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File:Superluminalmotion.gif
In astronomy, superluminal motion is the apparently faster-than-light motion seen in someradio galaxies, quasars and recently also in some galactic sources called microquasars. All of these sources are thought to contain a black hole, responsible for the ejection of mass at high velocities. When first observed in the early 1970s, superluminal motion was taken to be a piece of evidence against quasars having cosmological distances. Although a few astrophysicists still argue in favor of this view, most believe that apparent velocities greater than the velocity of light are optical illusions and involve no physics incompatible with the theory of special relativity. ==Explanation==This phenomenon is caused because the jets are travelling very near the speed of light and at a very small angle towards the observer. Because at every point of their path the high-velocity jets are emitting light, the light they emit does not approach the observer much more quickly than the jet itself. To be more clear, the jet is essentially "chasing" the light it emits. This causes the light emitted over hundreds of years of travel to not  have hundreds of lightyears of distance between it, the light thus arrives at the observer over a much smaller time period (ten or twenty years) giving the illusion of faster than light travel. This explanation depends on the jet making a sufficiently narrow angle with the observer's line-of-sight to explain the degree of superluminal motion seen in a particular case.[1] Superluminal motion is often seen in two opposing jets, one moving away and one toward Earth. If Doppler shifts are observed in both sources, the velocity and the distance can be determined independently of other observations. ===Some contrary evidence===As early as 1983, at the "superluminal workshop" held at Jodrell Bank Observatory, referring to the seven then-known superluminal jets, 
Schilizzi ... presented maps of arc-second resolution [showing the large-scale outer jets] ... which ... have revealed outer double structure in all but one (3C 273) of the known superluminal sources. An embarrassment is that the average projected size [on the sky] of the outer structure is no smaller than that of the normal radio-source population.[2]
 In other words the jets are evidently not, on average, close to our line-of-sight. (Their apparent length would appear much shorter if they were.) In 1993, Thomson et al. suggested that the (outer) jet of the quasar 3C 273 is nearly collinear to our line-of-sight. Superluminal motion of up to ~9.6c has been observed along the (inner) jet of this quasar.[3] Superluminal motion of up to 6c has been observed in the inner parts of the jet of M87. To explain this in terms of the "narrow-angle" model, the jet must be no more than 19° from our line-of-sight.[4] But evidence suggests that the jet is in fact at about 43° to our line-of-sight.[5] The same group of scientists later revised that finding and argue in favour of a superluminal bulk movement in which the jet is embedded.[6] Suggestions of turbulence and/or "wide cones" in the inner parts of the jets have been put forward to try to counter such problems, and there seems to be some evidence for this.[7] ====Signal Velocity====The model identifies a difference between the information carried by the wave at its signal velocity c, and the information about the wave fronts apparent rate of change of position. If you envisage a light pulse in a wave guide (glass tube) moving across an observers field of view, the pulse can only move at c through the guide. If that pulse is also directed towards the observer he will receive that wave information, at c.  If the wave guide is moved in the same direction as the pulse the information on its position, passed to the observer as lateral emissions from the pulse, changes.  He may see the rate of change of position as apparently representing motion faster than c when calculated, like the edge of a shadow across a curved surface.  This is a different signal, containing different information, to the pulse and does not break the 2nd postulate of SR. c is strictly maintained in all local fields. ==Derivation of the relativistic explanation==A relativistic jet coming out of the center of an active galactic nucleus is moving along AB with a velocity v. We are observing the jet from the point O. At time $ t_1 $ a light ray leaves the jet from point A and another ray leaves at time $ t_2 $ from point B. Observer at O receives the rays at time $ t_1^\prime $ and $ t_2^\prime $ respectively.: $ AB \ = \ v\delta t $: $ AC \ = \ v\delta t \cos\theta $: $ BC \ = \ v\delta t \sin \theta $: $ t_2-t_1 \ = \ \delta t $ : $ t_1^\prime = t_1 + \frac{D_L+v\delta t \cos\theta}{c} $: $ t_2^\prime =t_2+ \frac{D_L}{c} $ : $ \delta t^\prime = t_2^\prime - t_1^\prime = t_2 - t_1 - \frac{v\delta t \cos\theta}{c} = \delta t - \frac{v\delta t \cos\theta}{c} = \delta t (1-\beta \cos\theta) $, where $ \beta=\frac{v}{c} $ : $ \delta t = \frac{\delta t^\prime}{1-\beta\cos\theta} $ : $ BC \ = \ D_L\sin\phi \approx \phi D_L = v\delta t \sin \theta \Rightarrow \phi D_L = v\sin\theta\frac{\delta t^\prime}{1-\beta\cos\theta} $ Apparent transverse velocity along CB, $ v_T = \frac{\phi D_L}{\delta t^\prime}=\frac{v\sin\theta}{1-\beta\cos\theta} $ : $ \beta_T = \frac{v_T}{c} = \frac{\beta\sin\theta}{1-\beta\cos\theta} $ : $ \frac{\partial\beta_T}{\partial\theta} = \frac{\partial}{\partial\theta} \left[\frac{\beta\sin\theta}{1-\beta\cos\theta}\right] = \frac{\beta\cos\theta}{1-\beta\cos\theta} - \frac{(\beta\sin\theta)^2}{(1-\beta\cos\theta)^2} = 0 $ : $ \Rightarrow \beta\cos\theta (1-\beta\cos\theta)^2 = (1 - \beta\cos\theta) (\beta\sin\theta)^2 $ : $ \Rightarrow \beta\cos\theta (1-\beta\cos\theta) = (\beta\sin\theta)^2 \Rightarrow \beta\cos\theta - \beta^2\cos^2\theta = \beta^2sin^2\theta \Rightarrow \cos\theta_{max} = \beta $ : $ \Rightarrow \sin\theta_{max} = \sqrt{1-\cos^2\theta_{max}} = \sqrt{1-\beta^2} = \frac{1}{\gamma} $, where $ \gamma=\frac{1}{\sqrt{1-\beta^2}} $ : $ \therefore \beta_T^{max} = \frac{\beta\sin\theta_{max}}{1-\beta\cos\theta_{max}} = \frac{\beta/ \gamma}{1-\beta^2} = \beta\gamma $ If $ \gamma \gg 1 $ (i.e. when velocity of jet is close to the velocity of light) then $ \beta_T^{max} > 1 $ despite the fact that $ \beta < 1 $. And of course $ \beta_T > 1 $ means apparent transverse velocity along CB, the only velocity on sky that we can measure, is larger than the velocity of light in vacuum, i.e. the motion is apparently superluminal. ==History==In 1966 Martin Rees predicted that "an object moving relativistically in suitable directions may appear to a distant observer to have a transverse velocity much greater than the velocity of light".[8] A few years later (in 1969 and 1970) such sources were indeed discovered as very distant astronomical radio sources, such as radio galaxies and quasars.[9][10][11] They were called superluminal (lit. "above light") sources. The discovery was a spectacular result of a new technique called Very Long Baseline Interferometry, which allowed astronomers to set limits to the angular size of components and to determine positions to better than milli-arcseconds and in particular to determine the change in positions on the sky, called proper motions in a timespan of typically years. The apparent velocity is obtained by multiplying the observed proper motion by the distance and could be up to 6 times the speed of light. In the Introduction to a workshop on superluminal radio sources, Pearson and Zensus reported
"The first indications of changes in the structure of some sources were obtained by an American-Australian team in a series of transpacific VLBI observations between 1968 and 1970 (Gubbay et al. 1969[9]). Following the early experiments, they had realised the potential of the NASA tracking antennas for VLBI measurements and set up an interferometer operating between California and Australia. The change in the source visibility that they measured for 3C 279, combined with changes in total flux density, indicated that a component first seen in 1969 had reached a diameter of about 1 milliarcsecond, implying expansion at an apparent velocity of at least twice the speed of light. Aware of Rees's model,[8] (Moffet et al. 1972[12]) concluded that their measurement presented evidence for relativistic expansion of this component. This interpretation, although by no means unique, was later confirmed, and in hindsight it seems fair to say that their experiment was the first interferometric measurement of superluminal expansion."[13]
 In 1994, a Galactic speed record was obtained with the discovery of a superluminal source in our own Galaxy, the cosmic x-ray source GRS 1915+105. The expansion occurred on a much shorter timescale. Several separate blobs were seen to expand in pairs within weeks by typically 0.5 arcsec.[14]  Because of the analogy with quasars, this source was called a microquasar. ==Notes==
  1. See http://www.mhhe.com/physsci/astronomy/fix/student/chapter24/24f10.html for a graph of angle versus apparent speeds for two given actual relativistic speeds.
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  12. ==Further reading==
    • Template loop detected: Template:Cite book
    • Template loop detected: Template:Cite book
    • {{cite book | first=Robert | last=Heinlein | authorlink= | date=1980 | title=Expanded Universe | edition= | publisher=Ace Books | location=New York |
  13. ==Further reading==
    • Template loop detected: Template:Cite book
    • Template loop detected: Template:Cite book
    • {{cite book | first=Robert | last=Heinlein | authorlink= | date=1980 | title=Expanded Universe | edition= | publisher=Ace Books | location=New York |
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 ==See also==*Ultra-high-energy cosmic ray*Faster-than-light*Superluminal communication ==External links==* A more detailed explanation.* A mathematical deduction of superluminal motion.* Superluminal motion Flash Applet.  fr:Vitesse_supraluminique#En_astrophysique 
File:Superluminalmotion.gif
In astronomy, superluminal motion is the apparently faster-than-light motion seen in someradio galaxies, quasars and recently also in some galactic sources called microquasars. All of these sources are thought to contain a black hole, responsible for the ejection of mass at high velocities. When first observed in the early 1970s, superluminal motion was taken to be a piece of evidence against quasars having cosmological distances. Although a few astrophysicists still argue in favor of this view, most believe that apparent velocities greater than the velocity of light are optical illusions and involve no physics incompatible with the theory of special relativity. ==Explanation==This phenomenon is caused because the jets are travelling very near the speed of light and at a very small angle towards the observer. Because at every point of their path the high-velocity jets are emitting light, the light they emit does not approach the observer much more quickly than the jet itself. To be more clear, the jet is essentially "chasing" the light it emits. This causes the light emitted over hundreds of years of travel to not  have hundreds of lightyears of distance between it, the light thus arrives at the observer over a much smaller time period (ten or twenty years) giving the illusion of faster than light travel. This explanation depends on the jet making a sufficiently narrow angle with the observer's line-of-sight to explain the degree of superluminal motion seen in a particular case.[1] Superluminal motion is often seen in two opposing jets, one moving away and one toward Earth. If Doppler shifts are observed in both sources, the velocity and the distance can be determined independently of other observations. ===Some contrary evidence===As early as 1983, at the "superluminal workshop" held at Jodrell Bank Observatory, referring to the seven then-known superluminal jets, 
Schilizzi ... presented maps of arc-second resolution [showing the large-scale outer jets] ... which ... have revealed outer double structure in all but one (3C 273) of the known superluminal sources. An embarrassment is that the average projected size [on the sky] of the outer structure is no smaller than that of the normal radio-source population.[2]
 In other words the jets are evidently not, on average, close to our line-of-sight. (Their apparent length would appear much shorter if they were.) In 1993, Thomson et al. suggested that the (outer) jet of the quasar 3C 273 is nearly collinear to our line-of-sight. Superluminal motion of up to ~9.6c has been observed along the (inner) jet of this quasar.[3] Superluminal motion of up to 6c has been observed in the inner parts of the jet of M87. To explain this in terms of the "narrow-angle" model, the jet must be no more than 19° from our line-of-sight.[4] But evidence suggests that the jet is in fact at about 43° to our line-of-sight.[5] The same group of scientists later revised that finding and argue in favour of a superluminal bulk movement in which the jet is embedded.[6] Suggestions of turbulence and/or "wide cones" in the inner parts of the jets have been put forward to try to counter such problems, and there seems to be some evidence for this.[7] ====Signal Velocity====The model identifies a difference between the information carried by the wave at its signal velocity c, and the information about the wave fronts apparent rate of change of position. If you envisage a light pulse in a wave guide (glass tube) moving across an observers field of view, the pulse can only move at c through the guide. If that pulse is also directed towards the observer he will receive that wave information, at c.  If the wave guide is moved in the same direction as the pulse the information on its position, passed to the observer as lateral emissions from the pulse, changes.  He may see the rate of change of position as apparently representing motion faster than c when calculated, like the edge of a shadow across a curved surface.  This is a different signal, containing different information, to the pulse and does not break the 2nd postulate of SR. c is strictly maintained in all local fields. ==Derivation of the relativistic explanation==A relativistic jet coming out of the center of an active galactic nucleus is moving along AB with a velocity v. We are observing the jet from the point O. At time $ t_1 $ a light ray leaves the jet from point A and another ray leaves at time $ t_2 $ from point B. Observer at O receives the rays at time $ t_1^\prime $ and $ t_2^\prime $ respectively.: $ AB \ = \ v\delta t $: $ AC \ = \ v\delta t \cos\theta $: $ BC \ = \ v\delta t \sin \theta $: $ t_2-t_1 \ = \ \delta t $ : $ t_1^\prime = t_1 + \frac{D_L+v\delta t \cos\theta}{c} $: $ t_2^\prime =t_2+ \frac{D_L}{c} $ : $ \delta t^\prime = t_2^\prime - t_1^\prime = t_2 - t_1 - \frac{v\delta t \cos\theta}{c} = \delta t - \frac{v\delta t \cos\theta}{c} = \delta t (1-\beta \cos\theta) $, where $ \beta=\frac{v}{c} $ : $ \delta t = \frac{\delta t^\prime}{1-\beta\cos\theta} $ : $ BC \ = \ D_L\sin\phi \approx \phi D_L = v\delta t \sin \theta \Rightarrow \phi D_L = v\sin\theta\frac{\delta t^\prime}{1-\beta\cos\theta} $ Apparent transverse velocity along CB, $ v_T = \frac{\phi D_L}{\delta t^\prime}=\frac{v\sin\theta}{1-\beta\cos\theta} $ : $ \beta_T = \frac{v_T}{c} = \frac{\beta\sin\theta}{1-\beta\cos\theta} $ : $ \frac{\partial\beta_T}{\partial\theta} = \frac{\partial}{\partial\theta} \left[\frac{\beta\sin\theta}{1-\beta\cos\theta}\right] = \frac{\beta\cos\theta}{1-\beta\cos\theta} - \frac{(\beta\sin\theta)^2}{(1-\beta\cos\theta)^2} = 0 $ : $ \Rightarrow \beta\cos\theta (1-\beta\cos\theta)^2 = (1 - \beta\cos\theta) (\beta\sin\theta)^2 $ : $ \Rightarrow \beta\cos\theta (1-\beta\cos\theta) = (\beta\sin\theta)^2 \Rightarrow \beta\cos\theta - \beta^2\cos^2\theta = \beta^2sin^2\theta \Rightarrow \cos\theta_{max} = \beta $ : $ \Rightarrow \sin\theta_{max} = \sqrt{1-\cos^2\theta_{max}} = \sqrt{1-\beta^2} = \frac{1}{\gamma} $, where $ \gamma=\frac{1}{\sqrt{1-\beta^2}} $ : $ \therefore \beta_T^{max} = \frac{\beta\sin\theta_{max}}{1-\beta\cos\theta_{max}} = \frac{\beta/ \gamma}{1-\beta^2} = \beta\gamma $ If $ \gamma \gg 1 $ (i.e. when velocity of jet is close to the velocity of light) then $ \beta_T^{max} > 1 $ despite the fact that $ \beta < 1 $. And of course $ \beta_T > 1 $ means apparent transverse velocity along CB, the only velocity on sky that we can measure, is larger than the velocity of light in vacuum, i.e. the motion is apparently superluminal. ==History==In 1966 Martin Rees predicted that "an object moving relativistically in suitable directions may appear to a distant observer to have a transverse velocity much greater than the velocity of light".[8] A few years later (in 1969 and 1970) such sources were indeed discovered as very distant astronomical radio sources, such as radio galaxies and quasars.[9][10][11] They were called superluminal (lit. "above light") sources. The discovery was a spectacular result of a new technique called Very Long Baseline Interferometry, which allowed astronomers to set limits to the angular size of components and to determine positions to better than milli-arcseconds and in particular to determine the change in positions on the sky, called proper motions in a timespan of typically years. The apparent velocity is obtained by multiplying the observed proper motion by the distance and could be up to 6 times the speed of light. In the Introduction to a workshop on superluminal radio sources, Pearson and Zensus reported
"The first indications of changes in the structure of some sources were obtained by an American-Australian team in a series of transpacific VLBI observations between 1968 and 1970 (Gubbay et al. 1969[9]). Following the early experiments, they had realised the potential of the NASA tracking antennas for VLBI measurements and set up an interferometer operating between California and Australia. The change in the source visibility that they measured for 3C 279, combined with changes in total flux density, indicated that a component first seen in 1969 had reached a diameter of about 1 milliarcsecond, implying expansion at an apparent velocity of at least twice the speed of light. Aware of Rees's model,[8] (Moffet et al. 1972[12]) concluded that their measurement presented evidence for relativistic expansion of this component. This interpretation, although by no means unique, was later confirmed, and in hindsight it seems fair to say that their experiment was the first interferometric measurement of superluminal expansion."[13]
 In 1994, a Galactic speed record was obtained with the discovery of a superluminal source in our own Galaxy, the cosmic x-ray source GRS 1915+105. The expansion occurred on a much shorter timescale. Several separate blobs were seen to expand in pairs within weeks by typically 0.5 arcsec.[14]  Because of the analogy with quasars, this source was called a microquasar. ==Notes==
  1. See http://www.mhhe.com/physsci/astronomy/fix/student/chapter24/24f10.html for a graph of angle versus apparent speeds for two given actual relativistic speeds.
  2. Template:Cite journal
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  8. 8.0 8.1 Template:Cite doi
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  12. ==Further reading==
    • Template loop detected: Template:Cite book
    • Template loop detected: Template:Cite book
    • {{cite book | first=Robert | last=Heinlein | authorlink= | date=1980 | title=Expanded Universe | edition= | publisher=Ace Books | location=New York |
  13. ==Further reading==
    • Template loop detected: Template:Cite book
    • Template loop detected: Template:Cite book
    • {{cite book | first=Robert | last=Heinlein | authorlink= | date=1980 | title=Expanded Universe | edition= | publisher=Ace Books | location=New York |
  14. Template:Cite journal
 ==See also==*Ultra-high-energy cosmic ray*Faster-than-light*Superluminal communication ==External links==* A more detailed explanation.* A mathematical deduction of superluminal motion.* Superluminal motion Flash Applet.  fr:Vitesse_supraluminique#En_astrophysique 

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