Category: Physics: Foundations of Measurement

The Pretty-good Twenty-nine

On By rolcottIn Physics: Foundations of Measurement, Physics: Fundamentals, UncategorizedLeave a comment

Time for coffee and a scone. As I step into Al’s coffee shop he’s taking his Jupiter poster down from behind the cash register.

“Hey, Al, I liked that poster. You decide you prefer plain wall?”

“Nah, Sy, I got a new one here. Help me get it up over the hook.”

A voice from behind us. “Ya got it two degrees outta plumb, clockwise.” Vinnie, of course. Al taps the frame to true it up.

Teachers, click here to download a large-format printable copy.

“Hey, Sy, in the middle, that’s the same seven units we just finished talking about — amps for electric current, kelvins for temperature, meters for length, kilograms for mass, seconds for time, moles for counting atoms and such, and that candela one you don’t like. What’s all the other bubbles about? For that matter, what’s the poster about, Al?”

“What it’s about, Vinnie, is on May 20 the whole world goes to a new set of measurement standards, thanks to some international bureau.”

“Le Bureau International des Poids et Mesures.” It’s Newt Barnes in from the Physics building. “The bubbles in that central ring are the BIPM’s selections for fundamental standards. Each one’s fixed by precisely defined values of one or more universal physical constants. For instance, a ruler calibrated on Earth will match up perfectly with one calibrated on Mars because both calibrations depend on the wavelength of radiation from a cesium-based laser and that’s the same everywhere.”

“How about the other bubbles and the rings around them?”

“They’re all derived quantities, simple combinations of the fundamental standards.”

“Hey, I see one I recognize. That °C has gotta be degrees centigrade ’cause it’s right next to kelvins. Centigrade’s the same as kelvins plus , uh, 273?”

“There you go, Al. What’s ‘rad’ and ‘sr’, Newt?”

“Symbols for radian and steradian, Vinnie. They both measure angles like degrees do, but they fit the BIPM model because they’re ratios of lengths and length is one of the fundamentals. Divide a circle’s circumference by its radius and what do you get?”

“Twice pi.”

“Right, call it 2π radians and that’s a full circle. Half a circle is π radians, a right angle is π/2 radians and so on. Works for any size circle, right? Anyone remember the formula for the area of a sphere?”

“4πr2, right?”

“Exactly. If you divide any sphere’s area by the square of its radius you get 4π steradians. Any hemisphere is 2π steradians and so on. Steradians are handy for figuring things like light and gravity that decrease as the square of the distance.”

Something occurs to me. “I’m looking at those bigger bubbles that enclose the derived quantities. Seems to me that each one covers a major area of physical science. The green one with newtons for force, pascals for pressure, joules for energy and watts for power — that’d be Newtonian physics. The red circle with volts plus coulombs for charge, ohms for resistance, farads for capacitance, siemens for electrical conductance — all that’s electronics. Add in henries for inductance, webers for magnetic flux and teslas for flux density and you’ve got Maxwellian electromagnetism.”

“You’re on to something, Sy. Chemistry’s there with moles and katals, also known as moles per second, for catalytic activity. How does your idea fit the cluster attached to seconds?”

“They’re all per-second rates, Newt. The hertz is waves per second for periodic things like sound or light-as-a-wave. The other three are about radioactivity — bequerels is fissions per second; grays and sieverts are measures of radiation exposure per kilogram.”

“Vinnie says you don’t like candelas, so you probably don’t like lumens or luxes either. What’s your gripe with them?”

“All three are supposed to quantify visible light from a source, as opposed to the total emission at all wavelengths. But the definition of ‘visible’ zeros in on one wavelength in the green because that’s where most people are most sensitive. Candelas aren’t valid for a person who’s color-blind in the green, nor for something like a red laser that has no green lightwaves. I call bogosity, and lumens and luxes are both candela-based.”

“These 29 standards are as good on Mars as they are here on Earth?”

“That’s the plan.”

~~ Rich Olcott

The Magnificent Seven

On By rolcottIn Physics: Foundations of Measurement, Physics: Fundamentals, UncategorizedLeave a comment

“Hey, Sy, you said there’s seven fundamental standards. We’ve talked about the second and the meter and the kilogram and the ampere. What’s left?”

“The mole, the kelvin and the candela, Al. They’re all kinda special-purpose but each has its charms. The mole, for instance, is cute and fuzzy and has its very own calendar date.”

“You’re pulling our legs, Sy. A cute unit of measure? No way.”

“Hear me out, Vinnie. How many shoes in a dozen pairs?”

“Huh? Two dozen, that’s twenty-four.”

“Sure, but it’s easier to work in dozens. How many hydrogen atoms in a dozen H2O molecules?”

“Two dozen, of course. Are we going somewhere here?”

“Next step. A mole is like a dozen on steroids, about 6×1023 whatevers. How many hydrogen atoms in a mole of H2O molecules?”

“Two moles, I suppose, or 12×1023.”

“You got the idea.”

“Cute.”

“A-hah! Gotcha for one.”

“Fair hit. How about the fuzzy part and the date?”

“The fuzzy has to do with isotopes. Every element has an atomic number and an atomic weight. The atomic number counts protons in the nucleus –all atoms of an element have the same atomic number. But different isotopes of an element have different numbers of neutrons. The ‘weight’ is protons plus neutrons, averaged across the isotopes. If you’re holding a mole of an element, you’re holding its atomic weight in grams. The fuzzy happens because samples of an element from different sources can have different mixtures of isotopes. You may have some special diamonds that contain nothing but carbon-12. A mole of those atoms masses exactly 12 grams. My sample is enriched with 10% of carbon-13. Mole-for-mole, my carbon is a tad heavier than yours. In fact, 6×1023 of my atoms mass 12.10 grams. That’s an extreme example but you get the idea.”

“Fuzzy, a little, OK. And the date thing?”

“June 23 is Mole Day, celebrated by Chemistry teachers everywhere.”

“What’s the kelvin about then?”

“Temperature. And most solid-state electronics. Zero kelvin is absolute zero, the coldest temperature something can get, when the maximum heat has been sucked out and all its atoms have minimum vibrational energy. From there you heat it up degree by degree until you get to where water can co-exist as liquid, solid and water vapor. It used to be the standard to call that temperature 273.16 K.”

“Used to be? Water doesn’t do that any more?”

“Oh, it still does, but the old standard had problems. It used five different ‘official’ techniques and 16 different calibration checks to cover the range from 3 K up to the melting point of copper. Some of those standards, like the melting pressure of helium-3, are not only inconvenient but expensive. Others led to measured intermediate temperatures that disagree depending on which direction you’re going. The defined standards did nothing for the plasma people who work above 1500 K. It was a mess.”

“So how does the new standard fix that?”

“It exploits new tech, especially in solid-state science. The Boltzmann constant, kB, is sort of the quantum of heat capacity at the microscopic level. The product kBT is a threshold energy. Practically everything that happens at the quantum level depends on the ratio of some process energy divided by kBT. If the ratio’s high the process runs; if it’s low, nothing. In-between, the response is predictably temperature-dependent. Thanks to a plethora of new solid-state thermal sensors that depend on that logic, we now have a handle on the range from microkelvins to kilokelvins and above.”

“Pretty good. What’s the last one?”

“It’s the one I’m least happy about, the candela. It’s a unit for how bright a light source is, sort-of. Take the source’s power output at all optical frequencies and ‘correct’ that by how much each frequency would stimulate a mathematically modeled ‘standard human eye.’ Isolate the ‘corrected’ watts at 555 nanometers, multiply by Kcd=683. It’s a time-hallowed metric that lighting designers depend upon, but it skips over little things like we actually see with rod cells and three kinds of cone cells, none of which match the standard curve. Kcd is just too human-centered to be a universal constant.”

“Humans ain’t universal. We’re not even on Mars.”

“Yet.”

~~ Rich Olcott

Beautiful Realization

On By rolcottIn Physics: Foundations of Measurement, Physics: Fundamentals, UncategorizedLeave a comment

“Whaddaya mean, Sy, ‘charge and resistance and voltage all playing beautiful together‘? How’s that beautiful?”

“It is when they play together in a Kibble Balance, Vinnie. That beautifully-designed device solved the realization problem for two of the revised fundamental standards of measurement. Here’s the one for electricity.”

“That’s odd. It says ‘electric current’ but the number’s about charge. And I don’t see anything in there about voltage or resistance.”

“True. The electronic charge e is one of our universal constants. It and the speed of light and Planck’s constant h are the same on Mars as they are here on Earth. Take a cesium-based laser from Earth to Mars and its frequency doesn’t change. That’s why the revisions are measure-anywhere standards, no need to carry something to Paris to compare it to a physical object.”

“This is another one of those definition tricks, isn’t it? Like the cesium frequency — we defined the second by saying it’s the time required for so-and-so many waves of that light beam. Here, it’s not like someone measured the charge in coulombs, it’s we’re gonna make the coulomb exactly big enough so when we do measure an electron it’ll match up.”

“You’re not wrong, Vinnie, but it’s not quite that arbitrary. Lots of people did measure the electron against the old standard. This number represents the most accurate estimate across all the measurements. The standards board just froze it there. It’s the same strategy they took with the other six fundamental standards — each of them sits on top of a well-known constant.”

“Like Newton’s gravitational constant?”

“Sorry, Al, not that one. It’s universal, alright, but it’s only known to four significant figures, nowhere near the 8-or-better level the metrologists demand.”

“So tell us about the beauty part, Sy.”

I grab some paper napkins from the dispenser at our table. Al gives me a look. In his opinion Vinnie uses way too many of those and he doesn’t want it to spread. “Just using what I need to make a point, Al. Vinnie, I know you like pictures better than algebra but bear with me.”

“Yeah, you went through the kilogram thing pretty quick what with the garlic and all.”

“Oooh, yeah.” <scribbling on the first napkin> “Well anyway, here’s a sketch of the Kibble Balance rigged for weighing but let’s just pay attention to the parts in the dark blue oval. That zig-zag line labeled RK is a resistor that exploits the quantum Hall effect. Quantum math says its resistance is given by RK=h/e2. That’s exactly 25812.80756 ohms.”

“That a lot more digits than gravity.”

“Nice catch, Al. Now the second component in the oval is a quantum voltmeter. If you put a voltage V across it, the Josephson junction inside passes an alternating current whose frequency is f=V/CJ, where CJ=h/2e.” <scribbling on the second napkin> “Put another way. the frequency tells you the voltage from V=f×CJ and that’s the same as V=f×h/2e.” <scribbling on the third napkin> “The current iW going through RK is V/RK and that’s going to be iW=(f×CJ)/(RK)=f×(CJ/RK)=f×(h/2e)/(h/e2)=(f/2)×e. You with me?”

“Gimme a minute… You’re saying that the current is going to be half some frequency, which we can measure, times the charge on an electron. Yeah, that makes sense, ’cause the current is electrons and you got us counting electrons. Hey, wait, what happened to the h?”

“Canceled out in the fraction, just the way that e canceled out in the fraction for the kilogram.”

“Cute.”

“Better than cute, it’s beautiful. The same equipment, the Kibble Balance plus a gravimeter, gives you the realization of a kilogram depending only on h, AND the realization of the ampere depending only on e. Once you know the standards for time, which depends only on that cesium frequency, and for length, which depends only on time and the speed of light, you can get standards for mass and electric current in the NIST lab here on Earth or up on Mars or anywhere.”

“Almost anywhere.”

“What’s your exception?”

“In space, where there’s no gravity.”

“Einstein covered that with his Equivalence Principle.”

~~ Rich Olcott

The Currant Affair

On By rolcottIn Physics: Electromagnetism, Physics: Foundations of Measurement, Physics: Fundamentals, UncategorizedLeave a comment

Al has a new sign up at his coffee shop, “Scone of the day — Current.” He chuckles when I quietly point out the spelling error. “I know how to spell currant, Sy. I’m just gonna enjoy telling people that whatever I’m taking from the oven is the current flavor.” I’m high-fiving him for that, just as Vinnie slams in and yells out, “Hey, Al, you got your sign spelled wrong. Got any cranberry ones in there?”

Al gives me a look. I shrug. Vinnie starts in on me. “Hey, Sy, that was pretty slick what that Kibble guy did. All the measurements and calculations had the mass standard depending on three universal constants but then suddenly there was only two.”

Al pricks up his ears. “Universal constants, Sy?”

“We think so. Einstein said that the speed of light c is the same everywhere. That claim has withstood a century of testing so the International Bureau of Weights and Measures took that as their basis when they redefined the meter as the standard of length. Planck’s constant h is sometimes called the quantum of action. It shows up everywhere in quantum-related phenomena and appears to be fundamental to the way the Universe works. Bryan Kibble’s team created a practical way to have a measure-anywhere standard of mass and it just happens to depend only on having good values for c and h.”

“What’s the one that Vinnie said dropped out?”

“I knew you’d ask that, Al. It’s e, the charge on an electron. The proton and every other sub-atomic particle we’ve measured has a charge that’s some integer multiple of e. Sometimes the multiplier is one, sometimes it’s zero, sometimes it’s a negative, but e appears to be a universal quantum of charge. Millikan’s oil drop experiment is the classic example. He measured the charge on hundreds of ionized droplets floating in an electric field between charged plates. Every droplet held some integer multiple between 1 and 150 of 1.6×10-19 Coulomb.”

“That’s a teeny bit of electricity. I remember from Ms Kendall’s class that one coulomb is one ampere flowing for one second. Then a microampere flowing for a microsecond is, uhh, 6 million electrons. How did they make that countable?”

“Ah, you’ve just touched on the ‘realization problem,’ which is not about getting an idea but about making something real, turning a definition into a practical measurement. Electrical current is a good example. Here’s the official definition from 60 years ago. See any problems with it, Vinnie?”

“Infinitely long wires that are infinitely thin? Can’t do it. That’s almost as goofy as that 1960 definition of a second. And how does the force happen anyway?”

“The force comes from electrons moving in each wire electromagnetically pushing on the electrons in the other wire, and that’s a whole other story. The question here is, how could you turn those infinities into a real measurement?”

“Lemme guess. In the 1960 time standard they did a math trick to model a fake Sun and based the second on how the fake Sun moves. Is this like that, with fake wires?”

“Nice shot, Vinnie. One of the methods worked like that — take a pair of wires with a known resistance, bend them along a pair of parabolas or some other known curve set close together, apply a voltage and measure the force. Then you use Maxwell’s equations to ‘correct’ the force to what it would have been with the infinite wires the right distance apart. Nobody was comfortable with that.”

“Not surprised — too many ways to do it wrong, and besides, that’s an awfully small force to measure.”

“Absolutely. Which is why there were so many competing standards, some dating back to the 1860s when we were still trying to figure out what electricity is. Some people used a standard resistor R and the voltage V from a standard chemical cell. Then they defined their standard current I from I=V/R. Some measured power P and calculated I2=P/R. Other people standardized charge from the electrostatic force F=q1q2/r2 between two charged objects; they defined current as charge passed per second. It was a huge debate.”

“Who won?”

“Charge and R and V, all playing together and it’s beautiful.”

~~ Rich Olcott

Revenge of The Garlic Calzone

On By rolcottIn Physics: Foundations of Measurement, Physics: Fundamentals, Physics: Quantum Mechanics, UncategorizedLeave a comment

“So what’s the next two steps?” Vinnie asks.

“I’m thinking a dose of the pink stuff and a glass of milk. That garlic calzone’s just not giving up.”

“Nah, we were talking about the new mass standard and how it uses a Kibble Balance protocol you said had three steps but you only got to the gravity-measuring step. You wanna talk to take your mind off your gut, do some more of that.”

“<burp-sigh> OK, assume we did an accurate measurement of gravity’s acceleration g right next to the Balance.” <pulling Old Reliable from its holster...> “Here’s the device in the protocol’s second step, ‘weighing mode’. Bottom to top we’ve got a permanent magnet A and a coil of wire B that’s hooked up to some electronics. The coil floats in the magnetic field because it’s carrying an electric current from that adjustable power source C. The balance’s test pan D rides on the coil and supports our target mass E. Up top, laser interferometer F keeps track of the test pan’s position. Got all that?”

“Mass goes in the pan, got it.”

“Good. You adjust the current through the coil until the interferometer tells you the test pan is floating motionless. Here’s where the electronics come into play. The same current goes through resistor RK, a quantum Hall effect device chilling in a magnetic field and a bath of liquid helium. Quantum math says its resistance is h/e², where e is the charge on an electron and h is Planck’s constant. Those’re both universals like Einstein’s lightspeed c. RK comes to 25812.807557 ohms. You remember the V-I-R diagram?”

“Once Ms Kendall drills it into your brain it’s there forever. Volts equals current in amps times resistance in ohms.”

“Yep. In the Kibble Balance we evaluate the coil’s balancing current by measuring the voltage drop across RK. The voltmeter uses a Josephson junction, another quantum thingie. At a voltage V the junction passes a small alternating current whose frequency is f=V/CJ, where CJ=h/2e. Count the frequency and you can calculate the voltage. DivideV by RK to get the current iW going through the resistor. Everything here meets the count-based, stable, reproducible-anywhere standard.”

“I suppose the w suffixes mean ‘weigh mode’ and m in the bottom equation is the mass. Makes sense that heavier masses need more current to float them. What’s G?”

“Hold on, I got another burp coming … <bo-o-o-O-O-ORP!>”

“Impressive.”

“Thanks, I suppose. G rolls up all those geometry factors — size, shape and power of the magnet and so forth — that you complained about when I said ‘motor-generator.’ We take care of that in the third step. Here’s the diagram for that.”

“Looks pretty much the same.”

“We took out the target mass and the power source, and see, there’s v-subscripts for ‘velocity mode.’ We move the coil vertically while
the atomic clock ticks and the interferometer tracks the pan’s position. That lets us calculate speed s. The coil moving through the magnetic field generates a voltage V=fvCj=sG. Because the geometry factor G is identical between modes, the linkage between coil speed and output power is exactly the same as the linkage between current and input power. That’s the middle equation — velocity-mode voltage divided by speed equals weighing-mode force divided by current.”

“That’s weird.”

“But true, and so elegant. Every variable in that equation save the mass comes from a high-accuracy, high-precision reproducible standard. That makes mass a measure-anywhere dimension, too. But wait, there’s more.”

“Too much math already.”

“Just a little more. Plug all these equations together and you get the bottom one. That’s exciting.”

“Doesn’t look exciting to me.”

“It goes back to the universal constants thing. The first factor in th middle is a ratio of count-derived quantities. Plug the quantum definitions into the second factor and you get CJ²/RK=(h²/4e²)(e²/h)=h/4. What that says is mass is expressible in units of Planck’s constant. That’s deep stuff! What’s exciting is that the standards people used that result in defining the kilogram.”

“Well, blow me down. And one more of your garlic burps or any more math just might.”

~~ Rich Olcott

The Case of The Garlic Calzone

On By rolcottIn Physics: Foundations of Measurement, Physics: Fundamentals, UncategorizedLeave a comment

I’m on an after-lunch hike through the park, trying to digest one of Pizza Eddie’s roasted garlic calzones. Vinnie’s walking a path that joins mine. “Hey, Sy. Whoa, lemme get upwind of you. You did the garlic calzone again, huh?”

“Yeah, and this time Eddie went two cloves over the line and didn’t roast them enough. Talk to me, take my mind off it, OK?”

“Sure. Uhhh… Let’s get back to kilograms which I got started on from a magazine article saying they’re chucking the old kilogram for something better. We were talking about that but got sidelined with measuring time and distance. So what’s the better thing?”

“They weren’t really sidelines, Vinnie, they were setting-up exercises. The technical world needs a set of measurement standards that are stable and precisely reproducible anywhere, any time. The old kilogram, the IPK, isn’t any of that. It’s a polished cylinder of platinum-iridium alloy in a Paris vault. You can’t reproduce it exactly, just very close. All you can do is bring a candidate object to Paris, measure the mass difference between it and the IPK, and then carry your newly-certified junior standard home to calibrate other masses on down the line. And hope you don’t scratch yours or get fingermarks on it en route.”

“But if we’re talking mass, why did time and distance standards even come into the conversation?”

“Several becauses. High-accuracy time measurement is fundamental to all the modern standards; much of the laser technology that supports the new time standard also plays into the other revised standards; and the time standard is the simplest one to describe and implement. No matter where you are, you can build a cesium-atom maser and fire it up. Start counting peaks in the maser beam and when you reach the defined number you’ve been counting for exactly one second. <burp> Excuse me.”

“You’re ‘scused. Yeah, the distance thing is pretty simple, too, now they’ve defined the speed of light as a standard. Is the mass standard that simple?”

“Nowhere near. In fact, it’s easier to describe the technique than to explain why it meets the requirements. It depends upon an apparatus called the Kibble Balance, named in honor of the late Bryan Kibble who devoted two decades of his life to perfecting the machine. Like with the spring balance we talked about, you estimate an object’s mass by comparing the force of gravity on it to some opposing force that you can quantify. The object in question goes on the Balance’s test pan. The opposing ‘pan’ is essentially a motor-generator, just a permanent magnet and a moving coil of wire.”

“Alright, I know enough about motors to see that’s complicated. To figure the balance of forces you gotta know the magnet’s strength and geometry, the coil’s resistance and geometry and speed, the voltage across it, the current through it… They’re none of them exact numbers. And you gotta account for how gravity can be different somewhere else like on Mars. Hard to see how that’s much of an improvement.”

“That’s the beauty of it. Kibble’s machine and measurement protocol are designed so that many of the finicky quantities drop out of the calculation. What’s left is high-accuracy counting-type numbers.”

“Measurement protocol? It’s not just ‘load the test pan and read a dial’?”

“Nope, it’s a three-step process. First step is to measure g, the acceleration of gravity in the Kibble room. Galileo showed all masses accelerate the same so any mass will do. National standards labs can’t just take a value from a book. At their level of rigor g has measurably different values on different floors of the building. You need a high-accuracy gravimeter — a vertical evacuated pipe with a laser interferometer pointing up from the bottom. Drop a mirrored test mass down the pipe while an atomic clock records exactly when the falling mass passes each of hundreds of checkpoints. Two adjacent distance-time pairs gives you one velocity, two adjacent velocity-time pairs gives you one acceleration, average them all together. <BURP!> You got any antacid tablets?”

“Do I look like somebody with a first aid kit in my purse? Don’t answer that. Here.”

“Thanks. No more garlic calzones, ever.”

~~ Rich Olcott

Trombones And Echoes

On By rolcottIn Physics: Foundations of Measurement, Physics: Waves, UncategorizedLeave a comment

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

What Time Is It on Mars?

On By rolcottIn Astronomy: Planetary Science, Physics: Foundations of Measurement, Physics: Light and Relativity, Uncategorized2 Comments

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

A Clock You Can Count On And Vice-versa

On By rolcottIn Physics: Foundations of Measurement, Physics: Waves, UncategorizedLeave a comment

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

On By rolcottIn Physics: Foundations of Measurement, Uncategorized2 Comments

<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