The Spectrum of Lightning

Forked Lightning Spectra

Denis Joye captured these lightning spectra during a thunderstorm over Paris. They reveal the extreme conditions inside a lightning stroke.

He used a 540 line/mm diffraction grating in front of the camera lens. A slit is usually needed to get good line spectra. Here the very narrow lightning strokes make a slit quite unnecessary.

We see sharp spectrum emission lines superimposed on weaker continuum light.

Putting Some Spin On It

University of St Andrews scientists create ‘fastest man-made spinning object’

The team then used the miniscule forces of laser light to hold the sphere with the radiation pressure of light – rather like levitating a beach ball with a jet of water.

They exploited the property of polarisation of the laser light that changed as the light passed through the levitating sphere, exerting a small twist or torque.

Light, of course, can have angular momentum, so if the ball was changing the light from linear to circular polarization (or vice versa), the angular momentum change would have to come from the ball, so it would spin.

If my calculator skills are not failing me, the ball had around 10^17 h-bar of angular momentum, which isn’t a lot for a macroscopic object. 10^17 photons is less than a tenth of a Watt-second’s worth of visible light, or 10 mW for less than 2 minutes.

Nick over at Fine Structure points out that the Nature Communications paper is currently free.

The technique they are using is actually using the material as a half-wave plate, which is twice as effective at imparting angular momentum to the sphere as I had described. When circularly polarized light is incident upon it it switches the direction of the polarization, imparting 2*h-bar of angular momentum.

Don't Stop Me if You've Heard This Before

It’s time for the seemingly semi-annual announcement (which you may have already seen) about the new work coming out of some lab (often it’s NIST), where a new experimental technique, or new atom or ion, or some other ingenuity or heroic effort allows them to come up with a better frequency standard measurement. In this month’s game of Clock Clue it’s NIST (plus collaborators), in an optical lattice, with neutral Ytterbium.

Ytterbium Clock Sets New Stability Mark

An international team of researchers has built a clock whose quantum-mechanical ticking is stable to within 1.6 x 10^-18 (a little better than two parts in a quintillion).

This is pretty awesome work (do they get bored with being awesome on a regular basis?) But now comes my standard disclaimer: this isn’t really a clock, it’s a frequency standard. Side note: I had a communication from someone doing a little background on a similar situation and they made the comment that it seems that people in the timing community are kind of sensitive about the distinction between frequency standards and clocks. I don’t know this to be true — I’m the only one who seems to spend any effort making the distinction. I’m not terribly upset by it (I understand why clock is used) and I can’t speak for anyone else. Everyone in the community already knows, so they aren’t confused by it, and they probably don’t care all that much about what goes on in the popular press. But I blog, and this is the sort of thing that matters more in the science communication field, and it affects me when someone says they read about a new clock that NIST build and am I working on that too? And if it happens to me, I’m sure it’s part of certain discussions that happen above my pay grade.

In other words, it matters with respect to people who fund these efforts. I’m reasonably sure there are higher-level inquiries, asking if we’re working on this sort of thing, and why the hell not, and/or not understanding the difference in measuring frequency and time. If you don’t see the difference, you might think that there’s a duplication of effort going on. Even if you get the distinction, you might think this is a technology we should be investigating*.

So let me explain with an analogy that might be easier to understand than timing.

Imagine you are navigating a vessel in eternal fog — there is no way to do any kind of observing for a navigational fix. You want to follow a path — let’s say you want to go exactly north, so you can think of a line drawn on a map, going north, from where you are. That’s the course you wish to follow. (we’re assuming a flat earth here, so all lines north are parallel)

You have a compass that’s pretty good but not perfect. There is going to be some steering “noise” because of this. If the compass exhibits 1 degree of error, that means your velocity vector is going to randomly point anywhere from 1 degree port to 1 degree starboard, randomly. On average your direction will be correct, but that’s for your velocity vector. For your displacement, which is what’s important to you, there will be a random walk, because that’s what the integral of white noise becomes — a random walk. Put another way, even though the direction averages to zero, the errors do not cancel — being off by some angle to port is not immediately followed by being off to starboard by the same amount — the steering error is never undone. It accumulates with each random jiggle of the compass, and there’s nothing you can do about it.

The result is that your good compass means you will random walk some distance to the side of your ideal path that you’d have for a perfect compass. You’re traveling north, and when you reach your destination you might have a random walk to the east by a mile, and that’s bad. You want a better compass.

Let’s say you have a much, much better compass. Good to an arc second instead of a degree — that’s 3600 times better. If you could use it all the time, your 1 mile lateral random walk becomes a few feet. For all intents and purposes, it’s perfect.

However, for some reason, you can’t use it all the time. (insert any plot twist you like for a reason why). Let’s say you can only use it half a day. While you’re using it you accumulate essentially no error in your path, but when you are stuck using the old compass, you still accumulate your error. Since you can use the perfect compass half the time, your random walk error is cut in half, even though the new compass is 3600 times better. The actual improvement in performance is a combination of two things: the precision and the duty cycle.

It’s the same with clocks. Since you are counting “ticks” to keep time, it means that time is an integral of frequency — any clock with white frequency noise will random walk away from perfect time. And you can only count ticks when a clock is running. What do you do when it’s not running? It’s the worst clock in the world when it’s not running! So you have to a have a flywheel — some other clock (in practice a group of them, sometimes called a timing ensemble) to keep time when your über-cool device isn’t running. Even if you add a device that’s 100 times better, its improvement to your timekeeping is limited by its duty cycle, just as with the compasses.

In this case, they ran for 7 hours to make one stability measurement. How often can they do that? Every 3 days? That’s a 10% duty cycle, and even though its stability is 100 times better than currently used clock systems, it would only represent a 10% improvement in your timing ensemble’s performance. Depending on the size of your ensemble, you might see the same (or better) improvement just by adding another continuously-running clock to it, and averaging them all together — ideally, the stability of an ensemble of identical clocks depends on the square root of the number of clocks.

The Ytterbium device is really neat, with stability of a part in 10^18 being a big achievement. There is a lot of neat physics you can do with one, or better yet, two of them. But for the application of timekeeping, the ability to run essentially continuously is very important, and timekeeping is primarily what a clock is for. The better analogy in this case is a stopwatch rather than a clock, just in case you care about the distinction. That doesn’t make for a good headline, though: NIST builds a better stopwatch sounds a bit dismissive and I don’t want to diminish the accomplishment in any way, which is why clock is going to be used even though it’s technically wrong. Until the technology becomes robust enough to run all the time, though, it’s not something that’s going to become part of a true clock.

*it happened when Bose-Einstein Condensates were in the news. Lots of questions about whether we were going to make a clock out of a BEC.

Rapunzel, Rapunzel

I’ve been hearing about Mark Kasevich’s super fountain tower for a while (including someone who was involved in funding it who was trying dazzle me a little. It worked.) A 10m tall device is imposing; one might ask what you can do with such a device that you can’t do with something that fits in one room. The answer is some really neat interferometry:

Viewpoint: A New Starting Point for Atom Interferometry

Point Sources and Towers: “Multiaxis Inertial Sensing with Long-Time Point Source Atom Interferometry”

An Anniversary, of Sorts

This isn’t going to be about physics. In fact, the only connection is that I was teaching physics when this happened. This is about what happened one night, 28 years ago: Ex-sailor Releases Hostage After Siege At Navy Base. LT Steve Gabriel (who taught Chemistry, Materials and Radiological Fundamentals, aka CMR) was taken hostage by a former student.

About the same time, Gabriel also called security while he was being held

“Security” would be me, since I was standing the Command Duty Officer watch at the time. CDO is a 24-hour watch that one stands, and you are responsible for, well, everything when the commanding officer (CO, aka captain) is gone. Imagine borrowing a car from someone — you’re responsible for it until you return the keys. Except that the CO doesn’t actually own the car — s/he was assigned to it by someone else, and is ultimately responsible for it. If the car starts making sounds, you’re going to call the captain up and make sure it’s not a problem, and the CO is not prone to yell at you for checking, because the last thing they want is to get the car back with a surprise problem. “My CDO was an idiot” is not an excuse, because that only prompts one to ask why you lent the keys to an idiot. The navy is not fond of excuses, especially ones that sound like they are passing the buck.

On a quiet watch, the kind you hope for every time, there are no incidents to worry about. You do your rounds, do the paperwork that’s required and get a few hours of sleep. If it was during the week you’d teach and not have to worry about the CDO part during the day, while the captain was there. After you took charge the other watchstanders all did their jobs (there was a duty chief petty officer for each building, and someone from the first lieutenant’s staff, in charge of the evening cleaning crews and other duties, plus a dozen or so people as unarmed security watchstanders, working the phones and checking traffic into and out of the buildings, making sure you had your security badge, or weren’t leaving with any classified documents)

On a good night, aside from a stroll or two around the buildings, you got to sit around and hear the enlisted guys tell sea stories. I was 23, just a year out of college and still an Ensign and had no stories to tell (yet), other than some drunken stupidity, but even then, exotic-port navy drunken stupidity made for much better stories. It was fun to listen to that, and some of the things that happen at sea. But on this evening, there wasn’t going to be much time for sea stories.

Physicist proves impossibility of quantum time crystals

Bruno’s proof demonstrates that setting a system of particles in motion around a one-dimensional magnetic ring always increases the ground-state energy of the system so that it’s no longer in its ground state, which prohibits the existence of a rotating ground-state system. The proof covers systems rotating at any finite angular velocity.

I had linked to this some time back because the press release was bad and made some overly bold extrapolations. Interesting that a periodic system as described can’t be in a ground state.

There are also probably a couple of “I reject quantum theory” crackpots who will be disappointed, as this seems to rule out some of the favorite classical atom models. Oh, who am I kidding. They are impervious.

Tackling the Block Problem Some More

More on the problem posted yesterday. Such a simple setup, and it’s generated a lot of positive discussion in the physics blogohedron (including twitter), which is a sign that I’m not the only one who thinks it’s a great demo.

As I stated, the kinetic energy of a particle of momentum p is given by p^/2m (since KE = 1/2 mv^2 and p = mv). We can estimate how much of the initial kinetic energy is lost; since momentum is the same before and after the collision, all we need to know is the mass of “moving things” before and after. The ratio of the initial and final KE is then just m/(m+M), where m is the mass of the projectile and M is the mass of the target. If this is a 10g bullet and a 1kg block of wood, then only 1% of the kinetic energy remains after the collision.

Let’s assume the block of wood went up about a meter in the video. To do that the speed is about 4.4 m/s right after the collision, which gives the bullet+block system a kinetic energy of 9.8 Joules (which is what you’d better expect to 2 digits for a ~1 kg system rising a meter). That means the bullet had a kinetic energy of 970 Joules! It was also traveling at ~440 m/s prior to impact.

Elastic collisions are different. KE is conserved, and the incident particle recoils. This gives you a momentum equation and a kinetic equation to solve, with the final velocities being the two unknowns, so you can solve for them in terms of the initial velocity of the projectile. Do a little math and you get the results.

If we solve for the final speed of the two objects but use the same masses and speeds, the block will start up at a speed of 8.7 m/s — almost twice as fast, so there is almost 4 times the kinetic energy (38 Joules). The projectile (more like a super-ball rather than a bullet, and probably a harder target) will end up going -431 m/s. The negative sign means its going down, as you expect — it will recoil, just not quite as fast. That’s 930 Joules, and 930 + 38 is about 970 (the same to the two digits I kept in the calculations)

If you play around with those formulas, you can see the target always goes in the direction of the projectile, but the projectile can recoil if the target is more massive, come to a stop if it has the same mass as the target, or will continue on in the same direction if it is more massive. I hope that matches intuition.

The rotating case is a little more complicated to work out, since you have more variables. Since the ball recoils and the block rotates, that’s another set of equations, and there’s the issue of the ball not bouncing straight down, which literally (and I literally mean literally; thanks a lot, OED) brings another dimension to the problem, though this effect is probably small for this problem and could be ignored.

After This, Veritasium Will Saw a Woman in Half

Some physics sleight-of-hand. I like it.

I have to admit, my first instinct was that the rotating block should not have gone as high, but I quickly realized why this was wrong. I don’t know if the folks in the video who are truly puzzled or acting that way for the sake of the video, because from other science videos I’ve seen, they are smart cookies.

There is not any extra energy that has to be “created” for the rotating case, because this is a completely inelastic collision. Kinetic energy is not a conserved quantity (!), total energy is. KE is only conserved in elastic collisions. There is more kinetic energy in the rotating case, and that’s just fine! And that’s the misdirection — everyone is puzzling over a quantity that’s not constant, implying that it should be. But this is why it’s a great demo — you have to identify and avoid a misconception to get the answer.

So it’s possible they are just playing to the audience to try and get you to think something mystical is going on here, or they “got it” soon after the first reaction was taped.

Now, what is conserved in these interactions is momentum, both linear and angular, since at the moment of impact there are no external forces or torques we have to worry about; we ignore gravity, since the effect during the short time of impact is very, very small. The impulse would be mgt, where t is the time of impact, and that’s small compared to the momentum of a fast-moving projectile. We’re physicists, and we set small effects to be zero. Too messy otherwise.

In the straight-on case, we have a linear momentum p, and momentum and kinetic energy have a simple relationship: KE = p^2/2m. So the kinetic energy is dictated by the momentum of the bullet (nail) just before it strikes the block, and it will go to whatever height where the energy has changes to potential energy, because in that case, mechanical energy is conserved: KE + PE is a constant when no work is done.

Concluding: If the nail has the same momentum in each case, the block must rise to the same height, rotation be damned.

Rotationally, it’s similar. The angular momentum is L = r X p, (or rp, at the point of impact), and angular momentum has a similar relation to rotational KE as the linear case does. Mass becomes moment of inertia, and you have L^2/2I as your rotational energy.

But the rotational energy does not come at the expense of the linear (which is different experience than rolling a ball or disk down an incline, where they must share). Because of the collision, KE is not conserved, and all we are doing in the rotating case is turning little less of the lost KE into sound, deformation of the wood, and a temperature increase, and using it to rotate the block.

Leon's Getting Laaarger

Why Do Solids Expand When Heated?

Higher temperatures mean higher energy levels. At higher energy levels, the average atom separation is also larger. When you increase the temperature for most objects, they expand. Of course, this assumes that the more complicated ball and spring model works for solids as well as for molecular hydrogen, but it mostly does.

There’s this as well, which is a snapshot of how physicists think:

The simple spring model is much easier to use and works for some things. Like all models, if it works we us it.

It explains why we e.g. model things as harmonic oscillators all the time. It works.

My Voice is My Passport. Verify Me.

As I wrote on Friday, there’s a potential danger in thinking that your experience is typical or widespread. I ran across a topic where this applies — online pseudonyms. I obviously don’t; I work in a small slice of applied science, so I think it would be hard to put up repeated posts about timekeeping and not be found out, but more importantly, I’m not in a situation where need to hide who I am. But that isn’t true of all bloggers.

Tell me again how pseudonyms are lame

Pseudonyms are essential online

I think it’s important to draw the distinction between an anonymous online presence and a pseudonym. A pseudonym at least presents a consistent persona. Even though you don’t know the person’s name, there is an identity associated with the ideas. Criticism aimed at anonymous writing doesn’t necessarily apply to someone using a pseudonym.