## Sunday, April 12, 2015

### Photonic Booms: How images can move faster than light, and what they can tell us.

If you sweep a laser pointer across the moon, will the spot move faster than the speed of light? Every physics major encounters this question at some point, and the answer is yes, it will. If you sweep the laser pointer it in an arc, the velocity of the spot increases with the distance to the surface you point at. On Earth, you only have to rotate the laser in a full arc within a few seconds, then it will move faster than the speed of light on the moon!

This simplified explanation would be all there is to say were the moon a disk, but the moon isn’t a disk and this makes the situation more interesting. The speed of the spot also increases the more parallel the surface you aim at is relative to the beam’s direction. And so the spot’s speed increases without bound as it reaches the edge of the visible part of the moon.

That’s the theory. In practice of course your average laser pointer isn’t strong enough to still be visible on the moon.

This faster-than-light motion is not in conflict with special relativity because the continuous movement of the spot is an illusion. What actually moves are the photons in the laser beam, and they move at the always same speed of light. But different photons illuminate different parts of the surface in a pattern synchronized by the photon’s collective origin, which appears like a continuous movement that can happen at arbitrary speed. It isn’t possible in this way to exchange information faster than the speed of light because information can only be sent from the source to the surface, not between the illuminated parts on the surface.

That is for what the movement of the spot on the surface is concerned. Trick question: If you sweep a laser pointer across the moon, what will you see? Note the subtle difference – now you have to take into account the travel time of the signal.

Let us assume for the sake of simplicity that you and the moon are not moving relative to each other, and you sweep from left to right. Let us also assume that the moon reflects diffusely into all directions, so you will see the spot regardless of where you are. This isn’t quite right but good enough for our purposes.

Now, if you were to measure the speed of the spot on the surface of the moon it would appear on the left moving faster than the speed of light initially, then slowing down as it approaches the place on the moon’s surface that is orthogonal to the beam, then speed up again. But that’s not what you would see on Earth. That’s because the very left and very right edges are also farther away and so the light takes longer to reach us. You would instead see a pair of spots appear close by the left edge and then separate, one of them disappearing at the left edge, the other moving across the moon to disappear on the other edge. The point where the spot pair seems to appear is the position where the velocity of the spot on the surface drops from above the speed of light to below.

This pair creation of spots happens for the same reason you hear a sonic boom when a plane passes by faster than the speed of sound. That’s because the signal (the sound or the light) is slower than what is causing the signal (the plane or the laser hitting the surface of the moon). The spot pair creation is thus signal of a “photonic boom,” a catchy phrase coined by Robert Nemiroff, Professor for astrophysics at Michigan Technological University, and one of the two people behind the Astronomy Picture Of the Day that clogs our facebook feeds every morning.

The most surprising thing about this spot pair creation is that nobody ever thought through this until December 2014, when Nemiroff put out a paper in which he laid out the math of the photonic booms. The above considerations for a perfectly spherical surface can be put in more general terms, taking into account also relative motion between the source and the reflecting surface. The upshot is that the spot pair creation events carry information about the structure of the surface that they are reflected on.

But why, you might wonder, who cares about spots on the Moon? To begin with, if you were to measure the structure of any object, say an asteroid, by aiming at it with laser beams and recording the reflections, then you would have to take into account this effect. Maybe more interestingly, these spot pair creations probably occur in astrophysical situations. Nemiroff in his paper for example mentions the binary pulsar 3U 0900-40, whose x-rays may be scattering off the surface of its companion, a signal that one will misinterpret without knowing about photonic booms.

The above considerations don’t only apply to illuminated spots but also to shadows. Shadows can be cast for example by opaque clouds on reflecting nebula, resulting in changes of brightness that may appear to move faster than the speed of light. There are many nebula that show changes in brightness thought to be due to such effects, like for example the Hubble Nebula (HVN: NGC 2260). Again, one cannot properly analyze these situations without taking into account the spot pair creation effect.

In his January paper, Nemiroff hints at an upcoming paper “in preparation” with a colleague, so I think we will hear more about the photonic booms in the near future.

In 2015, Special Relativity is 110 years old, but it still holds surprises for us.

This post first appeared on Starts with A Bang with the title "Photonic Booms".

1. http://www.stsci.edu/ftp/science/m87/press.txt (1999, oopsie)
http://spiff.rit.edu/classes/phys200/lectures/superlum/superlum.html
http://en.wikipedia.org/wiki/Superluminal_motion

Superluminal observations are not superluminal phenomena. Tomographic object reconstruction; observation that is time-asymmetric. Sweet. Our universe is not exactly mirror-symmetric at any scale, explicitly (Weak interaction) and as a racemate trace wandering around exact cancellation. Observations are diagnostic not anomalous: black swans, black flamingos, black experiment. Enjoy the view.

2. Wouldn't we expect to see this effect in light received from the gaseous shell(s) surrounding a pulsar? As the pulsar spins it should illuminate the shell of surrounding material, and create a superluminal "source" (assuming there is a distinct enough shell of material). I would think this is easier than trying to resolve light reflected off the limb of a relatively tiny solid spherical body.

By the way, I think the links in Uncle Al's message refer to a different effect, in which the source is actually sub-luminal, but one can mis-interpret the signal and mistaken conclude that the source was superluminal. The subject of this post refers to actual superluminal sources, i.e., the sequence of source events is spacelike separated, like a moving shadow.

3. Amos,

Yes, I think one would expect that.

4. With apologies to everybody who has so far enjoyed the exchange in my comment section, I've had to turn on comment moderation. I've really gotten tired of all the bullshit comments that aren't making any interesting contributions.

Please make sure that your comment is on topic, this means in this case about the paper under discussion, and I'll almost certainly approve it.

I am not even remotely interested in your personal opinion about what is wrong with mainstream physics, why special relativity is wrong, or what you think is the solution to the black hole information loss problem. Please take your so-called insights elsewhere.

5. Amos,

Yes, were a shell close enough to a pulsar and near enough to a spherical geometry, one might expect spot pair events to be created on the shell from the pulsar's sweeping beam. Such a simple case might not be evident in nature, though. As a thought experiment what happens can be really cool looking, though, with spot pairs being both created an annihilated in quite a light show as the beam rotates.

As you indicated, the paper (now published: PASA 32, 1, 2015: http://dx.doi.org/10.1017/pasa.2014.46) cites another case of a pulsar beam sweeping by a companion star, which might be more common in nature. See Milgrom & Avni (1976) and Chester (1979) in the reference list. Even if the star is "tiny", it is likely bigger than the pulsar and the key factor is distance between the two. Since the example star (binary pulsar 3U 0900-40) is likely both close to the pulsar and spherical, pair events might be evident, faintly, in the time series of the pulses.

- RJN

6. Back in the late 1970s there was an ad for an oscilloscope with a beam faster than light in the sense that its trace could cross the screen in less time than a beam of light starting at one edge could reach the other. (i.e. The beam could move from one edge to the other of a 6" wide screen in less than 0.5 nanoseconds.)

Given the rapid rise of digital circuit speeds at the time, this was a useful gadget. It suggested, however, that oscilloscopes were going to get bigger and bigger to keep up with logic gates as their response moved into the femtoseconds.

7. I've been thinking about another idea. instead of a laser pointer, a light bulb. the light from the light bulb radiates and can be seen (absorbed) by body "A" which is a million miles away from the light bulb. The light can also be seen by body "B" which is also a million miles away from the light bulb...but 2 million miles from A. That is, A and B are on opposite sides of the light bulb. Let's say A has the ability to choose whether or not to absorb light as a photon from the light bulb (I don't know if that is possible). Then A could send a morse code message to B instaneously. That is, absorbing a light photon would be a 0 and not absorbing a light photon would be a one.

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