Superluminal motion

Superluminal motion

In astronomy, superluminal motion is the apparently faster-than-light motion seen in some radio 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 1980s, 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 emiting 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.

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, 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.

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.

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. But evidence suggests that the jet is in fact at about 43° to our line-of-sight. The same group of scientists later revised that finding and argue in favour of a superluminal bulk movement in which the jet is embedded.

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.

Laser Ranging

NASA's lunar laser ranging experiment was supposed to be a specific and precise test of the invariance of c and Special Relativity. The first two papers were published in Dec. 2009. The results were apparently inconsistent with either SR or Lorentz invariance of c. They were consistent with GPS data when corrected to consistently account for the Sagnac effect. Measured speed appeared superluminal, exceeding canonical value by 200ms (which was "the speed of the observatory along the line of sight due to rotation during measurement"). Article suggested that, if c were to remain invariant, a preferred frame would be required. In this case an observer in the preferred frame could measure the apparent superluminal motion of light travelling at c within another frame in relative motion, as the Discrete Field Model, and would suggest an alternative explanation for the gas jets of galaxy M87 (see below).

It was subsequently shown that these lunar ranging measurements have been misinterpreted, and the experiment, as analyzed, did not actually measure the speed of light in the moving reference frame. All measurements of c in the experiment were actually performed from a stationary frame only, which resulted in expected, correct values of c (within 8.3 ± 3.2 m/s as stated in the article). For that same set of data, the author then performed Galilean transformations, and erroneously got a different speed of light inside the moving frame. The author updated his paper.

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.

Messier 87 etc. Gas Jets

An alternative explanation for the Gas Jets moving at 6c is derived from the Discrete Field Model and is consistent with the NASA Lunar Ranging results (above). The magnetic field of the super massive rotating black hole will be contorted to a "tube" at the poles, ejecting the particles. The jet is proposed as a moving "field" gradually slowing and diffusing, but with new particles travelling in its core at close to c within its own moving frame, and more new ones at c in their frame. Newer core particles would be more radiant. From the Hubble space telescopes "preferred" frame they would in this case appear to be moving at 6c, but none would exceed c in the quantum field they are moving within.

Derivation of the relativistic explanation

A relativistic jet coming out of the center of an AGN 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 $\beta ={\frac {v}{c}}$

$\delta t={\frac {\delta t^{\prime }}{1-\beta \cos \theta }}$

$BC\ =\ D_{L}\sin \phi =\phi D_{L}=v\delta t\sin \theta \Rightarrow \phi D_{L}=v\sin \theta {\frac {\delta t^{\prime }}{1-\beta \cos \theta }}$

Apparent transverse velocity along CB, $v_{T}={\frac {\phi D_{L}}{\delta t^{\prime }}}={\frac {v\sin \theta }{1-\beta \cos \theta }}$

$\beta _{T}={\frac {v_{T}}{c}}={\frac {\beta \sin \theta }{1-\beta \cos \theta }}$

${\frac {\partial \beta _{T}}{\partial \theta }}={\frac {\partial }{\partial \theta }}\left[{\frac {\beta \sin \theta }{1-\beta \cos \theta }}\right]={\frac {\beta \cos \theta }{1-\beta \cos \theta }}-{\frac {(\beta \sin \theta )^{2}}{(1-\beta \cos \theta )^{2}}}=0$

$\Rightarrow \beta \cos \theta (1-\beta \cos \theta )^{2}=(1-\beta \cos \theta )(\beta \sin \theta )^{2}$

$\Rightarrow \beta \cos \theta (1-\beta \cos \theta )=(\beta \sin \theta )^{2}\Rightarrow \beta \cos \theta -\beta ^{2}\cos ^{2}\theta =\beta ^{2}sin^{2}\theta \Rightarrow \cos \theta _{max}=\beta$

$\Rightarrow \sin \theta _{max}={\sqrt {1-\cos ^{2}\theta _{max}}}={\sqrt {1-\beta ^{2}}}={\frac {1}{\gamma }}$, 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 (Nature 211, 468) 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".

A few years later (in 1970) such sources were indeed discovered as very distant astronomical radio sources, such as radio galaxies and quasars. 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 determine positions 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 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 (I.F. Mirabel and L.F. Rodriguez, Nature 371, 48, "A superluminal source in the Galaxy") to expand in pairs within weeks by typically 0.5 arcsec. Because of the analogy with quasars, this source was called a microquasar.

Superluminal motion of Electromagnetic Waves

Surface Waves

The quantum of a surface electromagnetic wave is a tachyon whose velocity of motion, equivalent to the energy flow velocity of the wave. can be faster than light speed c in vacuum.

Electric energy in Metals

The dispersion relation of a low frequency electromagnetic field in conductors is corresponding to the energy-momentum equation of a tachyon. Actually, the velocity of such a tachyon just equals that of the energy of the field which is much greater than light speed c= 299,792,458 m/s in vacuum.

See also

• Faster-than-light
• Superluminal communication

External links

• A more detailed explanation.
• A mathematical deduction of superluminal montion.
• Superluminal motion Flash Applet.