"How can one see matter moving faster than light?"

By Chris Stewart

Modern observing techniques and technologies allow us to see farther into space, to measure the properties of the bodies we observe with unprecedented accuracy, to see more clearly, with higher resolution and in a greater range of wavelengths than ever before. Consequently, an astounding range of truly remarkable astronomical discoveries is with increasing frequency being announced. Yet the discovery of luminous jets of matter ejected by certain quasars, and which are apparently travelling at speeds significantly in excess of that of light, is without doubt one of the most unexpected, puzzling and yet generally ignored of the last two decades. These measurements, notably by means of very long baseline interferometry, constitute some of the most painstakingly performed and accurate ever attempted. Given our current understanding of the physics of the universe, the results are at first glance in total conflict with our best models of how matter can behave. How can this be? As it turns out, the jets are indeed travelling extremely fast. The quasars have enormous energy reserves and are in fact quite capable of accelerating the jets to a significant percentage of the speed of light. That we see them as travelling faster, is simply a quirk of perspective coupled with the finite speed of light itself. Let us indulge now in a little story to illustrate the point by way of analogy.

Imagine you are in Johannesburg and I am in Cape Town, a separation by road of some 1500km. I decide on the spur of the moment to visit you, instructing Gulliver -- my erstwhile young assistant -- to inform you that I am leaving at this very minute. For me, the trip is an excuse to "go for a burn" on my lovingly restored 20-year-old Moto Guzzi Le Mans. Mounting it, I set off and manage to average exactly 199km/h over the whole journey. Gulliver, fearful of losing his job, has neglected to tell me that the batteries in his cell phone are flat. Also, the local phones are down because the Telkom lines in the area have been the unfortunate victims of "alternative shopping", so for the same reason he can’t even e-mail either. Being a resourceful if rather scatterbrained chap, he nips next door to the local Yakawhonsu dealer and buys the latest big-bore riceburner out of the money he has saved by skimping on his housekeeping budget (obviously I pay him too much). On this, he manages to set off at exactly the same time as I, in the hopes of getting to Jo’burg first to deliver the message. Of course he is not nearly such an experienced rider but -- having a typical adolescent’s disregard for the normal fear of smearing oneself over the landscape, plus the advantage of a more powerful modern bike -- he averages precisely 200km/h.

Exactly half-way to Jo’burg, I pause for an instant in Blikkiesfontein to take a leak and refuel (these Guzzies are moereva light on juice). At this point, I give the pump jockey a big tip and ask him to let you know I am now in Blikkies. Now, he is seriously impressed by me, the Guzzi and the big tip, so he rushes in to phone. Unfortunately the tannie who has manned the local telephone exchange for the last twenty years is out having melktert and koeksusters with her friends in Gatsonderwater and no-one else knows how to drive this technological dinosaur. He has a flash of inspiration: his brother in-law, Frikkie "Slagyster" van der Vyfer, is the head of the local Hells Angels chapter. This luminary is renowned amongst the lunatic fringe as a bezerko rider who never refuses a challenge. He is also the only one from Blikkies who knows his way around Jo’burg, having got lost there so often while passing through on the way to the biker rallies. So the pump jockey bets his swaer that he can’t deliver the message before I get to Joeys, and unbeknownst to me the dice is on. As I pull away, so does Slagyster. He doesn’t have nearly as nice a bike as the Guzzi, but he has recognised me as being one of the DJs at the rallies. He also knows that if he loses the dice he will be too ashamed to ever enjoy a rally again in case he sees me there; his friends will see to that, ragging him unmercifully forever about losing a dice to an middle-aged DJ on a 20-year-old bike. To him, upholding his reputation as the fearless leader of the local Angels chapter is much more important than preserving his poor machine, so he abuses it mightily to stay ahead. He manages to match my first messenger’s speed of exactly 200km/h. I, exhibiting my usual mechanical affinity, continue complacently to average my 199.

Now we must quickly do some basic maths. Since I was travelling at 199km/h, I managed to do the 750 km to Blikkies in 226 minutes, and of course the same from there to Jo’burg. Gulliver, doing 200km/h, would have passed through Blikkies only one minute ahead of my arrival there. Similarly, Slagyster is doing 200, so he gets to Jo’burg one minute ahead of me. Because Slagyster and I left Blikkies one minute after Gulliver passed through, and the two of them are doing the same speed, Slagyster also gets to your office one minute behind Gulliver. (We are assuming here that an "average" speed includes all pitstops, so they don’t count.)

Unaware of this gruelling tableau unfolding on the roads, you are happily working away at your desk, solemnly scrutinising the latest Sky & Telescope tucked inside an old financial report. Gulliver, tired and fagged out after a long burn but totally hyped-up on adrenaline from the unaccustomed rush, bursts in to your secretary’s office. He breathlessly delivers my message verbatim, as any good messenger should. She buzzes you to say I am leaving Cape town at that instant. "Ah, good," you say, assuming she must have received a phone call. A minute later, Slagyster arrives to say I am in Blikkies, which fact your now somewhat confused secretary efficiently conveys to you as well. "Something is wrong here," you think, "Assuming there were anyone left in the SADF who knows how to fly and service the thing, even our hottest airforce jet couldn’t get from Cape Town to Blikkies in one minute. It would have to travel at 45000km/h to do that. In fact, even if it could do that speed, it would just melt from the friction!" And just one minute after that... I myself walk in, picking dead bugs off my visor and grinning broadly. I have apparently done Cape Town to Jo’burg in two minutes flat, without even the benefit of the Space Shuttle’s ceramic tiles to fend off the heat. (So now you know the origins of the phrase "going for a burn".) This is clearly a record time, but then these old Guzzis are not just tough, they are also moereva fast, as we all know.

This story describes a situation that is actually possible (if little fanciful, given the prevalence of speed-cops and the state of my wallet). Let’s relate the players in this flight of fantasy to what’s going on with the quasars. In the story, you equate to "the observer"; your secretary is your "measuring equipment"; my two messengers are "photons of light"; I of course am "the jet of matter"; and Cape Town is "the quasar". As you can see, it is possible for perfectly valid information to be quite reasonably misinterpreted if taken purely at face value. Consider too that here I have described sending off only two messengers who -- by travelling only that little bit faster -- just manage to stay ahead of me. I could have despatched messengers at each point along my route as I got there; they would have arrived in sequence and -- given their times of arrival and their statements as to their points of origin -- you would get a consistent picture of my seemingly phenomenal speed. Obviously I chose numbers that were easy to work with and would give an impressive result, but the important issue here is not what order of magnitude our speeds were, but that there was a very small difference between my speed and that of my erstwhile messengers.

Let’s now take the (thankfully) hypothetical case of a quasar only 100 light years away from Earth. This distance means that any event in the vicinity of the quasar can only be seen by us one hundred years later, since that’s how long the light (travelling at the speed ‘c’) would take to get from it to us. Now, let’s assume that at time ‘T’, a jet of plasma is ejected by the quasar in a direction almost exactly towards us. It achieves a speed of, say, 0.99c. Being highly energetic, it is very luminous. Nonetheless, the laws of physics still dictate that the light it emits can only travel at c. So, at time ‘T + 50 years’, the light emitted at the time the jet was ejected has travelled half way towards us (i.e. 50 light years), while the jet itself has travelled only 49,5 light years. Any light that the jet emits at this point must of course also travel at c, while the jet itself continues at 0,99c. At time ‘T + 100’ years, the light from the initial event reaches us; we see the jet being ejected from the quasar. At this point, the jet itself is still one light year away from us and the light it emitted at the halfway point is only 0,5 light years away from us. So six months later, at time ‘T + 100,5 years’, that light arrives and, voila!, we see the jet has apparently moved 50 light years distance in only six months. It appears that the jet must be travelling at 100 times the speed of light! At each instant during its travel towards us, the jet continues to emit light that manages to just pull away from it. Again, these photons will arrive in sequence and will present a consistent picture of the jet’s phenomenal speed being far in excess of that of light. At time ‘T + 101 years’ the Earth, having been blasted by intense radiation for a year now, is finally engulfed by the plasma jet. Even those fortunate souls possessing space-faring Guzzi equivalents are in danger of annihilation. Clearly, it is just as well that in reality quasars are pretty much the most distant objects that we can see in the entire universe, because that gives the light a long time to pull away from the matter, leaving it far behind. So don’t panic: death by quasar is not in our immediate future.

OK, now that you have digested these two illustrative accounts you will be wondering what astronomers have observed in reality. Before I actually get to that, I must point out a couple of other facts about what is practically possible for us to observe. Firstly, we see things "moving" in the sky because their position with respect to the background (their celestial co-ordinates) and other objects out there change with time. The very long baseline interferometers mentioned earlier allow very small angular displacements to be measured. Because the quasars are so far away, the ability to measure the angular progress of any jets which they might eject is a truly impressive achievement. The jets might be fast-moving and thus cover enormous distances in short order, but their distance from us is so great that the apparent angular separation between the jets and their parent bodies is infinitesimal. Secondly, if a quasar were to emit a jet of plasma directly towards us, we would not see it as a separate entity. This is primarily because the quasar itself is so much bigger and brighter, so the image of the jet would be swamped by that of the quasar itself. Possibly, after careful investigation of the composite image, we might notice some puzzling Doppler effects in the spectrum that could eventually be correctly interpreted by some genius out there (of which there are indeed a fair number). Thirdly and more importantly, objects travelling directly towards or away from us are not seen to move with respect to the background sky, i.e. they do not change their celestial co-ordinates with time. We do not therefore directly perceive their motion; it is only by secondary effects such as the Doppler shifts in their spectra that we can determine that they are in fact moving. And the information we get from that process may be difficult to interpret, but it does not lead to the same confusing conclusion as that highlighted in our earlier little stories. (An aside... Quasars are so far away that they appear to be receding from us at a truly great rate. As a result, the energetic ultraviolet radiation they actually emitted is so drastically Doppler red-shifted that they are seen by us in the infrared!)

With these concepts in mind, we can finally draw this explanation to a conclusion. You should hopefully understand from what I have said so far that, if a quasar were to eject a plasma jet at exactly 90 degrees to our line of sight, we would see it travelling at its actual speed. But if its motion were to be directed just a bit towards us, it would simultaneously get closer to us (i.e. have a "longitudinal" component to its velocity) and move across our field of view (i.e. have a "transverse" component to its velocity, which we directly discern as movement). As its direction of movement gets closer and closer to our line of sight, then the previously described illusion becomes more and more pronounced -- but the transverse component of its actual motion becomes smaller, cancelling this out to some extent. At very small angles, where we can only just separate the image of the jet from its parent quasar, the illusion is at its greatest but the transverse component is at its minimum. The net result is that the apparent multiplication of the object’s speed is not as great as those described in the stories, where things were exaggerated for effect. However, it is still significant.

Right, so what is actually being observed in the real world? Amongst others, an astronomer by the name of T. Pearson became interested in a jet of material some 70000 light years in length that had escaped from the quasar known as 3C 273. He decided to regularly observe a very bright nodule within the jet. When he first observed it in 1977, it was separated from the quasar by a distance of 62 light years. When he next observed it three years later, he found to his great astonishment that it was now separated by 87 light years. In other words, between 1977 and 1980, it had apparently moved a distance of 25 light years, which would imply that it was travelling at just over eight times the speed of light. That’s indeed rather impressive. [The determination of the actual speed of the nodule and its angle to our line of sight is, as they say, left as an exercise for the student... You can take that to mean that I don’t happen to know.]

Well, I hope this has been both entertaining and, if you will forgive the pun, enlightening. It would be better to have suitable illustrations to assist in the explanation; perhaps someone would like to contribute such to the next edition of Canopus? Or -- better -- perhaps someone can take up the challenge of presenting this as a "mini Bateman lecture" at the next ASSA meeting, complete with suitable drawings unfolding on the whiteboard. (Eben/Danie/Evan/Tom/etc., are you listening?). May I suggest Jean Michel Jarre’s "Chronologie" as suitable backing music to this epic extravaganza? Of course, I would also be more than happy to have any flaws in my understanding of this interesting phenomenon pointed out. And ecstatic if someone could explain it more simply. Lastly, just so that you can place this article in a temporal context, you may be interested to know that Stanley Kubrick died as I was writing it. (Not that I am suggesting that there is any connection, mind you.)

My best regards to all of you; I hope to see you soon...

Chris Stewart,
Brussels,
March 1999