Elevator, Locked And Loaded

Vinnie’s on his phone again.  “Michael!  Where are you, man?  We’re still trapped in this elevator!  Ah, geez.”  <to me>  “Guy can’t find the special lever.”  <to phone>  “Well, use a regular prybar, f’petesake.”  <to me>  “Says he doesn’t want to damage the new door.”  <to phone>  “Find something else, then.  It’s way past dinner-time, I’m hungry, and Sy’s starting to look good, ya hear what I’m sayin’?  OK, OK, the sooner the better.”  <to me>  “Michael’s says he’s doin’ the best he can.”

“I certainly hope so.  Try chewing on one of your moccasins there.  It’d complain less than I would and probably taste better.”

“Don’t worry about it.  Yet.”  <looks at Old Reliable’s display, takes his notebook from a pocket, scribbles in it>  “That 1960 definition has more digits than the 1967 one.  Why’d they settle for less precision in the new definition?  Lemme guess — 1960s tech wasn’t up to counting frequencies any higher so they couldn’t get any better numbers?”

“Nailed it, Vinnie.  The International Bureau of Weights and Measures blessed the cesium-microwave definition just as laser technology began a whole cascade of advancements.  It started with mode-locking, which led to everything from laser cooling to optical clockwork.”

“We got nothing better to do until Michael. Go ahead, ‘splain those things.”

“Might as well, ’cause this’ll take a while. What do you know about how a laser works?”

“Just what I see in my magazines. You get some stuff that can absorb and emit light in the frequency range you like. You put that stuff in a tube with mirrors at each end but one of them’s leaky. You pump light in from the side. The stuff absorbs the light and sends it out again in all different directions. Light that got sent towards a mirror starts bouncing back and forth, getting stronger and stronger. Eventually the absorber gets saturated and squirts a whoosh of photons all in sync and they leave through the leaky mirror. That’s the laser beam. How’d I do?”

“Pretty good, you got most of the essentials except for the ‘saturated-squirting’ part. Not a good metaphor. Think about putting marbles on a balance board. As long as the board stays flat you can keep putting marbles on there. But if the board tilts, just a little bit, suddenly all the marbles fall off. It’s not a matter of how many marbles, it’s the balance. But what’s really important is that there’s lots of boards, one after the other, all down the length of the laser cavity, and they interact.”

“How’s that important?”

“Because then waves can happen. Marbles coming off of board 27 disturb boards 26 and 28. Their marbles unbalance boards 25 and 29 and so on. Waves of instability spread out and bounce off those mirrors you mentioned. New marbles coming in from the marble pump repopulate the boards so the process keeps going. Here’s the fun part — if a disturbance wave has just the right wavelength, it can bounce off of one mirror, travel down the line, bounce back off the other mirror, and just keep going. It’s called a standing wave.”

“I heard this story before, but it was about sound and musical instruments. Standing waves gotta exactly match the tube length or they die away.”

“Mm-hm, wave theory shows up all over Physics. Laser resonators are just another case.”

“You got a laser equivalent to overtones, like octaves and fourths?”

“Sure, except that laser designers call them modes. If one wave exactly fits between the mirrors, so does a wave with half the wavelength, or 1/3 or 1/4 and so on. Like an organ pipe, a laser can have multiple active modes. But it makes a difference where each mode is in its cycle. Here, let me show you on Old Reliable … Both graphs have time along the horizontal. Reading up from the bottom I’ve got four modes active and the purple line on top is what comes out of the resonator. If all modes peak at different times you just get a hash, but if you synchronize their peaks you get a series of big peaks. The modes are locked in. Like us in this elevator.”

“Michael! Get us outta here!”

~~ Rich Olcott

Advertisements

The New System’s in Tune

<We interrupt our running story line to bring you this important development…>

“Morning, Sy.  What can I get you?”

“My usual mugfull of black, Al.  What’s the Scone-of-The-Day?”

“I’m calling this The Trappist.  It’s got raspberry jam!”

“Why that name?”

“In honor of TRAPPIST-1, you know, that star they just found a bunch of planets around.”

“Your coffee shop being right next to the Astronomy building, I guess you’ve heard a lot about it.”

“Sy, you couldn’t believe.  The planetologists are going nuts of course, even though no-one’s actually seen the planets, and the astrometrics folks are lining up for telescope time ’cause they’ve got a whole new class of stars to monitor and of course the astrophysicists get to figure out how the system even works.”

“Astrometrics folks?  New class of stars?”

“Yeah, the high-precision star-measurers.  They didn’t used to pay attention to the small, dim stars because why bother.  But now … woo-hoo, whole new ballgame.”

“Nobody’s seen those planets?  How do they know they’re there?”

“Process of elimination, Sy.  The TRAPPIST telescopes picked up repetitive dark blips in the light coming from that star.  It’s a close, fast-moving star so there’s no sense supposing it’s like going behind or in front of a regular array of rocks or stars or something.  It’s not wobbling side-to-side like it would if it was a binary so it’s not traveling along with another star.  If the blips were sunspots going around as the star rotates there’d be only one rhythm, but these blips come in too complicated for that.  Besides, the star’s low-activity, too cool for lotsa sunspots.  Gotta be planets eclipsing it.”

trappist-1-system-450
NASA’s artistic (and cute) rendition
of the TRAPPIST-1 system
Note the close-in steam and the frost further out

“Sounds pretty good, but…”

“Hey Sy, there was something else, maybe you could explain it.  One astrophysics guy was real impressed that the planets had residences.  I didn’t understand that.”

“Residences?  That’s a new one on me.”

“Had something to do with the blip periods.  Yeah, here’s the paper napkin he wrote ’em all down on.”

Object
TRAPPIST-1x
Period, days
Resonance
Actual /
Expected
b
1.51
c
2.42
5c:8b
1.002
d
4.05
3d:5c
1.004
e
6.10
2e:3d
1.004
f
9.20
2f:3e
1.006
g
12.35
3g:4f
1.007
h
20?
5h:8g
1.012?

“Oh, resonances! That I recognize, and yeah, those numbers are much more convincing.  Remember my post about gear logic?”

“Sorry, Sy, that must’ve been a long time ago and who has time to read?”

“I understand.  OK, that post explained how planets that survive the early chaos of a forming solar system tend to wind up in orbits whose relative year-lengths form ratios of small whole numbers.  In our system, for instance, the length of Pluto’s year is exactly 3/2 of Neptune’s, Neptune’s year is twice that of Uranus, and so on.  If a planet doesn’t synch up with its neighbors, it’ll collide with someone or be flung out of the system.  Put another way, a system’s not stable if its planetary orbit periods are just any old numbers.  Make sense?”

“I suppose, so…?”

“So look at this guy’s table.  The periods of each pair of adjacent objects follow that rule almost exactly.  Five times c‘s period is less than 0.25% away from eight times b‘s, and so on all the way out to h, which I take it has an uncertain period because the guy put in that question mark.  In fact, I think this system follows the rule more tightly than our Solar System does.  As far as I’m concerned that regularity in the periods makes the case for TRAPPIST-1 having planets.  You hear anything else?”

“Yeah, there was a lot of excitement about the middle three planets being in some kind of Goldilocks zone.  What’s that about?”

“Hah, I’d be excited, too.  If a planet’s too close to the star, like Mercury is to ours, it’ll be too hot for liquid water.  If the planet’s too far, any water it has would be frozen stiff.  Either way, not good for life to grow there.  In the Goldilocks zone, it’s…”

“Just right, huh, Sy?”

“On the nose, Al.  I’m going to have to read up on TRAPPIST-1.”

~~ Rich Olcott