# A Clock You Can Count On And Vice-versa

We’re both leery of the Acme Building’s elevators after escaping from one, so Vinnie and I take the stairs down to Pizza Eddie’s. “Faster, Sy, that order we called in will be cold when we get there.”

“Maybe not, Vinnie. Depends on his backlog.”

“Hey, before all this started, we were talking about the improved time standard and you said something about optical clockwork. I gather it’s got something to do with lasers and such.”

“It sure does. Boils down to Science preferring count-based units over ratios because they’re more precise. If you count something twice you should get exactly the same answer each time; if you’re measuring a ratio against a ruler or something, duplicate measurements might not agree. For instance, you can probably tell me how many steps there are between floors — “

“Fourteen”

“— more precisely than you can tell me the floor-to-floor height in feet or meters. And more accurately, too.”

“How can it be more accurate? I’ve got a range-finder gadget that reads out to a tenth of an inch. Or a millimeter if you set the switch for that.”

“Because that reading is subject to all sorts of potential errors — maybe you’re pointing it at an angle, or its temperature calibration is off, or you’re moving and there’s a Doppler effect. It may give you exactly the same reading twice in a row —”

“I always measure twice before I cut once.”

“Of course you do. My point is, that device might give you very precise but inaccurate answers that are way off. You’d have to calibrate its readings against a trustworthy standard to be sure.”

“Suppose my range-finder’s as precise as my step-counting. How can step-counting be better?”

“Because the step is defined as the measurement unit. There’s no calibration issues or instrumental drift or ‘it depends on how good the carpenter was,’ a step is a step. Step counting is accurate by definition. Nearly all our conventional units of measurement have some built-in ‘‘it depends’ factors that drive the measurement folks crazy. Like the foot, for instance — every time a new king came to power, his foot became the new standard and every wood and cloth merchant in the kingdom had to revise their inventory listings.”

“OK, so that’s basically why the time-measurement people wanted to get away from that ‘a second is a fraction of a day back when‘ definition — too many ‘it depends’ factors and they wanted something they could count. Got it. So back in what, 1967? they switched to a time standard where they could count waves and they went to the ‘a second is so many waves‘ thing. I also got that their first shot was to use microwaves ’cause that’s what they could count. But that was half-a-century ago. Haven’t they moved up the spectrum since then, say to visible light?”

“Not quite. They had to get tricky. Think about it. Yellow-orange light’s wavelength is about 600 nanometers or 600×10-9 meters. Divide that by the speed of light, 3×108 meters/second, and you get that each wave whizzes by in only 2×10-15 seconds. Our electronics still can’t count that fast, but we can cheat. Uhhh … which would be easier to answer — how many floors in this building or how many steps?”

“Floors, of course, there’s a lot fewer of them.”

“But the step count would track the floor count, regular as clockwork, because an exact number of steps separates each pair of floors. If you know one count, arithmetic tells you the other. The same logic can work with lightwaves. Soon after the engineers developed mode-locking theory and a few tricks like frequency combs, they figured out ways to stabilize a maser by mode-locking it to a laser. It’s like gearing down a once-a-second pendulum to regulate the hour-hand of a clock, so of course they called it optical clockwork even though there’s no gears.”

“Maser?”

“A maser does microwaves the way a laser does lightwaves. Every tick from a cesium-based maser is about 47,000 ticks from a strontium-based laser. Mode-lock them together and your clock’s good within a few seconds over the age of the Universe.”

“Hiya, Eddie.”

“Hiya, Vinnie. Perfect timing. Those pizzas you called for, they’re just comin’ outta the oven.”

~~ Rich Olcott

# In A Pinch And Out Again

<Vinnie’s phone rings> “Yeah, Michael? That ain’t gonna work, Micheal.” <to me> “Michael wants to hoist us out through the elevator cab’s ceiling hatch.” <to phone> “No, it’s a great idea, Michael, it’d be no problem for Sy, he’s skinny, but no way am I gonna fit through that hatch. Yeah, keep looking for the special lever. Hey, call Eddie downstairs for some pizza you can send through the hatch. Yeah, you’re right, pizza grease and elevator grease don’t mix. Right, we’ll wait, like we got any choice. Bye.” <to me> “You heard.”

“Yeah, I got the drift. Plenty more time to talk about the improved portable kilogram standard.”

“I thought we were talking about lasers. No, wait, we got there by talking about the time standard.”

“We were and we did, but all the improved measurements are based on laser tech. Mode-locking, optical tweezers and laser cooling, for instance, are key to the optical clockwork you need for a really good time standard.”

“Optical tweezers?”

“Mm-hm, that’s yet another laser-related Nobel Prize topic. There’s been nearly a dozen so far. Optical tweezers use light beams to grab and manipulate small particles. Really small, like cells or molecules or even single atoms.”

“Grabbing something with light? How’s that work?”

“Particles smaller than a light beam get drawn in to where the beam’s electric field varies the most. With a tightly-focused laser beam that special place is just a little beyond its focus point. You can use multiple beams to trap particles even more tightly where the beams cross.”

“Is that how ‘laser cooling’ works? You hold an atom absolutely still and it’s at absolute zero?”

“Nice idea, Vinnie, but your atom couldn’t ever reach absolute zero because everything has a minimum amount of zero-point energy. But you’re close to how the most popular technique is set up. It’s elegant. You start with a thin gas of the atoms you want to work with. Their temperature depends on their average kinetic energy as they zip around, right?”

“Yeah, so you want to slow them down.”

“Now you shine in two laser beams, one pointing east and one pointing west, and their wavelengths are just a little to the red of what those atoms absorb. Imagine yourself sitting on one of those atoms coming toward the east-side laser.”

Blue shift! I’m coming toward the waves so I see them scrunched together at a wavelength where my atom can absorb a photon. But what about the other laser?”

“You’d see its wavelength red-shifted away from your atom’s sweet spot and the atom doesn’t absorb that photon. But we’re not done. Now your excited atom relaxes by emitting a photon in some random direction. Repeat often. The north-south momentum change after each cycle averages out to zero but east-west momentum always goes down. The gas temperature drops.”

“Cool.”

All this talk of particles balanced in force fields gives me an idea. “Vinnie, d’ya think we stopped closer to the fifth floor or the sixth?”

“I think we’re almost down to five.”

“Good, that gives us a better chance. Where were you standing when we stopped?”

“Right by the buttons, like always. Whaddaya got in mind?”

“Michael said that’s a new elevator door, right? No offense, you’re heavy and I’m no light-weight. Both of us were standing at the very front of the cab. I’m thinking maybe our unbalanced weight tilted the cab just enough to catch an edge on some part of the door mechanism they didn’t put in quite right. Let’s switch places and both jump up and while we’re in the air wallop the top of the cab’s back wall as hard as we can. OK, on three — one, two, three!” “

<B-BLAMkchitKKzzzzzrrrrrrr-T>

“Michael. It’s Vinnie. We’re out. Yeah, ‘s wunnerful, I’m glad you’re glad. Look, something was sorta outta place in the new door mechanism on five and now it’s way outta place and the cab’s probably here for the duration. Call your repair guys, but before you do that bring up some Caution tape and something that’ll block the door open. Quick-like, right? I’m holding this door but I ain’t gonna be a statue long ’cause I’m hungry.”

~~ Rich Olcott

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

# Time in A Bottle, Sort Of

We’re in the Acme Building’s elevator, headed down to Eddie’s for pizza, when there’s a sudden THUNK.  Vinnie’s got his cellphone out and speed-dialed before I’ve registered that we’ve stopped.  “Michael, it’s me, Vinnie.  Hi.  Me and Sy are in elevator three and it just stopped between floors.  Yeah, between six and five.  Of course I know that’s where, I always count floors.  Look, you get us outta here quick and I won’t have to call the rescue squad and you don’t have paperwork, OK?  Warms my heart to hear you say that.  Right.  And there’s pizza in it for you when we’re out.  Thanks, Michael.”  <to me>  “Says it’ll be a few minutes.  You good for climbing out when he levers the doors?”

“Sure, no problem.  Might as well keep on about why the kilogram definition changed.  Oddly enough, the story starts with one of the weirdest standards in Science.  Here, I’ll pull it up on Old Reliable…”

“OK, that’s a weird number in the fraction, but what’s weird about the whole definition?”

“Think about it — when they defined this standard in 1960, it essentially said, ‘Go back sixty years, see how long it took for the Sun to return to exactly where it was in the sky a year earlier, capture exactly that weird fraction of the one-year interval in a bottle and bring it back to the present for comparison with an interval you want to report a time for.  Sound doable to you?”

“Mmm, no.  But these guy’s weren’t stupid.  There had to be a way.”

“The key is in those words, ephemeris time.”

“Something like Greenwich Time?  How would that help?”

“Greenwich Mean Time would be better — ‘mean’ as in ‘average.’  You know the Earth doesn’t spin perfectly, right?”

“Yeah, it wobbles.  The Pole Star won’t be at the pole in a few thousand years.”

“That’s the idea but things are messier than that.  For instance, when a large mass moves around, like a big volcano eruption or a major ice-sheet breakup or monsoon rains using Indian Ocean water to drench Southwest Asia, that causes a twitch in the rotation.”

“Hard to see how those twitches would be measurable.”

“They are when you’re working at 9-digit precision, which atomic clocks exceeded long ago.  Does your GPS unit have that spiffy dual-frequency function for receiving satellite time signals?”

“Sure does  — good to within a foot.”

“That’d be about 30 centimeters.  Speed of light’s 3×108 meters per second so you’re depending on satellite radio time-checks good to about, um, 100 nanoseconds, in a data field holding week number and seconds down to nanoseconds.  So you’d expect measurement jitter within … about 2 parts in 1015.  Pretty good, and on that scale those twitches count.”

“What do they do about them?”

“Well, you can’t fix Earth, but you can measure the twitches very carefully and then average over them.  Basically, you list all the Sun-position measurements made over many years, along with the corresponding time as reported by then-current science’s best clocks.  Use those observations to build a mathematical model of where an averaged fake Sun would appear to be at any given moment if it were absolutely regular, no twitches.  When the fake Sun would be at its highest during a given day, that’s noon GMT.”

“Fine, but what’s that got to do with your weird definition?”

“You can run your mathematical model backward in time to see how many times your best-we’ve-got-now clock would tick between fake noon and fake 12:00:01 on that date.  That calibrates your clock.”

“Seems a little circular to me — Sun to clock to model to fake-Sun to clock.”

“Which is why, now that we’ve got really good clocks, they’ve changed the operational definition by dropping the middleman.  The most precise measurements for anything depend on counting.  We now have technology that can count individual peaks in a lightwave signal.  These days the second is defined this way.  If a counter misses one peak, that’s one part in 10 million, three counts per year.  That’s so much better than Solar time they sometimes have to throw in a ‘leap-second’ so the years can keep up with the clocks.”

“Michael’s way overdue.  I’m callin’ him again.”

~~ Rich Olcott

# An Official Mass Movement

A December nip’s in the air.  I’m in my office trying to persuade the heating system to be more generous, when Vinnie wanders in carrying a magazine.  “I been reading about how a pound won’t be a pound any more.”

This takes me a moment to work out.  “Ah, you’re talking kilograms, not pounds, right?”

“Pound, kilogram, same difference, they’re both weights.”

“No, they’re not.  A kilogram at the bottom of the sea would still be a kilogram at the top of a mountain, but a pound high up weighs less than a pound lower down.”

“In what alternate universe does that make sense?”

“In any universe where Galileo’s observations and Newton’s equations are valid.  Thanks to them we know the difference between weight and mass.”

“Which is…?”

“That’s where things get subtle and it took Newton to tease them apart.  It’s the difference between quantifying something with a spring scale and quantifying it with a balance.  Say you put a heavy object on a scale.  It pulls down on the spring and the spring pulls up on the object.  When everything stops moving, the upward and downward forces are equal.  Given the spring’s stretch-per-pound relationship, you can measure the stretch and figure out how many pounds of force the object exerts.”

“Yeah, so…?”

“So now you put the same object on one pan of a balance.  You put kilogram blocks on the other pan until the balance beam levels out.  The beam goes level because the two sides of the balance carry the same mass.  Count the blocks and you know your object’s mass in kilograms.”

“Like I said, same difference.”

“Nope, because you’ve done two different operations.  On a balance your object will match up with the same number of blocks wherever you go with them.  Balance measurements are all about mass.  With the spring scale you compared gravity’s force against some other kind of force.  If you go somewhere else where gravity’s weaker, say to the top of Mt Everest, the scale will show a different weight even though the mass hasn’t changed.”

“How much different?”

“Not much for most purposes — about two pounds per ton between sea-level and Mt Everest’s peak.  But that’s a huge variation for physicists who look for clues to the Universe in the 5th or 6th decimal place.  High tech science and engineering need measurements, like mass, that are precise, stable and reproducible in many labs.  You noticed that both of my example measurements are too approximate for the techs.”

“Sure, the scale thing can be off because the spring can get wonky with use.  Um, and you can only measure the stretch within a percent or so probably.  But you can count the kilogram blocks — that ought to be a pretty good number.”

“Count-based metrics are indeed the most precise, but they’re problematic in their own way.  For one thing, maybe the object isn’t an exact number of kilograms.  Best you can do is say it’s between and n+1 kilograms.  But it’s worse than that.  The kilogram blocks can get wonky, too — finger-marks, corrosion, all of that.”

“But you can counter that by comparing the daily-use blocks with a standard you don’t use much.”

“Which sooner or later gets wonky with use so you have re-calibrate it to a whole chain of calibration blocks going back to a lovingly preserved great-grandmaster standard block, but what do we do when we get to Mars where it’d be difficult to get the local standard back to Earth for a re-calibration?”

“I see the problem.  Is that why a kilogram won’t be a kilogram any more?”

“Well, that’s why The Kilogram won’t be Le grand K, the great-grandmaster standard — a carefully monitored hunk of platinum-iridium that’s actually kept in a guarded, climate-controlled vault in a Paris basement.  It’s taken out only once every few years to compare with its kin.  Even so it appears to have lost 50 micrograms since 1889.  We think.  So they’re demoting it.”

“What’re they replacing it with?  Not another lump of metal, then?”

“Oh, no, they need something that’s precisely reproducible anywhere, preferably something that’s count-based.  The new standard will be official soon.  It’s a great physics story.”

~~ Rich Olcott