Redshift

# Redshift

Overview
In physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

(especially astrophysics
Astrophysics
Astrophysics is the branch of astronomy that deals with the physics of the universe, including the physical properties of celestial objects, as well as their interactions and behavior...

), redshift happens when light
Light
Light or visible light is electromagnetic radiation that is visible to the human eye, and is responsible for the sense of sight. Visible light has wavelength in a range from about 380 nanometres to about 740 nm, with a frequency range of about 405 THz to 790 THz...

seen coming from an object is proportion
Proportionality (mathematics)
In mathematics, two variable quantities are proportional if one of them is always the product of the other and a constant quantity, called the coefficient of proportionality or proportionality constant. In other words, are proportional if the ratio \tfrac yx is constant. We also say that one...

ally increased in wavelength
Wavelength
In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...

, or shifted to the red
Red
Red is any of a number of similar colors evoked by light consisting predominantly of the longest wavelengths of light discernible by the human eye, in the wavelength range of roughly 630–740 nm. Longer wavelengths than this are called infrared , and cannot be seen by the naked eye...

end of the spectrum
Visible spectrum
The visible spectrum is the portion of the electromagnetic spectrum that is visible to the human eye. Electromagnetic radiation in this range of wavelengths is called visible light or simply light. A typical human eye will respond to wavelengths from about 390 to 750 nm. In terms of...

. More generally, where an observer
Observer (physics)
The term observer has a number of non-equivalent uses in science.-Special relativity:The term observer in special relativity refers most commonly to an inertial reference frame....

Electromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space...

outside the visible spectrum
Electromagnetic spectrum
The electromagnetic spectrum is the range of all possible frequencies of electromagnetic radiation. The "electromagnetic spectrum" of an object is the characteristic distribution of electromagnetic radiation emitted or absorbed by that particular object....

, "redder" amounts to a technical shorthand for "increase in electromagnetic wavelength
Wavelength
In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...

" — which also implies lower frequency
Frequency
Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...

and photon
Photon
In physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...

energy in accord with, respectively, the wave and quantum theories of light.

Redshifts are attributable to the Doppler effect
Doppler effect
The Doppler effect , named after Austrian physicist Christian Doppler who proposed it in 1842 in Prague, is the change in frequency of a wave for an observer moving relative to the source of the wave. It is commonly heard when a vehicle sounding a siren or horn approaches, passes, and recedes from...

, familiar in the changes in the apparent pitch
Pitch (music)
Pitch is an auditory perceptual property that allows the ordering of sounds on a frequency-related scale.Pitches are compared as "higher" and "lower" in the sense associated with musical melodies,...

es of sirens and frequency
Frequency
Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...

of the sound waves
Sound
Sound is a mechanical wave that is an oscillation of pressure transmitted through a solid, liquid, or gas, composed of frequencies within the range of hearing and of a level sufficiently strong to be heard, or the sensation stimulated in organs of hearing by such vibrations.-Propagation of...

emitted by speeding vehicles; an observed redshift due to the Doppler effect occurs whenever a light source moves away from an observer.
Discussion

Encyclopedia
In physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

(especially astrophysics
Astrophysics
Astrophysics is the branch of astronomy that deals with the physics of the universe, including the physical properties of celestial objects, as well as their interactions and behavior...

), redshift happens when light
Light
Light or visible light is electromagnetic radiation that is visible to the human eye, and is responsible for the sense of sight. Visible light has wavelength in a range from about 380 nanometres to about 740 nm, with a frequency range of about 405 THz to 790 THz...

seen coming from an object is proportion
Proportionality (mathematics)
In mathematics, two variable quantities are proportional if one of them is always the product of the other and a constant quantity, called the coefficient of proportionality or proportionality constant. In other words, are proportional if the ratio \tfrac yx is constant. We also say that one...

ally increased in wavelength
Wavelength
In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...

, or shifted to the red
Red
Red is any of a number of similar colors evoked by light consisting predominantly of the longest wavelengths of light discernible by the human eye, in the wavelength range of roughly 630–740 nm. Longer wavelengths than this are called infrared , and cannot be seen by the naked eye...

end of the spectrum
Visible spectrum
The visible spectrum is the portion of the electromagnetic spectrum that is visible to the human eye. Electromagnetic radiation in this range of wavelengths is called visible light or simply light. A typical human eye will respond to wavelengths from about 390 to 750 nm. In terms of...

. More generally, where an observer
Observer (physics)
The term observer has a number of non-equivalent uses in science.-Special relativity:The term observer in special relativity refers most commonly to an inertial reference frame....

Electromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space...

outside the visible spectrum
Electromagnetic spectrum
The electromagnetic spectrum is the range of all possible frequencies of electromagnetic radiation. The "electromagnetic spectrum" of an object is the characteristic distribution of electromagnetic radiation emitted or absorbed by that particular object....

, "redder" amounts to a technical shorthand for "increase in electromagnetic wavelength
Wavelength
In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...

" — which also implies lower frequency
Frequency
Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...

and photon
Photon
In physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...

energy in accord with, respectively, the wave and quantum theories of light.

Redshifts are attributable to the Doppler effect
Doppler effect
The Doppler effect , named after Austrian physicist Christian Doppler who proposed it in 1842 in Prague, is the change in frequency of a wave for an observer moving relative to the source of the wave. It is commonly heard when a vehicle sounding a siren or horn approaches, passes, and recedes from...

, familiar in the changes in the apparent pitch
Pitch (music)
Pitch is an auditory perceptual property that allows the ordering of sounds on a frequency-related scale.Pitches are compared as "higher" and "lower" in the sense associated with musical melodies,...

es of sirens and frequency
Frequency
Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...

of the sound waves
Sound
Sound is a mechanical wave that is an oscillation of pressure transmitted through a solid, liquid, or gas, composed of frequencies within the range of hearing and of a level sufficiently strong to be heard, or the sensation stimulated in organs of hearing by such vibrations.-Propagation of...

emitted by speeding vehicles; an observed redshift due to the Doppler effect occurs whenever a light source moves away from an observer. Cosmological
Cosmology
Cosmology is the discipline that deals with the nature of the Universe as a whole. Cosmologists seek to understand the origin, evolution, structure, and ultimate fate of the Universe at large, as well as the natural laws that keep it in order...

redshift is seen due to the expansion of the universe
Metric expansion of space
The metric expansion of space is the increase of distance between distant parts of the universe with time. It is an intrinsic expansion—that is, it is defined by the relative separation of parts of the universe and not by motion "outward" into preexisting space...

, and sufficiently distant light sources (generally more than a few million light years
Light Years
Light Years is the seventh studio album by Australian recording artist Kylie Minogue. It was released on 25 September 2000 by Parlophone and Mushroom Records. The album's style was indicative of her return to "mainstream pop dance tunes"....

away) show redshift corresponding to the rate of increase of their distance from Earth. Finally, gravitational redshift
Gravitational redshift
In astrophysics, gravitational redshift or Einstein shift describes light or other forms of electromagnetic radiation of certain wavelengths that originate from a source that is in a region of a stronger gravitational field that appear to be of longer wavelength, or redshifted, when seen or...

s are a relativistic
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

effect observed in electromagnetic radiation moving out of gravitational field
Gravitational field
The gravitational field is a model used in physics to explain the existence of gravity. In its original concept, gravity was a force between point masses...

s. Conversely, a decrease in wavelength is called blueshift and is generally seen when a light-emitting object moves toward an observer or when electromagnetic radiation moves into a gravitational field.

Although observing redshifts and blueshifts have several terrestrial applications (e.g., Doppler radar
A Doppler radar is a specialized radar that makes use of the Doppler effect to produce velocity data about objects at a distance. It does this by beaming a microwave signal towards a desired target and listening for its reflection, then analyzing how the frequency of the returned signal has been...

A radar speed gun is a small doppler radar unit used to measure the speed of moving objects, including vehicles, pitched baseballs, runners and other moving objects. Radar speed guns may be hand-held, vehicle-mounted or static...

s), redshifts are most famously seen in the spectroscopic
Astronomical spectroscopy
Astronomical spectroscopy is the technique of spectroscopy used in astronomy. The object of study is the spectrum of electromagnetic radiation, including visible light, which radiates from stars and other celestial objects...

observations of astronomical objects.

A special relativistic
Special relativity
Special relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...

redshift formula (and its classical approximation
Classical physics
What "classical physics" refers to depends on the context. When discussing special relativity, it refers to the Newtonian physics which preceded relativity, i.e. the branches of physics based on principles developed before the rise of relativity and quantum mechanics...

) can be used to calculate the redshift of a nearby object when spacetime
Spacetime
In physics, spacetime is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space as being three-dimensional and time playing the role of a fourth dimension that is of a different sort from the spatial dimensions...

is flat
Minkowski space
In physics and mathematics, Minkowski space or Minkowski spacetime is the mathematical setting in which Einstein's theory of special relativity is most conveniently formulated...

. However, many cases such as black hole
Black hole
A black hole is a region of spacetime from which nothing, not even light, can escape. The theory of general relativity predicts that a sufficiently compact mass will deform spacetime to form a black hole. Around a black hole there is a mathematically defined surface called an event horizon that...

s and Big Bang cosmology require that redshifts be calculated using general relativity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

. Special relativistic, gravitational, and cosmological redshifts can be understood under the umbrella of frame transformation laws
Frame of reference
A frame of reference in physics, may refer to a coordinate system or set of axes within which to measure the position, orientation, and other properties of objects in it, or it may refer to an observational reference frame tied to the state of motion of an observer.It may also refer to both an...

. There exist other physical processes that can lead to a shift in the frequency of electromagnetic radiation, including scattering
Scattering
Scattering is a general physical process where some forms of radiation, such as light, sound, or moving particles, are forced to deviate from a straight trajectory by one or more localized non-uniformities in the medium through which they pass. In conventional use, this also includes deviation of...

and optical effects
Physical optics
In physics, physical optics, or wave optics, is the branch of optics which studies interference, diffraction, polarization, and other phenomena for which the ray approximation of geometric optics is not valid...

; however, the resulting changes are distinguishable from true redshift and not generally referred as such (see section on physical optics and radiative transfer).

## History

The history of the subject began with the development in the 19th century of wave mechanics
Wave
In physics, a wave is a disturbance that travels through space and time, accompanied by the transfer of energy.Waves travel and the wave motion transfers energy from one point to another, often with no permanent displacement of the particles of the medium—that is, with little or no associated mass...

and the exploration of phenomena associated with the Doppler effect
Doppler effect
The Doppler effect , named after Austrian physicist Christian Doppler who proposed it in 1842 in Prague, is the change in frequency of a wave for an observer moving relative to the source of the wave. It is commonly heard when a vehicle sounding a siren or horn approaches, passes, and recedes from...

. The effect is named after Christian Doppler
Christian Doppler
Christian Andreas Doppler was an Austrian mathematician and physicist.-Life and work:Christian Doppler was raised in Salzburg, Austria, the son of a stonemason. Doppler could not work in his father's business because of his generally weak physical condition...

, who offered the first known physical explanation for the phenomenon in 1842. The hypothesis was tested and confirmed for sound waves by the Dutch
Netherlands
The Netherlands is a constituent country of the Kingdom of the Netherlands, located mainly in North-West Europe and with several islands in the Caribbean. Mainland Netherlands borders the North Sea to the north and west, Belgium to the south, and Germany to the east, and shares maritime borders...

Christophorus Henricus Diedericus Buys Ballot was a Dutch chemist and meteorologist after whom Buys Ballot's law and the Buys Ballot table are named.-Biography:...

in 1845. Doppler correctly predicted that the phenomenon should apply to all wave
Wave
In physics, a wave is a disturbance that travels through space and time, accompanied by the transfer of energy.Waves travel and the wave motion transfers energy from one point to another, often with no permanent displacement of the particles of the medium—that is, with little or no associated mass...

s, and in particular suggested that the varying color
Color
Color or colour is the visual perceptual property corresponding in humans to the categories called red, green, blue and others. Color derives from the spectrum of light interacting in the eye with the spectral sensitivities of the light receptors...

s of star
Star
A star is a massive, luminous sphere of plasma held together by gravity. At the end of its lifetime, a star can also contain a proportion of degenerate matter. The nearest star to Earth is the Sun, which is the source of most of the energy on Earth...

s could be attributed to their motion with respect to the Earth. While this attribution turned out to be incorrect (stellar colors are indicators primarily of a star's temperature
Color temperature
Color temperature is a characteristic of visible light that has important applications in lighting, photography, videography, publishing, manufacturing, astrophysics, and other fields. The color temperature of a light source is the temperature of an ideal black-body radiator that radiates light of...

, not motion) Doppler would later be vindicated by verified redshift observations.

The first Doppler redshift was described by French physicist Hippolyte Fizeau
Hippolyte Fizeau
Armand Hippolyte Louis Fizeau was a French physicist.-Biography:Fizeau was born in Paris. His earliest work was concerned with improvements in photographic processes. Following suggestions by François Arago, Léon Foucault and Fizeau collaborated in a series of investigations on the interference of...

in 1848, who pointed to the shift in spectral line
Spectral line
A spectral line is a dark or bright line in an otherwise uniform and continuous spectrum, resulting from a deficiency or excess of photons in a narrow frequency range, compared with the nearby frequencies.- Types of line spectra :...

s 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
William Huggins
Sir William Huggins, OM, KCB, FRS was an English amateur astronomer best known for his pioneering work in astronomical spectroscopy.-Biography:...

was the first to determine the velocity of a star moving away from the Earth by this method. In 1871, optical redshift was confirmed when the phenomenon was observed in Fraunhofer lines
Fraunhofer lines
In physics and optics, the Fraunhofer lines are a set of spectral lines named for the German physicist Joseph von Fraunhofer . The lines were originally observed as dark features in the optical spectrum of the Sun....

using solar rotation, about 0.1 Å in the red.
In 1887, Vogel and Scheiner discovered the annual Doppler effect, the yearly change in the Doppler shift of stars located near the ecliptic due to the orbital velocity of the Earth. In 1901, Aristarkh Belopolsky
Aristarkh Apollonovich Belopolsky
Aristarkh Apollonovich Belopolsky , Moscow – 16 May 1934, Pulkovo, Leningrad) was a Russian astronomer....

verified optical redshift in the laboratory using a system of rotating mirrors.

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 until about 1934 by Willem de Sitter
Willem de Sitter
Willem de Sitter was a Dutch mathematician, physicist and astronomer.-Life and work:Born in Sneek, De Sitter studied mathematics at the University of Groningen and then joined the Groningen astronomical laboratory. He worked at the Cape Observatory in South Africa...

, perhaps indicating that up to that point its German equivalent, Rotverschiebung, was more commonly used.

Beginning with observations in 1912, Vesto Slipher
Vesto Slipher
Vesto Melvin Slipher was an American astronomer. His brother Earl C. Slipher was also an astronomer and a director at the Lowell Observatory....

discovered that most spiral nebulae had considerable redshifts. Slipher first reports on his measurement in the inaugural volume of the Lowell Observatory Bulletin. Three years later, he wrote a review in the journal Popular Astronomy
Popular Astronomy (US magazine)
Popular Astronomy was a magazine for amateur astronomers published between 1893 and 1951. It was the successor to The Sidereal Messenger, which ceased publication in 1892. Each yearly volume of Popular Astronomy contained 10 issues, for a total of 59 volumes.The first editor, from 1893-1911, was...

. 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
Celestial sphere
In astronomy and navigation, the celestial sphere is an imaginary sphere of arbitrarily large radius, concentric with the Earth and rotating upon the same axis. All objects in the sky can be thought of as projected upon the celestial sphere. Projected upward from Earth's equator and poles are the...

, all but three having observable "positive" (that is recessional) velocities. Subsequently, Edwin Hubble
Edwin Hubble
Edwin Powell Hubble was an American astronomer who profoundly changed the understanding of the universe by confirming the existence of galaxies other than the Milky Way - our own galaxy...

discovered an approximate relationship between the redshifts of such "nebulae" (now known to be galaxies
Galaxy
A galaxy is a massive, gravitationally bound system that consists of stars and stellar remnants, an interstellar medium of gas and dust, and an important but poorly understood component tentatively dubbed dark matter. The word galaxy is derived from the Greek galaxias , literally "milky", a...

in their own right) and the distance
Distance
Distance is a numerical description of how far apart objects are. In physics or everyday discussion, distance may refer to a physical length, or an estimation based on other criteria . In mathematics, a distance function or metric is a generalization of the concept of physical distance...

s to them with the formulation of his eponymous Hubble's law
Hubble's law
Hubble's law is the name for the astronomical observation in physical cosmology that: all objects observed in deep space are found to have a doppler shift observable relative velocity to Earth, and to each other; and that this doppler-shift-measured velocity, of various galaxies receding from...

. These observations corroborated Alexander Friedman's 1922 work, in which he derived the famous Friedmann equations
Friedmann equations
The Friedmann equations are a set of equations in physical cosmology that govern the expansion of space in homogeneous and isotropic models of the universe within the context of general relativity...

. They are today considered strong evidence for an expanding universe and the Big Bang
Big Bang
The Big Bang theory is the prevailing cosmological model that explains the early development of the Universe. According to the Big Bang theory, the Universe was once in an extremely hot and dense state which expanded rapidly. This rapid expansion caused the young Universe to cool and resulted in...

theory.

## Measurement, characterization, and interpretation

The spectrum
Visible spectrum
The visible spectrum is the portion of the electromagnetic spectrum that is visible to the human eye. Electromagnetic radiation in this range of wavelengths is called visible light or simply light. A typical human eye will respond to wavelengths from about 390 to 750 nm. In terms of...

of light that comes from a single source (see idealized spectrum illustration top-right) can be measured. To determine the redshift, one searches for features in the spectrum such as absorption lines
Spectral line
A spectral line is a dark or bright line in an otherwise uniform and continuous spectrum, resulting from a deficiency or excess of photons in a narrow frequency range, compared with the nearby frequencies.- Types of line spectra :...

, emission lines
Spectral line
A spectral line is a dark or bright line in an otherwise uniform and continuous spectrum, resulting from a deficiency or excess of photons in a narrow frequency range, compared with the nearby frequencies.- Types of line spectra :...

, or other variations in light intensity
Light intensity
Several measures of light are commonly known as intensity. These are obtained by dividing either a power or a luminous flux by a solid angle, a planar area, or a combination of the two...

. If found, these features can be compared with known features in the spectrum of various chemical compounds found in experiments where that compound is located on earth. A very common atomic element
Chemical element
A chemical element is a pure chemical substance consisting of one type of atom distinguished by its atomic number, which is the number of protons in its nucleus. Familiar examples of elements include carbon, oxygen, aluminum, iron, copper, gold, mercury, and lead.As of November 2011, 118 elements...

in space is hydrogen
Hydrogen
Hydrogen is the chemical element with atomic number 1. It is represented by the symbol H. With an average atomic weight of , hydrogen is the lightest and most abundant chemical element, constituting roughly 75% of the Universe's chemical elemental mass. Stars in the main sequence are mainly...

. The spectrum of originally featureless light shone through hydrogen will show a signature spectrum specific to hydrogen that has features at regular intervals. If restricted to absorption lines it would look similar to the illustration (top right). If the same pattern of intervals is seen in an observed spectrum from a distant source but occurring at shifted wavelengths, it can be identified as hydrogen too. If the same spectral line is identified in both spectra but at different wavelengths then the redshift can be calculated using the table below. Determining the redshift of an object in this way requires a frequency- or wavelength-range. In order to calculate the redshift one has to know the wavelength of the emitted light in the rest frame of the source, in other words, the wavelength that would be measured by an observer located adjacent to and comoving with the source. Since in astronomical applications this measurement cannot be done directly, because that would require travelling to the distant star of interest, the method using spectral lines described here is used instead. Redshifts cannot be calculated by looking at unidentified features whose rest-frame frequency is unknown, or with a spectrum that is featureless or white noise
White noise
White noise is a random signal with a flat power spectral density. In other words, the signal contains equal power within a fixed bandwidth at any center frequency...

(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
Speed of light
The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...

), then z is defined by the equations:
Calculation of redshift,
Based on wavelength Based on frequency

After z is measured, the distinction between redshift and blueshift is simply a matter of whether z is positive or negative. See the formula section below for some basic interpretations that follow when either a redshift or blueshift is observed. For example, Doppler effect
Doppler effect
The Doppler effect , named after Austrian physicist Christian Doppler who proposed it in 1842 in Prague, is the change in frequency of a wave for an observer moving relative to the source of the wave. It is commonly heard when a vehicle sounding a siren or horn approaches, passes, and recedes from...

blueshifts (z < 0) are associated with objects approaching (moving closer to) the observer with the light shifting to greater energies
Energy
In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...

. Conversely, Doppler effect redshifts (z > 0) are associated with objects receding (moving away) from the observer with the light shifting to lower energies. Likewise, gravitational blueshifts are associated with light emitted from a source residing within a weaker gravitational field
Gravitational field
The gravitational field is a model used in physics to explain the existence of gravity. In its original concept, gravity was a force between point masses...

observed within a stronger gravitational field, while gravitational redshifting implies the opposite conditions.

## Redshift formulae

In general relativity one can derive several important special-case formulae for redshift in certain special spacetime geometries, as summarized in the following table. In all cases the magnitude of the shift (the value of z) is independent of the wavelength.
Redshift Summary
Redshift type Geometry Formula
Relativistic Doppler Minkowski space
Minkowski space
In physics and mathematics, Minkowski space or Minkowski spacetime is the mathematical setting in which Einstein's theory of special relativity is most conveniently formulated...

(flat spacetime)

for small

for motion completely in the radial direction.

for motion completely in the transverse direction.
Cosmological redshift FLRW spacetime (expanding Big Bang universe)
Gravitational redshift any stationary spacetime
Stationary spacetime
In general relativity, specifically in the Einstein field equations, a spacetime is said to be stationary if it admits a Killing vector that is asymptotically timelike....

(e.g. the Schwarzschild geometry)

(for the Schwarzschild geometry,

### 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
Doppler effect
The Doppler effect , named after Austrian physicist Christian Doppler who proposed it in 1842 in Prague, is the change in frequency of a wave for an observer moving relative to the source of the wave. It is commonly heard when a vehicle sounding a siren or horn approaches, passes, and recedes from...

. Consequently, this type of redshift is called the Doppler redshift. If the source moves away from the observer with velocity
Velocity
In physics, velocity is speed in a given direction. Speed describes only how fast an object is moving, whereas velocity gives both the speed and direction of the object's motion. To have a constant velocity, an object must have a constant speed and motion in a constant direction. Constant ...

v, which is much less than the speed of light (), the redshift is given by
(since )

where c is the speed of light
Speed of light
The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...

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

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
Relativistic Doppler effect
The relativistic Doppler effect is the change in frequency of light, caused by the relative motion of the source and the observer , when taking into account effects described by the special theory of relativity.The relativistic Doppler effect is different from the non-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
Time dilation
In the theory of relativity, time dilation is an observed difference of elapsed time between two events as measured by observers either moving relative to each other or differently situated from gravitational masses. An accurate clock at rest with respect to one observer may be measured to tick at...

of special relativity
Special relativity
Special relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...

which can be corrected for by introducing the Lorentz factor
Lorentz factor
The Lorentz factor or Lorentz term appears in several equations in special relativity, including time dilation, length contraction, and the relativistic mass formula. Because of its ubiquity, physicists generally represent it with the shorthand symbol γ . It gets its name from its earlier...

γ into the classical Doppler formula as follows:

This phenomenon was first observed in a 1938 experiment performed by Herbert E. Ives and G.R. Stilwell, called the Ives-Stilwell experiment
Ives-Stilwell experiment
The Ives–Stilwell experiment exploits the transverse Doppler effect . This was the first direct, quantitative confirmation of the time dilation factor. Together with the Michelson–Morley and Kennedy–Thorndike experiments, it forms one of the fundamental tests of special relativity theory...

.

Since the Lorentz factor is dependent only on the magnitude
Magnitude (mathematics)
The magnitude of an object in mathematics is its size: a property by which it can be compared as larger or smaller than other objects of the same kind; in technical terms, an ordering of the class of objects to which it belongs....

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
Line-of-sight propagation
Line-of-sight propagation refers to electro-magnetic radiation or acoustic wave propagation. Electromagnetic transmission includes light emissions traveling in a straight line...

which yields different results for different orientations. If θ is the angle between the direction of relative motion and the direction of emission in the observer's frame (zero angle is directly away from the observer), the full form for the relativistic Doppler effect becomes:

and for motion solely in the line of sight (θ = 0°), this equation reduces to:

For the special case that the light is approaching at right angle
Right angle
In geometry and trigonometry, a right angle is an angle that bisects the angle formed by two halves of a straight line. More precisely, if a ray is placed so that its endpoint is on a line and the adjacent angles are equal, then they are right angles...

s (θ = 90°) to the direction of relative motion in the observer's frame, 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 when 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

In the early part of the twentieth century, Slipher, Hubble and others made the first measurements of the redshifts and blueshifts of galaxies beyond the Milky Way
Milky Way
The Milky Way is the galaxy that contains the Solar System. This name derives from its appearance as a dim un-resolved "milky" glowing band arching across the night sky...

. They initially interpreted these redshifts and blueshifts as due solely to the Doppler effect, but later Hubble discovered a rough correlation between the increasing redshifts and the increasing distance of galaxies. Theorists almost immediately realized that these observations could be explained by a different mechanism for producing redshifts. Hubble's law
Hubble's law
Hubble's law is the name for the astronomical observation in physical cosmology that: all objects observed in deep space are found to have a doppler shift observable relative velocity to Earth, and to each other; and that this doppler-shift-measured velocity, of various galaxies receding from...

of the correlation between redshifts and distances is required by models of cosmology derived from general relativity that have a metric expansion of space
Metric expansion of space
The metric expansion of space is the increase of distance between distant parts of the universe with time. It is an intrinsic expansion—that is, it is defined by the relative separation of parts of the universe and not by motion "outward" into preexisting space...

. As a result, photons propagating through the expanding space are stretched, creating the cosmological redshift.

There is a distinction between a redshift in cosmological context as compared to that witnessed when nearby objects exhibit a local
Local reference frame
In theoretical physics, a local reference frame refers to a coordinate system or frame of reference that is only expected to function over a small region or a restricted region of space or spacetime....

Doppler-effect redshift. Rather than cosmological redshifts being a consequence of relative velocities, the photons instead increase in wavelength and redshift because of a feature of the spacetime
Spacetime topology
Spacetime topology, the topological structure of spacetime, is a subject studied primarily in general relativity. This physical theory models gravitation as a Lorentzian manifold and the concepts of topology thus become important in analysing local as well as global aspects of spacetime...

through which they are traveling that causes space to expand
Metric expansion of space
The metric expansion of space is the increase of distance between distant parts of the universe with time. It is an intrinsic expansion—that is, it is defined by the relative separation of parts of the universe and not by motion "outward" into preexisting space...

. Due to the expansion increasing as distances increase, the distance between two remote galaxies can increase at more than 3 m/s, but this does not imply that the galaxies move faster than the speed of light at their present location which is forbidden by Lorentz covariance
Lorentz covariance
In standard physics, Lorentz symmetry is "the feature of nature that says experimental results are independent of the orientation or the boost velocity of the laboratory through space"...

.

#### Mathematical derivation

The observational consequences of this effect can be derived using the equations
Friedmann-Robertson-Walker metric
The Friedmann–Lemaître–Robertson–Walker metric is an exact solution of Einstein's field equations of general relativity; it describes a homogeneous, isotropic expanding or contracting universe that may be simply connected or multiply connected...

from general relativity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

that describe a homogeneous and isotropic universe
Cosmological Principle
In modern physical cosmology, the cosmological principle is the working assumption that observers on Earth do not occupy an unusual or privileged location within the universe as a whole, judged as observers of the physical phenomena produced by uniform and universal laws of physics...

.

To derive the redshift effect, use the geodesic equation for a light wave, which is

where
• is the spacetime interval
• is the time interval
• is the spatial interval
• is the speed of light
• is the time-dependent cosmic scale factor
Scale factor (Universe)
The scale factor or cosmic scale factor parameter of the Friedmann equations is a function of time which represents the relative expansion of the universe. It is sometimes called the Robertson-Walker scale factor...

• is the curvature
Curvature
In mathematics, curvature refers to any of a number of loosely related concepts in different areas of geometry. Intuitively, curvature is the amount by which a geometric object deviates from being flat, or straight in the case of a line, but this is defined in different ways depending on the context...

per unit area.

For an observer observing the crest of a light wave at a position and time , the crest of the light wave was emitted at a time in the past and a distant position . Integrating over the path in both space and time that the light wave travels yields:

In general, the wavelength of light is not the same for the two positions and times considered due to the changing properties of the metric. When the wave was emitted, it had a wavelength . The next crest of the light wave was emitted at a time

The observer sees the next crest of the observed light wave with a wavelength to arrive at a time

Since the subsequent crest is again emitted from and is observed at , the following equation can be written:

The right-hand side of the two integral equations above are identical which means

or, alternatively,

For very small variations in time (over the period of one cycle of a light wave) the scale factor is essentially a constant ( today and previously). This yields

which can be rewritten as

Using the definition of redshift provided above, the equation

is obtained. In an expanding universe such as the one we inhabit, the scale factor is monotonically increasing
Monotonic function
In mathematics, a monotonic function is a function that preserves the given order. This concept first arose in calculus, and was later generalized to the more abstract setting of order theory....

as time passes, thus, z is positive and distant galaxies appear redshifted.

----

Using a model of the expansion of the universe, redshift can be related to the age of an observed object, the so-called cosmic time
Cosmic time
Cosmic time is the time coordinate commonly used in the Big Bang models of physical cosmology. It is defined for homogeneous, expanding universes as follows: Choose a time coordinate so that the universe has the same density everywhere at each moment in time Cosmic time (also known as time since...

–redshift relation
. Denote a density ratio as Ω0:

with ρcrit the critical density demarcating a universe that eventually crunches from one that simply expands. This density is about three hydrogen atoms per thousand liters of space. At large redshifts one finds:

where H0 = present-day Hubble constant, and z = redshift.

#### Distinguishing between cosmological and local effects

For cosmological redshifts of z < 0.01 additional Doppler redshifts and blueshifts due to the peculiar motions
Peculiar velocity
Peculiar motion or peculiar velocity refers to the true velocity of an object, relative to a rest frame.-Galactic astronomy:In galactic astronomy, the term peculiar motion refers to the motion of an object through space.Local objects are usually related in terms of proper motion and radial...

of the galaxies relative to one another cause a wide scatter
Variance
In probability theory and statistics, the variance is a measure of how far a set of numbers is spread out. It is one of several descriptors of a probability distribution, describing how far the numbers lie from the mean . In particular, the variance is one of the moments of a distribution...

from the standard Hubble Law. The resulting situation can be 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.

The redshifts of galaxies include both a component related to recessional velocity from expansion of the universe, and a component related to peculiar motion (Doppler shift). The redshift due to expansion of the universe depends upon the recessional velocity in a fashion determined by the cosmological model chosen to describe the expansion of the universe, which is very different from how Doppler redshift depends upon local velocity. Describing the cosmological expansion origin of redshift, cosmologist Edward Robert Harrison
Edward Robert Harrison
Edward R. Harrison was a British astronomer and cosmologist, who spent much of his career at the University of Massachusetts and University of Arizona...

said, “Light leaves a galaxy, which is stationary in its local region of space, and is eventually received by observers who are stationary in their own local region of space. Between the galaxy and the observer, light travels through vast regions of expanding space. As a result, all wavelengths of the light are stretched by the expansion of space. It is as simple as that.... Steven Weinberg
Steven Weinberg
Steven Weinberg is an American theoretical physicist and Nobel laureate in Physics for his contributions with Abdus Salam and Sheldon Glashow to the unification of the weak force and electromagnetic interaction between elementary particles....

clarified, "The increase of wavelength from emission to absorption of light does not depend on the rate of change of a(t) [here a(t) is the Robertson-Walker scale factor] at the times of emission or absorption, but on the increase of a(t) in the whole period from emission to absorption.”

Popular literature often uses the expression "Doppler redshift" instead of "cosmological redshift" to describe the redshift of galaxies dominated by the expansion of spacetime, but the cosmological redshift is not found using the relativistic Doppler equation which is instead characterized by special relativity
Special relativity
Special relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...

; thus v > c is impossible while, in contrast, v > c is possible for cosmological redshifts because the space which separates the objects (for example, 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 system
Coordinate system
In geometry, a coordinate system is a system which uses one or more numbers, or coordinates, to uniquely determine the position of a point or other geometric element. The order of the coordinates is significant and they are sometimes identified by their position in an ordered tuple and sometimes by...

s. Expressing this precisely requires working with the mathematics of the Friedmann-Robertson-Walker metric
Friedmann-Robertson-Walker metric
The Friedmann–Lemaître–Robertson–Walker metric is an exact solution of Einstein's field equations of general relativity; it describes a homogeneous, isotropic expanding or contracting universe that may be simply connected or multiply connected...

.

If the universe were contracting instead of expanding, we would see distant galaxies blueshifted by an amount proportional to their distance instead of redshifted.

### Gravitational redshift

In the theory of general relativity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

, there is time dilation within a gravitational well. This is known as the gravitational redshift
Gravitational redshift
In astrophysics, gravitational redshift or Einstein shift describes light or other forms of electromagnetic radiation of certain wavelengths that originate from a source that is in a region of a stronger gravitational field that appear to be of longer wavelength, or redshifted, when seen or...

or Einstein Shift. The theoretical derivation of this effect follows from the Schwarzschild solution of the Einstein equations
Einstein field equations
The Einstein field equations or Einstein's equations are a set of ten equations in Albert Einstein's general theory of relativity which describe the fundamental interaction of gravitation as a result of spacetime being curved by matter and energy...

which yields the following formula for redshift associated with a photon traveling in the gravitational field
Gravitational field
The gravitational field is a model used in physics to explain the existence of gravity. In its original concept, gravity was a force between point masses...

of an uncharged, nonrotating
Rotation
A rotation is a circular movement of an object around a center of rotation. A three-dimensional object rotates always around an imaginary line called a rotation axis. If the axis is within the body, and passes through its center of mass the body is said to rotate upon itself, or spin. A rotation...

, spherically symmetric mass:

where
• is the gravitational constant
Gravitational constant
The gravitational constant, denoted G, is an empirical physical constant involved in the calculation of the gravitational attraction between objects with mass. It appears in Newton's law of universal gravitation and in Einstein's theory of general relativity. It is also known as the universal...

,
• is the mass
Mass
Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...

of the object creating the gravitational field,
• is the radial coordinate of the source (which is analogous to the classical distance from the center of the object, but is actually a Schwarzschild coordinate
Schwarzschild coordinates
In the theory of Lorentzian manifolds, spherically symmetric spacetimes admit a family of nested round spheres. In such a spacetime, a particularly important kind of coordinate chart is the Schwarzschild chart, a kind of polar spherical coordinate chart on a static and spherically symmetric...

), and
• is the speed of light
Speed of light
The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...

.

This gravitational redshift result can be derived from the assumptions of special relativity
Special relativity
Special relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...

and the equivalence principle
Equivalence principle
In the physics of general relativity, the equivalence principle is any of several related concepts dealing with the equivalence of gravitational and inertial mass, and to Albert Einstein's assertion that the gravitational "force" as experienced locally while standing on a massive body is actually...

; the full theory of general relativity is not required.

The effect is very small but measurable on Earth using the Mössbauer effect
Mössbauer effect
The Mössbauer effect, or recoilless nuclear resonance fluorescence‎, is a physical phenomenon discovered by Rudolf Mössbauer in 1958. It involves the resonant and recoil-free emission and absorption of γ radiation by atomic nuclei bound in a solid...

and was first observed in the Pound-Rebka experiment
Pound-Rebka experiment
The Pound–Rebka experiment is a well known experiment to test Albert Einstein's theory of general relativity. It was proposed by Robert Pound and his graduate student Glen A. Rebka Jr. in 1959, and was the last of the classical tests of general relativity to be verified...

. However, it is significant near a black hole
Black hole
A black hole is a region of spacetime from which nothing, not even light, can escape. The theory of general relativity predicts that a sufficiently compact mass will deform spacetime to form a black hole. Around a black hole there is a mathematically defined surface called an event horizon that...

, and as an object approaches the event horizon
Event horizon
In general relativity, an event horizon is a boundary in spacetime beyond which events cannot affect an outside observer. In layman's terms it is defined as "the point of no return" i.e. the point at which the gravitational pull becomes so great as to make escape impossible. The most common case...

the red shift becomes infinite. It is also the dominant cause of large angular-scale temperature fluctuations in the cosmic microwave background radiation
In cosmology, cosmic microwave background radiation is thermal radiation filling the observable universe almost uniformly....

(see Sachs-Wolfe effect
Sachs-Wolfe effect
The Sachs–Wolfe effect, named after Rainer Kurt Sachs and Arthur Michael Wolfe, is a property of the cosmic microwave background radiation , in which photons from the CMB are gravitationally redshifted, causing the CMB spectrum to appear uneven...

).

## Observations in astronomy

The redshift observed in astronomy can be measured because the emission
Emission spectrum
The emission spectrum of a chemical element or chemical compound is the spectrum of frequencies of electromagnetic radiation emitted by the element's atoms or the compound's molecules when they are returned to a lower energy state....

and absorption spectra for atom
Atom
The atom is a basic unit of matter that consists of a dense central nucleus surrounded by a cloud of negatively charged electrons. The atomic nucleus contains a mix of positively charged protons and electrically neutral neutrons...

s are distinctive and well known, calibrated from spectroscopic experiments
Spectroscopy
Spectroscopy is the study of the interaction between matter and radiated energy. Historically, spectroscopy originated through the study of visible light dispersed according to its wavelength, e.g., by a prism. Later the concept was expanded greatly to comprise any interaction with radiative...

in laboratories
Laboratory
A laboratory is a facility that provides controlled conditions in which scientific research, experiments, and measurement may be performed. The title of laboratory is also used for certain other facilities where the processes or equipment used are similar to those in scientific 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. Although distant objects may be slightly blurred and lines broadened, it is by no more than can be explained by thermal or mechanical motion
Motion (physics)
In physics, motion is a change in position of an object with respect to time. Change in action is the result of an unbalanced force. Motion is typically described in terms of velocity, acceleration, displacement and time . An object's velocity cannot change unless it is acted upon by a force, as...

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 and explanations for redshift such as tired light
Tired light
Tired light is a class of hypothetical redshift mechanisms that was proposed as an alternative explanation for the redshift-distance relationship. These models have been proposed as alternatives to the metric expansion of space of which the Big Bang and the Steady State cosmologies are the most...

are not generally considered plausible.

Spectroscopy, as a measurement, is considerably more difficult than simple photometry
Photometry (astronomy)
Photometry is a technique of astronomy concerned with measuring the flux, or intensity of an astronomical object's electromagnetic radiation...

, which measures the brightness
Brightness
Brightness is an attribute of visual perception in which a source appears to be radiating or reflecting light. In other words, brightness is the perception elicited by the luminance of a visual target...

of astronomical objects through certain filter
Filter (optics)
Optical filters are devices which selectively transmit light of different wavelengths, usually implemented as plane glass or plastic devices in the optical path which are either dyed in the mass or have interference coatings....

s. When photometric data is all that is available (for example, the Hubble Deep Field
Hubble Deep Field
The Hubble Deep Field is an image of a small region in the constellation Ursa Major, constructed from a series of observations by the Hubble Space Telescope. It covers an area 2.5 arcminutes across, two parts in a million of the whole sky, which is equivalent in angular size to a 65 mm tennis...

and the Hubble Ultra Deep Field
Hubble Ultra Deep Field
The Hubble Ultra-Deep Field is an image of a small region of space in the constellation Fornax, composited from Hubble Space Telescope data accumulated over a period from September 24, 2003, through to January 16, 2004...

), astronomers rely on a technique for measuring photometric redshift
Photometric redshift
A photometric redshift is an estimate for the distance of an astronomical object, such as a galaxy or quasar. The technique uses photometry to determine the redshift, and hence, through Hubble's...

s. Due to the broad wavelength ranges in photometric filters and the necessary assumptions about the nature of the spectrum at the light-source, error
Observational error
Observational error is the difference between a measured value of quantity and its true value. In statistics, an error is not a "mistake". Variability is an inherent part of things being measured and of the measurement process.-Science and experiments:...

s for these sorts of measurements can range up to δz = 0.5, and are much less reliable than spectroscopic determinations. However, photometry does at least allow 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
Infrared
Infrared light is electromagnetic radiation with a wavelength longer than that of visible light, measured from the nominal edge of visible red light at 0.74 micrometres , and extending conventionally to 300 µm...

rather than at the yellow-green color associated with the peak of its blackbody spectrum, and the light intensity will be reduced in the filter by a factor of four, . Both the photon count rate and the photon energy are redshifted. (See K correction
K correction
K correction is a correction to an astronomical object's magnitude that allows a measurement of a quantity of light from an object at a redshift z to be converted to an equivalent measurement in the rest frame of the object. If one could measure all the light from an object at all wavelengths , a...

for more details on the photometric consequences of redshift.)

### Local observations

In nearby objects (within our Milky Way
Milky Way
The Milky Way is the galaxy that contains the Solar System. This name derives from its appearance as a dim un-resolved "milky" glowing band arching across the night sky...

galaxy) observed redshifts are almost always related to the line-of-sight
Line-of-sight propagation
Line-of-sight propagation refers to electro-magnetic radiation or acoustic wave propagation. Electromagnetic transmission includes light emissions traveling in a straight line...

velocities associated with the objects being observed. Observations of such redshifts and blueshifts have enabled astronomers to measure velocities
Velocity
In physics, velocity is speed in a given direction. Speed describes only how fast an object is moving, whereas velocity gives both the speed and direction of the object's motion. To have a constant velocity, an object must have a constant speed and motion in a constant direction. Constant ...

and parametrize the mass
Mass
Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...

es of the orbiting star
Star
A star is a massive, luminous sphere of plasma held together by gravity. At the end of its lifetime, a star can also contain a proportion of degenerate matter. The nearest star to Earth is the Sun, which is the source of most of the energy on Earth...

s in spectroscopic binaries, a method first employed in 1868 by British astronomer William Huggins
William Huggins
Sir William Huggins, OM, KCB, FRS was an English amateur astronomer best known for his pioneering work in astronomical spectroscopy.-Biography:...

. 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
Extrasolar planet
An extrasolar planet, or exoplanet, is a planet outside the Solar System. A total of such planets have been identified as of . It is now known that a substantial fraction of stars have planets, including perhaps half of all Sun-like stars...

around other stars and have even made very detailed differential measurements
Rossiter-McLaughlin effect
The Rossiter–McLaughlin effect is a spectroscopic phenomenon observed when either an eclipsing binary's secondary star or an extrasolar planet is seen to transit across the face of the primary or parent star. As the main star rotates on its axis, one quadrant of its photosphere will be seen to be...

of redshifts during planetary transits to determine precise orbital parameters. Finely detailed measurements of redshifts are used in helioseismology
Helioseismology
Helioseismology is the study of the propagation of wave oscillations, particularly acoustic pressure waves, in the Sun. Unlike seismic waves on Earth, solar waves have practically no shear component . Solar pressure waves are believed to be generated by the turbulence in the convection zone near...

to determine the precise movements of the photosphere
Photosphere
The photosphere of an astronomical object is the region from which externally received light originates. The term itself is derived from Ancient Greek roots, φῶς, φωτός/phos, photos meaning "light" and σφαῖρα/sphaira meaning "sphere", in reference to the fact that it is a spheric surface perceived...

of the Sun
Sun
The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...

. Redshifts have also been used to make the first measurements of the rotation rates of planet
Planet
A planet is a celestial body orbiting a star or stellar remnant that is massive enough to be rounded by its own gravity, is not massive enough to cause thermonuclear fusion, and has cleared its neighbouring region of planetesimals.The term planet is ancient, with ties to history, science,...

s, velocities of interstellar cloud
Interstellar cloud
Interstellar cloud is the generic name given to an accumulation of gas, plasma and dust in our and other galaxies. Put differently, an interstellar cloud is a denser-than-average region of the interstellar medium. Depending on the density, size and temperature of a given cloud, the hydrogen in it...

s, the rotation of galaxies, and the dynamics
Dynamics (mechanics)
In the field of physics, the study of the causes of motion and changes in motion is dynamics. In other words the study of forces and why objects are in motion. Dynamics includes the study of the effect of torques on motion...

of accretion onto neutron star
Neutron star
A neutron star is a type of stellar remnant that can result from the gravitational collapse of a massive star during a Type II, Type Ib or Type Ic supernova event. Such stars are composed almost entirely of neutrons, which are subatomic particles without electrical charge and with a slightly larger...

s and black hole
Black hole
A black hole is a region of spacetime from which nothing, not even light, can escape. The theory of general relativity predicts that a sufficiently compact mass will deform spacetime to form a black hole. Around a black hole there is a mathematically defined surface called an event horizon that...

s which exhibit both Doppler and gravitational redshifts. Additionally, the temperature
Temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...

s of various emitting and absorbing objects can be obtained by measuring Doppler broadening
In atomic physics, Doppler broadening is the broadening of spectral lines due to the Doppler effect caused by a distribution of velocities of atoms or molecules. Different velocities of the emitting particles result in different shifts, the cumulative effect of which is the line broadening.The...

— effectively redshifts and blueshifts over a single emission or absorption line. By measuring the broadening and shifts of the 21-centimeter hydrogen line
Hydrogen line
The hydrogen line, 21 centimeter line or HI line refers to the electromagnetic radiation spectral line that is created by a change in the energy state of neutral hydrogen atoms. This electromagnetic radiation is at the precise frequency of 1420.40575177 MHz, which is equivalent to the vacuum...

in different directions, astronomers have been able to measure the recessional velocities
Recessional velocity
Recessional Velocity is a term used to describe the rate at which an object is moving away, typically from Earth.-Application to Cosmology:This term is generally only used in reference to distant Galaxies. The most common reason for the use of this term is Hubble's Law, which states that the...

of interstellar gas, which in turn reveals the rotation curve of our Milky Way. Similar measurements have been performed on other galaxies, such as Andromeda. As a diagnostic tool, redshift measurements are one of the most important spectroscopic measurements
Astronomical spectroscopy
Astronomical spectroscopy is the technique of spectroscopy used in astronomy. The object of study is the spectrum of electromagnetic radiation, including visible light, which radiates from stars and other celestial objects...

### Extragalactic observations

The most distant objects exhibit larger redshifts corresponding to the Hubble flow
Hubble's law
Hubble's law is the name for the astronomical observation in physical cosmology that: all objects observed in deep space are found to have a doppler shift observable relative velocity to Earth, and to each other; and that this doppler-shift-measured velocity, of various galaxies receding from...

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
In cosmology, cosmic microwave background radiation is thermal radiation filling the observable universe almost uniformly....

; the numerical value of its redshift is about ( corresponds to present time), and it shows the state of the Universe
Universe
The Universe is commonly defined as the totality of everything that exists, including all matter and energy, the planets, stars, galaxies, and the contents of intergalactic space. Definitions and usage vary and similar terms include the cosmos, the world and nature...

about 13.7 billion years ago, and 379,000 years after the initial moments of the Big Bang
Big Bang
The Big Bang theory is the prevailing cosmological model that explains the early development of the Universe. According to the Big Bang theory, the Universe was once in an extremely hot and dense state which expanded rapidly. This rapid expansion caused the young Universe to cool and resulted in...

.

The luminous point-like cores of quasar
Quasar
A quasi-stellar radio source is a very energetic and distant active galactic nucleus. Quasars are extremely luminous and were first identified as being high redshift sources of electromagnetic energy, including radio waves and visible light, that were point-like, similar to stars, rather than...

s were the first "high-redshift" objects discovered before the improvement of telescopes allowed for the discovery of other high-redshift galaxies.

For galaxies more distant than the Local Group
Local Group
The Local Group is the group of galaxies that includes Earth's galaxy, the Milky Way. The group comprises more than 30 galaxies , with its gravitational center located somewhere between the Milky Way and the Andromeda Galaxy...

and the nearby Virgo Cluster
Virgo Cluster
The Virgo Cluster is a cluster of galaxies whose center is 53.8 ± 0.3 Mly away in the constellation Virgo. Comprising approximately 1300 member galaxies, the cluster forms the heart of the larger Local Supercluster, of which the Local Group is an outlying member...

, but within a thousand megaparsecs
Parsec
The parsec is a unit of length used in astronomy. It is about 3.26 light-years, or just under 31 trillion kilometres ....

or so, the redshift is approximately proportional to the galaxy's distance. This correlation was first observed by Edwin Hubble
Edwin Hubble
Edwin Powell Hubble was an American astronomer who profoundly changed the understanding of the universe by confirming the existence of galaxies other than the Milky Way - our own galaxy...

and has come to be known as Hubble's law
Hubble's law
Hubble's law is the name for the astronomical observation in physical cosmology that: all objects observed in deep space are found to have a doppler shift observable relative velocity to Earth, and to each other; and that this doppler-shift-measured velocity, of various galaxies receding from...

. Vesto Slipher
Vesto Slipher
Vesto Melvin Slipher was an American astronomer. His brother Earl C. Slipher was also an astronomer and a director at the Lowell Observatory....

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
The cosmic distance ladder is the succession of methods by which astronomers determine the distances to celestial objects. A real direct distance measurement of an astronomical object is possible only for those objects that are "close enough" to Earth...

to formulate his Law. In the widely accepted cosmological model based on general relativity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

, 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
Hubble's law
Hubble's law is the name for the astronomical observation in physical cosmology that: all objects observed in deep space are found to have a doppler shift observable relative velocity to Earth, and to each other; and that this doppler-shift-measured velocity, of various galaxies receding from...

follows in part from the Copernican principle
Copernican principle
In physical cosmology, the Copernican principle, named after Nicolaus Copernicus, states that the Earth is not in a central, specially favored position. More recently, the principle has been generalized to the relativistic concept that humans are not privileged observers of the universe...

. Because it is usually not known how luminous
Luminosity
Luminosity is a measurement of brightness.-In photometry and color imaging:In photometry, luminosity is sometimes incorrectly used to refer to luminance, which is the density of luminous intensity in a given direction. The SI unit for luminance is candela per square metre.The luminosity function...

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
Gravitation
Gravitation, or gravity, is a natural phenomenon by which physical bodies attract with a force proportional to their mass. Gravitation is most familiar as the agent that gives weight to objects with mass and causes them to fall to the ground when dropped...

of galaxies with each other and clusters cause a significant scatter
Variance
In probability theory and statistics, the variance is a measure of how far a set of numbers is spread out. It is one of several descriptors of a probability distribution, describing how far the numbers lie from the mean . In particular, the variance is one of the moments of a distribution...

in the normal plot of the Hubble diagram. The peculiar velocities
Peculiar velocity
Peculiar motion or peculiar velocity refers to the true velocity of an object, relative to a rest frame.-Galactic astronomy:In galactic astronomy, the term peculiar motion refers to the motion of an object through space.Local objects are usually related in terms of proper motion and radial...

associated with galaxies superimpose a rough trace of the mass
Mass
Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...

of virialized objects in the universe. This effect leads to such phenomena as nearby galaxies (such as the Andromeda Galaxy
Andromeda Galaxy
The Andromeda Galaxy is a spiral galaxy approximately 2.5 million light-years from Earth in the constellation Andromeda. It is also known as Messier 31, M31, or NGC 224, and is often referred to as the Great Andromeda Nebula in older texts. Andromeda is the nearest spiral galaxy to the...

) exhibiting blueshifts as we fall towards a common barycenter
Barycentric coordinates (astronomy)
In astronomy, barycentric coordinates are non-rotating coordinates with origin at the center of mass of two or more bodies.The barycenter is the point between two objects where they balance each other. For example, it is the center of mass where two or more celestial bodies orbit each other...

, and redshift maps of clusters showing a Fingers of God
Fingers of God
Fingers of God is an effect in observational cosmology that causes clusters of galaxies to be elongated in redshift space, with an axis of elongation pointed toward the observer. It is caused by a Doppler shift associated with the peculiar velocities of galaxies in a cluster...

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
Mass to light ratio
In astrophysics and physical cosmology the mass to light ratio, normally designated with the symbol \Upsilon is the quotient between the total mass of a spatial volume and its luminosity...

(the ratio of a galaxy's mass in solar masses to its brightness in solar luminosities), an important tool for measuring dark matter
Dark matter
In astronomy and cosmology, dark matter is matter that neither emits nor scatters light or other electromagnetic radiation, and so cannot be directly detected via optical or radio astronomy...

.

The Hubble law's linear relationship between distance and redshift assumes that the rate of expansion of the universe is constant. However, when the universe was much younger, the expansion rate, and thus the Hubble "constant", was larger than it is today. For more distant galaxies, then, whose light has been travelling to us for much longer times, the approximation of constant expansion rate fails, and the Hubble law becomes a non-linear integral relationship and dependent on the history of the expansion rate since the emission of the light from the galaxy in question. Observations of the redshift-distance relationship can be used, then, to determine the expansion history of the universe and thus the matter and energy content.

While it was long believed that the expansion rate has been continuously decreasing since the Big Bang, recent observations of the redshift-distance relationship using Type Ia supernova
Type Ia supernova
A Type Ia supernova is a sub-category of supernovae, which in turn are a sub-category of cataclysmic variable stars, that results from the violent explosion of a white dwarf star. A white dwarf is the remnant of a star that has completed its normal life cycle and has ceased nuclear fusion...

e have suggested that in comparatively recent times the expansion rate of the universe has begun to accelerate
Accelerating universe
The accelerating universe is the observation that the universe appears to be expanding at an increasing rate, which in formal terms means that the cosmic scale factor a has a positive second derivative, implying that the velocity at which a given galaxy is receding from us should be continually...

.

### Highest redshifts

Currently, the objects with the highest known redshifts are galaxies and the objects producing gamma ray bursts. The most reliable redshifts are from spectroscopic data, and the highest confirmed spectroscopic redshift of a galaxy is that of
UDFy-38135539
UDFy-38135539
UDFy-38135539 is the Hubble Ultra Deep Field identifier for a galaxy which has been calculated to have a light travel time of 13.1 billion years with a present comoving distance of around 30 billion light-years...

at a redshift of , corresponding to just 600 million years after the Big Bang.
The previous record was held by
IOK-1
IOK-1
IOK-1 is a distant galaxy in Coma Berenices. When discovered in 2006, it was the oldest and most distant galaxy ever found, at redshift 6.96....

, at a redshift , corresponding to just 750 million years after the Big Bang. Slightly less reliable are Lyman-break
Lyman-alpha forest
In astronomical spectroscopy, the Lyman-alpha forest is the sum of absorption lines arising from the Lyman-alpha transition of the neutral hydrogen in the spectra of distant galaxies and quasars....

redshifts, the highest of which is the lensed galaxy A1689-zD1 at a redshift and the next highest being . The most distant observed gamma ray burst
Gamma ray burst
Gamma-ray bursts are flashes of gamma rays associated with extremely energetic explosions that have been observed in distant galaxies. They are the most luminous electromagnetic events known to occur in the universe. Bursts can last from ten milliseconds to several minutes, although a typical...

was GRB 090423
GRB 090423
GRB 090423 is a gamma-ray burst detected by the Swift Gamma-Ray Burst Mission on April 23, 2009 at 07:55:19 UTC. The afterglow of GRB 090423 was detected in the infrared, and allowed astronomers to determine that the redshift of GRB 090423 is z = 8.2, which makes GRB 090423 the second...

, which had a redshift of . The most distant known quasar, ULAS J1120+0641
ULAS J1120+0641
ULAS J1120+0641 is a quasar, the discovery of which was reported on 29 June 2011. , it is the most distant known quasar, and it was the first quasar discovered beyond a redshift of 7. Various news reports, including those provided by the Associated Press, have stated that it is the brightest object...

, is at . The highest known redshift radio galaxy (TN J0924-2201) is at a redshift and the highest known redshift molecular material is the detection of emission from the CO molecule from the quasar SDSS J1148+5251 at

Extremely red objects (EROs) are astronomical sources of radiation that radiate energy in the red and near infrared part of the electromagnetic spectrum. These may be starburst galaxies that have a high redshift accompanied by reddening from intervening dust, or they could be highly redshifted elliptical galaxies with an older (and therefore redder) stellar population. Objects that are even redder than EROs are termed hyper extremely red objects (HEROs).

The cosmic microwave background has a redshift of , corresponding to an age of approximately 379,000 years after the Big Bang and a current comoving distance
Comoving distance
In standard cosmology, comoving distance and proper distance are two closely related distance measures used by cosmologists to define distances between objects...

of more than 46 billion light years. The yet-to-be-observed first light from the oldest Population III stars, not long after atoms first formed and the CMB ceased to be absorbed almost completely, may have redshifts in the range of . Other high-redshift events predicted by physics but not presently observable are the cosmic neutrino background
Cosmic neutrino background
The cosmic neutrino background is the universe's background particle radiation composed of neutrinos.Like the cosmic microwave background radiation , the CνB is a relic of the big bang, and while the CMB dates from when the universe was 379,000 years old, the CνB decoupled from matter when the...

from about two seconds after the Big Bang (and a redshift in excess of ) and the cosmic gravitational wave background
Cosmic gravitational wave background
The cosmic gravitational wave background is a relic of the Cosmic inflation that can be measured directly or indirectly by examining the polarization of the Cosmic microwave background radiation...

emitted directly from inflation at a redshift in excess of .

### Redshift surveys

Telescope
A telescope is an instrument that aids in the observation of remote objects by collecting electromagnetic radiation . The first known practical telescopes were invented in the Netherlands at the beginning of the 1600s , using glass lenses...

s and improvements in spectroscopes
Astronomical spectroscopy
Astronomical spectroscopy is the technique of spectroscopy used in astronomy. The object of study is the spectrum of electromagnetic radiation, including visible light, which radiates from stars and other celestial objects...

, 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
Great Wall (astronomy)
The Great Wall , sometimes specifically referred to as the CfA2 Great Wall, is one of the largest known super-structures in the Universe...

, a vast supercluster
Supercluster
Superclusters are large groups of smaller galaxy groups and clusters and are among the largest known structures of the cosmos. They are so large that they are not gravitationally bound and, consequently, partake in the Hubble expansion.-Existence:...

of galaxies over 500 million light-year
Light-year
A light-year, also light year or lightyear is a unit of length, equal to just under 10 trillion kilometres...

s wide, provides a dramatic example of a large-scale structure that redshift surveys can detect.

The first redshift survey was the CfA Redshift Survey
CfA Redshift Survey
The Center for Astrophysics Redshift Survey was the first attempt to map the large-scale structure of the universe. It began in 1977 with the initial data collection completed in 1982...

, started in 1977 with the initial data collection completed in 1982. More recently, the 2dF Galaxy Redshift Survey
2dF Galaxy Redshift Survey
In astronomy, the 2dF Galaxy Redshift Survey , 2dF or 2dFGRS is a redshift survey conducted by the Anglo-Australian Observatory with the 3.9m Anglo-Australian Telescope between 1997 and 11 April 2002. The data from this survey were made public on 30 June 2003...

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
Data set
A data set is a collection of data, usually presented in tabular form. Each column represents a particular variable. Each row corresponds to a given member of the data set in question. Its values for each of the variables, such as height and weight of an object or values of random numbers. Each...

was released 30 June 2003. (In addition to mapping large-scale patterns of galaxies, 2dF established an upper limit on neutrino
Neutrino
A neutrino is an electrically neutral, weakly interacting elementary subatomic particle with a half-integer spin, chirality and a disputed but small non-zero mass. It is able to pass through ordinary matter almost unaffected...

mass.) Another notable investigation, the Sloan Digital Sky Survey
Sloan Digital Sky Survey
The Sloan Digital Sky Survey or SDSS is a major multi-filter 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 was named after the Alfred P...

(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 quasar
Quasar
A quasi-stellar radio source is a very energetic and distant active galactic nucleus. Quasars are extremely luminous and were first identified as being high redshift sources of electromagnetic energy, including radio waves and visible light, that were point-like, similar to stars, rather than...

s beyond z = 6. The DEEP2 Redshift Survey
DEEP2 Redshift Survey
The DEEP2 Survey or DEEP2 is a Redshift survey of the Redshift~1 universe. It uses the Keck telescopes to measure the spectra and hence redshifts of approximately 60,000 galaxies....

uses the Keck telescopes
Keck telescopes
The W. M. Keck Observatory is a two-telescope astronomical observatory at an elevation of near the summit of Mauna Kea in Hawai'i. The primary mirrors of each of the two telescopes are in diameter, making them the second largest optical telescopes in the world, slightly behind the Gran Telescopio...

with the new "DEIMOS" spectrograph
Spectrograph
A spectrograph is an instrument that separates an incoming wave into a frequency spectrum. There are several kinds of machines referred to as spectrographs, depending on the precise nature of the waves...

; 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
Radiative transfer is the physical phenomenon of energy transfer in the form of electromagnetic radiation. The propagation of radiation through a medium is affected by absorption, emission and scattering processes. The equation of radiative transfer describes these interactions mathematically...

and physical optics
Physical optics
In physics, physical optics, or wave optics, is the branch of optics which studies interference, diffraction, polarization, and other phenomena for which the ray approximation of geometric optics is not valid...

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 such physical phenomena as coherence effects
Wolf effect
The Wolf Effect is a frequency shift in the electromagnetic spectrum.The phenomenon occurs in several closely related phenomena in radiation physics, with analogous effects occurring in the scattering of light. It was first predicted by Emil Wolf in 1987 and subsequently confirmed in the...

or the scattering
Scattering
Scattering is a general physical process where some forms of radiation, such as light, sound, or moving particles, are forced to deviate from a straight trajectory by one or more localized non-uniformities in the medium through which they pass. In conventional use, this also includes deviation of...

Electromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space...

whether from charged
Electric charge
Electric charge is a physical property of matter that causes it to experience a force when near other electrically charged matter. Electric charge comes in two types, called positive and negative. Two positively charged substances, or objects, experience a mutual repulsive force, as do two...

elementary particle
Elementary particle
In particle physics, an elementary particle or fundamental particle is a particle not known to have substructure; that is, it is not known to be made up of smaller particles. If an elementary particle truly has no substructure, then it is one of the basic building blocks of the universe from which...

s, from particulates, or from fluctuations of the index of refraction in a dielectric medium as occurs in the radio phenomenon of radio whistlers
A whistler is a very low frequency electromagnetic wave which can be generated, for example, by lightning. Frequencies of terrestrial whistlers are 1 to 30 kHz, with maximum usually at 3 to 5 kHz. Although they are electromagnetic waves, they occur at audio frequencies, and can be...

. While such phenomena are sometimes referred to as "redshifts" and "blueshifts", 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
Entropy
Entropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...

results in the predominance of many low-energy
Energy
In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...

photons over few high-energy ones (while conserving total energy
Conservation of energy
The nineteenth century law of conservation of energy is a law of physics. It states that the total amount of energy in an isolated system remains constant over time. The total energy is said to be conserved over time...

). 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
Function (mathematics)
In mathematics, a function associates one quantity, the argument of the function, also known as the input, with another quantity, the value of the function, also known as the output. A function assigns exactly one output to each input. The argument and the value may be real numbers, but they can...

of wavelength. Furthermore, scattering from random
Randomness
Randomness has somewhat differing meanings as used in various fields. It also has common meanings which are connected to the notion of predictability of events....

media
Matter
Matter is a general term for the substance of which all physical objects consist. Typically, matter includes atoms and other particles which have mass. A common way of defining matter is as anything that has mass and occupies volume...

generally occurs at many angle
Angle
In geometry, an angle is the figure formed by two rays sharing a common endpoint, called the vertex of the angle.Angles are usually presumed to be in a Euclidean plane with the circle taken for standard with regard to direction. In fact, an angle is frequently viewed as a measure of an circular arc...

s, and z is a function of the scattering angle. If multiple scattering occurs, or the scattering particles have relative motion, then there is generally distortion of spectral line
Spectral line
A spectral line is a dark or bright line in an otherwise uniform and continuous spectrum, resulting from a deficiency or excess of photons in a narrow frequency range, compared with the nearby frequencies.- Types of line spectra :...

s as well.

In interstellar astronomy
Interstellar medium
In astronomy, the interstellar medium is the matter that exists in the space between the star systems in a galaxy. This matter includes gas in ionic, atomic, and molecular form, dust, and cosmic rays. It fills interstellar space and blends smoothly into the surrounding intergalactic space...

, visible spectra
Visible spectrum
The visible spectrum is the portion of the electromagnetic spectrum that is visible to the human eye. Electromagnetic radiation in this range of wavelengths is called visible light or simply light. A typical human eye will respond to wavelengths from about 390 to 750 nm. In terms of...

can appear red
Red
Red is any of a number of similar colors evoked by light consisting predominantly of the longest wavelengths of light discernible by the human eye, in the wavelength range of roughly 630–740 nm. Longer wavelengths than this are called infrared , and cannot be seen by the naked eye...

der due to scattering processes in a phenomenon referred to as interstellar reddening — similarly Rayleigh scattering
Rayleigh scattering
Rayleigh scattering, named after the British physicist Lord Rayleigh, is the elastic scattering of light or other electromagnetic radiation by particles much smaller than the wavelength of the light. The particles may be individual atoms or molecules. It can occur when light travels through...

causes the atmospheric
Earth's atmosphere
The atmosphere of Earth is a layer of gases surrounding the planet Earth that is retained by Earth's gravity. The atmosphere protects life on Earth by absorbing ultraviolet solar radiation, warming the surface through heat retention , and reducing temperature extremes between day and night...

reddening of the Sun
Sun
The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...

seen in the sunrise
Sunrise
Sunrise is the instant at which the upper edge of the Sun appears above the horizon in the east. Sunrise should not be confused with dawn, which is the point at which the sky begins to lighten, some time before the sun itself appears, ending twilight...

or sunset
Sunset
Sunset or sundown is the daily disappearance of the Sun below the horizon in the west as a result of Earth's rotation.The time of sunset is defined in astronomy as the moment the trailing edge of the Sun's disk disappears below the horizon in the west...

and causes the rest of the sky
Sky
The sky is the part of the atmosphere or outer space visible from the surface of any astronomical object. It is difficult to define precisely for several reasons. During daylight, the sky of Earth has the appearance of a pale blue surface because the air scatters the sunlight. The sky is sometimes...

to have a blue
Blue
Blue is a colour, the perception of which is evoked by light having a spectrum dominated by energy with a wavelength of roughly 440–490 nm. It is considered one of the additive primary colours. On the HSV Colour Wheel, the complement of blue is yellow; that is, a colour corresponding to an equal...

color. This phenomenon is distinct from redshifting because the spectroscopic lines
Atomic spectral line
In physics, atomic spectral lines are of two types:* An emission line is formed when an electron makes a transition from a particular discrete energy level of an atom, to a lower energy state, emitting a photon of a particular energy and wavelength...

are not shifted to other wavelengths in reddened objects and there is an additional dimming
Extinction (astronomy)
Extinction is a term used in astronomy to describe the absorption and scattering of electromagnetic radiation by matter between an emitting astronomical object and the observer. Interstellar extinction—also called Galactic extinction, when it occurs in the Milky Way—was first...

and distortion associated with the phenomenon due to photons being scattered in and out of the line-of-sight
Line-of-sight propagation
Line-of-sight propagation refers to electro-magnetic radiation or acoustic wave propagation. Electromagnetic transmission includes light emissions traveling in a straight line...

.

For a list of scattering processes, see Scattering
Scattering
Scattering is a general physical process where some forms of radiation, such as light, sound, or moving particles, are forced to deviate from a straight trajectory by one or more localized non-uniformities in the medium through which they pass. In conventional use, this also includes deviation of...

.

### Articles

• Odenwald, S. & Fienberg, RT. 1993; "Galaxy Redshifts Reconsidered" in Sky & Telescope Feb. 2003; pp31–35 (This article is 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
Scientific American
Scientific American is a popular science magazine. It is notable for its long history of presenting science monthly to an educated but not necessarily scientific public, through its careful attention to the clarity of its text as well as the quality of its specially commissioned color graphics...