NationMaster - Encyclopedia: Relativistic Doppler effect

The relativistic Doppler effect is the change in frequency (and wavelength) of light, caused by the relative motion of the source and the observer (as in the classical Doppler effect), when taking into account effects of the special theory of relativity. Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ... For other uses, see Frequency (disambiguation). ... For other uses, see Wavelength (disambiguation). ... For other uses, see Light (disambiguation). ... A source of waves moving to the left. ... For a less technical and generally accessible introduction to the topic, see Introduction to special relativity. ...

The relativistic Doppler effect is different from the non-relativistic Doppler effect as the equations include the time dilation effect of special relativity. They describe the total difference in observed frequencies and possess the required Lorentz symmetry. A source of waves moving to the left. ... Time dilation is the phenomenon whereby an observer finds that anothers clock which is physically identical to their own is ticking at a slower rate as measured by their own clock. ... For a less technical and generally accessible introduction to the topic, see Introduction to special relativity. ... In physics, Lorentz symmetry is the invariance of physical laws under the Lorentz transformations. ...

1 The mechanism (a simple case)
2 General results
3 See also
4 External links

The mechanism (a simple case)

Assume the observer and the source are moving away from each other with a relative velocity $v,$ . Let us consider the problem from the reference frame of the source. A frame of reference in physics is a set of axes which enable an observer to measure the aspect, position and motion of all points in a system relative to the reference frame. ...

Suppose one wavefront arrives at the observer. The next wavefront is then at a distance $lambda=c/f_e,$ away from him (where $lambda,$ is the wavelength, $f_e,$ is the frequency of the wave the source emitted, and $c,$ is the speed of light). Since the wavefront moves with velocity $c,$ and the observer escapes with velocity $v,$ , the time observed between crests is In optics, a wavefront is the locus (a line or surface in an electromagnetic wave) of points having the same phase. ... For other uses, see Wavelength (disambiguation). ... For other uses, see Frequency (disambiguation). ... The speed of light in a vacuum is an important physical constant denoted by the letter c for constant or the Latin word celeritas meaning swiftness.[1] It is the speed of all electromagnetic radiation, including visible light, in a vacuum. ...

$t = frac{lambda}{c-v} = frac{1}{(1-v/c)f_e}.$

However, due to the relativistic time dilation, the observer will measure this time to be Time dilation is the phenomenon whereby an observer finds that anothers clock which is physically identical to their own is ticking at a slower rate as measured by their own clock. ...

$t_o = frac{t}{gamma} = frac{1}{gamma(1-v/c)f_e},$

where $gamma = 1/sqrt{1-v^2/c^2}$ , so the corresponding frequency is

$f_o = frac{1}{t_o} = gamma (1-v/c) f_e = sqrt{frac{1-v/c}{1+v/c}},f_e.$

The ratio $f_e / f_o,$ is called the Doppler factor of the source relative to the observer. (This terminology is particularly prevalent in the subject of astrophysics: see relativistic beaming.) Spiral Galaxy ESO 269-57 Astrophysics is the branch of astronomy that deals with the physics of the universe, including the physical properties (luminosity, density, temperature, and chemical composition) of celestial objects such as stars, galaxies, and the interstellar medium, as well as their interactions. ... Relativistic beaming is the process by which the relativistic effect modifies the apparent luminosity of a relativistic jet. ...

General results

For motion along the line of sight

If the observer and the source are moving directly away from each other with velocity $v,$ , the observed frequency $f_o,$ is different from the frequency of the source $f_e,$ as For other uses, see Frequency (disambiguation). ...

$f_o = sqrt{frac{1-v/c}{1+v/c}},f_e,$

where $c,$ is the speed of light. The speed of light in a vacuum is an important physical constant denoted by the letter c for constant or the Latin word celeritas meaning swiftness.[1] It is the speed of all electromagnetic radiation, including visible light, in a vacuum. ...

The corresponding wavelengths are related by For other uses, see Wavelength (disambiguation). ...

$lambda_o = sqrt{frac{1+v/c}{1-v/c}},lambda_e,$

and the resulting redshift $z,$ can be written as This article is about the physical phenomenon. ...

$z + 1 = frac{lambda_o}{lambda_e} = sqrt{frac{1+v/c}{1-v/c}}.$

In the non-relativistic limit—i.e. when $v ll c,$ —the approximate expressions are

$frac{Delta f}{f} simeq -frac{v}{c}; qquad frac{Delta lambda}{lambda} simeq frac{v}{c}; qquad z simeq frac{v}{c}.$

Note: In all the expressions in this section it is assumed that the observer and the source are moving away from each other. If they are moving towards each other, $v,$ should be taken negative.

For motion in an arbitrary direction

If, in the reference frame of the observer, the source is moving away with velocity $v,$ at an angle $theta_o,$ relative to the direction from the observer to the source (at the time when the light is emitted), the frequency changes as A frame of reference in physics is a set of axes which enable an observer to measure the aspect, position and motion of all points in a system relative to the reference frame. ...

$f_o = frac{f_s}{gammaleft(1+frac{vcostheta_o}{c}right)},$ (1)

where $gamma = frac{1}{sqrt{1-v^2/c^2}}.$

In the particular case when $costheta_o=0 ,$ one obtains the transverse Doppler effect In special relativity, the transverse Doppler effect is the nominal redshift component associated with transverse (i. ...

$f_o=frac {f_s} {gamma} ,$ . (2)

However, if the angle $theta_s,$ is measured in the reference frame of the source (at the time when the light is received by the observer), the expression is A frame of reference in physics is a set of axes which enable an observer to measure the aspect, position and motion of all points in a system relative to the reference frame. ...

$f_o = gammaleft(1-frac{vcostheta_s}{c}right)f_s.$ (3)

$cos theta_o ,$ and $cos theta_s ,$ are tied to each other via the relativistic aberration formula: It has been suggested that this article or section be merged into relativistic aberration. ...

$cos theta_o=frac{cos theta_s-frac{v}{c}}{1-frac{v}{c} cos theta_s} ,.$ (4)

The relativistic aberration formula explains why, for $cos theta_s =0 ,$ one obtains a second formula for the transverse Doppler effect:

$f_o=f_s gamma ,.$ (5)

(5) is obtained easily by substituting $cos theta_o =-frac {v}{c} ,$ into (1). Turns out that (5) is more useful than (2) being the form used routinely in the Ives-Stilwell experiment.

In the non-relativistic limit, both formulæ become It has been suggested that this article or section be merged into relativistic aberration. ... In special relativity, the transverse Doppler effect is the nominal redshift component associated with transverse (i. ... The Ives-Stilwell experiment exploits the Transverse Doppler effect (TDE) described by Albert Einstein in his 1905 paper. ...

$frac{Delta f}{f} simeq -frac{vcostheta}{c}.$

Visualization

Diagram 1. Demonstration of aberration of light and relativistic Doppler effect.

In diagram 1, the blue point represents the observer. The x,y-plane is represented by yellow graph paper. As the observer accelerates, he sees the graph paper change colors. Also he sees the distortion of the x,y-grid due to the aberration of light. The black vertical line is the y-axis. The observer accelerates along the x-axis. If the observer looks to the left, (behind him) the lines look closer to him, and since he is accelerating away from the left side, the left side looks red to him. (redshift) When he looks to the right (in front of him) because he is moving towards the right side, he sees the right side as green, blue, and purple, respectively as he accelerates. (blueshift) Note that the distorted grid is just the observer's perspective, it is all still a consistent yellow graph, but looks more colored and distorted as the observer changes speed.
Image File history File links No higher resolution available. ... The aberration of light (also referred to as astronomical aberration or stellar aberration) is an astronomical phenomenon which produces an apparent motion of celestial objects. ... The aberration of light (also referred to as astronomical aberration or stellar aberration) is an astronomical phenomenon which produces an apparent motion of celestial objects. ... This article is about the physical phenomenon. ... Blue shift is the opposite of redshift, the latter being much more noted due to its importance to modern astronomy. ...

External links

Warp Special Relativity Simulator Computer program demonstrating the relativistic doppler effect.
[1] Presentation of the Guido Saathoff modern reenactment of the Ives-Stilwell experiment
The Doppler Effect at MathPages

Categories: Special relativity | Doppler effects

Results from FactBites:

Doppler effect - Wikipedia, the free encyclopedia (1485 words)
	The Doppler effect, named after Christian Andreas Doppler, is the apparent change in frequency and wavelength of a wave that is perceived by an observer moving relative to the source of the waves.
	The use of the Doppler effect for light in astronomy depends on the fact that the spectra of stars are not continuous.
	Another use of the Doppler effect which is found mostly in astronomy, is the estimation of the temperature of a gas which is emitting a spectral line.

Article about "Doppler effect" in the English Wikipedia on 24-Apr-2004 (981 words)
	The Doppler effect is the apparent change in frequency or wavelength of a wave that is perceived by an observer moving relative to the source of the waves.
	The total Doppler effect may therefore result from both motion of the source and motion of the observer.
	It has been used to measure the speed at which stars and galaxies are approaching or receding from us, to detect that an apparently single star is, in fact, a close binary and even to measure the speed of rotation of stars and galaxies.

More results at FactBites »

COMMENTARY

Share your thoughts, questions and commentary here

Want to know more?
Search encyclopedia, statistics and forums:

Feeds | Contact
The Wikipedia article included on this page is licensed under the GFDL.
Images may be subject to relevant owners' copyright.
All other elements are (c) copyright NationMaster.com 2003-5. All Rights Reserved.
Usage implies agreement with terms.

Contents

The mechanism (a simple case) GA_googleFillSlot("encyclopedia_square");