Apparent superluminal velocity in M82 source

[jackiefrost]

An April 18 newscientist.com article, http://www.newscientist.com/article/dn18775-mysterious-radio-waves-emitted-from-nearby-galaxy.html" reports recent observations of a radio source in M82 with an apparent horizontal motion of 4x speed of light.

Yet it does seem to be moving – and fast: its apparent sideways velocity is four times the speed of light. Such apparent "superluminal" motion has been seen before in high-speed jets of material squirted out by some black holes. The stuff in these jets is moving towards us at a slight angle and traveling at a fair fraction of the speed of light, and the effects of relativity produce a kind of optical illusion that makes the motion appear superluminal.

Could someone comment on what particular relativistic effects would cause an "optical illusion" of superluminal velocities. What specific empirical measurements are they referring to that would indicate apparent superluminal velocities?

 

[sylas]

An April 18 newscientist.com article, http://www.newscientist.com/article/dn18775-mysterious-radio-waves-emitted-from-nearby-galaxy.html" reports recent observations of a radio source in M82 with an apparent horizontal motion of 4x speed of light.

Could someone comment on what particular relativistic effects would cause an "optical illusion" of superluminal velocities. What specific empirical measurements are they referring to that would indicate apparent superluminal velocities?

It is a common effect that occurs when an object is moving at high velocity almost towards you. It is not a relativistic effect so much as a consequence of the finite speed of light.

Suppose, for example, that something is moving at an angle of θ away from directly towards you, at a velocity v, and you know that it is a distance away from you d.

Suppose that two signals are sent from this object, separated in time Δt. (Forget any relativistic effects. Everything is done in your own reference from.) Now over that time, it moves a distance v.Δt. We break this into two components; it is closer to you by v.Δt.cos(θ), and it has moved orthogonal to the line of sight by v.Δt.sin(θ). The latter corresponds to an apparent horizontal movement across the sky.

Note, however, the second signal has less distance to go to reach you. Therefore it arrives after a shorter period of time Δt(1 - (v/c).cos(θ)). This is simply subtracting the time it would have taken light to go that extra distance towards you, which is (v/c).Δt.cos(θ).

If you forget to consider this advantage in time, you might think that the time the object took was the time between the two signals to be observed, rather than the time between the two signals being emitted.

The apparent horizontal velocity of the object is thus a = v.sin(θ)/(1 - (v/c).cos(θ)).

Using units with c = 1, if you differentiate this with respect to θ, assuming v fixed, you get

$$\begin{align*} a & = \frac{v \sin \theta}{1 - v \cos \theta} \\ \frac{\partial a}{\partial \theta} & = v\frac{\cos \theta ( 1 - v \cos \theta ) - \sin \theta ( v \sin \theta )}{(1 - v \cos \theta)^2} \\ & = c \frac{\cos \theta - v}{(1 - v \cos \theta)^2} \end{align*}$$​

Thus, when v = cos(θ) you get a maximum apparent velocity, which works out to be

$$\frac{v}{\sqrt{1-v^2}}$$​

If I have the maths right, then you can get an apparent horizontal velocity of 4c if the v was about 97% lightspeed, and the particle was moving at about 14 degrees off directly towards you.

Cheers -- sylas

 

[Ich]

Could someone comment on what particular relativistic effects would cause an "optical illusion" of superluminal velocities.

It's not really a relativistic effect, it's simply light travel time. The object approaches you at close to the speed of light, so the light sent from different positions reaches the observer in fast forward.
The acoustic analogue is fast approaching jet fighter. From what you hear, you'd guess that it traveled at Mach 10, so quickly changes the sound. The extreme is a sonic boom, when all the sound arrives in a single moment.

 

[jackiefrost]

Sorry for the long delay. Both your explanations and the analysis makes good sense. Thank you both very much.

 

[sardar]

I would like to provide some insight into the reported observations of apparent superluminal velocity in the M82 source. First and foremost, it is important to understand that the concept of superluminal velocity, or faster-than-light motion, is not possible according to our current understanding of physics. The speed of light is considered to be the ultimate speed limit in the universe.

In this case, the observed apparent superluminal velocity is a result of relativistic effects, specifically the Doppler effect and time dilation. The Doppler effect is the apparent change in frequency of a wave due to the relative motion between the source and observer. In the case of the M82 source, it is emitting radio waves at a high speed towards us, causing a shift in the observed frequency. This shift can make it appear as though the source is moving faster than the speed of light.

Additionally, time dilation is a consequence of Einstein's theory of relativity, which states that time can appear to pass at different rates for observers in relative motion. In the case of the M82 source, the material in the high-speed jet is moving towards us at a slight angle, causing a difference in the perceived passage of time. This can also contribute to the illusion of superluminal velocities.

It is important to note that these effects are only apparent and do not actually violate the laws of physics. They are a result of the complex nature of relativity and the way we perceive motion and time. In fact, similar observations of apparent superluminal velocities have been seen before in other high-speed jets from black holes.

As for the specific empirical measurements mentioned in the article, it is likely referring to the observed frequency shift and changes in the perceived passage of time, which can be measured using specialized instruments and techniques.

In conclusion, while the reported observations of apparent superluminal velocity in the M82 source may seem puzzling, they can be explained by known relativistic effects and do not indicate any violation of the laws of physics. Further research and observations will continue to shed light on the complex nature of the universe and help us better understand these phenomena.