Editing Redshift (section)

===Doppler effect===
{{Main|Doppler effect|Relativistic Doppler effect}}
[[Image:Suzredshift.gif|thumb|[[Doppler effect]], yellow (~575 [[Nanometre|nm]] wavelength) ball appears greenish (blueshift to ~565 nm wavelength) approaching observer, turns [[Orange (colour)|orange]] (redshift to ~585 nm wavelength) as it passes, and returns to yellow when motion stops. To observe such a change in color, the object would have to be traveling at approximately 5,200 [[Metre per second|km/s]], or about 32 times faster than the speed record for the [[Parker Solar Probe|fastest space probe]].]]
[[File:Redshift blueshift.svg|thumb|Redshift and blueshift]]

If a source of the light is moving away from an observer, then redshift ({{math|''z'' > 0}}) occurs; if the source moves towards the observer, then [[blueshift]] ({{math|''z'' < 0}}) occurs. This is true for all electromagnetic waves and is explained by the [[Doppler effect]]. Consequently, this type of redshift is called the ''Doppler redshift''. If the source moves away from the observer with [[velocity]] {{math|''v''}}, which is much less than the speed of light ({{math|''v'' ≪ ''c''}}), the redshift is given by

:<math>z \approx \frac{v}{c}</math>   (since <math>\gamma \approx 1</math>)

where {{math|''c''}} is the [[speed of light]]. In the classical Doppler effect, the frequency of the source is not modified, but the recessional motion causes the illusion of a lower frequency.

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

:<math>1 + z = \left(1 + \frac{v}{c}\right) \gamma.</math>

This phenomenon was first observed in a 1938 experiment performed by Herbert E. Ives and G.R. Stilwell, called the [[Ives–Stilwell experiment]].<ref>{{cite journal | last1 = Ives | first1 = H. | last2 = Stilwell | first2 = G. | year = 1938 | title = An Experimental study of the rate of a moving atomic clock | journal = Journal of the Optical Society of America | volume = 28 | issue = 7| pages = 215–226 | doi=10.1364/josa.28.000215 | bibcode = 1938JOSA...28..215I}}</ref>

Since the Lorentz factor is dependent only on the [[magnitude (mathematics)|magnitude]] of the velocity, this causes the redshift associated with the relativistic correction to be independent of the orientation of the source movement. In contrast, the classical part of the formula is dependent on the [[scalar resolute|projection]] of the movement of the source into the [[Line-of-sight propagation|line-of-sight]] which yields different results for different orientations. If {{math|''θ''}} is the angle between the direction of relative motion and the direction of emission in the observer's frame<ref>{{cite book|last=Freund|first=Jurgen|title=Special Relativity for Beginners|date=2008|publisher=World Scientific|page=120|isbn=978-981-277-160-5}}</ref> (zero angle is directly away from the observer), the full form for the relativistic Doppler effect becomes:

:<math>1+ z = \frac{1 + v \cos (\theta)/c}{\sqrt{1-v^2/c^2}}</math>

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

:<math>1 + z = \sqrt{\frac{1+v/c}{1-v/c}}</math>

For the special case that the light is moving at [[right angle]] ({{math|''θ'' {{=}} 90°}}) to the direction of relative motion in the observer's frame,<ref>{{cite book|last=Ditchburn|first=R. |title=Light|date=1961|publisher=Dover|page=329|isbn=978-0-12-218101-6}}</ref> the relativistic redshift is known as the [[Relativistic Doppler effect|transverse redshift]], and a redshift:

:<math>1 + z = \frac{1}{\sqrt{1-v^2/c^2}}</math>

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.<ref>
See "[http://www.physics.uq.edu.au/people/ross/phys2100/doppler.htm Photons, Relativity, Doppler shift] {{Webarchive|url=https://web.archive.org/web/20060827063802/http://www.physics.uq.edu.au/people/ross/phys2100/doppler.htm |date=2006-08-27 }} " at the University of Queensland
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