Trombones And Echoes

Vinnie’s fiddling with his Pizza Eddie’s pizza crumbs. “Hey, Sy, so we got the time standard switched over from that faked 1900 Sun to counting lightwave peaks in a laser beam. I understand why that’s more precise ’cause it’s a counting measure, and it’s repeatable and portable ’cause they can set up a time laser on Mars or wherever that uses the same identical kinds of atoms to do the frequency stuff. All this talk I hear about spacetime, I’m thinkin’ space is linked to time, right? So are they doing smart stuff like that for measuring space?”

“They did in 1960, Vinnie. Before that the meter was defined to be the distance between two carefully positioned scratches on a platinum-iridium bar that was lovingly preserved in a Paris basement vault. In 1960 they went to a new standard. Here, I’ll bring it up on Old Reliable. By the way, it’s spelled m-e-t-e-r stateside, but it’s the same thing.”

“Mmm… Something goofy there. Look at the number. You’ve been going on about how a counted standard is more precise than one that depends on ratios. How can you count 0.73 of a cycle?”

“You can’t, of course, but suppose you look at 100 meters. Then you’d be looking at an even 165,076,373 of them, OK?”

“Sorta, but now you’re counting 165 million peaks. That’s a lot to ask even a grad student to do, if you can trust him.”

“He won’t have to. Twenty-three years later they went to this better definition.”

“Wait, that depends on how accurate we can measure the speed of light. We get more accurate, the number changes. Doesn’t that get us into the ‘different king, different foot-size’ hassle?”

“Quite the contrary. It locks down the size of the unit. Suppose we develop technology that’s good to another half-dozen digits of precision. Then we just tack half-a-dozen zeroes onto that fraction’s denominator after its decimal point. Einstein said that the speed of light is the same everywhere in the Universe. Defining the meter in terms of lightspeed gives us the same kind of good-everywhere metric for space that the atomic clocks give us for time.”

“I suppose, but that doesn’t really get us past that crazy-high count problem.”

“Actually, we’ve got three different strategies for different length scales. For long distances we just use time-of-flight. Pick someplace far away and bounce a laser pulse off of it. Use an atomic clock to measure the round-trip time. Take half that, divide by the defined speed of light and you’ve got the distance in meters. Accuracy is limited only by the clock’s resolution and the pulse’s duration. The Moon’s about a quarter-million miles away which would be about 2½ seconds round-trip. We’ve put reflectors up there that astronomers can track to within a few millimeters.”

“Fine, but when distances get smaller you don’t have as many clock-ticks to work with. Then what do you do?”

“You go to something that doesn’t depend on clock-ticks but is still connected to that constant speed of light. Here, this video on Old Reliable ought to give you a clue.”

“OK, the speed which is a constant is the number of peaks that’s the frequency times the distance between them that’s the wavelength. If I know a wavelength then arithmetic gets me the frequency and vice-versa. Fine, but how do I get either one of them?”

“How do you tune a trombone?”

“Huh? I suppose you just move the slide until you get the note you want.”

“Yup, if a musician has good ear training and good muscle memory they can set the trombone’s resonant tube length to play the right frequency. Table-top laser distance measurements use the same principle. A laser has a resonant cavity between two mirrors. Setting the mirror-to-mirror distance determines the laser’s output. When you match the cavity length to something you want to measure, the laser beam frequency tells you the distance. At smaller scales you use interference techniques to compare wavelengths.”

Vinnie gets a gleam in his eye. “Time-of-flight measurement, eh?” He flicks a pizza crumb across the room.

In a flash Eddie’s standing over our table. “Hey, hotshot, do that again and you’re outta here!”

“Speed of light, Sy?”

“Pretty close, Vinnie.”

~~ Rich Olcott

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What Time Is It on Mars?

I’m puffing a little after hiking up a dozen flights of stairs. That whole bank of Acme Building elevators is closed off while the repair crew tries to free up the one that trapped us. The crowd waiting for the other bank is forgetaboutit. I unlock my office door and there’s Vinnie, tinkering with the thermostat. “Geez, Sy, it’s almost as cold in here as it is out in the hall. Hey, ya think there’s anything to the rumor that building management is gonna rent out that elevator as office space? And how does time work on Mars?”

“Morning, Vinnie. You’re right, I don’t think so, and where’d that last question come from?”

“I been thinking about those ultra-accurate clocks and how they’d play into that relativity stuff we talked about with Ramona.” <short lull in the conversation as we both consider Ramona> “Suppose there’s one of those clocks in a satellite going around Earth. If I remember right, it’s going ZIP around the planet so its clock ought to run faster than my wristwatch, but it’s further out of Earth’s gravity well so its clock ought to run slower. Which would win?”

“You remembered right — you’ve got Special Relativity and General Relativity in a couple of nutshells, and yes, they sometimes work in opposite directions. You have to look at the numbers. Give me a sec to work up a few examples on Old Reliable… OK, let’s start with the speed part. That’s Special Relativity because they both start with ‘SP’.”

“Cute.”

“I thought so.  OK, here’s a handful of locations and their associated straight-line speeds relative to some star far away. That last column shows a difference factor for a clock at each location compared to a far-away motionless clock in a zero gravitational field. Multiply the factor by 86,400 seconds per day to get the time difference per day. The fastest thing on the list is that spacecraft we’re sending to the Sun by way of some slingshot maneuvers around Venus to speed it up. The Special Relativity difference comes to less than two nanoseconds per day. That’s barely in the range we can detect. It’s way less for everyplace else. ”

“Hey, Mars is down at the bottom. Lemme think why… OK, slower rotation than Earth’s, AND smaller radius so you don’t move as far for the same degrees of spin, so the formula barely subtracts anything from 1.0, right?”

“Yup, the slower you go compared to lightspeed the smaller the time adjustment. The difference between unity and the ratio for a point on Mars’ surface is so small that Old Reliable suffered a floating-point underflow trying to calculate it. That’s hard to make it do. Bottom line, the SR effect doesn’t really kick in unless you’re going faster than practically everything larger than an atom.”

“So how about the gravity wells? I’ll bet the deeper the well, the more time gets stretched.”

“Good bet. The well gets deeper as the attracting mass increases. But your clock feels less of a squeeze if it’s further away. The net effect is controlled by the mass-to-distance ratio inside that square root. Worst case in this table is at the top. A clock embedded in the Sun’s photosphere loses 0.00212*(86400 sec/day)=183 seconds compared to a far-away motionless clock in free-fall. We here on Earth lose 912 milliseconds a day total, but the astronauts on the ISS lose about 3 milliseconds less than we do because they’re further away from Earth’s center.”

“Yeah, I read about those twin astronauts. The one flying on the ISS didn’t get older as fast as the one that stayed on Earth.”

“About a second’s-worth over a year. So, do you have your relativity and Mars-time answer?”

“Sorta. But what time is it up there right now?”

“Hey, Mars is a whole world and has different times at different places just like Earth does. Wherever you are on Mars, ‘noon’ is when the Sun is overhead. Mars spins about 3% slower than Earth does — noon-to-noon there is Earth’s 24 hours plus 37 minutes and change. Add in the net 340-millisecond relativistic daily drift away from Earth time. No way can you sync up Earth and Mars times.”

“Nothin’s simple, huh?”

~~ Rich Olcott

For the VLA, Timing Is Everything

Eddie’s pizza is especially tasty after a long walk down a stairwell. Vinnie and I are polishing off the last of our crumbs when he says, “OK, so we got these incredibly accurate clocks. Two questions. What do we use them for besides sending out those BBC pips, and what do they have to do with the new kilogram standard?”

“Pips? Oh, the top-of-the-hour radio station beeps we used to depend upon to set our watches. Kept us all up-to-the-minute, us and the trains and planes — but we don’t need 10-digit accuracy for that. What we do get from high-quality time signals is the ability to create distributed instruments.”

“Distributed instruments?”

“Ones with pieces in different places. You know about the Jansky Very Large Array, that huge multi-dish radio telescope in New Mexico?”

Karl G. Jansky Very Large Array, photo by Mihaiscanu
via Wikimedia Commons licensed under Creative Commons

“Been there. Nice folks in Pie Town up the road.”

“Did you look around?”

“Of course. What I didn’t understand is why they got 27 dishes and they’re all pointed the same direction. You’d think one would be enough for looking at something.”

“Ah, that’s the thing. All of them together make one telescope.”

<sets smartphone to calculator mode> “Lessee … dish is 25 meters across, πD2/4, 27 dishes, convert square meters to… Geez, 3¼ acres! A single dish that size would be a bear to keep steady in the wind down there. No wonder they split it up.”

“That was one concern, but the total area’s not as important as the distance between the pairs.”

“Why’s that even relevant?”

“Because radio telescopes don’t work the way that optical ones do. No lens or mirror, just a big dish that accepts whatever comes in along a narrow beam of radio waves.”

“How narrow?”

“About the size of the full Moon.”

“That can cover a lot of stars and galaxies.”

“It sure can, which is why early radio astronomy was pretty low-resolution. Astronomers needed a way to pick out the signals from individual objects within that field of view. Turns out two eyes are better than one.”

“3D vision?”

“Kinda related, but not really. Our two eyes give us 3D vision because each eye provides a slightly different picture of close-by objects, say, less than about 5 yards away. For everything further, one eye’s view is no different from the other’s. You’d get the same effect if distant things were painted on a flat background, which is how come a movie set backdrop still looks real.”

“You’re saying that the stars are so far away that each dish gets the same picture.”

“Yeah.”

“So why have more than one?”

“They don’t get the picture at the same time. With an atomic clock you can take account of when each signal arrives at each dish. Here’s a diagram I did up on Old Reliable. It’s way out of scale but it makes the point, I think. We’ve got two dishes at the bottom here, and those purple dots are two galaxies. Each dish sees them on top of each other and can’t distinguish which one sent that peaky signal. What’s important is, the dish on the right receives the signal later. See that red bar? That’s the additional path length the signal has to travel to reach the second dish.”

“Can’t be much later, light travels pretty fast.”

“About 30 centimeters per nanosecond, which adds up. When the VLA dishes are fully spread out, the longest dish-to-dish distance is about 36 kilometers which is about 120 microseconds as the photon flies. That’s over a million ticks on the cesium clock – no problem tracking the differences.”

“Same picture a little bit later. Doesn’t seem worth the trouble.”

“What makes it worth the trouble is what you can learn from the total space-time pattern after you combine the signals mathematically. Under good conditions the VLA can resolve signals from separate objects only 40 milliarcseconds apart, about 1/45000 the diameter of the Moon. That’s less than the width of a dime seen from 50 miles away.”

“The time pattern is how the dishes act like a single spread-around telescope, huh? Without the high-precision time data, they’re just duplicates?”

“Atomic clocks let us see the Universe.”

~~ Rich Olcott

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

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

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.”

Clock image from vecteezy.com

~~ 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

Why So Big?

“How come so big, kid?”

“Beg pardon, Mr Feder?”

“Mars has the biggest volcanoes and all, like that canyon you can’t even see across.  Earth’s bigger than Mars, right?  How come we don’t have stuff like that?”

“Maybe we do but we’ve not found it yet.  Earth’s land area is only 4% greater than the surface area of Mars.  Our ocean floor and what’s beneath the Greenland and Antarctic ice sheets are like a whole second planet twice as big as the land we’ve explored so far.  Some people refer to the Mid-Atlantic Ridge as a 10000-mile-long volcano.  No-one knows for sure what-all else is down there.  Even on land we’ve probably had enormous landforms like Alba Mons but on the geologic timescale they don’t last long here.”

“So like I said, how come?”

“Because of what we have that Mars doesn’t.  Massive forces of erosion — wind, water, Goldilocks temperatures — that grind down landforms something fierce.”

Watney_s route 420
Mark Watney’s travel route in The Martian.
Image by ESA/DLR/FU Berlin
under Creative Commons license

“Wait, Mars has winds.  What about those dust storms, and that windstorm that damn near destroyed Watney’s spaceship?”

“Um, Watney’s a fictional character.  The dust storms do exist, though —  one of them created a blackout that may have killed the Opportunity rover’s solar power.  But Martian dust grains are about the size of smoke particles.  Doesn’t take much of a wind to get those grains into the air and keep them there even in Martian atmosphere that’s only 1% as thick as Earth’s.  A 120-mph wind on Earth would blow you over, but one on Mars would just give you a gentle push.  Martian winds can barely roll a sand grain along the ground.  They definitely can’t sandblast a volcano like Earth winds can.  Which, by the way is why planetologists panned that storm scene in your The Martian movie.  Couldn’t happen.  The film production team admitted that.  The rest of the science was pretty good, though.”

“OK then, water.  You talking like dripping water can wear a hole in a rock?”

“More like water in quantity — glaciers carving off mountaintops and rivers digging canyons and ocean waves smashing shorelines to sandy powder.  Dripping water works, too — water’s corrosive enough even at low temperatures that it can dissolve most kinds of rock if you give it enough time.  But Mars has no glaciers or rivers or oceans.  Probably no dripping water, either”

“You were kidding about Goldilocks, right?  Talk about fictional characters!”

“Not in this case.  To planetologists, ‘Goldilocks’ is a technical term.  You know, ‘not too cold, not too warm…”

“‘Just right,’ yeah, yeah.  But just right for what?  What’s Mars got that’s Goldilocks-ish?”

“Sorry, it’s Earth that has the Goldilocks magic, not Mars, and what’s just right is that we’re in the right temperature range for water to exist in gas and liquid and solid forms.  Mars’ surface is way too cold for liquid water.”

“Wait, I read that they’d found liquid water there.”

“Not on the surface.  The radar experiment aboard European Space Agency’s Mars Express spacecraft found an indication of liquid water, but it’s a kilometer below the surface.  Twenty kilometers wide, maybe a meter thick — more of a pond than the ‘lake’ the media were talking about.”

“Why should it make a difference that Earth’s Goldilocks-ish?  I mean, we’re comfortable but we’re not rocks.  What’s that got to do with the volcanoes?”

“Recycling, Mr Feder, recycling.  On Mars, if enough gaseous water molecules could get together to make rain, which they can’t, they’d freeze to the ground and stay there for a long, long time.  On Earth, though, most rain stays liquid and you get ground water or run-off which eventually evaporates and rains down again.  The same molecules get many, many chances to grind down a mountain.”

“But Earth water can freeze, too.”

“Remember we’re Goldilocks-ish.  Liquid water soaks into a cracked rock where it freezes, expands to pry off a chip or two, and thaws to freeze again.  Water’s freeze-thaw cycle can do a lot of damage if it gets to repeat often enough.”

“So Mars has big stuff because…”

“The planet’s too cold to wear it away.”

~~ Rich Olcott

Raindrops landing in a red-brown puddle
Adapted image from Clipart-library.com

The Big Splash? Maybe.

You’ve not seen half of it, Mr Feder.  Mars has the Solar System’s tallest volcano, most massive volcano, biggest planetary meteor strike, deepest and longest  canyon…”

“Wait, kid, I’ve been to the Grand Canyon.  Thing is … BIG!  What’d they say?  A mile deep, 18 miles wide, 250 miles long.  No way Mars can beat that.”

“Valles Marineris is 4½ miles deep, 120 miles wide and 2500 miles long.  The Grand Canyon meanders, packing its length into only 150 miles of bee-line distance.  Marineris stretches straight as a string.  No river carved that formation, but the planetologists can’t agree on what did.”

Labeled Mars map 2 420
Mars map from NASA/JPL/GSFC

“They got evidence, don’t they?”

“Not enough.  Different facts point in different directions and no overall theory has won yet.  Most of it has to do with the landforms.  Start with the Tharsis Bulge, big as a continent and rising kilometers above Mars’ average altitude.  Near the Bulge’s highest point, except for the volcanoes, is a fractured-looking region called Noctis Labyrinthus.  Starting just west of  the Labyrinth a whole range of wrinkly highlands and mountains arcs around south and then east to point towards the eastern end of Marineris.  Marineris completes the arc by meeting the Labyrinth to its west.  Everything inside that arc is higher than everything else around it.  Except for the volcanoes, of course.”

“Looks like something came up from underneath to push all that stuff up.”

“Mm-hm, but we don’t know what, or what drove it, or even how fast everything happened.  There are theories all over the place”

“Like what?”

“Well, maybe it’s upwellng from a magma hotspot, like the one under the Pacific that’s been creating Hawaiian Islands one at a time for the past 80 million years.  Some people think the upwelling mostly lifted the existing crust like expanding gas bubbles push up the crust of baking bread.  Other people think that the upwelling’s magma broke through the crust to form enormous lava flows that covered up whatever had been there before.”

“You said ‘maybe.'”

“Yeah.  Another group of theories sees a connection between Tharsis and Hellas Basin, which is almost exactly on the other side of the planet.  Hellas is the rock-record of a mega-sized meteorite strike, the third largest confirmed one in the Solar System.  Before you ask, the other two are on the Moon.  Like I said, it’s a group of theories.  The gentlest one, if you can call it that, is that energy from the impact rippled all around the planet to focus on the point opposite the impact.  That would have disrupted the local equilibrium between crustal weight and magma’s upward pressure.  An imbalance like that would encourage uplift, crustal cracking and, ultimately, Valles Marineris.”

“Doesn’t sound very gentle.”

“It wouldn’t have been but it might even have been nastier.  Another possibility is that the meteorite may not have stopped at the crust.  It could have hit hard enough, and maybe with enough spin, to drill who knows how far through the fluid-ish body of the planet, raising the Bulge just by momentum and internal slosh.  Worst case, some of Tharsis’ rock might even have come from the intruder.”

Realistic Orange-red Liquid Splash Vector
Adapted from an image by Vecteezy

“Wow, that would have been a sight to see!”

“Yeah, from a distance.  Any spacecraft flying a Mars orbit would be in jeopardy from rock splatter.  We’ve found meteors on Earth that we know originated on Mars because they have bubbles holding trapped gas that matches the isotope signature of Martian atmosphere.  A collision as violent as the one I just described could certainly have driven rocky material past escape velocity and on its way to us.  Oh, by the way and speaking of sights — you’d be disappointed if you actually visited Valles Marineris.”

“How could anything that ginormous be a disappointment?”

“You could look down into it but you probably couldn’t see the far side.  Mars is smaller than Earth and its surface curves downward more rapidly.  Suppose you stood on one side of the valley’s floor where it’s 4 miles deep.  The opposite wall, maybe 100 miles away, would be beyond your 92-mile horizon limit for an object that tall.”

“Aw, phooey!”

~~ Rich Olcott