Three Shades of Dark

The guy’s got class, I’ll give him that. Astronomer-in-training Jim and Physicist-in-training Newt met his challenges so Change-me Charlie amiably updates his sign.

But he’s not done. “If dark matter’s a thing, how’s it different from dark energy? Mass and energy are the same thing, right, so dark energy’s gotta be just another kind of dark matter. Maybe dark energy’s what happens when real matter that fell into a black hole gets squeezed so hard its energy turns inside out.”

Jim and Newt just look at each other. Even Cap’n Mike’s boggled. Someone has to start somewhere so I speak up. “You’re comparing apples, cabbages and fruitcake. Yeah, all three are food except maybe for fruitcake, but they’re grossly different. Same thing for black holes, dark matter and dark energy — we can’t see any of them directly but they’re grossly different.”

EHT's image of the black hole at the center of the Messier 87 galaxy
Black hole and accretion disk, image by the Event Horizon Telescope Collaboration

Vinnie’s been listening off to one side but black holes are one of his hobbies. “A black hole’s dark ’cause its singularity’s buried inside its event horizon. Whatever’s outside and somehow gets past the horizon is doomed to fall towards the singularity inside. The singularity itself might be burn-your-eyes bright but who knows, ’cause the photons’re trapped. The accretion disk is really the only lit-up thing showing in that new EHT picture. The black in the middle is the shadow of the horizon, not the hole.”

Jim picks up the tale. “Dark matter’s dark because it doesn’t care about electromagnetism and vice-versa. Light’s an electromagnetic wave — it starts when a charged particle wobbles and it finishes by wobbling another charged particle. Normal matter’s all charged particles — negative electrons and positive nuclei — so normal matter and light have a lot to say to each other. Dark matter, whatever it is, doesn’t have electrical charges so it doesn’t do light at all.”

“Couldn’t a black hole have dark matter in it?”

“From what little we know about dark matter or the inside of a black hole, I see no reason it couldn’t.”

“How about normal matter falls in and the squeezing cooks it, mashes the pluses and minuses together and that’s what makes dark matter?”

“Great idea with a few things wrong with it. The dark matter we’ve found mostly exists in enormous spherical shells surrounding normal-matter galaxies. Your compressed dark matter is in the wrong place. It can’t escape from the black hole’s gravity field, much less get all the way out to those shells. Even if it did escape, decompression would let it revert to normal matter. Besides, we know from element abundance data that there can’t ever have been enough normal matter in the Universe to account for all the dark matter.”

Newt’s been waiting for a chance to cut in. “Dark energy’s dark, too, but it works in the opposite direction from the other two. Gravity from normal matter, black holes or otherwise, pulls things together. So does gravity from dark matter which is how we even learned that it exists. Dark energy’s negative pressure pulls things apart.”

“Could dark energy pull apart a black hole or dark matter?”

Big Cap’n Mike barges in. “Depends on if dark matter’s particles. Particles are localized and if they’re small enough they do quantum stuff. If that’s what dark matter is, dark energy can move the particles apart. My theory is dark matter’s just ripples across large volumes of space so dark energy can change how dark matter’s spread around but it can’t break it into pieces.”

Vinnie stands up for his hobby. “Dark energy can move black holes around, heck it moves galaxies, but like Sy showed us with Old Reliable it’s way too weak to break up black holes. They’re here for the duration.”

Newt pops him one. “The duration of what?”

“Like, forever.”

“Sorry, Hawking showed that black holes evaporate. Really slowly and the big ones slower than the little ones and the temperature of the Universe has to cool down a bit more before that starts to get significant, but not even the black holes are forever.”

“How long we got?”

“Something like 10106 years.”

“That won’t be dark energy’s fault, though.”

~~ Rich Olcott

Advertisements

Dark Shadows

Change-me Charlie’s still badgering Astronomer-in-training Jim and Physicist-in-training Newt about “Dark Stuff,” though he’s switched his target from dark matter to dark energy. “OK, the expansion of the Universe is speeding up. How does dark energy do that?”

Jim steps up to bat. “At this point dark energy’s just a name. We frankly have no idea what the name represents, although it seems appropriate.”

“Why’s that?”

“Gravity pulls things together, right, and we have evidence that galaxies are flying away from each other. When you pick something up your muscles give it gravitational potential energy that becomes kinetic energy when you let go and it drops. In space, a galaxy moving away from its neighbors gains gravitational potential energy relative to them. If the Energy Conservation Law holds, that energy has to come from somewhere. ‘Dark energy’ is what we call the somewhere, but naming something and understanding it are two different things.”

Newt chips in. “Einstein came at it from a different direction. His General Relativity field equations contained two numbers for observation to fill in — G, Newton’s gravitational constant, and lambda (Λ), which we now call the Cosmological Constant. Lambda measures the energy density of empty space. The equations say the balance between lambda and gravity controls whether the Universe expands, contracts or stays static. Lambda‘s just a little bit positive so the universe is expanding.”

“Same conclusion, different name. Neither one says where the energy comes from.”

That’s my cue. “True, but Einstein’s work goes deeper. Newtonian physics maps the Universe onto a stable grid of straight lines. In General Relativity those lines are deformed and twisted under the influence of massive objects. Vinnie and I talked about how gravity’s a fictitious force arising from that deformation. Like John Wheeler said, ‘Mass tells space-time how to curve, and space-time tells mass how to move.’ Anyway, when you throw dark energy’s lambda into the mix, the grid lines themselves go into motion. Dark energy torques the spacetime fabric that pulls galaxies together.”

“So dark energy pulls things apart by spreading out the grid they’re built on? If that’s so how come I’m still in one piece?”

“Nothing personal, but you’re too small and dense to notice. So am I, so is the Earth.”

“Why should that make a difference?”

“Time for a thought experiment. Think of the Sun. The atoms inside its surface are trying to get out, right? What’s holding them in?”

“The Sun’s gravity.”

“Just like pressure on the skin of a balloon. In either case, as long as things are stable the pressure on an enclosing real or mathematical surface rises and falls with the amount of enclosed energy density and it doesn’t matter which we talk about. Energy density’s easier to think about. With me so far?”

“I guess.”

“Let’s run a few horseback numbers on Old Reliable here. Start with protons and neutrons trying to leave an atomic nucleus. Here’s the total binding energy of an iron-56 nucleus divided by its volume…”

“… so the nuclear particles would fly apart except for the inward pressure exerted by the nuclear forces. Now we’ll go up a level and consider electrons trying to leave a helium atom. They’re held in by the electromagnetic force…”

“Still a lot of inward pressure but less than nuclear by fifty-five powers of ten. Gravity next. That’s what keeps us from flying off into space. I’ll use Earth’s escape velocity to cheat-quantify it…”

“Ten billion times weaker than the electromagnetism that holds our atoms and molecules together. Dark energy’s mass density is estimated to be about 10-27 kilograms per cubic meter. I’ll use that and Einstein’s E=mc2to calculate its pull-us-apart pressure.”

“A quintillion times weaker still.”

“So what you’re saying is, dark energy tries to pull everything apart by stretching out that spacetime grid, but it’s too weak to actually do anything to stuff that’s held together by gravity, electromagnetism or the two nuclear forces.”

“Mostly. Nuclear forces are short-range so distance doesn’t matter. Gravity and electromagnetism get weaker with the square of the distance. Dark energy only gets competitive working on objects that are separated much further than even neighboring galaxies. You’re not gonna get pulled apart.”

~~ Rich Olcott

Dark Horizon

Charlie's table sign says "Dark Energy is bogus"

Change-me Charlie attacks his sign with a rag and a marker, rubbing out “Matter” and writing in “Energy.” Turns out his sign is a roll-up dry-erase display and he can update it on site. Cool. I guess with his rotating-topic strategy he needs that. “OK, maybe dark matter’s a thing, but dark energy ain’t. No evidence, someone just made that one up to get famous!”

And of course Physicist-in-training Newt comes back at him. “Lots of evidence. You know about the Universe expanding?”

“Prove it.” At least he’s consistent.

<sigh> “You know how no two snowflakes are exactly alike but they can come close? It applies to stars, too. Stars are fairly simple in a complicated way. If you tell me a star’s mass, age and how much iron it has, I can do a pretty good job of computing how bright it is, how hot it is, its past and future life history, all sort of things. As many stars as there are, we’re pretty much guaranteed that there’s a bunch of them with very similar fundamentals.”

“So?”

“So when a star undergoes a major change like becoming a white dwarf or a neutron star or switching from hydrogen fusion to burning something else, any other star that has the same fundamentals will behave pretty much the same way. They’d all flare with about the same luminosity, pulsate with about the same frequency —”

“Wait. Pulsate?”

“Yeah. You’ve seen campfires where one bit of flame coming out of a hotspot flares up and dies back and flares up and dies back and you get this pulsation —”

“Yeah. I figured that happens with a sappy log where the heat gasifies a little sap then the spot cools off when outside air gets pulled in then the cycle goes again.”

“That could be how it works, depending. Anyhow, a star in the verge of mode change can go through the same kind of process — burn one kind of atom in the core until heat expansion pushes fuel up out of the fusion zone; that cools things down until fuel floods back in and off we go again. The point is, that kind of behavior isn’t unique to a single star. We’ve known about variable stars for two centuries, but it wasn’t until 1908 that Henrietta Swan Leavitt told us how to determine a particular kind of variable star’s luminosity from its pulsation frequency.”

“Who cares?”

“Edwin Hubble cared. Brightness dies off with the distance squared. If you compare the star’s intrinsic luminosity with how bright the star appears here on Earth, it’s simple to calculate how far away the star is. Hubble did that for a couple dozen galaxies and showed they had to be far outside the Milky Way. He plotted red-shift velocity data against those distances and found that the farther away a galaxy is from us, the faster it’s flying away even further.”

“A couple dozen galaxies ain’t much.”

“That was for starters. Since the 1930s we’ve built a whole series of ‘standard candles,’ different kinds of objects whose luminosities we can convert to distances out to 400 million lightyears. They all agree that the Universe is expanding.”

“Well, you gotta expect that, everything going ballistic from the Big Bang.”

“They don’t go the steady speed you’re thinking. As we got better at making really long-distance measurements, we learned that the expansion is accelerating.”

“Wait. I remember my high-school physics. If there’s an acceleration, there’s gotta be a force pushing it. Especially if it’s fighting the force of gravity.”

“Well there you go. Energy is force times distance and you’ve just identified dark energy. But standard candles aren’t the only kind of evidence.”

“There’s more?”

“Sure — ‘standard sirens‘ and ‘standard rulers.’ The sirens are events that generate gravitational waves we pick up with LIGO facilities. The shape and amplitude of the LIGO signals tell us how far away the source was — and that information is completely immune to electromagnetic distortions.”

“And the rulers?”

“They’re objects, like spiral galaxies and intergalactic voids, that we have independent methods for connecting apparent size to distance.”

“And the candles and rulers and sirens all agree that acceleration and dark energy are real?”

“Yessir.”

~~ Rich Olcott

Dancing in The Dark

Change-me Charlie at his argument table

The impromptu seminar at Change-me Charlie’s “Change My Mind” table is still going strong, but it looks like Physicist-in-training Newt and Astronomer-in-training Jim have met his challenge. He’s switched from arguing that dark matter doesn’t exist to asking how it worked in the Bullet Cluster’s massive collision between two collections of galaxies with their clouds of plasma and dark matter. “OK, the individual galaxies are so spread out they slide past each other without slowing down but the plasma clouds obstruct each other by friction. Wouldn’t friction in the dark matter hold things back, too?”

Jim’s still standing in front of the table. “Now that’s an interesting question, so interesting that research groups have burned a bazillion computer cycles trying to answer it.”

“Interesting, yes, but that interesting?”

“For sure. What we know about dark matter is mostly what it doesn’t do. It doesn’t give off light, it doesn’t absorb light, it doesn’t seem to participate in the strong or weak nuclear forces or interact with normal matter by any means other than gravity, and no identifiable dark matter particles have been detected by bleeding-edge experiments like IceCube and the Large Hadron Collider. So people wonder, does dark matter even interact with itself? If we could answer that question one way or the other, that ought to tell us something about what dark matter is.”

“How’re we gonna do that?”

Newt’s still perched on Charlie’s oppo chair. “By using computers and every theory tool on the shelf to run what-if? simulations. From what we can tell, nearly everywhere in the Universe normal matter is embedded in a shell of dark matter. The Bullet Cluster and a few other objects out there appear to break that rule and give us a wonderful check on the theory work.”

The Bullet Cluster, 1E 0657-56 (NASA image)

“Like for instance.”

“Simple case. What would the collision would looked like if dark matter wasn’t involved? Some researchers built a simulation program and loaded it with a million pretend plasma particles in two cluster-sized regions moving towards each other from 13 million pretend lightyears apart. They also loaded in position and momentum data for the other stars and galaxies shown in the NASA image. The simulation tracked them all as pretend-time marched along stepwise. At each time-step the program applied known or assumed laws of physics to compute every object’s new pretend position and momentum since the prior step. Whenever two pretend-particles entered the same small region of pretend-space, the program calculated a pretend probability for their collision. The program’s output video marked each successful collision with a pink pixel so pinkness means proton-electron plasma. Here’s the video for this simulation.”

“Doesn’t look much like the NASA picture. The gas just spreads out, no arc or cone to the sides.”

“Sure not, which rules out virtually all models that don’t include dark matter. So now the team went to a more complicated model. They added a million dark matter particles that they positioned to match the observed excess gravity distribution. Those’re marked with blue pixels in the videos. Dark matter particles in the model were allowed to scatter each other, too, under control of a self-interaction parameter. The researchers ran the simulations with a whole range of parameter values, from no-friction zero up to about twice what other studies have estimated. Here’s the too-much case.”

“Things hold together better with all that additional gravity, but it’s not a good match either.”

“Right, and here’s the other end of the range — no friction between dark matter particles. Robertson, the video’s author/director, paused the simulation in the middle to insert NASA’s original image so we could compare.”

“Now we’re getting somewhere.”

“It’s not a perfect match. Here’s an image I created by subtracting a just-after-impact simulation frame from the NASA image, then amplifying the red. There’s too much left-over plasma at the outskirts, suggesting that maybe no-friction overstates the case and maybe dark matter particles interact, very slightly, beyond what a pure-gravity theory predicts.”

“Wait, if the particles don’t use gravity, electromagnetism or the nuclear forces on each other, maybe there’s a fifth force!”

“New Physics!”

A roar from Cap’n Mike — “Or they’re not particles!”

~~ Rich Olcott

Dark Passage

Change-me Charlie’s not giving up easily. “You said that NASA picture did three things, but you only told us two of them — that dark matter’s a thing and that it’s separate from normal matter. What’s the third thing? What exactly is in that picture? Does it tell us what dark matter is?”

The Bullet Cluster ( 1E 0657-56 )

Physicist-in-training Newt’s ready for him. “Not much of a clue about what dark matter is, but a good clue about how it behaves. As to what’s in the picture, we need some background information first.”

“Go ahead, it’s not dinner-time yet.”

“First, this isn’t two stars colliding. It’s not even two galaxies. It’s two clusters of galaxies, about 40 all together. The big one on the left probably has the mass of a couple quintillion Suns, the small one about 10% of that.”

“That’s a lot of stars.”

“Oh, most of it’s definitely not stars. Maybe only 1-2%. Those stars and the galaxies they form are embedded in ginormous clouds of proton-electron plasma that make up 5-20% of the mass. The rest is that dark matter you don’t like.”

“Quadrillions of stars are gonna make a super-super-nova when they collide!”

“Well, no. That doesn’t even happen when two galaxies collide. The average distance between neighboring stars in a galaxy is 200-300 times the diameter of a star so it’s unlikely that any two of them will come even close. Next level up, the average distance between galaxies in a cluster is about 60 galaxy diameters or more, depending. The galaxies will mostly just slide past each other. The real colliders are the spread-out stuff — the plasma clouds and of course the dark matter, whatever that is.”

Astronomer-in-training Jim cuts in. “Anyway, the collision has already happened. The light from this configuration took 3.7 billion years to reach us. The collision itself was longer ago than that because the bullet’s already passed through the big guy. From that scale-bar in the bottom corner I’d say the centers are about 2 parsecs apart. If I recall right, their relative velocity is about 3000 kilometers per second so…” <poking at his smartphone> “…the peak intersection was about 700 million years earlier than that. Call it 4.3 billion years ago.”

“So what’s with the cotton candy?”

Newt looks puzzled. “Cotton… oh, the pink pixels. They’re markers for where NASA’s Chandra telescope saw X-rays coming from.”

“What can make X-rays so far from star radiation that could set them going?”

“The electrons do it themselves. An electron emits radiation every time it collides with another charged particle and changes direction. When two plasma clouds interpenetrate you get twice as many particles per unit volume and four times the collision rate so the radiation intensity quadruples. There’s always some X-radiation in the plasma because the temperature in there is about 8400 K and particle collisions are really violent. The Chandra signal pink shows the excess over background.”

“The blue in the Jim’s picture is supposed to be what, extra gravity?”

“Basically, yeah. It’s not easy to see from the figure, but there are systematic distortions in the images of the background galaxies in the blue areas. Disks and ellipsoids appear to be bent, depending on where they sit relative to the clusters’ centers of mass. The researchers used Einstein’s equations and lots of computer time to work back from the distortions to the lensing mass distributions.”

“So what we’ve got is a mostly-not-from-stars gravity lump to the left, another one to the right, and a big cloud in the middle with high-density hot bits on its two sides. Something in the middle blew up and spread gas around mostly in the direction of those two clusters. What’s that tell us?”

“Sorry, that’s not what happened. If there’d been a central explosion the excess to the right would be arc-shaped, not a cone like you see. No, this really is the record of one galaxy cluster bursting through another one. Particle-particle friction within the plasma clouds held them back while the embedded galaxies and dark matter moved on.”

“OK, the galaxies aren’t close-set enough for them to slow each other down, but wouldn’t friction in the dark matter hold things back, too?”

“Now that’s an interesting question…”

~~ Rich Olcott

The Prints of Darkness

There’s a commotion in front of Al’s coffee shop. Perennial antiestablishmentarian Change-me Charlie’s set up his argument table there and this time the ‘establishment’ he’s taking on is Astrophysics. Charlie’s an accomplished chain-yanker and he’s working it hard. “There’s no evidence for dark matter, they’ve never found any of the stuff and there’s tons of no-dark-matter theories to explain the evidence.”

Big Cap’n Mike’s shouts from the back of the crowd. “What they’ve been looking for and haven’t found is particles. By my theory dark matter’s an aspect of gravity which ain’t particles so there’s no particles for them to find.”

Astronomer-in-training Jim spouts off right in Charlie’s face. “Dude, you can’t have it both ways. Either there’s no evidence to theorize about, or there’s evidence.”

Physicist-in-training Newt Barnes takes the oppo chair. “So what exactly are we talking about here?”

“That’s the thing, guy, no-one knows. It’s like that song, ‘Last night I saw upon the stair / A little man who wasn’t there. / He wasn’t there again today. / Oh how I wish he’d go away.‘ It’s just buzzwords about a bogosity. Nothin’ there.”

I gotta have my joke. “Oh, it’s past nothing, it’s a negative.”

“Come again?”

“The Universe is loaded with large rotating but stable structures — solar systems, stellar binaries, globular star clusters, galaxies, galaxy clusters, whatever. Newton’s Law of Gravity accounts nicely for the stability of the smallest ones. Their angular momentum would send them flying apart if it weren’t for the gravitational attraction between each component and the mass of the rest. Things as big as galaxies and galaxy clusters are another matter. You can calculate from its spin rate how much mass a galaxy must have in order to keep an outlying star from flying away. Subtract that from the observed mass of stars and gas. You get a negative number. Something like five times more negative than the mass you can account for.”

“Negative mass?”

“Uh-uh, missing positive mass to combine with the observed mass to account for the gravitational attraction holding the structure together. Zwicky and Rubin gave us the initial object-tracking evidence but many other astronomers have added to that particular stack since then. According to the equations, the unobserved mass seems to form a spherical shell surrounding a galaxy.”

“How about black holes and rogue planets?”

Newt’s thing is cosmology so he catches that one. “No dice. The current relative amounts of hydrogen, helium and photons say that the total amount of normal matter (including black holes) in the Universe is nowhere near enough to make up the difference.”

“So maybe Newton’s Law of Gravity doesn’t work when you get to big distances.”

“Biggest distance we’ve got is the edge of the observable Universe. Jim, show him that chart of the angular power distribution in the Planck satellite data for the Cosmological Microwave Background.” <Jim pulls out his smart-phone, pulls up an image.> “See the circled peak? If there were no dark matter that peak would be a valley.”

Charlie’s beginning to wilt a little. “Ahh, that’s all theory.”

The Bullet Cluster ( 1E 0657-56 )

<Jim pulls up another picture.> “Nope, we’ve got several kinds of direct evidence now. The most famous one is this image of the Bullet Cluster, actually two clusters caught in the act of colliding head-on. High-energy particle-particle collisions emit X-rays that NASA’s Chandra satellite picked up. That’s marked in pink. But on either side of the pink you have these blue-marked regions where images of further-away galaxies are stretched and twisted. We’ve known for a century how mass bends light so we can figure from the distortions how much lensing mass there is and where it is. This picture does three things — it confirms the existence of invisible mass by demonstrating its effect, and it shows that invisible mass and visible mass are separate phenomena. I’ve got no pictures but I just read a paper about two galaxies that don’t seem to be associated with dark matter at all. They rotate just as Newton would’ve expected from their visible mass alone. No surprise, they’re also a lot less dense without that five-fold greater mass squeezing them in.”

“You said three.”

“Gotcha hooked, huh?

~~ Rich Olcott

The Pretty-good Twenty-nine

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

“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

“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

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