Category: Physics

Flasks Of Money

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

<chirp, chirp> “Moire here.”

“Hiya, Sy, it’s me again.”

“Hi, Eddie. I thought you were done with your deliveries tonight. That was a good stromboli, by the way, just the right amount of zing and sauce.”

“Thanks. Yeah, I’m done for the day, but I was thinking while I drove home. We said that the Feds and the banks together can tinker with the money supply so there’s no Conservation of Money like we got Conservation of Energy. But then we said that it matters to keep money in local businesses instead of letting it drain away somewhere else. That says there’s only so much to go around like the amount doesn’t change. So which is it?”

“Good point. You’ve touched on another contrasting parallel between Physics and Economics. In Physics we mostly understand how atoms work and we’ve got a pretty good handle on the forces that control objects big enough to see. J Willard Gibbs, probably the foremost physicist of the late 1800s, devised Statistical Mechanics to bridge the gap between the two levels. The idea is to start with the atoms or molecules. They’re quantum objects, of course, so we can’t have much precise information at that level. What we can get, though, is averages and spreads on one object’s properties — speed, internal energy levels, things like that. Imagine we have an ensemble of those guys, mostly identical but each with their own personal set of properties. Gibbs showed us how to apply low-level averages and spreads across the whole ensemble to calculate upper-level properties like magnetic strength and heat capacity.”

“Ensemble. Fancy word.”

“Not my word, blame Gibbs. He invented the field so we go with his terminology. Atoms weren’t quite a respectable topic of conversation at the time so he kept things general and talked about ‘macroscopic properties‘ which we can measure directly and ‘microscopic properties‘ which were mysterious at the time. Think of three flasks holding samples of some kind of gas, OK?”

“No problem.”

“The first flask is stoppered, no gas can get in or out but energy can pass through the flask’s wall. Gibbs would call the confined collection of molecules a ‘canonical ensemble‘. Because the wall transmits energy we can use an external thermometer to measure the ensemble’s temperature. Other than that, all we know about the contents is the number of particles and the volume the particles can access.”

“Canonical?”

“In Gibbs’ usage it means that he’s pared things down to an abstract essence. It doesn’t matter whether what’s inside is atoms or fruitflies, his logic still holds. Now for flask number two. It’s heavily insulated so whatever energy it had inside originally, that’s what it’s got now. We can’t measure the temperature in this one. Gibbs would consider the particles in there to be a ‘microcanonical ensemble,’ with the ‘micro’ indicating the energy restriction.”

“Where there’s a microcanonical there’s gotta be a macrocanonical.”

“You’d think, but Gibbs used the term ‘grand canonical ensemble‘ instead. That’s flask number three, which has neither insulation nor stopper. Both energy and matter are free to enter or leave the ensemble. Gibbs’ notion of canonical ensembles and the math that grows out of them have been used in every kind of analysis from solid state physics to cybersecurity.”

“OK, I think I see where you’re going here. Money acts sorta like energy so you’re gonna lay out three kinds of economy restriction.”

“You’re way ahead of me and the economists, Eddie. They’ve only got two levels, though they do use reasonable names for them — microeconomics and macroeconomics. For them the micro level is about individuals, businesses, the markets they play in and how they spend their incomes. Supply-demand thinking gets used a lot.”

“That figures. What about macro?”

“Macro level is about regions and countries and the world. Supply‑demand plays here, too, except the macroeconomists worry about how demand for money itself affects its value compared to everything else.”

“They got bridges like Gibbs built?”

“Nope. Atoms are simple, people are complicated. The economists are still arguing about the basics. Anyway, the economists’ micro level assumes local money stays local and has a stable value.”

“Keeping my business stable is good.”

~~ Rich Olcott

What Goes Around

On By rolcottIn Physics: Money, UncategorizedLeave a comment

<shout from outside my office door> “Stromboli Express. Get ’em while they’re hot!”

“The door’s open, Eddie, and you’re right on schedule.”

“I aim to please, Sy. Which ain’t easy while I’m wearing this virus mask.”

“On you it looks good, Eddie. Just leave the order on the credenza. How’s my account?”

“Still good from that last twenty. I gotta say, I appreciate you keeping your tab on the plus side. You, Vinnie, all you singles, your orders are keeping me in business despite that corporate PizzaDoodle shop that opened up.”

“Doing my part to keep the money local, Eddie. Besides, you do good pizza.”

“What difference does keeping the money local make? Anything to do with money being energy?”

“Whoa, where did that come from?”

“You told me, Sy. When prices get higher than a perfect supply‑demand market would set them, it’s from inefficiency like what happens to machine energy that gets turned into heat by friction.”

“Ah, you stretched my metaphor a little too far. Money behaves like energy in some ways but not in others. For one thing, Conservation of Energy applies universally, we think, but Conservation of Money not so much.”

“The dollars in my wallet don’t multiply, that’s for sure.”

“Individuals aren’t allowed to fiddle the money supply — that’s called counterfeiting. But the 1930s Great Depression taught us that purposefully creating and destroying money is part of the government’s job. Banks can vary the money supply, too, sort of.”

“Yeah, I’ve seen videos of the Mint’s printing presses and them grinding up ratty old used bills.”

“That’s the least of what they do these days. Depending on which way you define ‘money’, only about a fifth of the money supply is cash currency.”

“There’s definitions of money?”

“Mm-hm. That’s one of the keys to the part the banks play. One definition is just the currency, like you’d think. The economists pay attention to a broader definition. When you deposit tonight’s receipts in the bank, the cash doesn’t just sit in a vault. For that matter, your credit card and debit card take can’t sit in a vault. What does the bank do? It keeps a certain percentage of its deposited dollars as a reserve in case you want to pull dollars out to pay Joey for his sausage or something. The rest of those dollars can be loaned out. The loaned dollars generally get deposited for a while before they’re spent and a fraction of those deposits can be loaned out … you see where this is going.”

“Whoa, so I put on a hundred and that turns into maybe four, five hundred or more by when the dust settles. I see what you mean about banks creating money even if it’s not real money.”

“Oh, it’s real money — officially blessed marks in a ledger or more likely, bits in computers instead of paper and coins, but it counts. Anyhow, the second definition of ‘money’ combines currency and deposits from all those loans.”

“So what’s to prevent the bank from loaning out all their money and riding this pony over and over again? That’s what I’d want to do, pull in interest on like, infinite loans.”

“That’s where the government steps in. Depositors need to be sure they can make withdrawals. The Feds don’t tell banks, ‘You can only loan out a certain number of dollars.‘ What they do say is, “Your reserves have to total up to at least x fraction of your deposits.’ The Feds are free to change the value of x up or down depending on whether they want to shrink or expand the money supply.”

“Closing down or opening up the spigot and Conservation of Money ain’t a thing, gotcha. But what does that have to do with you guys keeping money local?”

“Think back to that $20 bill that went from you to Vinnie to Al to me to you. What would have happened if Al had decided to invest in some weird coffee beans instead of buying those magazines from me?”

“The dollars would fly away from our local bank and they wouldn’t be there for an x fraction loan for my business. Gotcha.”

~~ Rich Olcott

Supply, Demand And Friction

On By rolcottIn Physics: Money, UncategorizedLeave a comment

<chirp, chirp> “Moire here. Open for business on a reduced schedule.”

“Hiya, Sy. It’s Eddie, taking orders for tonight’s pizza deliveries. My 6:15 wave is full-up, can I schedule you for 6:45? Whaddaya like tonight?”

“Yeah, a little later’s OK, Eddie. Mmmm, I think a stromboli this time. Rolled up like that, it ought to stay hot longer.”

“Good idea. Hey, I been thinking about that ‘velocity of money‘ thing and the forces that change where it goes. Isn’t that just another name for ‘supply and demand’? Bad weather messes up the wheat crop, I gotta pay more for pizza flour, that kinda thing.”

“That’s one of the oldest theories in economics, the idea that low supply increases prices and conversely. Economists often use two hyperbolas to describe the trade-off. Unfortunately, the idea’s only sorta true and only for certain markets. Oh, and it’s only sorta related to how fast money flows through the economy.”

“C’mon, Sy, you’re talking to a professional here. I watch my costs pretty close. Supply-demand tells my story — a bad tomato harvest drives my red sauce price through the roof.”

“No question it works for some products where there’s many independent buyers, many independent sellers, everyone has the same information, and a few other technical only-ifs. It’s what they call a perfect market. How many different companies do you buy flour from?”

“Three or four in town here. I switch around. Keeps ’em on their toes and holds their price down.”

“Competition’s a good thing, right? No buyer pays more than they absolutely must and no seller takes less than their competition does. Negative feedback all over the place. If one vendor figures out an advantage and can make money selling the same stuff for a lower price, everyone else copies them and the market price settles into a new lower equilibrium and there’s no advantage any more.”

“Yeah, that’s the way it works for flour.”

“And a few other commodities like grains and metals and West Texas crude. Economic theorists love the perfect-market model because it sets prices so nicely. Physicists love ideal cases, too — frictionless pulleys on infinitely sharp pivots, that kind of thing, where you can ignore the practical details. Most markets have lots of practical considerations that gum up the works.”

“Devil’s in the details, huh?”

“Sure. I seem to recall you’ve got a favorite sausage supplier.”

“Yeah, my brother-in-law Joey. OK, he’s family, but he does good work — fresh meat ground exactly the way I want it, got a good nose for spices, dependable delivery, what’s not to like?”

“Is he more expensive?””

“A little, a little, but it’s worth it.”

“So hereabouts there’s an imperfect market for sausage. The economists might tally Joey’s extra profit from that premium price to an accounting column labeled ‘Goodwill.’ A physicist would have another name for it.”

“Goodwill. Joey’d like that. So what would the physicist call it?”

“Real mechanical systems are never perfectly energy‑efficient. Energy is always lost to friction. In my money‑physics framework money’s lost to friction. It’s the reason you pay a premium above what would be perfect‑market price for sausage. Nothing wrong with that so long as you know you’re doing it and why. Most real markets are loaded with friction of various sorts. Think of market regulators as mechanics, running around with oil cans as they reduce inefficiency and friction.”

“What other frictions … lemme think. Monopoly, for sure — some big chain takes over my market, drives me the rest of the way out of business and then they can charge whatever they want. Umm … collusion, either direction. Advertising, maybe, but that’s mostly legal.”

“You got the idea. So, how is business?”

“Are you kidding? Way off. I had to lay off people, now it’s just me baking and delivering.”

“Would you buy flour these days at the usual price?”

“Nah. At the rate things are going what I got will last me for a l‑o‑o‑n‑g time. I got no place to put any more.”

“Your customers aren’t buying, you’re not buying, money’s not changing hands. The velocity of money’s so low that supply-demand isn’t capable of setting price. That’s deflation, not market friction.”

“Either way, it hurts.”

~~ Rich Olcott

The Buck Rolls On, We Hope

On By rolcottIn Physics: Money, UncategorizedLeave a comment

<knock, knock> “Door’s open. Come in but maintain social distance.”

“Hiya, Sy. Here’s your pizza, still hot and everything but no pineapple.”

“Thanks, Eddie. Just put it on the credenza. There’s a twenty there waiting for you. Put the balance on my tab.”

“Whoa, I recognize this bill. It’s the one that Vinnie won off me at the after‑hours dice game last month before all this started. See, I initialed it down here on the corner ’cause Vinnie usually don’t do that well. How’d you get it from him?”

“I didn’t get it from Vinnie, I got it from Al when I sold him a batch of old astronomy magazines. Vinnie must have finally paid off his tab at Al’s coffee shop.”

“Funny how that one bill just went in a circle. Financed some risky business, paid off a loan, bought stuff, and here I get it again so I can buy stuff to make more pizza. That’s a lotta work for one piece of paper.”

“Mm-hm. Everyone’s $20 better off now, all because the bill kept moving. Chalk it off to ‘the velocity of money.‘ If Vinnie didn’t spend that money the velocity’d be zero and none of the rest would have happened.”

“That sounds suspiciously like Physics, Sy.”

“Guilty as charged, Eddie. Just following along with what Isaac Newton started back when he was staying at his mother’s place, hiding out from the bubonic plague.”

Newton, after a day at the beach
while wearing an anti-viral mask

“What’s that got to do with money? Was Newton a banker?”

“Not quite, although the last 30 years of his life he headed up England’s Royal Mint. The core of his work during his Science years was all about change and rate of change. His Laws of Motion quantified what it takes to cause change. He developed his version of calculus to bridge between how fast change happens and how much change has happened.”

“Hey, that’s those graphs you showed me, with the wave on the top line and the slope underneath.”

“Bingo. Pandemics are a long way from the simple systems that Newton studied, but the important point is that to study his planets and pendulums he developed general strategies for tackling complex situations. He started with just a few basic concepts, like position and speed, and expanded on them.”

“Speed’s speed, what’s to expand?”

“Newton expanded the notion of speed to velocity, which also includes direction. From Newton’s point of view, the velocity of a planet in orbit is continuously changing even if its miles per hour is as steady as … a planet.”

“Who cares?”

“Newton did, because he wanted to know what makes the change happen. His starting point was if there’s any motion, it’s got to be at constant speed and in a straight line unless some force causes a velocity change. That’s where his notion of gravity came from — he invented the idea of ‘the force of gravity‘ to account for us not flying off the rotating Earth and the Earth not zooming away from the Sun. His methods set the model that physicists have followed ever since — if we see motion, we measure how fast it’s happening and then we look for the force or forces that can explain that.”

“Now I see where you’re going. That ‘velocity of money‘ thing is about how fast the paper changes hands, isn’t it? Wait, if Vinnie had put that twenty up on his wall as a trophy, then the chain would’ve been broken.”

“Right, or if Al had diverted it to buy, say, coffee beans. That’s why we say velocity of money and not speed, because the direction of flow counts.”

“Smelling more and more like Physics, Sy. Like, there’s astrophysics and biophysics and you’re coming up with econophysics.”

“Well, yeah, but I didn’t invent the term. It’s already out there, with textbooks and academic study groups and everything. It’s just interesting to use economics as a metaphor for physics and vice-versa. The fun is in seeing where the metaphors break down.”

“I see one already, Sy. Those forces — we all had different reasons to kick the bill along.”

“Good point. Now we figure out those forces.”

~~ Rich Olcott

Sisyphus on A Sand Dune

On By rolcottIn Physics: Entropy and Thermodynamics, UncategorizedLeave a comment

I’m walking the park’s paths on a lovely early Spring day when, “There you are, Moire. I got a question!”

“As you always do, Mr Feder. What’s your question this time?”

“OK, this guy’s saying that life is all about fighting entropy but entropy always increases anyway. I seen nothing in the news about us fighting entropy so where’s he get that? Why even bother if we’re gonna lose anyway? Where’s it coming from? Can we plug the holes?”

“That’s 4½ questions with a lot of other stuff hiding behind them. You’re going to owe me pizza at Eddie’s AND a double-dip gelato.”

“You drive a hard bargain, Moire, but you’re on.”

“Deal. Let’s start by clearing away some underbrush. You seem to have the idea that entropy’s a thing, like water, that it flows around and somehow seeps into our Universe. None of that’s true.”

“That makes no sense. How can what we’ve got here increase if it doesn’t come from somewhere?”

“Ah, I see the problem — conservation. Physicists say there are two kinds of quantities in the Universe — conserved and non‑conserved. The number of cards in a deck is is a conserved quantity because it’s always 52, right?”

“Unless you’re in a game with Eddie.”

“You’ve learned that lesson, too, eh? With Eddie the system’s not closed because he occasionally adds or removes a card. Unless we catch him at it and that’s when the shouting starts. So — cards are non-conserved if Eddie’s in the game. Anyway, energy’s a conserved quantity. We can change energy from one form to another but we can’t create or extinguish energy, OK?”

“I heard about that. Sure would be nice if we could, though — electricity outta nothing would save the planet.”

“It would certainly help, and so would making discarded plastic just disappear. Unfortunately, mass is another conserved quantity unless you’re doing subatomic stuff. Physicists have searched for other conserved quantities because they make calculations simpler. Momentum‘s one, if you’re careful how you define it. There’s about a dozen more. The mass of water coming out of a pipe exactly matches the mass that went in.”

“What if the pipe leaks?”

“Doesn’t matter where the water comes out. If you measure the leaked mass and the mass at the pipe’s designed exit point the total outflow equals the inflow. But that gets me to the next bit of underbrush. Energy’s conserved, that’s one of our bedrock rules, but energy always leaks and that’s another bedrock rule. The same rule also says that matter always breaks into smaller pieces if you give it a chance though that’s harder to calculate. We measure both leakages as entropy. Wherever you look, any process that converts energy or matter from one form to another diverts some fraction into bits of matter in random motion and that’s an increase of entropy. One kind of entropy, anyway.”

“Fine, but what’s all this got to do with life?”

“It’s all to get us to where we can talk about entropy in context. You’re alive, right?”

“Last I looked.”

“Ever break a bone?”

<taps his arm> “Sure, hasn’t everybody one time or another?”

“Healed up pretty well, I see. Congratulations. Right after the break that arm could have gone in lots of directions it’s not supposed to — a high entropy situation. So you wore a cast while your bone cells worked hard to knit you together again and lower that entropy. Meanwhile, the rest of your body kept those cells supplied with energy and swept away waste products. You see my point?”

“So what you’re saying is that mending a broken part uses up energy and creates entropy somewhere even though the broken part is less random. I got that.”

“Oh, it goes deeper than that. If you could tag one molecule inside a living cell you’d see it bouncing all over the place until it happens to move where something grabs it to do something useful. Entropy pushes towards chaos, but the cell’s pattern of organized activity keeps chaos in check. Like picnicking on a windy day — only constant vigilance maintains order. That’s the battle.”

“Hey, lookit, Eddie’s ain’t open. I’ll owe you.”

“Pizza AND double-dip gelato.”

~~ Rich Olcott

A Far And Dusty Traveler

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

Cathleen takes the mic. “Quick coffee and scone break, folks, then Jim will continue our ‘IR, Spitzer And The Universe‘ symposium.” <pause> “OK, we’re back in business. Jim?”

“Thanks, Cathleen. Well, we’ve discussed finding astronomical molecules with infra-red. Now for a couple of other IR applications. First up — looking at things that are really far away. Everyone here knows that the Universe is expanding, right?”

<general murmur of assent, although the probably-an-Art-major looks startled>

“Great. Because of the expansion, light from a far-away object gets stretched out to longer wavelengths on its way to us. Say a sodium atom shot a brilliant yellow-gold 590-nanometer photon at us, but at the time the atom was 12.5 million lightyears away. By the time that wave reaches us it’s been broadened to 3540 nanometers, comfortably into the infra-red. Distant things are redder, sometimes too red to see with an optical telescope. The Spitzer Space Telescope‘s infra-red optics let us see those reddened photons. And then there’s dust.”

<voice from the crowd> “Dust?”

“Cosmic dust, pretty much all the normal matter that’s not clumped into stars and planets. Some of it is leftovers from early times in the Universe, but much of it is stellar wind. Stars continuously spew particles in their normal day-to-day operation. There’s a lot more of that when one explodes as a nova or supernova. Dust particles come in all sizes but most are smaller than the ones in tobacco smoke.”

<same voice> “If they’re so small, why do we care about them?”

“Two reasons. First, there’s a lot of them. Maybe only a thousand particles per cubic kilometer of space, but there’s a huge number of cubic kilometers in space and they add up. More important is what the dust particles are made of and where we found them. Close inspection of the dust is like doing astronomical archaeology, giving us clues about how stars and galaxies evolved.”

<Vinnie, skeptical as always> “So what’s infra-red got to do with dust?”

“Depends on what kind of astronomy you’re interested in. Dust reflects and emits IR light. Frequency patterns in the light can tell us what that dust made of. On the other hand there’s the way that dust doesn’t interact with infra-red.”

<several voices> “Wait, what?”

The Milky Way from Black Rock Desert NV
By Steve Jurvetson via Flickr, Wikimedia Commons, CC BY 2.0

“If Al’s gotten his video system working … ah, he has and it does. Look at this gorgeous shot of the Milky Way Galaxy. See all the dark areas? That’s dust blocking the visible light. The scattered stars in those areas are simply nearer to us than the clouds. We’d like to study what’s back beyond the clouds, especially near the galaxy’s core. That’s a really interesting region but the clouds block its visible light. Here’s the neat part — the clouds don’t block its infra-red light.”

<other voices> “Huh?” “Why wouldn’t they?”

“It’s the size of the waves versus the size of the particles. Take an extreme case — what’s the wavelength of Earth’s ocean tides?”

<Silence, so I speak up.> “Two high tides a day, so the wavelength is half the Earth’s circumference or about 12’500 miles.”

“Right. Now say you’re at the beach and you’re out there wading and the water’s calm. Would you notice the tide?”

“No, rise or fall would be too gentle to affect me.”

“Now let’s add a swell whose peak-to-peak wavelength is about human-height scale.”

“Whoa, I’d be dragged back and forth as each wave passes.”

“Just for grins, let’s replace that swell with waves the same height but only a millimeter apart. Oh, and you’re wearing SCUBA equipment.”

“Have mercy! Well, I should be able to stand in place because I wouldn’t even feel the peaks and troughs as separate waves, just a foamy massage. Thanks for the breathing assistance, though.”

“You’re welcome, and thanks for helping with the thought experiment. Most cosmic dust particles are less than 100 nanometers across. Infra-red wavelengths run 100 to 1000 times longer than that. Infra-red light from those cloud-hidden stars just curves around particles that can stop visible lightwaves cold. Spitzer Space Telescope and its IR-sensitive kin provide deeper and further views than visible light allows.”

~~ Rich Olcott

Above The Air, Below The Red

On By rolcottIn Astronomy: Multi-messenger, Astronomy: Techniques, Physics: Light and Relativity, UncategorizedLeave a comment

Vinnie and I walk into Al’s coffee shop just as he sets out a tray of scones. “Odd-looking topping on those, Al. What is it?”

“Dark cherry and dark chocolate, Sy. Something about looking infra-red. Cathleen special-ordered them for some Astronomy event she’s hosting in the back room. Carry this tray in there for me?”

Vinne grabs the tray and a scone. “Sure, Al. … Mmm, tasty. … Hi, Cathleen. Here’s your scones. What’s the event?”

“It’s a memorial symposium for the Spitzer Space Telescope, Vinnie. Spitzer‘s been an infra-red workhorse for almost 17 years and NASA formally retired it at the end of January.”

“What’s so special about infra-red? It’s just light, right? We got the Hubble for that.”

“A perfect cue for Jim’s talk. <to crowd> Grab a scone and settle down, everyone. Welcome to our symposium, ‘IR , Spitzer And The Universe.’ Our first presentation today is entitled ‘What’s So Special About Infra-red?‘ Jim, you’re on.”

“Thanks, Cathleen. This is an introductory talk, so I’ll keep it mostly non-technical. So, question for everybody — when you see ‘IR‘, what do you think of first?”

<shouts from the crowd> “Pizza warmer!” “Invisible light!” “Night-vision goggles!”

“Pretty much what I expected. All relevant, but IR’s much more than that. To begin with, many more colors than visible light. We can distinguish colors in the rainbow because each color’s lightwave has a different frequency. Everybody OK with that?”

<general mutter of assent>

“OK. Well, the frequency at the violet end of the visible spectrum is a bit less than double the frequency at the red end. In music when you double the frequency you go up an octave. The range of colors we see from red to violet is less than an octave, about like going from A-natural to F-sharp on the piano. The infra-red spectrum covers almost nine octaves. An 88-key piano doesn’t even do eight.”

<voice from the crowd, maybe an Art major> “Wow, if we could see infra-red think of all the colors there’d be!”

“But you’d need a whole collection of specialized eyes to see them. With light, every time you go down an octave you reduce the photon’s energy capacity by half. Visible light is visible because its photons have just enough energy to cause an electronic change in our retinas’ photoreceptor molecules. Five octaves higher than that, the photons have enough energy to knock electrons right out of a molecule like DNA. An octave lower than visible, almost nothing electronic.”

<Vinnie’s always-skeptical voice> “If there’s no connecting with electrons, how does electronic infra-red detection work?”

“Two ways. A few semiconductor configurations are sensitive to near- and mid-infra-red photons. The Spitzer‘s sensors are grids of those configurations. To handle really low-frequency IR you have to sense heat directly with bolometer techniques that track expansion and contraction.”

<another skeptical voice> “OK then, how does infra-red heating work?”

“Looks like a paradox, doesn’t it? Infra-red photons are too low-energy to make a quantum change in a molecule’s electronic arrangement, but we know that the only way photons can have an effect is by making quantum changes. So how come we feel infra-red’s heat? The key is, photons can interact with any kind of charged structure, not just electrons. If a molecule’s charges aren’t perfectly balanced a photon can vibrate or rotate part of a molecule or even the whole thing. That changes its kinetic energy because molecular motion is heat, right? Fortunately for the astronomers, gas vibrations and rotations are quantized, too. An isolated water molecule can only do stepwise changes in vibration and rotation.”

“Why’s that fortunate?”

“Because that’s how I do my research. Every kind of molecule has its own set of steps, its own set of frequencies where it can absorb light. The infra-red range lets us do for molecules what the visual range lets us do for atoms. By charting specific absorption bands we’ve located and identified interstellar clouds of water, formaldehyde and a host of other chemicals. I just recently saw a report of ‘helonium‘, a molecular ion containing helium and hydrogen, left over from when the Universe began. Infra-red is so cool.”

“No, it’s warm.”

Image suggested by Alex

~~ Rich Olcott

The Sight And Sound of Snow

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

<ring> “Moire here.”

“Uncle Sy! Uncle Sy! It’s snowing! It’s snowing!”

“Yes, Teena, it started last night after you went to bed. But it’s real early now and I haven’t had breakfast yet. I’ll be over there in a little while and we can do snow stuff.”

“Yaaay! I’ll have breakfast, too. Mommie, can we have oatmeal with raisins?” <click>

<knock, knock> “Uncle Sy! You’re here! I wanna go sledding! Get my sled out, please?”

“G’morning, Sis. G’morning, Teena. Get your snowsuit and boots on, Sweetie. Want to come along, Sis? It’s a cold, dry snow, not much wind.”

“No, I’ll just stay warm and get the hot chocolate ready.”

“Bless you for that, Sis. OK, young’un, ready to go?”

“Ready! Pull me on the sled to the sledding hill, Uncle Sy!”

“Ooo, it’s so quiet. Why’s it always quiet when snow’s falling, Uncle Sy? Is the world holding its breath? And why is snow white? When I hold snow in my hand it melts and then it’s no-color.”

“Always the good questions. Actually, these two are related and they both have to do with the shape of snowflakes. Here, hold out your arm and let’s see if you can catch a few. No, don’t try to chase them, the breeze from your arm will blow them away. Just let them fall onto your arm. That’s right. Now look at them real close.”

“They’re all spiky, not flat and pretty like the ones in my picture book!”

“That’s because they grew fast in a really cold cloud and didn’t have time to develop evenly. You have to work slow to make something that’s really pretty.”

“But if they’re spiky like this they can’t lay down flat together and be cozy!”

“Ah, that’s the key. Fresh spiky snowflakes make fluffy snow, which is why skiers love it. See how the flakes puff into the air when I scuff my boot? Those tiny spikes break off easily and make it easy for a ski to glide over the surface. Your sled, too — you’ve grown so big I’d be hard-put to pull you over wet snow. That fluffiness is why <hushed voice> it’s so quiet now.”

“Shhh … <whispered> yeah … <back to full voice> Wait, how does fluffy make quiet?”

“Because sound waves … Have we talked about sound waves? I guess we haven’t. OK, clap your hands once.”

<CLAP!>

“Good. When your hands came together they pushed away the air molecules that were between them. Those molecules pushed on the next molecules and those pushed on the next ones on and on until they got to your ear and you heard the sound. Make sense?”

“Ye-aa-uh. Is the push-push-push the wave?”

“Exactly. OK, now imagine that a wave hits a wall or some packed-down icy snow. What will happen?”

“It’ll bounce off like my paddle-ball toy!”

“Smart girl. Now imagine that a wave hits fluffy snow.”

“Um … it’ll get all lost bouncing between all the spikes, right?”

“Perfect. That’s exactly what happens. Some of the wave is scattered by falling snowflakes and much of what’s left spreads into the snow on the ground. That doesn’t leave much sound energy for us to hear.”

“You said that snow’s white because of what snow does to sound, but look, it’s so bright I have to squint my eyes!”

“That’s not exactly what I said, I said they’re related. Hmm… ah! You know that ornament your Mommie has hanging in the kitchen window?”

“The fairy holding the glass jewel? Yeah, when the sunlight hits it there’s rainbows all over the room! I love that!”

A beam or white light passing through two prisms. The first produces a spectrum and the second remixes the colors to white.

“I do, too. White light like sunlight has all colors in it and that jewel splits the colors apart so you can see them. Well, suppose that jewel is surrounded by other jewels that can put the colors together again. Here’s a picture on my cellphone for a clue.”

“White goes to rainbow and back to white again … I’ll bet the snowflakes act like little jewels and bounce all the colors around but the light doesn’t get trapped and it comes out and we see the WHITE again! Right?”

“So right that we’re going home for hot chocolate.”

“Yaaay!”

~~ Rich Olcott

PS – A Deeper Look.

Better A Saber Than A Club?

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

There’s a glass-handled paper-knife on my desk, a reminder of a physics experiment gone very bad back in the day. “Y’know, Vinnie, this knife gives me an idea for another Star Trek weapons technology.”

“What’s that, Sy?”

“Some kinds of wave have another property in addition to frequency, amplitude and phase. What do you know about seismology?”

“Not a whole lot. Uhh … earthquakes … Richter scale … oh, and the Insight lander on Mars has seen a couple dozen marsquakes in the first six months it was looking for them.”

“Cool. Well, where I was going is that earthquakes have three kinds of waves. One’s like a sound wave — it’s called a P‑wave or pressure wave and it’s a push-pull motion along the direction the wave is traveling. The second is called an S‑wave or shear wave. It generates motion in some direction perpendicular to the wave’s path.”

“Not only up-and-down?”

“No, could be any perpendicular direction. Deep in the Earth, rock can slide any which-way. One big difference between the two kinds is that a P‑wave travels through both solid and molten rock, but an S‑wave can’t. Try to apply shearing stress to a fluid and you just stir it around your paddle. The side-to-side shaking isn’t transmitted any further along the wave’s original path. The geophysicists use that difference among other things to map out what’s deep below ground.”

“Parallel and perpendicular should cover all the possibilities. What’s the third kind?”

“It’s about what happens when either kind of deep wave hits the surface. A P‑wave will use up most of its energy bouncing things up and down. So will an S‑wave that’s mostly oriented up-and-down. However, an S‑wave that’s oriented more-or-less parallel to the surface will shake things side-to-side. That kind’s called a surface wave. It does the most damage and also spreads out more broadly than a P- or S‑wave that meets the surface with the same energy.”

“This is all very interesting but what does it have to do with Starfleet’s weapons technology? You can’t tell a Romulan captain what direction to come at you from.”

“Of course not, but you can control the polarization angle in your weapon beams.”

“Polarization angle?”

Plane-polarized electromagnetic wave
Electric (E) field is red
Magnetic (B) field is blue
(Image by Loo Kang Wee and
Fu-Kwun Hwang from Wikimedia Commons)

“Yeah. I guess we sort of slid past that point. Any given S‑wave vibrates in only one direction, but always perpendicular to the wave path. Does that sound familiar?”

“Huh! Yeah, it sounds like polarized light. You still got that light wave movie on Old Reliable?”

“Sure, right here. The red arrow represents the electric part of a light wave. Seismic waves don’t have a magnetic component so the blue arrow’s not a thing for them. The beam is traveling along the y‑axis, and the electric field tries to move electrons up and down in the yz plane. A physicist would say the light beam is plane‑polarized. S‑waves are polarized the same way. See the Enterprise connection?”

“Not yet.”

“Think about the Star Trek force-projection weapons — regular torpedoes, photon torpedoes, ship-mounted phasers, tractor beams, Romulan pulse cannons and the like. They all act like a P‑wave, delivering push-pull force along the line of fire. Even if Starfleet’s people develop a shield-shaker that varies a tractor beam’s phase, that’s still just a high-tech version of a club or cannon ball. Beamed S‑waves with polarization should be interesting to a Starfleet weapons designer.”

“You may have something. The Bridge crew talks about breaking through someone’s shield. Like you’re using a mace or bludgeon. A polarized wave would be more like an edged knife or saber. Why not rip the shield instead? Those shields are never perfect spheres around a ship. If your beam’s polarization angle happens to match a seam where two shield segments come together — BLOOEY!”

“That’s the idea. And you could jiggle that polarization angle like a jimmy — another way to confuse the opposition’s defense system.”

“I’m picturing a Klingon ship’s butt showing through a rip in its invisibility cloak. Haw!”

~~ Rich Olcott

How To Wave A Camel

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

“You’re sayin’, Sy, no matter what kind of wave we got, we can break it down by amplitude, frequency and phase?”

“Right, Vinnie. Your ears do that automatically. They grab your attention for the high-amplitude loud sounds and the high-frequency screechy ones. Goes back to when we had to worry about predators, I suppose.”

“I know about music instruments and that, but does it work for other kinds of waves?”

“It works for waves in general. You can match nearly any shape with the right combination of sine waves. There’s a few limitations. The shape has to be single-valued — no zig-zags — and it has to be continuous — no stopping over here and starting over there..”

“Ha! Challenge for you then. Use waves to draw a camel. Better yet– make it a two-humped camel.”

“A Bactrian camel, eh? OK, there’s pizza riding on this, you understand. <keys clicking> All right, image search for Bactrian camel … there’s a good one … scan for its upper profile … got that … tack on some zeroes fore and aft … dump that into my Fourier analysis engine … pull the coefficients … plot out the transform — wait, just for grins, plot it out in stages on top of the original … here you are, Vinnie, you owe me pizza.”

“OK, what is it?”

“Your Bactrian camel.”

“Yeah, I can see that, but what’s with the red line and the numbers?”

“OK, the red line is the sum of a certain number of sine waves with different frequencies but they all start and end at the same places. The number says how many waves were used in the sum. See how the ‘1‘ line is just a single peak, ‘3‘ is more complicated and so on? But I can’t just add sine waves together — that’d give the same curve no matter what data I use. Like in a church choir. The director doesn’t want everyone to sing at top volume all the time. Some passages he wants to bring out the alto voices so he hushes the men and sopranos, darker passages he may want the bases and baritones to dominate. Each section has to come in with its own amplitude.”

“So you give each sine wave an amplitude before you add ’em together. Makes sense, but how do you know what amplitudes to give out?”

“That gets into equations, which I know you don’t like. In practice these days you get all the amplitudes in one run of the Fast Fourier Transform algorithm, but it’s easier to think of it as the stepwise process that they used before the late 1960s. You start with the lowest-frequency sine wave that fits between the start- and end-points of your data.”

“Longest wavelength to match the data length, gotcha.”

“Mm-hm. So you put in that wave with an amplitude near the average value of your data in the middle art of the range. That’s picture number 1.”

“Step 2 is to throw in the next shorter wavelength that fits, right? Half the wavelength, with an amplitude to match the differences between your data and wave 1. And then you keep going.”

“You got the idea. Early physicists and their grad students used up an awful lot of pencils, paper and calculator time following exactly that strategy. Painful. The FFT programs freed them up to do real thinking.”

“So you get a better and better approximation from adding more and more waves. What stopped you from getting it perfect?”

“Two things — first, you can’t use more waves than about half the number of data points. Second, you see the funny business at his nose? Those come from edges and sudden sharp changes, which Fourier doesn’t handle well. That’s why edges look flakey in JPEG images that were saved in high-compression mode.”

“Wait, what does JPEG have to do with this?”

“JPEG and most other kinds of compressed digital image, you can bet that Fourier-type transforms were in play. Transforms are crucial in spectroscopy, astronomy, weather prediction, MP3 music recordings –“

Suddenly Vinnie’s wearing a big grin. “I got a great idea! While that Klingon ship’s clamped in our tractor beam, we can add frequencies that’d make them vibrate to Brahms’ Lullaby.”

“Bad idea. They’d send back Klingon Opera.”

~~ Rich Olcott