Tag: Susan Kim

The Threshold of Stuffiness

On By rolcottIn Chemistry, Physics: Fundamentals, UncategorizedLeave a comment

<chirp chirp> “Moire here.”

“Hi, Sy, it’s Susan Kim. I read your humidifier piece and I’ve got your answer for you.”

“Answer? I didn’t know I’d asked a question.”

“Sure you did. You worked out that your humidifier mostly keeps your office at 45% relative humidity by moisturizing incoming air that’s a lot drier than that. As a chemist I like how you brought in moles to check your numbers. Anyway, you wondered how to figure the incoming airflow. I’ve got your answer. It’s a scaling problem.”

“Mineral scaling? No, I don’t think so. The unit’s mostly white plastic so I wouldn’t see any scaling, but it seems to be working fine. I’ve been using de-ionized water and following the instructions to rinse the tank with vinegar every week or so.”

“Nope, not that kind of scale, Sy. You’ve got a good estimate from a small sample and you wondered how to scale it up, is all.”

“Sample? How’d I take a sample?”

“You gave us the numbers. Your office is 1200 cubic feet, right, and it took 88 milliliters of water to raise the relative humidity to where you wanted it, right, and the humidifier used a 1000 milliliters of water to keep it there for a day, right? Well, then. If one roomful of air requires 88 milliliters, then a thousand milliliters would humidify (1000/88)=11.4 room changes per day.”

“Is that a good number?”

“I knew you’d ask. According to the ventilation guidelines I looked up, ‘Buildings occupied by people typically need between 5 and 10 cubic feet per minute per person of fresh air ventilation.‘ You’re getting 11.4 roomfuls per day, times your office volume of 1200 cubic feet, divided by 1440 minutes per day. That comes to 9.5 cubic feet per minute. On the button if you’re alone, a little bit shy if you’ve got a client or somebody in there. I’d say your building’s architect did a pretty good job.”

“I like the place, except for when the elevators act up. All that figuring must have you thirsty. Meet me at Al’s and I’ll buy you a mocha latte.”

“Sounds like a plan.”

“Hi, folks. Saw you coming so I drew your usuals, mocha latte for Susan, black mud for Sy. Did I guess right?”

“Al, you make mocha lattes better than anybody.”

“Thanks, Susan, I do my best. Go on, take a table.”

“Susan, I was thinking while I walked over here. My cousin Crystal doesn’t like to wear those N95 virus masks because she says they make her short of breath. Her theory is that they trap her exhaled CO2 and those molecules get in the way of the O2 molecules she wants to breathe in. What does chemistry say to that theory?”

“Hmm. Well, we can make some estimates. N95 filtration is designed to block 95% of all particles larger than 300 nanometers. A couple thousand CO2 molecules could march abreast through a mesh opening that size no problem. An O2 molecule is about the same size. Both kinds are so small they never contact the mesh material so there’s essentially zero likelihood of differential effect.”

“So exhaled CO2 isn’t preferentially concentrated. Good. How about the crowd‑out idea?”

“Give me a second. <tapping on phone> Not supported by the numbers, Sy. There’s one CO2 for every 525 O2‘s in fresh air. Exhaled air is poorer in O2, richer in CO2, but even there oxygen has a 4‑to‑1 dominance.”

“But if the mask traps exhaled air…”

“Right. The key number is the retention ratio, what fraction of an exhaled breath the mask holds back. A typical exhale runs about 500 milliliters, could be half that if you’ve got lung trouble, twice or more if you’re working hard. This mask looks about 300 milliliters just sitting on the table, but there’s probably only 100 milliliters of space when I’m wearing it. It’s just arithmetic to get the O2/CO2 ratio for each breathing mode, see?”

“Looks good.”

“Even a shallow breather still gets 79 times more O2 than CO2. Blocking just doesn’t happen.”

“I’ll tell Crys.”

~ Rich Olcott

Save The Whales? Burn Turpentine

On By rolcottIn Physics: Money, UncategorizedLeave a comment

“OK, Sy, I’ve told you the oil, wax and spermaceti story from my chemistry viewpoint. What got you reading up on whales?”

“A client asked a question that had me going down a rabbit hole that turned into a wormhole leading to a whole bunch of Biology and some Economics. Good thing I enjoy learning random facts.”

“OK, I’ll bite. What was the question?”

“Alright, Susan, see how you do with this. We need our eyes to be round so they can rotate in their sockets and still focus images on their retinas. They can hold that spherical shape against atmospheric pressure because they’re filled with watery stuff and they have a pump‑and‑drain mechanism inside that maintains a slight positive internal pressure. Whales dive down to where water pressures are a hundred atmospheres or more, enough to squeeze their lungs shut. They must use their vision sense down there because their retinal rod cells, the low‑light receptors, are sensitive to blue light. That’s what you’d need for hunting where the water above you filters out all the longer wavelengths. So why doesn’t the pressure down there crumple their eyeballs?”

“Oh, Sy, that’s easy. Water’s among the least compressible molecular liquids we know of. It takes an immense amount of pressure to reduce its volume even by 1%. Hunting-ground pressure isn’t nearly high enough to sabotage water‑filled eyeballs.”

“D’oh! So simple. And here I am, reading a dissection report on a sperm whale’s eyeball. Which, by the way, is about 22 times heavier than a human’s.”

“That’s where your wormhole led you?”

“No, actually, it led me to a econo-political argument about why kerosene got big in the 1860s.”

“Say what? I thought kerosene came in because sperm whales were getting hard to find.”

“That’s the story Big Oil likes. Apparently free-market enthusiasts have been lauding the petroleum industry as heroes dashing in with kerosene to save the whales and by the way, prospering completely independent of any government actions. Turns out History doesn’t support either claim. Ever hear of Camphine?”

“Nope.”

“Camphine saved the whales but then sank with nary a trace. I got most of the story from a PBS blog but pieced that together with a Wikipedia article and a bunch of old government statistics.. I charted the numbers and came up with some interesting correlations. Are you at your computer so I can email it to you?”

Data from W S Tower, “A History of The American Whale Fishery” (1907)

“Sure.”

“On its way.”

“Ooo, complicated. Care to read it to me?”

“Of course. Fun fact — fats from toothed whales are generally waxier than fat from baleen whales. Sperm whales just happen to be at the far end of that trend. Anyway, I concentrated on the sperm whale data. The red line is the total amount of spermaceti obtained from whales taken by US craft in each year,”

“Five million gallons in 1842? That’s ten thousand whales!”

“Mm-hm. The red line drops sharply after those peak years despite the whalers floating a bigger fleet — that’s the black line. The hunters found diminishing returns because the harvest just wasn’t sustainable. But people still wanted their spermaceti candles — the green line shows the price continued to rise until the mid‑1850s. Not only inside the US — the blue line shows exports rising because foreign whalers couldn’t supply demand from their own markets.”

“Bad prospects. What happened in the yellow part of the chart?”

“Competition from a new product called Camphine, a.k.a. ‘burning oil.’ In the mid‑1830s a guy in Maine and a couple of New Yorkers started making liquid substitutes for spermaceti. The products were mixtures of turpentine, grain alcohol and a little camphor for aroma. You needed a special lamp to burn it but you got a flame that rivaled sperm candles for brightness and color purity. Sold like gang‑busters, up to 200 million gallons per year, but the Civil War killed it off.”

“How?”

“Federal embargoes on Southern pine forest turpentine, Federal taxes on alcohol. Kerosene and the Pennsylvania oil wells in 1859 rode in decades late to save the whales. Camphine was helping but government trade and tax policies cut it off at the pass.”

~~ Rich Olcott

Candle, Candle, Burning Bright

On By rolcottIn Chemistry, Physics: Light and Relativity, UncategorizedLeave a comment

<chirp, chirp> “Moire here.”

“Hi, Sy, it’s Susan Kim. I did a little research after our chat. The whale oil story isn’t quite what we’re told.”

“Funny, I’ve been reading up on whales, too. So what’s your chemical discovery?”

“What do we get from a fire, Sy?”

“Light, heat and leftovers.”

“Mm-hm, and back in 18th Century America, there was plenty of wood and coal for heat. Light was the problem. I can’t imagine young Abe Lincoln reading by the flickering light of his fireplace — he must have had excellent eyesight. If you wanted a mostly steady light you burned some kind of fat, either wax candles or oil lamps.”

“Wait, aren’t fat and wax and oil three different things?”

“Not to a chemist. Fat’s the broadest category, covers molecules and mixtures with chains of ‑CH2‑ groups that don’t dissolve in water. Maybe the chains include a few oxygen atoms but the molecules are basically hydrocarbons. Way before we knew about molecules, though, we started classifying fats by whether or not the material is solid at room temperature. Waxes are solid, oils are liquid. You’re thinking about waxy‑looking coconut oil, aren’t you?”

“Well….”

“Coconuts grow where rooms are warm so we call it an oil, OK? I think it’s fun that you can look at a molecular structure and kind of predict whether the stuff will be waxy or oily.”

“How do you do that?”

“Mmm… It helps to know that a long chain of ‑CH2‑ groups tends to be straight‑ish but if there’s an ‑O‑ link in the chain the molecule can bend and even rotate there. Also, you get a kink in the chain wherever there’s a –CH=CH– double bond. We call that a point of unsaturation.”

“Ah, there’s a word I recognize, from foodie conversations. Saturated, unsaturated, polyunsaturated — that’s about double bonds?”

“Yup. So what does your physicist intuition make of all that?”

“I’d say the linear saturated molecules ought to pack together better than the bendy unsaturated ones. Better packing means lower entropy, probably one of those solid waxes. The more unsaturation or more ‑O‑ links, the more likely something’s an oil. How’d I do?”

“Spot on, Sy. Now carry it a step further. Think of a –CH2– chain as a long methane. How do suppose the waxes and oils compare for burning?”

“Ooo, now that’s interesting. O2 has much better access to fuel molecules if they’re in the gas phase so a good burn would be a two‑step process — first vaporization and then oxidation. Oils are already liquid so they’d go gaseous more readily than an orderly solid wax of the same molecular weight. Unless there’s something about the –O– links that ties molecules together…”

“Some kinds have hydrogen-bond bridging but most of them don’t.”

“OK. Then hmm… Are the double-bond kinks more vulnerable to oxygen attack?”

“They are, indeed, which is why going rancid is a major issue with the polyunsaturated kinds.”

“Oxidized hydrocarbon fragments can be stinky, huh? Then I’d guess that oil flames tend to be smellier than wax flames. And molecules we smell aren’t getting completely oxidized so the flame would probably be smokier, too. And sootier. Under the same conditions, of course.”

“Uh-huh. Would you be surprised if I told you that flames from waxes tend to be hotter than the ones from oils?”

“From my experience, not surprised. Beeswax candlelight is brighter and whiter than the yellow‑orange light I saw when the frying oil caught fire. Heat glow changes red to orange to yellow to white as the source gets hotter. Why would the waxes burn hotter?”

“I haven’t seen any studies on it. I like to visualize those straight chains as candles burning from the ends and staying alight longer than short oil fragments can, but that’s a guess. Ironic that a hydrogen flame is just a faint blue, even though it’s a lot hotter than any hydrocarbon flame. Carbon’s the key to flamelight. Anyway, the slaughter started when we learned a mature sperm whale’s head holds 500 gallons of waxy spermaceti that burns even brighter than beeswax.”

~~ Rich Olcott

  • Whale image adapted from a photo by Gabriel Barathieu CC BY SA 2.0

The Venetian Blind Problem

On By rolcottIn Astronomy: Planetary Science, Chemistry, Physics: Light and Relativity, UncategorizedLeave a comment

Susan Kim gives me the side‑eye. “Sy, I get real suspicious when someone shows me a graph with no axis markings. I’ve seen that ploy used too often by people pushing a bias — you don’t know what happens offstage either side and you don’t know whether an effect was large or small. Your animated chart was very impressive, how that big methane infrared absorption peak just happens to fill in the space between CO2 and H2O peaks. But how wide is the chart compared to the whole spectrum? Did you cherry‑pick a region that just happens to make your point?”

“Susan, how could you accuse me of such underhanded tactics? But I confess — you’re right, sort of. <more tapping on Old Reliable’s keyboard> The animation only covered the near‑IR wavelengths from 1.0 to 5.0 micrometers. Here’s the whole strip from 0.2 micrometers in the near UV, out to 70 micrometers in the far IR. Among other things, it explains the James Webb Space Telescope, right, Al?”

Spectrum of Earth’s atmosphere. Adapted
under the Creative Commons 3.0 license
from Robert Wohde’s work
with the HITRAN2004 spectroscopic database,

“I know the Webb’s set up for IR astronomy from space, Sy. Wait, does this graph say there’s too much water vapor blocking the galaxy’s IR and that’s why they’re putting the scope like millions of miles away out there?”

“Not quite. The mission designers’ problem was the Sun’s heat, not Earth’s water vapor. The solution was to use Earth itself to shield the device from the Sun’s IR emissions. The plan is to orbit the Webb around the Earth‑Sun L2 point, about a million miles further out along the Sun‑Earth line. Earth’s atmosphere being only 60 miles thick, most of it, the Webb will be quite safe from our water molecules. No, our steamy atmosphere’s only a problem for Earth‑based observatories that have to peer through a Venetian blind with a few missing slats at very specific wavelengths.”

“Don’t forget, guys, the water spectrum is a barrier in both directions. Wavelengths the astronomers want to look at can’t get in, but also Earth’s heat radiation at those wavelengths can’t get out. Our heat balance depends on the right amount of IR energy making it out through where those missing slats are. That’s where Sy’s chart comes in — it identifies the wavelengths under threat by trace gases that aren’t so trace any more.”

“And we’re back to your point, Susan. We have to look at the whole spectrum. I heard one pitch by a fossil fuel defender who based his whole argument on the 2.8‑micrometer CO2 peak. ‘It’s totally buried by water’s absorption,‘ he claimed. ‘Can’t possibly do us any further damage.’ True, so far as it goes, but he carefully ignored CO2‘s other absorption wavelengths. Pseudoscience charlatan, ought to be ashamed of himself. Methane’s not as strong an absorber as CO2, but its peaks are mostly in the right places to do us wrong. Worse, both gas concentrations are going up — CO2 is 1½ times what it was in Newton’s day, and methane is 2½ times higher.”

Data from EPA Climate Indicators Explorer

“Funny how they both go up together. I thought the CO2 thing was about humanity burning fossil fuels but you said methane operations came late to that game.”

“Right on both counts, Al. Researchers are still debating why methane’s risen so bad but I think they’re zeroing in on cow gas — belches and farts. By and large, industry has made the world’s population richer over the past two centuries. People who used to subsist on a grain diet can now afford to buy meat so we’ve expanded our herds. Better off is good, but there’s an environmental cost.”

Al gets a far-away look. “Both those gases have carbon in them, right? How about we burn methane without the carbon in, just straight hydrogen?”

Susan gets excited. “Several groups in our lab are working on exactly that possibility, Al. The 2H2+O2→2H2O reaction yields 30% more energy per oxygen atom than burning methane. We just need to figure out how to use hydrogen economically.”

~~ Rich Olcott

It’s A Trap!

On By rolcottIn Astronomy: Planetary Science, Physics: Light and Relativity, UncategorizedLeave a comment

Late morning, no-one else in his coffee shop so Al pulls up a chair. “OK, Susan, so coal’s a mess for ash and air pollution but also each carbon from coal gives us less energy than a carbon from methane. So why the muttering against switching to natural gas?”

“Big-ticket reasons, Al. One, natural gas isn’t pure methane. Mostly methane, sure, but depending on the source you get a whole collection of other things in the mix — heavier hydrocarbons like propane and butane, stinky sulfides and amines, even helium and mercury. Gas from a well has to be purified before you’d want it piped to your house.”

“Piped. Oh, yeah, pipelines. Probably a lot more efficient than coal transport but I see how they get problems, too.”

“Indeed they do. Pipelines break and leak and some idiots even use them for target practice. The worst kind of waste.”

“Yeah, when the oil gets out and ruins the land or someone’s water supply.”

“That’s bad locally, all right, but it’s when methane leaks out that the global damage starts.”

“Global?”

“Mm-hm, because methane’s a gas and mixes in with the rest of the atmosphere. If a pipeline or a truck or anything springs a leak in, say, Chicago, the methane molecules can go anywhere.”

“So?”

“So a couple of things. A decade in the atmosphere oxidizes most methane molecules to, guess what, CO2, the same problematic CO2 we get from burning coal. But before it degrades, methane’s an even bigger heat‑trapper than CO2 is.”

“Whaddaya mean, heat‑trapper?”

“Do you want to take this, Sy? It’s more Physics than Chemistry and besides, my mocha latte’s getting cold.”

“Hmm, there’s a bunch of moving parts in this. Al, you owe Susan a warm-up while I think.”

“Here ya go, Susan.”

“Thanks, Al. I’ll get you guys started. Why did my coffee get cold?”

“Good one, Susan. Al, it’s a universal principle — left to itself, energy spreads out. Heat finds ways to travel from a concentrated, high‑temperature source to low‑temperature absorbers. The exceptions occur when some extra process expends energy to pump heat in the other direction. So, that coffee naturally lost heat to the table by conduction, to the air by convection and to the general environment by radiation. The only thing that can stop those processes is perfect insulation. That’s the thing about the atmosphere.”

“Whoa, that’s a jump or three too fast.”

“OK, let’s follow a sunbeam aimed in the Earth’s direction. Its photons carry a wide range of energies, ultraviolet down to far infrared. On the way in, a UV photon hits an atmospheric ozone molecule and gets absorbed. No more UV photon but now the molecule is in an excited state. It calms down by joggling its neighbor molecules, that’s heat transfer, and maybe emitting a longer wavelength photon or two. Ozone filters out incoming UV and in the process spreads out the photon’s concentrated energy. What’s left in the sunbeam is visible and infrared light that gets down to us. You with me?”

“Makes sense so far.”

“Good. Next stage is that the visible and IR light heat the Earth, which then re-radiates the energy as infrared light mostly at longer wavelengths. The problem is that not all the IR gets out. Water molecules absorb some wavelengths in that range. Every absorption event means more heat distribution into the atmosphere when the molecule relaxes. Ocean evaporation maintains a huge number of IR‑blocking water molecules in the atmosphere.”

“I heard that ‘some‘ weasel‑word. Other wavelengths still make it through, right?”

I unholster Old Reliable, tap a few keys. “Here’s water’s absorption pattern in the mid‑to‑far‑infrared. A high peak means absorption centered at that wavelength. This is scaled per molecule per unit area, so double the molecules gives you double the absorption.”

Spectrum profiles from M. Etminan, et al., doi:10.1002/2016GL071930

“Lots of blank space between the peaks, though.”

“Which is where CO2 and methane get into the game. It’s like putting green and blue filters in front of a red one. With enough of those insulating molecules up there there’s no blank space and lots of imbalance from trapped heat.”

“Methane’s worse.”

“Lots worse.”

~~ Rich Olcott

Going from Worse to Bad

On By rolcottIn Astronomy: Planetary Science, Chemistry, Uncategorized3 Comments

Al delivers coffees to our table, then pauses. “Why methane?”

Susan Kim looks up from her mocha latte. “Sorry?”

“Why all the fuss about methane all of a sudden? I thought carbon dioxide was the baddie. Everybody’s switching from coal to natural gas which they say is just methane and now that’s a bad thing, too. I’m confused. You’re a chemist, unconfuse me.”

“You’re right, there’s mixed message out there. Here’s the bottom line. Methane’s bad, but coal’s a worse bad.”

“OK, but why?”

“Pass me a paper napkin so I can write down the chemical reactions. When we look at them in detail there’s all kinds of complicated reaction paths, but the overall processes are pretty simple. The burnable part of coal is carbon. In an efficient coal‑fired process what happens is
  C + O2 → CO2 + energy.
The C is carbon, of course and O2 is an oxygen molecule, two atoms linked together. Carbon atoms weigh 12 and each oxygen atoms weighs 16, so 12 grams of carbon produces 12+(2×16)=44 grams of CO2. Scaling up, 12 tons of carbon produces 44 tons of CO2 and so on. The energy scales up, too. and that’s what heats the boilers that make the steam that spins the turbines that make electricity.”

“I heard a couple of weasel words but go on to methane.”

“You caught them, eh? They’re important weasels and we’ll get to them. OK, methane is CH4 and its overall burn equation is
  CH4 + 2O2 → CO2 + 2H2O + energy.
Oxidizing those hydrogens releases about twice as much energy per carbon as the coal reaction does.”

“Already I see one big advantage for methane — more bang per CO2. So about those weasels…”

“Right. Well, coal isn’t just pure burnable carbon. It’s 350‑million‑year‑old trees and ferns and animal carcasses and swamp muck and mineral sediments, all pressure‑baked together. There’s sulfur and nitrogen in there, mixed in with nasty elements like mercury and arsenic.”

“The extras go up the smokestack along with the CO2, huh? Bad, for sure.”

“The good news is that coal-burning power plants are under the gun to clean up those emissions. The bad news is that effective mitigation technologies themselves cost energy. That lowers the net yield. But the inefficiency gets worse. Think coal trains.”

“Yeah, half the time I get held up on the way home by one of those hundred‑car strings, either full-up heading to the power plant or empties going back for another load.”

“Mm-hm. Transporting coal takes energy, and so does mining it and crushing it and pre‑treating to get rid of dirt and then taking care of the ashes. Even less net energy output per ton of smokestack CO2, even worse inefficiency. See why coal’s on its way out?”

“I guess all that didn’t matter when it was cheap to dig up and there wasn’t much competition.”

“You put your finger on it, Al. Coal got its foot in the door with steam engines 300 years ago when about the only other things you could burn were wood and whale oil. Crude oil got big in the mid‑1800s but it had to be refined and that made it expensive. Cheap natural gas wasn’t really a thing until fracking came along 50 years ago, but that brought a different set of issues.”

“Yeah, I’ve seen videos of people lighting their kitchen sink water on fire. And wasn’t there an earthquake thing in Oklahoma?”

“That was an interesting situation. Oklahoma’s in the middle of the continent, not a place you’d expect earthquakes, but they began experiencing flurries of shallow ones in 2011. The fracking process starts with water pumped at high pressure into gas-bearing strata to loosen things up. People suspected fracking was connected to the earthquakes. It was, but only indirectly. When fracked gas comes out of a well, water does, too. The rig operators pump that expelled water down old oil wells. Among other things, the state’s Corporation Commission is in charge of their hydrocarbon production. When the Commission ordered a 60% cut in the waste‑water down‑pumping, the earthquake rate dropped by 90%. Sometimes regulations are good things, huh?”

~~ Rich Olcott

Maybe It’s Just A Coincidence

On By rolcottIn Crazy Theories, Physics: Black Holes and Relativity, UncategorizedLeave a comment

Raucous laughter from the back room at Al’s coffee shop, which, remember, is situated on campus between the Physics and Astronomy buildings. It’s Open Mic night and the usual crowd is there. I take a vacant chair which just happens to be next to the one Susan Kim is in. “Oh, hi, Sy. You just missed a good pitch. Amanda told a long, hilarious story about— Oh, here comes Cap’n Mike.”

Mike’s always good for an offbeat theory. “Hey, folks, I got a zinger for you. It’s the weirdest coincidence in Physics. Are you ready?” <cheers from the physicists in the crowd> “Suppose all alone in the Universe there’s a rock and a planet and the rock is falling straight in towards the planet.” <turns to Al’s conveniently‑placed whiteboard> “We got two kinds of energy, right?”

Potential Energy    Kinetic Energy

Nods across the room except for Maybe-an-Art-major and a couple of Jeremy’s groupies. “Right. Potential energy is what you get from just being where you are with things pulling on you like the planet’s gravity pulls on the rock. Kinetic energy is what potential turns into when the pulls start you moving. For you Physics smarties, I’m gonna ignore temperature and magnetism and maybe the rock’s radioactive and like that, awright? So anyway, we know how to calculate each one of these here.”

PE = GMm/R    KE = ½mv²

“Big‑G is Newton’s gravitational constant, big‑M is the planet’s mass, little‑m is the rock’s mass, big‑R is how far apart the things are, and little‑v is how fast the rock’s going. They’re all just numbers and we’re not doing any complicated calculus or relativity stuff, OK? OK, to start with the rock is way far away so big‑R is huge. Big number on the bottom makes PE’s fraction tiny and we can call it zero. At the same time, the rock’s barely moving so little‑v and KE are both zero, close enough. Everybody with me?”

More nods, though a few of the physics students are looking impatient.

“Right, so time passes and the rock dives faster toward the planet Little‑v and kinetic energy get bigger. Where’s the energy coming from? Gotta be potential energy. But big‑R on the bottom gets smaller so the potential energy number gets, wait, bigger. That’s OK because that’s how much potential energy has been converted. What I’m gonna do is write the conversion as an equation.

GMm/R = ½mv²

“So if I tell you how far the rock is from the planet, you can work the equation to tell me how fast it’s going and vice-versa. Lemme show those straight out…”

v = √(2GM/R)    R = 2GM/v²

Some physicist hollers out. “The first one’s escape velocity.”

“Good eye. The energetics are the same going up or coming down, just in the opposite direction. One thing, there’s no little‑m in there, right? The rock could be Jupiter or a photon, same equations apply. Suppose you’re standing on the planet and fire the rock upward. If you give it enough little‑v speed energy to get past potential energy equals zero, then the rock escapes the planet and big‑R can be whatever it feels like. Big‑R and little‑v trade off. Is there a limit?”

A couple of physicists and an astronomy student see where this is going and start to grin.

“Newton physics doesn’t have a speed limit, right? They knew about the speed of light back then but it was just a number, you could go as fast as you wanted to. How about we ask how far the rock is from the planet when it’s going at the speed of light?”

R = 2GM/c²

Suddenly Jeremy pipes up. “Hey that’s the Event Horizon radius. I had that in my black hole term paper.” His groupies go “Oooo.”

“There you go, Jeremy. The same equation for two different objects, from two different theories of gravity, by two different derivations.”

“But it’s not valid for lightspeed.”

“How so?”

“You divided both sides of your conversion equation by little‑m. Photons have zero mass. You can’t divide by zero.”

Everyone in the room goes “Oooo.”

~~ Rich Olcott

A Neutral Party

On By rolcottIn Cosmology, UncategorizedLeave a comment

“Hi, folks, sorry I’m late to the party. What are we arguing about and which side am I on?”

“Hi, Vinnie. We started out talking about neutrality and Jim proved that we’re electrically neutral otherwise we’d spray ourselves apart because of like‑charge repulsons.”

“Yeah, an’ then we got into the Standard Module picture here and how it’s weird that the electron charge exactly cancels out the quark mixture in a proton even though electrons don’t have quarks and quarks don’t have exact charges.”

Jim’s on it. “Almost, Eddie. Quarks have exact charges, but they’re exact fractions. They just add up when you mix three of them to make a particle. Two of them, sometimes. Up‑quark, up‑quark and down‑quark is two‑thirds plus two‑thirds minus one‑third equals one. That’s one proton, exactly opposing one electron’s charge.”

Vinnie’s good at mental math. “What happens when you mix one‑third plus one‑third minus two‑thirds which is zero?”

“Two downs and an up. That’s a neutron.”

“Ups, downs, electrons, protons, neutrons — except for the neutrino the first column’s pretty much atoms, right? What’s with those other boxes?”

“We only see evidence for the other purple‑box quarks in collider records or nuclear reactions. Same for the muon and tau. They’re all way too unstable to contribute much to anything that hangs around. The guys in the red and gold boxes aren’t building blocks, they’re more like glue that holds everything else together. The green‑box neutrinos at the bottom are just weird and we’ll probably be a long time figuring them out.”

“Says here that neutrinos have zero charge, and so do most of the force thingies. Is that really zero or is it just too small to measure?”

“A true Chemistry‑style question, Susan. Charges we can count but you’re right, energy exchanges in a process have to be measured. The zero charges are really zero. For example, Pauli dreamed up the neutrino as an energy‑accounting trick for a nuclear process where all the charges went to known products but there was energy left over. If they existed at all, neutrinos could carry away that energy but they had to have zero charge. A quarter‑century later we detected some and they fit all the requirements.”

Vinnie perks up. “Zero charge so they doesn’t interact with light, teeny mass per each but there’s a hyper‑gazillion of them out there which oughtta add up to a lot of mass. Could neutrinos be what dark matter is?”

“Some researchers thought that for a while but the idea hasn’t held up to inspection. The neutrinos we know about come to about 1% of dark matter’s mass. Some people think there may be a really heavy fourth kind of neutrino that would make up the difference, but it’s a long shot and there’s no firm evidence for it so far. Dark matter doesn’t interact with photons, photons interact with electric charge, quarks have electric charge. If you’ve got quarks you’re not dark matter.”

“How about neutrons floating around?”
 ”Those molecular clouds I’ve read about Aren’t they neutral? Are there neutral stars?”
  ”How about neutron stars and black holes?”
   ”What’s a neutron star?”

“All good questions. Free neutrons are a bad bet, Vinnie — unless they’re bound with protons they usually emit an electron and become a proton within an hour. Susan, electrostatic forces would overwhelm gravity so we believe stars and molecular clouds must be electrically neutral or close to it. Anyway, stars and clouds can’t be dark matter because they’ve got quarks. Eddie, what do you suppose happens when a star uses up the fuel that keeps it big?”

“Since you ask it that way, I suppose it caves in.”

“Got it in one. If the star’s too big to collapse to be a white dwarf but too small to collapse to be a black hole, it collapses to be a neutron star. Really weird objects — a star‑and‑a‑half of of mass packed into a 10‑kilometer sphere, probably spinning super‑fast and possessing a huge magnetic field. From a ‘what is dark matter?‘ perspective, though, collapsed stars of any sort are still made of quarks and can’t qualify.”

“So what is dark matter then?”

“Good question.”

~~ Rich Olcott

  • Thanks to Alex, who asked a question.

Quarkery

On By rolcottIn Cosmology, Physics: Quantum Mechanics, UncategorizedLeave a comment

Susan, aghast. “But I thought the Standard Model was supposed to be the Theory of Everything.”

Jim, abashed. “A lot of us wish that phrase had never been invented. Against the mass of the Universe it’s barely the theory of anything.”

Me, typecast. “That’s a heavy claim, Jim. Big Physics has put many dollars and fifty years of head time into filling out that elegant table of elementary particles. I remember the celebration when the LHC finally found the Higgs boson in 2012. I’ve read that the Higgs field is responsible for the mass of the Universe.”

“A little bit true, Sy, sort of. We think it’s responsible for about 1% of the mass of all the matter we understand. There’s another mechanism that accounts for the other 99%.”

Eddie, downcast. “I’m lost, guys. What Standard Module are you talking about?”

“Do you remember the Periodic Table of the chemical elements?”

“A little. Science class had big poster up on the wall. Had all kinds of atoms in it, right?”

“Yup. Scientists spent centuries breaking down minerals and compounds to find substances that chemical methods couldn’t break down any further. Those were the chemical elements, things like iron and carbon and oxygen. The Periodic Table arranges elements so as to highlight similarities in how they’ll interact. The Standard Model carries that idea down to the sub‑subatomic level.”

“Wait, sub‑subatomic level?”

“Mm-hm. Chemists would say that ‘subatomic‘ is about electrons, protons and neutrons. Count an atom’s electrons. That and some fairly simple rules can tell you what structure types it prefers to participate in and what it reacts with. Count the protons and neutrons in its nucleus. That gives you its atomic weight and starts you on the road to figuring reaction quantities. That’s all that the chemists need to know about atoms. All due respect, Susan, but physicists want to dig deeper. That’s what the Standard Model is all about.”

“So you’re saying that the protons and neutrons are made of these … quarks and things? Is that what comes out of those collider experiments?”

“No on both, Eddie. You ever whack a light pole with a baseball bat?”

“Sure, who hasn’t?”

“The sounds that came out, do you think the pole was made of them?”

“Course not, and I never bought the Brooklyn Bridge, neither.”

“Calm down, Eddie, just making a point. Suppose before you whacked that pole you’d attached a whole string of sensitive microphones all up and down it, and then when you whacked it you recorded all the vibrations your whack set off. Do you think with the recorded frequencies and a lot of math a good audio engineer could tell you what the pole is made of and how thick the casing is?”

“Maybe.”

“That’s what’s going on with the colliders. They whack particles with other particles, record everything that comes out and use math to work out what must have happened to make that event happen. Theory together with data from a huge number of whacks let people like Heisenberg, Gell‑Mann, Ne’eman and Nishijima to the seventeen boxes in that table.”

“‘Splain those particles to me.”

“Don’t think particles, think collections of properties. The Periodic Table’s ‘iron‘ box is about having 26 electrons and combining with 24 grams of oxygen to form 80 grams of Fe2O3. In the Standard Model table, the boxes are about energy, charge, lifetime, some technical properties, and rules for which can interact with what. We’ve never seen a free‑standing quark particle and there’s good reason to think we never will. We mostly see only two‑ or three‑quark mixtures. Some of the properties, like charge, simply add together. It takes a mixture to make a particle.”

“Then how did they figure what goes into a box?”

“Theoreticians worked to find the minimum set of independent properties that could still describe observations. Different mixtures of up and down quarks, for instance, account for protons, neutrons and many mesons.”

Vinnie, at last. “Hi, folks, sorry I’m late to the party. What are we arguing about and which side am I on?”

Higgs candidate LHC event trace
Electrons (green) and muons (red) exiting the event

~~ Rich Olcott

Neutral

On By rolcottIn Cosmology, Physics: Gaps, UncategorizedLeave a comment

It’s that kind of an afternoon. Finished up one project, don’t feel much like starting another. Spring rain outside so instead of walking to Al’s for coffee I take the elevator down to Pizza Eddie’s on 2. Looks like other folks have the same feeling. “Afternoon, all. What’s the current topic of conversation?”

“Well, Sy, it started out as Star Wars versus Star Trek but then Jim said he could care less and Susan said that meant he did care and he said no, he’s ambivalent and she said that still meant he cared, and—”

“I get it, Eddie. Susan, why does ‘ambivalent‘ mean Jim cares?”

“Chemistry, Sy. ‘Valence‘ means ‘bonding‘ and ‘ambi-‘ means ‘both‘ so ‘ambi‑valent‘ means ‘bonded to both‘.”

“But Susan, ambidextrous means able to use both hands, not unable to use either hand. I want to say I don’t particularly like or dislike either one.”

“It’s like trying to decide between fire ants or hornets. You could say ‘No‑win,’ right?”

“No, that’s not it, either, Eddie. That’s ‘everybody loses.’ I’m smack in the middle.”

“Sounds like absolute neutrality. Hard to get there.”

“Don’t look at Chemistry. If I take an acid solution and add just enough base to get to neutral pH, there’s still tenth‑micromolar concentrations of acid and base in there. I guess we could call that ambivalent.”

“Neutrality’s hard for humans and chemicals, yeah, but that’s where the Universe is.”

“Why do you say that, Jim?”

“Because we’ve got proof right in front of us. Look, planets and stars and people exist as distinct objects, right? They’re not a finely-divided mist.”

“So?”

“So if the Universe were not exactly electrically neutral, then opposite charges repelling would split everything apart.”
 ”Wait, nothing would have a chance to form in the first place.”
   ”Wait, couldn’t you have lumps of like 99 positives and 100 negatives or whatever that just cancel out?”

“Eddie, when you say ‘cancel out’ you’re still talking about being absolutely neutral at the lump level. It’s like this table salt that has positive sodium ions and negative chlorides but the crystals are neutral or we’d get sparks when I pour some out like this.”
 ”Hey, don’t waste the salt. Costs money.”

“I still think it’s weird how all electrons have the same charge and it’s exactly the same as the proton charge. Protons are made of quarks, right, and electrons aren’t. So how can you take three of something and have that add up to exactly one of something different?”

“I can give you Feynman and Wheeler’s answer to part of that, Susan. The electron has an anti‑partner, the positron, which is exactly like the electron in every way except it has the opposite charge. When electron and positron meet they annihilate to produce a burst of high‑energy photons. But there’s a flip side — high‑energy photons sometimes interact to make an electron‑positron pair. Feynman and Wheeler were both jokers. They suggested that a positron could be an electron traveling backward in time. Wheeler said, ‘Maybe they’re all the same electron,’ zig‑zagging across eternity. But that doesn’t account for the quarks. A proton has two up‑quarks, each with a charge of negative 2/3 electron, and one down‑quark with a charge of positive 1/3 electron. Add ’em up — you exactly neutralize one electron. Fun, huh?”

“Fun, Jim, but I’m a chemist. On a two-pan balance I can weigh out equal quantities of molasses and rock dust but I don’t expect them to interact with any simple mathematical relationship. Why should the quark’s charge be any exact multiple or divisor of the electron’s? And why is the electron charge the size it is instead of some other number?”

“Well, there you’ve got me. The quantum chromodynamics Standard Model has been amazingly successful for quantitative predictions, but not so good for explaining things outside of its own terms. The math lays out the relationship between quark and electron charge, but doesn’t give us a physical ‘why.’ The theory has 19 ‘adjustable constants’ but no particular reason why they should have the specific values that fit the observations. Also, the theory doesn’t include gravity. It’s a little embarrassing.”

“Sounds like you’re ambivalent about the theory.”

~~ Rich Olcott