effects of spacetime expansion are minimal and dominated by the peculiar motions which cause Doppler redshift. This led to initial interpretation of the cosmological redshift by Slipher, Hubble and others as a Doppler effect, as their sources were nearby in astronomical terms. In reality, the properties of the source are not modified, but the photons will be stretched as the space through which they are traveling expands, increasing their wavelengths. This effect is prescribed by the current cosmological model as an observable manifestation of the time-dependent cosmic scale factor (${\displaystyle a}$) in the following way:

${\displaystyle 1+z={\frac {a_{\mathrm {now} }}{a_{\mathrm {then} }}}.}$

This type of redshift is also called the cosmological redshift or Hubble redshift. If the universe were contracting instead of expanding, we would see distant galaxies blueshifted by an amount proportional to their distance instead of redshifted.

These galaxies are not receding simply by means of a physical velocity in the direction away from the observer; instead, the intervening space is stretching, which accounts for the large-scale isotropy of the effect demanded by the cosmological principle. The difference between physical velocity and space expansion is clearly illustrated by the Expanding Rubber Sheet Universe, a common cosmological analogy used to describe the expansion of space. If two objects are represented by ball bearings and spacetime by a stretching rubber sheet, the Doppler effect is caused by rolling the balls across the sheet to create peculiar motion. The cosmological redshift occurs when the ball bearings are stuck to the sheet and the sheet is stretched. (Obviously there are dimensional problems with the model, as the ball bearings should be in the sheet and cosmological redshift produces higher velocities than Doppler if the distance between 2 objects is far enough.)

Despite there being a distinction between redshifts caused by the velocity of the objects and the redshifts associated with the expanding universe, astronomers (especially professional ones) sometimes refer to "recession velocity" in the context of the redshifting of distant galaxies from the expansion of the Universe, even though it is only an apparent recession. As a consequence, popular literature often uses the expression "Doppler redshift" instead of "cosmological redshift" to describe the motion of galaxies dominated by the expansion of spacetime, despite the fact that a "cosmological recessional speed" when calculated will not equal the velocity in the relativistic Doppler equation. In particular, Doppler redshift is bound by special relativity so v > c is impossible while, in contrast, v > c is possible for cosmological redshift because the space which separates the objects (e.g., a quasar from the Earth) can expand faster than the speed of light. More mathematically, the viewpoint that "distant galaxies are receding" and the viewpoint that "the space between galaxies is expanding" are related by changing coordinate systems. Expressing this precisely requires working with the mathematics of the Robertson-Walker metric.

Gravitational redshift

In the theory of general relativity, there is also time dilation within a gravitational well. This is known as the gravitational redshift or Einstein Shift. The theoretical derivation of this effect follows from the Schwarzschild solution of the Einstein equations which yields the following formula for redshift associated with a photon traveling in the gravitational field of an uncharged, nonrotating, spherically symmetric mass:

${\displaystyle 1+z={\frac {1}{\sqrt {1-\left({\frac {2GM}{rc^{2}}}\right)}}}}$,

where

• ${\displaystyle G}$ is the gravitational constant,
• ${\displaystyle M}$ is the mass of the object creating the gravitational field,
• ${\displaystyle r}$ is the radial coordinate of the observer (which is analogous to the classical distance from the center of the object, but is actually a Schwarzschild coordinate), and
• ${\displaystyle c}$ is the speed of light.

The effect is very small but measurable on Earth using the Mossbauer effect and was first observed in the Pound-Rebka experiment. However, it is significant near a black hole, and as an object approaches the event horizon, the red shift becomes infinite. It is also the dominant cause of large angular-scale temperature fluctuations in the cosmic microwave background radiation (see Sachs-Wolfe effect).

Observations in astronomy

The redshift observed in astronomy can be measured because the emission and absorption spectra for atoms are distinctive and well known, calibrated from spectroscopic experiments in laboratories on Earth. When the redshift of various absorption and emission lines from a single astronomical object is measured, z is found to be remarkably constant. (See Is the fine structure constant really constant?) Although distant objects may be slightly blurred and lines broadened, it is by no more than can be explained by thermal or mechanical motion of the source. For these reasons and others, the consensus among astronomers is that the redshifts they observe are due to some combination of the three established forms of Doppler-like redshifts. Alternative hypotheses are not generally considered plausible.

Spectroscopy, as a measurement, is considerably more difficult than simple photometry which measures the brightness of astronomical objects through certain filters. When photometric data is all that is available (for example, the Hubble Deep Field and the Hubble Ultra Deep Field), astronomers rely on a technique for measuring photometric redshifts. Due to the filter being sensitive to a range of wavelengths and the technique relying on making many assumptions about the nature of the spectrum at the light-source, errors for these sorts of measurements can range up to δz = 0.5, and are much less reliable than spectroscopic determinations. However, photometry does allow at least for a qualitative characterization of a redshift. For example, if a sun-like spectrum had a redshift of z = 1, it would be brightest in the infrared rather than at the yellow-green color associated with the peak of its blackbody spectrum, and the light intensity will also be reduced in the filter by a factor of 1+z (see K correction for more details on the photometric consequences of redshift).

Local observations

In nearby objects (within our Milky Way galaxy) observed redshifts are almost always related to the line of sight velocities associated with the objects being observed. Observations of such redshifts and blueshifts have enabled astronomers to measure velocities and parametrize the masses of the orbiting stars in spectroscopic binaries, a method first employed in 1868 by British astronomer William Huggins. Similarly, small redshifts and blueshifts detected in the spectroscopic measurements of individual stars are one way astronomers have been able to diagnose and measure the presence and characteristics of planetary systems around other stars. Measurements of redshifts to fine detail are also used in helioseismology to determine the precise movements of the photosphere of the Sun. Redshifts have also been used to make the first measurements of the rotation rates of planets, velocities of interstellar clouds, the rotation of galaxies, and the dynamics of accretion onto neutron stars and black holes which exhibit both Doppler and gravitational redshifts. Additionally, the temperatures of various emitting and absorbing objects can be obtained by measuring Doppler broadening — effectively redshifts and blueshifts over a single emission or absorption line. By measuring the broadening and shifts of the 21-centimeter hydrogen line in different directions, astronomers have been able to measure the recessional velocities of interstellar gas, which in turn reveals the rotation curve of our Milky Way. Similar measurements have also been performed on other galaxies, such as Andromeda. As a diagnostic tool, redshift measurements are one of the most important spectroscopic measurements made in astronomy.

Extragalactic observations

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The most distant objects exhibit larger redshifts corresponding to the Hubble flow of the universe. The largest observed redshift, corresponding to the greatest distance and furthest back in time, is that of the cosmic microwave background radiation; the numerical value of its redshift is about z = 1089 (z = 0 corresponds to present time), and it shows the state of the Universe about 13.7 billion years ago, and 379,000 years after the initial moments of the Big Bang.

The luminous point-like cores of active galactic nuclei (quasars) were the first "high-redshift" (${\displaystyle z>0.1}$) objects discovered before the improvement of telescopes allowed for the discovery of extended-source high-redshift galaxies. Currently, the highest measured quasar redshift is ${\displaystyle z=6.4}$, with the highest confirmed galaxy redshift being ${\displaystyle z=7.0}$ while as-yet unconfirmed reports from a gravitational lens observed in a distant galaxy cluster may indicate a galaxy with a redshift of ${\displaystyle z=10}$.

For galaxies more distant than the Local Group and the nearby Virgo Cluster, but within a thousand megaparsecs or so, the redshift is approximately proportional to the galaxy's distance. This correlation was first observed by Edwin Hubble and has come to be known as Hubble's law. Vesto Slipher was the first to discover galactic redshifts, in about the year 1912, while Hubble correlated Slipher's measurements with distances he measured by other means to formulate his Law. In the widely accepted cosmological model based on general relativity, redshift is mainly a result of the expansion of space: this means that the farther away a galaxy is from us, the more the space has expanded in the time since the light left that galaxy, so the more the light has been stretched, the more redshifted the light is, and so the faster it appears to be moving away from us. Hubble's law follows in part from the Copernican principle. Because it is usually not known how luminous objects are, measuring the redshift is easier than more direct distance measurements, so redshift is sometimes in practice converted to a crude distance measurement using Hubble's law.

Gravitational interactions of galaxies with each other and clusters cause a significant scatter in the normal plot of the Hubble diagram. The peculiar velocities associated with galaxies superimpose a rough trace of the mass of virialized objects in the universe. This effect leads to such phenomena as nearby galaxies (such as the Andromeda Galaxy) exhibiting blueshifts as we fall towards a common barycenter, and redshift maps of clusters showing a Finger of God effect due to the scatter of peculiar velocities in a roughly spherical distribution. This added component gives cosmologists a chance to measure the masses of objects independent of the mass to light ratio (the ratio of a galaxy's mass in solar masses to its brightness in solar luminosities), an important tool for measuring dark matter.

For more distant galaxies, the relationship between current distance and observed redshift becomes more complex. When one sees a distant galaxy, one is seeing the galaxy as it was sometime in the past, when the expansion rate of the Universe was different from what it is now. At these early times, we expect differences in the expansion rate for at least two reasons:

1. The gravitational attraction between galaxies has been acting to slow down the expansion of the Universe since then.
2. The possible existence of a cosmological constant or quintessence may be changing the expansion rate of the Universe

Recent observations have suggested the expansion of the Universe is not slowing down, as expected from the first point, but accelerating. It is widely, though not quite universally, believed that this is because there is a form of dark energy dominating the evolution of the universe. Such a cosmological constant also implies that the ultimate fate of the Universe is not a Big Crunch, but instead will continue to exist foreseeably (though most physical processes within the Universe will still come to an eventual end).

The expanding Universe is a central prediction of the Big Bang theory. If extrapolated back in time, the theory predicts a "singularity", a point in time when the Universe had infinite density. The theory of general relativity, on which the Big Bang theory is based, breaks down at this point. It is believed that a yet unknown theory of quantum gravity would take over before the density becomes infinite.

Redshift surveys

With the advent of automated telescopes and improvements in spectroscopes, a number of collaborations have been made to map the universe in redshift space. By combining redshift with angular position data, a redshift survey maps the 3D distribution of matter within a field of the sky. These observations are used to measure properties of the large-scale structure of the universe. The Great Wall, a vast supercluster of galaxies over 500 million light-years wide, provides a dramatic example of a large-scale structure that redshift surveys can detect.

The first redshift survey was the CfA Redshift Survey, started in 1977 with the initial data collection completed in 1982. More recently, the 2dF Galaxy Redshift Survey determined the large-scale structure of one section of the Universe, measuring z-values for over 220,000 galaxies; data collection was completed in 2002, and the final data set was released 30 June 2003. (In addition to mapping large-scale patterns of galaxies, 2dF also established an upper limit on neutrino mass.) Another notable investigation, the Sloan Digital Sky Survey (SDSS), is ongoing as of 2005 and aims to obtain measurements on around 100 million objects. SDSS has recorded redshifts for galaxies as high as 0.4, and has been involved in the detection of quasars beyond z = 6. The DEEP2 Redshift Survey uses the Keck telescopes with the new "DEIMOS" spectrograph; a follow-up to the pilot program DEEP1, DEEP2 is designed to measure faint galaxies with redshifts 0.7 and above, and it is therefore planned to provide a complement to SDSS and 2dF.

Effects due to physical optics or radiative transfer

The interactions and phenomena summarized in the subjects of radiative transfer and physical optics can result in shifts in the wavelength and frequency of electromagnetic radiation. In such cases the shifts correspond to a physical energy transfer to matter or other photons rather than being due to a transformation between reference frames. These shifts can be due to coherence effects (see Wolf effect) or due to the scattering of electromagnetic radiation whether from charged elementary particles, from particulates, or from fluctuations in a dielectric medium. While such phenomena are sometimes referred to as "redshifts" and "blueshifts", the physical interactions of the electromagnetic radiation field with itself or intervening matter distinguishes these phenomena from the reference-frame effects. In astrophysics, light-matter interactions that result in energy shifts in the radiation field are generally referred to as "reddening" rather than "redshifting" which, as a term, is normally reserved for the effects discussed above.

In many circumstances scattering causes radiation to redden because entropy results in the predominance of many low energy photons over few high energy ones (while conserving total energy). Except possibly under carefully controlled conditions, scattering does not produce the same relative change in wavelength across the whole spectrum; that is, any calculated z is generally a function of wavelength. Furthermore, scattering from random media generally occurs at many angles, and z is also a function of the scattering angle. If multiple scattering occurs, or the scattering particles have relative motion, then there is generally distortion of spectral lines as well.

In interstellar astronomy, visible spectra can appear redder due to scattering processes in a phenomenon referred to as interstellar reddening — similarly Rayleigh scattering causes the atmospheric reddening of the sun seen in the sunrise or sunset and causes the rest of the sky to have a blue color. This phenomenon is distinct from redshifting because the spectroscopic lines are not shifted to other wavelengths in reddened objects and there is an additional dimming and distortion associated with the phenomenon due to photons being scattered in and out of the line of sight.

For a list of scattering processes, see Scattering.

References

Notes

1. See Feynman, Leighton and Sands (1989) or any introductory undergraduate (and many high school) physics textbooks. See Taylor (1992) for a relativistic discussion.
2. ^ See Binney and Merrifeld (1998), Carroll and Ostlie (1996), Kutner (2003) for applications in astronomy.
3. See Misner, Thorne and Wheeler (1973) and Weinberg (1971).
4. See Misner, Thorne and Wheeler (1973) and Weinberg (1971) or any of the physical cosmology textbooks.
5. Doppler, Christian, "Beitrage zur fixsternenkunde" (1846), Prag, Druck von G. Haase sohne
6. Dev Maulik, "Doppler Sonography: A Brief History" in Doppler Ultrasound in Obstetrics And Gynecology (2005) by Dev (EDT) Maulik, Ivica Zalud
7. O'Connor, John J.; Robertson, Edmund F., "Redshift", MacTutor History of Mathematics Archive, University of St Andrews
8. ^ William Huggins, "Further Observations on the Spectra of Some of the Stars and Nebulae, with an Attempt to Determine Therefrom Whether These Bodies are Moving towards or from the Earth, Also Observations on the Spectra of the Sun and of Comet II." (1868) Philosophical Transactions of the Royal Society of London, Volume 158, pp. 529-564
9. Adams, Walter S., "No. 22. Preliminary catalogue of lines affected in sun-spots" (1908) Contributions from the Mount Wilson Observatory / Carnegie Institution of Washington, vol. 22, pp.1-21
10. W. de Sitter, "On distance, magnitude, and related quantities in an expanding universe, (1934) Bulletin of the Astronomical Institutes of the Netherlands, Vol. 7, p.205. He writes: "It thus becomes urgent to investigate the effect of the redshift and of the metric of the universe on the apparent magnitude and observed numbers of nebulae of given magnitude"
11. Slipher first reports on his measurement in the inaugural volume of the Lowell Observatory Bulletin, pp.2.56-2.57. His article entitled The radial velocity of the Andromeda Nebula reports making the first Doppler measurement on September 17, 1912. In his report Slipher writes: "The magnitude of this velocity, which is the greatest hitherto observed, raises the question whether the velocity-like displacement might not be due to some other cause, but I believe we have at present no other interpretation for it." Three years later, in the journal Popular Astronomy, Vol. 23, p. 21-24 , Slipher wrote a review entitled Spectrographic Observations of Nebulae. In it he states, "The early discovery that the great Andromeda spiral had the quite exceptional velocity of - 300 km(/s) showed the means then available, capable of investigating not only the spectra of the spirals but their velocities as well." Slipher reported the velocities for 15 spiral nebulae spread across the entire celestial sphere, all but three having observable "positive" (that is recessional) velocities.
12. Hubble, Edwin, "A Relation between Distance and Radial Velocity among Extra-Galactic Nebulae" (1929) Proceedings of the National Academy of Sciences of the United States of America, Volume 15, Issue 3, pp. 168-173 (Full article, PDF)
13. ^ This was recognized early on by physicists and astronomers working in cosmology in the 1930s. The earliest layman publication describing the details of this correspondence was Sir Arthur Eddington's book The Expanding Universe: Astronomy's 'Great Debate', 1900-1931, published by Press Syndicate of the University of Cambridge in 1933.
14. See, for example, this 25 May 2004 press release from NASA's Swift space telescope that is researching gamma-ray bursts: "Measurements of the gamma-ray spectra obtained during the main outburst of the GRB have found little value as redshift indicators, due to the lack of well-defined features. However, optical observations of GRB afterglows have produced spectra with identifiable lines, leading to precise redshift measurements."
15. Where z = redshift; v = velocity; c = speed of light; γ = Lorentz factor; a = scale factor; G = gravitational constant; M = object mass; r = radial Schwarzschild coordinate
16. H. Ives and G. Stilwell, An Experimental study of the rate of a moving atomic clock , J. Opt. Soc. Am. 28, 215-226 (1938)
17. See "Photons, Relativity, Doppler shift" at the University of Queensland
18. Measurements of the peculiar velocities out to 5 Mpc using the Hubble Space Telescope were reported in 2003 by Karachentsev et al. Local galaxy flows within 5 Mpc. 02/2003 Astronomy and Astrophysics, 398, 479-491.
19. The distinction is made clear in Harrison, E.R. 1981 Cosmology: The Science of the Universe (New York:Cambridge University Press).
20. This is only true in a universe where there are no peculiar velocities. Otherwise, redshifts combine as

    ${\displaystyle 1+z=(1+z_{\mathrm {Doppler} })(1+z_{\mathrm {expansion} })}$

    which yields solutions where certain objects that "recede" are blueshifted and other objects that "approach" are redshifted. For more on this bizarre result see Davis, T. M., Lineweaver, C. H., and Webb, J. K. "Solutions to the tethered galaxy problem in an expanding universe and the observation of receding blueshifted objects", American Journal of Physics (2003), 71 358-364.
21. Peebles (1993).
22. University of Massachusetts, Amherst professor Edward Harrison gives a review summary of this confusion in his paper The redshift-distance and velocity-distance laws (01/1993 Astrophysical Journal, Part 1 (ISSN 0004-637X), 403, no. 1, p. 28-31.)
23. Odenwald & Fieberg 1993
24. This is because the expansion of the spacetime metric is describable by general relativity and dynamically changing measurements as opposed to a rigid Minkowski metric. Space, not being composed of any material can grow faster than the speed of light since, not being an object, it is not bound by the speed of light upper bound.
25. M. Weiss, What Causes the Hubble Redshift?, entry in the Physics FAQ (1994), available via John Baez's website
26. See for example, Chant, C. A., "Notes and Queries (Telescopes and Observatory Equipment-The Einstein Shift of Solar Lines)" (1930) Journal of the Royal Astronomical Society of Canada, Vol. 24, p.390
27. R. V. Pound and G. A. Rebka Jr., Apparent weight of photons, Phys. Rev. Lett. 4, 337 (1960). This paper was the first measurement.
28. Sachs, R. K. (1967). "Perturbations of a cosmological model and angular variations of the cosmic microwave background". Astrophysical Journal. 147 (73). {{cite journal}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)
29. When cosmological redshifts were first discovered, Fritz Zwicky proposed an effect known as tired light. While usually considered for historical interests, it is sometimes, along with intrinsic redshift suggestions, utilized by nonstandard cosmologies. In 1981, H. J. Reboul summarised many alternative redshift mechanisms that had been discussed in the literature since the 1930s. In 2001, Geoffrey Burbidge remarked in a review that the wider astronomical community has marginalized such discussions since the 1960s. Burbidge and Halton Arp, while investigating the mystery of the nature of quasars, tried to develop alternative redshift mechanisms, and very few of their fellow scientists acknowledged let alone accepted their work.
30. For a review of the subject of photometry, consider Budding, E., Introduction to Astronomical Photometry, Cambridge University Press (September 24, 1993), ISBN: 0521418674
31. The technique was first described by Baum, W. A.: 1962, in G. C. McVittie (ed.), Problems of extra-galactic research, p. 390, IAU Symposium No. 15
32. Bolzonella, M.; Miralles, J.-M.; Pelló, R., Photometric redshifts based on standard SED fitting procedures, Astronomy and Astrophysics, 363, p.476-492 (2000).
33. A pedagogical overview of the K-correction by David Hogg and other members of the SDSS collaboration can be found at astro-ph.
34. The Exoplanet Tracker is the newest observing project to use this technique, able to track the redshift variations in multiple objects at once, as reported in Ge, Jian et al. The First Extrasolar Planet Discovered with a New-Generation High-Throughput Doppler Instrument, The Astrophysical Journal, 2006 648, Issue 1, pp. 683-695.
35. Libbrecht, Ken G., Solar and stellar seismology, Space Science Reviews, 1988 37 n. 3-4, 275-301.
36. In 1871 Hermann Carl Vogel measured the rotation rate of Venus. Vesto Slipher was working on such measurements when he turned his attention to spiral nebulae.
37. An early review by Oort, J. H. on the subject: The formation of galaxies and the origin of the high-velocity hydrogen, Astronomy and Astrophysics, 7, 381 (1970) .
38. Asaoka, Ikuko, X-ray spectra at infinity from a relativistic accretion disk around a Kerr black hole, Astronomical Society of Japan, Publications (ISSN 0004-6264), 41 no. 4, 1989, p. 763-778
39. Rybicki, G. B. and A. R. Lightman, Radiative Processes in Astrophysics, John Wiley & Sons, 1979, p. 288 ISBN:0471827592
40. An accurate measurement of the cosmic microwave background was achieved by the COBE experiment. The final published temperature of 2.73 K was reported in this paper: Fixsen, D. J.; Cheng, E. S.; Cottingham, D. A.; Eplee, R. E., Jr.; Isaacman, R. B.; Mather, J. C.; Meyer, S. S.; Noerdlinger, P. D.; Shafer, R. A.; Weiss, R.; Wright, E. L.; Bennett, C. L.; Boggess, N. W.; Kelsall, T.; Moseley, S. H.; Silverberg, R. F.; Smoot, G. F.; Wilkinson, D. T.. (1994). "Cosmic microwave background dipole spectrum measured by the COBE FIRAS instrument", Astrophysical Journal, 420, 445. The most accurate measurement as of 2006 was achieved by the WMAP experiment.
41. Fan, Xiahoui et al., A Survey of z>5.7 Quasars in the Sloan Digital Sky Survey. II. Discovery of Three Additional Quasars at z>6, The Astronomical Journal (2003), v. 125, Issue 4, pp. 1649-1659 .
42. Egami, E., et al., Spitzer and Hubble Space Telescope Constraints on the Physical Properties of the z~7 Galaxy Strongly Lensed by A2218, The Astrophysical Journal (2005), v. 618, Issue 1, pp. L5-L8 .
43. Pelló, R., Schaerer, D., Richard, J., Le Borgne, J.-F., & Kneib, J.P., ISAAC/VLT observations of a lensed galaxy at z = 10.0, Astronomy and Astrophysics (2004), 416, L35 .
44. Peebles (1993).
45. Peebles (1993).
46. Binney, James. Galactic dynamics. Princeton University Press. ISBN 0-691-08445-9. {{cite book}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)
47. P. J. E. Peebles and Bharat Ratra (2003). "The cosmological constant and dark energy". Reviews of Modern Physics. 75: 559–606.
48. S. Permutter et al. (The Supernova Cosmology Project) (1999). "Measurements of Omega and Lambda from 42 high redshift supernovae". Astrophysical J. 517: 565–86.
49. Adam G. Riess et al. (Supernova Search Team) (1998). "Observational evidence from supernovae for an accelerating universe and a cosmological constant". Astronomical J. 116: 1009–38.
50. Peebles (1993), Weinberg (1971), Misner, Thorne and Wheeler (1973).
51. M. J. Geller & J. P. Huchra, Science 246, 897 (1989). online
52. See the official CfA website for more details.
53. Shaun Cole et al. (The 2dFGRS Collaboration) (2005). "The 2dF galaxy redshift survey: Power-spectrum analysis of the final dataset and cosmological implications". Mon. Not. Roy. Astron. Soc. 362: 505–34.{{cite journal}}: CS1 maint: numeric names: authors list (link) 2dF Galaxy Redshift Survey homepage
54. SDSS Homepage
55. Marc Davis et al. (DEEP2 collaboration) (2002). "Science objectives and early results of the DEEP2 redshift survey". Conference on Astronomical Telescopes and Instrumentation, Waikoloa, Hawaii, 22-28 Aug 2002. {{cite conference}}: Unknown parameter |booktitle= ignored (|book-title= suggested) (help)CS1 maint: numeric names: authors list (link)

Articles

• Odenwald, S. & Fienberg, RT. 1993; "Galaxy Redshifts Reconsidered" in Sky & Telescope Feb. 2003; pp31-35 (This article is also useful further reading in distinguishing between the 3 types of redshift and their causes.)
• Lineweaver, Charles H. and Tamara M. Davis, "Misconceptions about the Big Bang", Scientific American, March 2005. (This article is useful for explaining the cosmological redshift mechanism as well as clearing up misconceptions regarding the physics of the expansion of space.)

Book references

• Binney, James (1998). Galactic Astronomy. Princeton University Press. ISBN 0-691-02565-7. {{cite book}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)
• Carroll, Bradley W. and Dale A. Ostlie (1996). An Introduction to Modern Astrophysics. Addison-Wesley Publishing Company, Inc. ISBN 0-201-54730-9.
• Feynman, Richard; Leighton, Robert; Sands, Matthew (1989). Feynman Lectures on Physics. Vol. 1. Addison-Wesley. ISBN 0-201-51003-0.{{cite book}}: CS1 maint: multiple names: authors list (link)
• Kutner, Marc (2003). Astronomy: A Physical Perspective. Cambridge University Press. ISBN 0-521-52927-1.
• Misner, Charles (1973). Gravitation. San Francisco: W. H. Freeman. ISBN 0-7167-0344-0. {{cite book}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)
• Peebles, P. J. E. (1993). Principles of Physical Cosmology. Princeton University Press. ISBN 0-691-01933-9.
• Taylor, Edwin F.; Wheeler, John Archibald (1992). Spacetime Physics: Introduction to Special Relativity (2nd ed.). W.H. Freeman. ISBN 0-7167-2327-1.{{cite book}}: CS1 maint: multiple names: authors list (link)
• Weinberg, Steven (1971). Gravitation and Cosmology. John Wiley. ISBN 0-471-92567-5.
• See also physical cosmology textbooks for applications of the cosmological and gravitational redshifts.

External links

• Gravitational redshift
• Ned Wright's Cosmology tutorial
• Article on redshift from SPACE.com
• Cosmic reference guide entry on redshift
• Mike Luciuk's Astronomical Redshift tutorial

Template:Link FA

• Astrophysics
• Doppler effects
• Physical cosmology
• Astronomical units of length