Editing Superluminal motion (section)

==Explanation==
Superluminal motion occurs as a special case of a more general phenomenon arising from the difference between the apparent speed of distant objects moving across the sky and their actual speed as measured at the source.<ref>{{cite journal |last1=Recami |first1=Erasmo |title=Considerations about the apparent superluminal expansions observed in astrophysics |journal=Il Nuovo Cimento |date=April 1986 |volume=93 |issue=1 |page=9|doi= 10.1007/BF02722327 |bibcode=1986NCimB..93..119R |s2cid=118034129 }}</ref>

In tracking the movement of such objects across the sky, a calculation of their speed can be determined by a simple distance divided by time formula.  If the distance of the object from the Earth is known and the angular speed of the object can be measured, then the speed can be calculated as:

{{block indent | em = 1.5 | text = ''apparent speed = distance to object × angular  speed.''}}

But this calculation does not yield the actual speed of the object, as it fails to account for the fact that the speed of light is finite. When measuring the movement of distant objects across the sky, there is a large time delay between what has been observed and what has occurred, due to the large distance the light from the distant object has to travel to reach us. The error in the above calculation comes from the fact that when an object has a component of velocity directed towards the Earth, as the object moves closer to the Earth that time delay becomes smaller. This means that the apparent speed as calculated above is <em>greater</em> than the actual speed. Correspondingly, if the object is moving away from the Earth, the above calculation underestimates the actual speed.

This effect in itself does not generally lead to superluminal motion being observed. But when the actual speed of the object is close to the speed of light, the apparent speed can be calculated as greater than the speed of light, as a result of the above effect. As the actual speed of the object approaches the speed of light, the effect is most pronounced as the component of the velocity towards the Earth increases. This means that in most cases, 'superluminal' objects are travelling almost directly towards the Earth. However it is not strictly necessary for this to be the case, and superluminal motion can still be observed in objects with appreciable velocities not directed towards the Earth.<ref>{{cite journal |last1=Meyer |first1=Eileen |title=Detection of an Optical/UV Jet/Counterjet and Multiple Spectral Components in M84 |journal=The Astrophysical Journal |date=June 2018 |volume=680 |issue=1 |page=9|bibcode=2018ApJ...860....9M |arxiv=1804.05122 |doi=10.3847/1538-4357/aabf39 |s2cid=67822924 |doi-access=free }}</ref>

Superluminal motion is most often observed in two opposing jets emanating from the core of a star or black hole. In this case, one jet is moving away from and one towards the Earth. If [[Doppler shift]]s 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,

<blockquote>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.<ref>{{Cite journal|doi=10.1038/302753a0|title=Superluminal motions: Astronomers still puzzled|date=1983|last1=Porcas|first1=Richard|journal=Nature|volume=302|issue=5911|pages=753–754|bibcode = 1983Natur.302..753P |doi-access=free}}</ref></blockquote>

In other words, the jets are evidently not, on average, close to the Earth's 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 the Earth's line-of-sight. Superluminal motion of up to ~9.6''c'' has been observed along the (inner) jet of this quasar.<ref>{{Cite journal|doi=10.1038/365133a0|title=Internal structure and polarization of the optical jet of the quasar 3C273|date=1993|last1=Thomson|first1=R. C.|last2=MacKay|first2=C. D.|last3=Wright|first3=A. E.|journal=Nature|volume=365|issue=6442|pages=133|bibcode = 1993Natur.365..133T |s2cid=4314344}};</ref><ref>{{Cite journal|doi=10.1038/290365a0|title=Superluminal expansion of quasar 3C273|date=1981|last1=Pearson|first1=T. J.|last2=Unwin|first2=S. C.|last3=Cohen|first3=M. H.|last4=Linfield|first4=R. P.|last5=Readhead|first5=A. C. S.|last6=Seielstad|first6=G. A.|last7=Simon|first7=R. S.|last8=Walker|first8=R. C.|journal=Nature|volume=290|issue=5805|pages=365|bibcode = 1981Natur.290..365P |s2cid=26508893}};</ref><ref>{{Cite journal|doi=10.1038/354374a0|title=Large-scale superluminal motion in the quasar 3C273|date=1991|last1=Davis|first1=R. J.|last2=Unwin|first2=S. C.|last3=Muxlow|first3=T. W. B.|journal=Nature|volume=354|issue=6352|pages=374|bibcode = 1991Natur.354..374D |s2cid=4271003}}</ref>

Superluminal motion of up to 6''c'' has been observed in the inner parts of the jet of [[Messier 87|M87]]. To explain this in terms of the "narrow-angle" model, the jet must be no more than 19° from the Earth's line-of-sight.<ref name="nature891">{{Cite journal|doi=10.1038/44780|date=1999|last1=Biretta|first1=John A.|title=Formation of the radio jet in M87 at 100 Schwarzschild radii from the central black hole|last2=Junor|first2=William|last3=Livio|first3=Mario|journal=Nature|volume=401|issue=6756|pages=891|bibcode = 1999Natur.401..891J |s2cid=205034376}} ; {{Cite journal|doi=10.1086/307499|title=Hubble Space TelescopeObservations of Superluminal Motion in the M87 Jet|date=1999|last1=Biretta|first1=J. A.|last2=Sparks|first2=W. B.|last3=MacChetto|first3=F.|journal=The Astrophysical Journal|volume=520|issue=2|pages=621|bibcode = 1999ApJ...520..621B |doi-access=free}}</ref> But evidence suggests that the jet is in fact at about 43° to the Earth's line-of-sight.<ref>{{Cite journal|doi=10.1086/175901|title=Detection of Proper Motions in the M87 Jet|date=1995|last1=Biretta|first1=J. A.|last2=Zhou|first2=F.|last3=Owen|first3=F. N.|journal=The Astrophysical Journal|volume=447|pages=582|bibcode = 1995ApJ...447..582B }}</ref> The same group of scientists later revised that finding and argue in favour of a superluminal bulk movement in which the jet is embedded.<ref>{{Cite journal|doi=10.1086/307499|title=Hubble Space TelescopeObservations of Superluminal Motion in the M87 Jet|date=1999|last1=Biretta|first1=J. A.|last2=Sparks|first2=W. B.|last3=MacChetto|first3=F.|journal=The Astrophysical Journal|volume=520|issue=2|pages=621|bibcode = 1999ApJ...520..621B |doi-access=free}}</ref>

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.<ref>{{cite journal|doi=10.1038/44780|date=1999|last1=Biretta|first1=John A.|title=Formation of the radio jet in M87 at 100 Schwarzschild radii from the central black hole|last2=Junor|first2=William|last3=Livio|first3=Mario|journal=Nature|volume=401|issue=6756|pages=891|bibcode = 1999Natur.401..891J |s2cid=205034376}}</ref>

====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 front's apparent rate of change of position. If a light pulse is envisaged in a wave guide (glass tube) moving across an observer's 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 second postulate of special relativity. ''c'' is strictly maintained in all local fields.