Tag: Electromagnetism

It’s All About The Coupling

On By rolcottIn UncategorizedLeave a comment

The game‘s over but there’s still pizza on the table so Eddie picks up the conversation. “So if gadolinoleum has even more unpaired electrons than iron, how come it’s not ferromagnetic like iron is?”

Vinnie’s tidying up the chips he just won. “I bet I know part of it, Eddie. Sy and me, we talked about magnetic domains some years ago. If I remember right, each iron atom in a chunk is a tiny little magnet, which I guess is the fault of its five unpaired electrons, but usually the atom magnets are pointing in all different directions so they all average out and the whole chunk doesn’t have a field. If you stroke the chunk with a magnet, that collects the little magnets into domains and the whole thing gets magnetic. How come gadomonium” <winks at Eddie, Eddie winks back> “doesn’t play the domain game, Susan?”

“It’s gadolinium, boys, please. As to the why, part’s at the atom level and part’s higher up. My lab neighbor Tammy schooled me on rare earth magnetism just last week. She does high‑temperature solid state chemistry with lanthanide‑containing materials. Anyway, she says it’s all about coupling.”

“I hope she told you more than that.”

The angular portion of the lowest-energy spherical harmonic modes
Credit: Inigo.quilez, under CCA SA 3.0 license

“She did. Say you’ve got a single gadolinium atom floating in space. Its environment is spherically symmetrical, no special direction to organize the wave‑orbitals hosting unpaired charges. Now turn on a magnetic field to tell the atom which way is up, call that the z‑axis. The atom’s wave‑orbital with zero angular momentum orients along z. Six more wave‑orbitals with non‑zero angular momentum spin one way or the other at various angles to the z‑axis. Those charges in motion build the atom’s personal magnetic field.”

“But we’re on Earth, not in space.”

“Bear with me. First, as a chemist I must say that most of the transition and lanthanide elements happily lose two electrons so in general we’re dealing with ions. Before you ask, Vinnie, that goes even for metals where the ions float in an electron sea. When Tammy said ‘coupling’ she was talking about how strongly one ion feels the neighboring fields. Iron and other ferromagnetic materials have a strong coupling, much stronger than the paramagnetics do.”

“Why’s the ferro- coupling so much stronger?”

“Two effects. You can read both of them right off the Periodic Table. Physical size, for one. Each row down in the table represents one electronic shell which takes up space. The atom or ion in any row is bigger than the ones above it. Yes, the heavy elements have more nuclear charge to pull electronic charge close, but shielding from their completed lower shells lets the outer charge cloud expand. Tammy told me that gadolinium’s ions are about 20% wider than iron’s.”

“Makes sense — you make the ions get further apart, they won’t connect so good. What’s the other effect?”

“It’s about how each orbital distributes its charge. There are tradeoffs between shell number, angular momentum and distance from the nucleus. Unpaired charge concentration in gadolinium’s high‑momentum 4f‑orbitals on the average stays inside of all its 3‑shell waves. The outermost charge shelters the unpaired waves inside it. That weakens magnetic coupling with unpaired charge in neighboring ions. Bottom line — gadolinium and its cousins are paramagnetic because they’re bigger and less sensitive than ferromagnetic iron is.”

“Then how come rare earth supermagnets the Chinese make are better than the cheapie ironic kinds we can make here?”

“The key is getting the right atoms into the right places in a crystalline solid. Neodymium magnets, for instance, have clusters of iron atoms around each lanthanide. The cluster arrangement aligns everyone’s z‑axes letting the unpaired charges gang up big‑time. You find materials like that mostly by luck and persistence. Tammy’s best samples are multi‑element oxides that arrange themselves in planar layers. Pick a component just 1% off the ideal size or cook your mixture with the wrong temperature sequence and the structure has completely different properties. Chinese scientists worked decades to perfect their recipes. USA chose to starve research in that area.”

~ Rich Olcott

Flipping An Edge Case

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

“Why’s the Ag box look weird in your chart, Susan?”

“That’s silver, Eddie. It’s an edge case. The pure metal’s diamagnetic. If you alloy silver with even a small amount of iron, the mixture is paramagnetic. How that works isn’t my field. Sy, it’s your turn to bet and explain.”

I match Eddie’s bet (the hand’s not over). “It’s magnetism and angular momentum and how atoms work, and there are parts I can’t explain. Even Feynman couldn’t explain some of it. Vinnie, what do you remember about electromagnetic waves?”

“Electric part pushes electrons up and down, magnetic part twists ’em sideways.”

“Good enough, but as Newton said, action begets reaction. Two centuries ago, Ørsted discovered that electrons moving along a wire create a magnetic field. Moving charges always do that. The effect doesn’t even depend on wires — auroras, fusion reactor and solar plasmas display all sorts of magnetic phenomena.”

“You said it’s about how atoms work.”

“Yes, I did. Atoms don’t follow Newton’s rules because electrons aren’t bouncing balls like those school‑book pictures show. An electron’s only a particle when it hits something and stops; otherwise it’s a wave. The moving wave carries charge so it generates a magnetic field proportional to the wave’s momentum. With me?”

“Keep going.”

“That picture’s fine for a wave traveling through space, but in an atom all the charge waves circle the nucleus. Linear momentum in open space becomes angular momentum around the core. If every wave in an atom went in the same direction it’d look like an electron donut generating a good strong dipolar magnetic field coming up through the hole.”

“You said ‘if’.”

“Yes, because they don’t do that. I’m way over‑simplifying here but you can think of the waves pairing up, two single‑electron waves going in opposite directions.”

“If they do that, the magnetism cancels.”

“Mm‑hm. Paired‑up configurations are almost always the energy‑preferred ones. An external magnetic field has trouble penetrating those structures. They push the field away so we classify them as diamagnetic. The gray elements in Susan’s chart are almost exclusively in paired‑up configurations, whether as pure elements or in compounds.”

“Okay, so what about all those paramagnetic elements?”

The angular portion of the lowest-energy spherical harmonic modes
Credit: Inigo.quilez, under CCA SA 3.0 license

“Here’s where we get into atom structure. An atom’s electron cloud is described by spherical harmonic modes we call orbitals, with different energy levels and different amounts of angular momentum — more complex shapes have more momentum. Any orbital hosting an unpaired charge has uncanceled angular momentum. Two kinds of angular momentum, actually — orbital momentum and spin momentum.”

“Wait, how can a wave spin?”

“Hard to visualize, right? Experiments show that an electron carries a dipolar magnetic field just like a spinning charge nubbin would. That’s the part that Feynman couldn’t explain without math. A charge wave with spin and orbital angular momentum is charge in motion; it generates a magnetic field just like current through a wire does. The math makes good predictions but it’s not something that everyday experience prepares us for. Anyway, the green and yellow‑orange‑ish elements feature unpaired electrons in high‑momentum orbitals buried deep in the atom’s charge cloud.”

“So what?”

“So when an external magnetic field comes along, the atom’s unpaired electrons join the party. They orient their fields parallel to the external field, in effect allowing it to penetrate. That qualifies the atom as paramagnetic. More unpaired electrons means stronger interaction, which is why iron goes beyond paramagnetic to ferromagnetic.”

“How does iron have so many?”

“Iron’s halfway across its row of ten transition metals—”

“I know where you’re going with this, Sy. It’ll help to say that these elements tend to lose their outer electrons. Scandium over on the left ionizes to Sc3+ and has zero d‑electrons. Then you add one electron in a d orbital for each move to the right.”

“Thanks, Susan. Count ’em off, Vinnie. Five steps over to iron, five added d‑electrons, all unpaired. Gadolinium, down in the lanthanides, beats that with seven half‑filled f‑orbitals. That’s where the strength in rare earth magnets arises.”

“So unpaired electrons from iron flip alloyed silver paramagnetic?”

“Vinnie wins this pot.”

~ Rich Olcott

Was Ramses Pharaoh-magnetic?

On By rolcottIn Chemistry, UncategorizedLeave a comment

Kareem puts in another couple of chips. “Hold your horses, Cal. The conversation‘s just getting interesting.”

Vinnie raises him a few chips. “Hey, Mr Geology. Just how rare are these lanthanide rare earths? And if they’re metals, how come they’re called earths?”

Source

“Not that rare.” <pulls up an image on his phone> “Here’s a quick abundance chart for the lanthanides and a few other elements averaged over all of Earth’s continental crust. Cerium’s more abundant than copper and 350 times more common than lead. Of course, that’s an average. Lanthanide concentrations in economically viable ores are much higher, just like with copper, lead, tin and other important non‑ferrous metals.”

“Funny zig-zag pattern there.”

“Good catch, Cal. Even‑number elements are generally more abundant than their odd‑numbered neighbors. That’s the Oddo-Harkins Rule in action—”

“ODDo-Harkins, haw!”

“You’re—” <Susan’s catches Vinnie’s frown and quickly drops few chips onto the pile> “Sorry, Vinnie. You’re not the first person to flag that pun. Two meteorite chemists named Giuseppe Oddo and William Harkins developed the rule a century ago. We’re pretty sure the pattern has to do with how stars fuse even‑numbered alpha particles to build up the elements heavier than hydrogen and helium. As to why the rare earths are called earths, back when Chemistry was just splitting away from alchemy, an ‘earth‘ was any crumbly mineral. Anybody heard of diatomaceous earth?”

Cal perks up. “Yeah, I got a bag of that dust in my garden shed to kill off slugs.”

“Mm‑hm. Powdery, mostly silica with some clay and iron oxide. The original ‘earth’ definition eventually morphed to denote minerals that dissolve in acid” <grin> “which diatomaceous earth doesn’t do. A few favorable Scandinavian mines gave the Swedish chemists lanthanide‑enriched ores to work on. Strictly speaking, in metallic form the lanthanides are rare earth metals, not rare earths, but people get sloppy.”

Eddie pitches in some chips. “So they’re <snort> chemical odd‑ities. Why would anyone but a chemist care about them?”

<sigh> “Magnetism.” <shows her laptop’s screen> “Here’s a chart that highlights the elements that are most magnetically active. The lanthanides are that colored strip below the main table. Chemically they’d all fit into that box with the red circle. They’re—”

“Wait, there’s more than one kind of magnetism?”

“Oh, yes. The distinction’s about how an element or material interacts with an external magnetic field. Most elements are at least weakly paramagnetic, which means they’re pulled into the field; diamagnets push away from it. Diamagnetic reaction is generally far weaker. Manganese is the strongest paramagnet, about 70 times stronger per atom than the strongest diamagnet, bismuth. Then there’s iron, cobalt and nickel — they do ferromagnetism, which means their atoms interact so strongly with the field that they get their neighbors to join in and make a permanent magnet.”

Schematic of a Gouy Balance

“How does anyone find out whether the field’s pulling or pushing?”

“Good question, Cal (you owe the pot, by the way). Basically, the idea is to somehow weigh a sample both with and without a surrounding field. Tammy’s lab down the hall from me has a nice Gouy Balance setup which is one way to make that measurement. The balance stands on a counter over a hole that leads down to a hollow glass tube that guards against air currents. There’s also a big powerful permanent magnet down there, mounted on a hinged arrangement. Your sample hangs on a piece of fishline hooked to the balance pan. Take a weight reading, swing the magnet into position just below the sample, read the weight again, do some arithmetic and you’re done. A higher weight reading when the field’s in place means your sample’s paramagnetic, less weight means it’s diamagnetic.”

“Why does that Ag box look weird in your table, sort of half‑brown and half‑gray?”

“That’s silver, Eddie. It’s an edge case. The pure metal’s diamagnetic but alloy a sample with even a small fraction of some ferromagnetic atoms and you’ve made it paramagnetic. Magnetism’s one test that people in the silver trade use to check if a coin or bar is pure. How that works isn’t my field. Sy, it’s your turn to bet and explain.”

~ Rich Olcott

That Lump in The Table

On By rolcottIn Astronomy: Planetary Science, Chemistry, UncategorizedLeave a comment

The Acme Building Science and Pizza Society is back in session. It’s Cal’s turn to deal the cards and the topic. “This TV guy was talking about rare earths that China’s got a lock on and it’s gonna mess up our economy, but he didn’t say what they are or why we should care about them. What’s goin’ on?”

Vinnie passes but Susan tosses a chip into the pot. “The rare earths are oxides of the lanthanide elements—”

“Wait, they’re from the planet that the Strange New Worlds engineering prof is from?”

“Put in a chip, Vinnie, you know the rules.” <He does.> “No, they have nothing to do with Pelia or her home planet. She’s a Lanthanite, these elements are lanthanides. Although these days we’re supposed to call them lanthanoids because ‑ides are ionic compounds like oxides.”

It’s not Kareem’s turn yet but he chuckles and flips in a chip. “Funny. The geology community settled on meteoroids as rocks floating in space, meteors when they flash through the sky, and meteorites when they hit the ground. I don’t think there’s such a thing as a meteoride. Sorry, Susan, go on.”

“As a matter of fact, Kareem, I once did a high‑rated downhill mountain bike path in Arizona called the Meteoride. Once. Didn’t wipe out but I admit I used my brakes a whole lot. Where was I? Oh, yes, the lanthanides. They’re a set of fourteen near‑identical twins, chemistry so similar that it took decades of heroic effort by 19th‑century Swedish chemists in the long, cold Swedish nights to separate and identify them.”

Benfey‘s “Periodic Snail” Image by DePiep under CC BY-SA 3.0

“Similar how?”

“They all act like aluminum.” <pulls laptop from her purse, points to two stickers on its lid> “You’ve all at least heard of the Periodic Table, right? Back in the mid-1800s, the chemists had isolated dozens of chemical elements, enough that they could start classifying them. They didn’t know what atoms were yet but they had developed ways to measure average atomic weights. Some theorists played with the idea of arranging elements with similar chemistries according to their atomic weights. Mendeleev did the best job, even predicting three elements to fill empty slots in his tabulation. These guys in the lime green row and the pale pink bulge were his biggest puzzlement.”

“Why’s that? They’re all spread out nice.”

“Because like I said, Vinnie, they all have pretty much the same chemistry. Aluminum’s a soft silvery metal, oxidizes readily to a 3+ ion and stays there. Same for almost all the lanthanides. Worse yet, all their atoms are nearly the same size, less than 8% difference from the largest to the smallest.”

“Why’s that make a difference?”

“Because they can all fit into the same crystalline structure. Nineteenth‑century chemistry’s primary technique for isolating a metallic element was to dissolve a likely‑looking ore, purify the solution, add an organic acid or something to make crystalline salts, burn away the organics, add more acid to dissolve the ash, purify the solution and re‑crystallize most it. Do that again and again until you have a provably pure product. All the lanthanide ions have the same charge and nearly the same size so the wrong ions could maliciously infiltrate your crystals. It took a lot of ingenious purification steps to isolate each element. There were many false claims.”

Kareem contributes another chip. “Mm‑hm, because geology doesn’t use chemically pure materials to create its ores. Four billion years ago when our planet was coated with molten magma, the asteroids striking Earth in the Late Heavy Bombardment brought megatons of stone‑making lithophile elements. The lanthanides are lithophiles so random mixtures of them tended to concentrate within lithic silicate and phosphate blobs that later cooled to form rocky ores. Industry‑scale operations can tease lanthanides out of ores but the processes use fierce chemicals and require close control of temperature and acidity. Tricky procedures that the Chinese spent billions and decades to get right. For the Chinese, those processes are precious national security assets.”

Cal’s getting impatient. “Hey, guys, are we playing cards or what?”

~ Rich Olcott

A No-Charge Transaction

On By rolcottIn Cosmology, Crazy Theories, Physics: Light and Relativity, UncategorizedLeave a comment

“I ain’t done yet, Sy. I got another reason for Dark Matter being made of faster‑then‑light tachyons.”

“I’m still listening, Vinnie.”

“Dark Matter gotta be electrically neutral, right, otherwise it’d do stuff with light and that doesn’t happen. I say tachyons gotta be neutral.”

“Why so?”

“Stands to reason. Suppose tachyons started off as charged particles. The electric force pushes and pulls on charges hugely stronger than gravity pulls—”

“1036 times stronger at any given distance.”

“Yeah, so right off the bat charged tachyons either pair up real quick or they fly away from the slower‑than‑light bradyon neighborhood leaving only neutral tachyons behind for us bradyon slowpokes to look at.”

“But we’ve got un‑neutral bradyon matter all around us — electrons trapped in Earth’s Van Allen Belt and Jupiter’s radiation belts, for example, and positive and negative plasma ions in the solar wind. Couldn’t your neutral tachyons get ionized?”

“Probably not much. Remember, tachyon particles whiz past each other too fast to collect into a star and do fusion stuff so there’s nobody to generate tachyonic super‑high‑energy radiation that makes tachyon ions. No ionized winds either. If a neutral tachyon collides with even a high-energy bradyon, the tachyon carries so much kinetic energy that the bradyon takes the damage rather than ionize the tachyon. Dark Matter and neutral tachyons both don’t do electromagnetic stuff so Dark Matter’s made of tachyons.”

“Ingenious, but you missed something way back in your initial assumptions.”

“Which assumption? Show me.”

“You assumed that tachyon mass works the same way that bradyon mass does. The math says it doesn’t.” <grabbing scratch paper for scribbling> “Whoa, don’t panic, just two simple equations. The first relates an object’s total energy E to its rest mass m and its momentum p and lightspeed c.”

E² = (mc²)² + (pc)²

“I recognize the mc² part, that’s from Einstein’s Equation, but what’s the second piece and why square everything again?”

“The keyword is rest mass.”

“Geez, it’s frames again?”

“Mm‑hm. The (mc²)² term is about mass‑energy strictly within the object’s own inertial frame where its momentum is zero. Einstein’s famous E=mc² covers that special case. The (pc)² term is about the object’s kinetic energy relative to some other‑frame observer with relative momentum p. When kinetic energy is comparable to rest‑mass energy you’re in relativity territory and can’t just add the two together. The sum‑of‑squares form makes the arithmetic work when two observers compare notes. Can I go on?”

“I’m still waitin’ to hear about tachyons.”

“Almost there. If we start with that equation, expand momentum as mass times velocity and re‑arrange a little, you get this formula

E = mc² / √(1 – v²/c²)

The numerator is rest‑mass energy. The v²/c² measures relative kinetic energy. The Lorentz factor down in the denominator accounts for that. See, when velocity is zero the factor is 1.0 and you’ve got Einstein’s special case.”

“Give me a minute. … Okay. But when the velocity gets up to lightspeed the E number gets weird.”

“Which is why c is the upper threshold for bradyons. As the velocity relative to an observer approaches c, the Lorentz factor approaches zero, the fraction goes to infinity and so does the object’s energy that the observer measures.”

“Okay, here’s where the tachyons come in ’cause their v is bigger than c. … Wait, now the equation’s got the square root of a negative number. You can’t do that! What does that even mean?”

“It’s legal, when you’re careful, but interpretation gets tricky. A tachyon’s Lorentz factor contains √(–1) which makes it an imaginary number. However, we know that the calculated energy has to be a real number. That can only be true if the tachyon’s mass is also an imaginary number, because i/i=1.”

“What makes imaginary energy worse than imaginary mass?”

“Because energy’s always conserved. Real energy stays that way. Imaginary mass makes no sense in Newton’s physics but in quantum theory imaginary mass is simply unstable like a pencil balanced on its point. The least little jiggle and the tachyon shatters into real particles with real kinetic energy to burn. Tachyons disintegrating may have powered the Universe’s cosmic inflation right after the Big Bang — but they’re all gone now.”

“Another lovely theory shot down.”

~ Rich Olcott

Got To Be Good-lookin’ ‘Cause He’s So Hard To See

On By rolcottIn Cosmology, Crazy Theories, UncategorizedLeave a comment

I’ll be sorry when Acme Building’s management swaps out our old‑style door locks for electronic ones. Vinnie has such fun lock‑picking his way past my office door in the morning. “Morning, Vinnie.”

“Morning, Sy. Hey, I got a new Crazy Theory for you. Nobody knows what Dark Matter is, right?”

“Right. All we know is that it has about five times as much mass as normal matter so it participates in gravitational interactions. Some of it seems to gather in spherical halos around galaxies and some of it seems to collect in spikes near their centers. Cosmologists are arguing about whether or not Dark Matter is particles, much less how they’d be quantized. And we call it Dark because it absolutely doesn’t care about electromagnetism.”

“That’s what I thought. I remember you said if Dark Matter did play with light waves at all it’d block our view of the CMB. So yeah, absolute. Good.”

“I gather your theory is about Dark Matter.”

“Mm-hm. I thought of a way that all that mass could be hiding in plain sight except we can’t see it.”

“Alright, I’m listening.”

“Tachyons.”

“Come again?”

“Tachyons — particles that fly around faster than light. I read an article about ’em. Some people say they can’t exist but hear me out, okay? The reason they’re not supposed to exist is ’cause it would take an infinite amount of energy to boost something up past lightspeed. I got that, but suppose they were born above lightspeed, back when the Big Bang singularity had energy packed so tight the Physics laws we know don’t apply. A lot of particles got flung out below lightspeed, but maybe even more got flung out above it.”

“What does this have to do with dark matter?”

“I’m gettin’ there. The thing with tachyons is, the article said it’d take infinite energy to slow one down to lightspeed. A tachyon rock hits a slow rock, it don’t stop ’cause the slow rock don’t have the juice for that. The collision may take a little energy from the tachyon rock but that just changes its trajectory.”

“Mmm, those tachyon rocks can’t be a thing. The — what can I call it? slow matter?”

“The article called ’em bradyons.”

“Thanks. We know that 92% of all … bradyonic atoms in the Universe are hydrogens. Rocks are made of silicon, oxygen and other atoms that are even heavier. Everything heavier than hydrogen and maybe some helium was created by nuclear reactions inside a star. Tachyonic atoms zooming beyond lightspeed couldn’t gather together to form a star or even join one. No significant tachyonic fusion, no tachyonic rocks.”

“Okay, they all stay tachy‑hydrogen, still not a problem. The point is, there could be a lot of them and they could add up to a lot of mass. So the next thing I asked is, where would tachyons hang out? Gotta be around galaxies, but being tachyons going super‑lightspeed they can’t just hang, they orbit around the centers. They’d spend the most time where they go slowest which is where they’re farthest away ’cause that’s how orbits work. But they’d be thickest close in ’cause of gravity but that’s where they go fastest.”

“Cute, so you’re predicting galaxies with halos of tachyons, plus spikes of them at each center. That just happens to be the dark matter distribution the astronomers find.”

“It gets better, Sy. I’m not so sure of this because math, but it feels right. I don’t think tachyons can do electromagnetism things.”

“Why not?”

“No blue glow — you know, that blue glow in nuclear reactors when electrons go through the cooling water faster than light?”

“Cherenkov radiation, happens when fast electrons polarize the water. The polarizing slows light in water relative to a vacuum.”

“Right, but tachyons in space travel through vacuum. They ought to polarize the vacuum like what fast electrons do to water. Electromagnetic tachyons orbiting galaxies ought to make a blue glow but there isn’t one, so tachyons don’t do electromagnetism things and that makes them Dark Matter.”

“You’re going to have to do better than that, Vinnie. Absence of evidence just might be evidence of absence. Maybe they’re not there to begin with.”

~ Rich Olcott

Properties of Space

On By rolcottIn Cosmology, Physics: Electromagnetism, Physics: Waves, UncategorizedLeave a comment

Vinnie gives me the side‑eye. “Wait, Sy. Back there you said Maxwell got the speed of light from the properties of space. What does any of that even mean?”

“Do you remember Newton’s equation for the force of gravity between two objects?”

“Of course not. Lessee… the force’d be bigger when either one gets bigger, and it’d get smaller when the distance between ’em gets bigger and there’s some constant number to make the units right, right?”

“Close enough, it’s the distance squared. The equation’s F=Gm1m2/r². The G is the constant you mentioned. It does more than turn mass‑units times mass‑units divided by length‑units‑squared into force‑units. It says how many force‑units. For one pair of objects at a certain distance, turn the G‑dial up and you get more force. Make sense?”

“Yeah, that looks right.”

“The value of G sets the force‑distance scale for how two objects attract each other everywhere in the Universe. That value is a property of space. So is the fact that the value is the same in all directions.”

“Huh! Never thought of it like a scale factor. Space has other properties like that?”

“Certainly. Coulomb’s Law for the electrostatic force between two charged objects has the same basic structure, FE=–(q1q2/r²)/CE. In any units you like you replace the q‘s with object charge amounts and r with the distance between them. For each set of change‑ and distance‑units there’s a well‑researched value of CE to convert your charge and distance numbers into force‑units. Under the covers, though, CE is a scale factor that controls the range of the electrostatic force. It’s the same everywhere in the Universe and it’s completely independent of Newton’s gravity scale factor.”

“Hey, what about ‘like charges repel, opposites attract’?”

“That’s what the minus sign’s in there for. If the q‘s have the same charge, the force is negative, that’s repulsion; opposite charges make for positive, attractive force.”

“If there’s a CE for electric there’s gotta be a CM for magnetic.”

“Sort of. The electrostatic force doesn’t care about direction. Magnetism does care so the equation’s more complicated. You’re right, though, there is a similar universal scale factor we might as well call CM.”

<chuckle> “Electric, magnetic, I don’t suppose we could mix those two somehow for an electromagnetic scale factor?”

<grin> “Did you read ahead in the book? Yes we can, and Maxwell’s equations showed us how. If you multiply the two C‘s together, you get one over the square of the speed of light. Re‑arranging a little, c=√(1/CECM), so c, the electromagnetic scale factor for velocity, is based on those space properties. Einstein showed that no material object can have a velocity greater than c.”

“I’ll take your word for the arithmetic, but how does that combination make for a speed limit?”

“There’s an easy answer you’re not going to like — it’s a speed because the units come out meters per second.”

“That’s a cheat. I don’t like it at all and it doesn’t account for the limit part. Explain it with Physics, no fancy equations.”

“Tough assignment. Okay, typical waves have a displacement force, like wind or something pushing up on an ocean wave, that works against a restoring force, such as gravity pulling down. Electromagnetic waves are different. The electric component supplies the up force, but the magnetic component twists sideways instead of restoring down. The wave travels as a helix. The CE and CM properties determine how tightly it spirals through space. That’s lightspeed.”

“And the limit part?”

“Einstein maintained that anything that happens must follow the same rules for all observers no matter how each is moving. The only way that can be true is if space is subject to the Lorentz contraction √[1-(v/vmax)²] for some universal maximum speed vmax. Maxwell’s electromagnetism equations showed that vmax is c. Okay?”

“I suppose.”

~ Rich Olcott

  • * Vinnie hates equations even with regular letters, Greek letters make it worse. Hence my using CE and CM instead of the conventional ε0 and μ0 notation. Sue me.

The Time Is Out of Joint

On By rolcottIn Cosmology, Crazy Theories, UncategorizedLeave a comment

Vinnie galumphs over to our table. “Hi, guys. Hey, Sy, I just read your Confluence post. I thought that we gave up on things happening simultaneous because of Einstein and relativity but I guess that wasn’t the reason.”

“Oh, things do happen simultaneously, no‑one claims they don’t, it’s just that it’s impossible for two widely‑separated observers to have evidence that two widely‑separated events happened simultaneously. That’s a very different proposition.”

“Ah, that makes me feel better. The ‘nothing is simultaneous‘ idea was making me itchy ’cause I know for sure that a good juggler lets go with one hand just as they’re catching with the other. How’s Einstein involved then?”

“Lightspeed’s a known constant. Knowing distance and lightspeed lets you calculate between‑event time, right? The key to simultaneity was understanding why lightspeed is a constant. We’d known lightspeed wasn’t infinite within the Solar System since Rømer’s time, but people doubted his number applied everywhere. Maxwell’s theory of electromagnetism derived lightspeed from the properties of space itself so it’s universal. Only in Newton’s Universe was it possible for two distant observers to agree that two also‑distant events were simultaneous.”

“Why was Newton’s Universe special?

“Space held still and didn’t bend. Astronomers A and B had a stable baseline between them. After measuring the baseline with light they could measure the angles each observed between the events. Some trigonometry let them send each other congratulatory messages on seeing a simultaneous pair of incidents. After Einstein’s work, they knew better.”

“It’s frames again, ain’t it?”

“Of course, Vinnie. A‘s frame is almost certainly moving relative to B‘s frame. Motion puts the Lorentz relativity factor into the game, making each astronomer’s clock run faster than the other’s. Worse, each astronomer sees that the other’s yardsticks are too short.”

Jeremy gives me a confused look.

“Space compression goes along with time dilation, Jeremy. Professor Hanneken will explain it all when your class gets to that unit. Bottom line, things can happen simultaneously in Einstein’s Universe, but no‑one can agree on which things.”

“Wait, if every frame has its own time‑rate, how can two spaceships rendezvous for an operation?”

“Good question, Jeremy. Einstein had an answer but complications hide under the covers. He suggested that A start a timer when sending a light pulse to a mirror at B. A waits for the reflection. B starts a timer when they see A‘s pulse. A measures the pulse’s round‑trip time. Each creates a clock that advances one tick for half of the round-trip time. B sets their clock back by one tick. That done, they agree to meet some number of ticks later.”

“Hmm… That should work, but you said there are complications.”

“There are always complications. For instance, suppose B is slingshotting around a black hole so that pulse and reflection travel different pathlengths. Or suppose one frame is rotating edge‑on to the other. In practice the ships would re‑sync repeatedly while approaching the rendezvous point.”

Vinnie erupts. “HAW! Successive approximation again!”

“Indeed. If we could extend the method to more than two participants we’d have a true Universal Coordinated Time.”

“Don’t we have that, Mr Moire? The Big Bang happened 14 billion years ago. Couldn’t we measure time from that?”

“Sort of. Last I looked the number was 13.787 plus‑or‑minus 20 million years. Too much slop for an instantaneous fleet‑level rendezvous like the final battle scene in StarTrek:Picard. But you’ve brought up an interesting question for a Crazy Theories seminar. One of Cosmology’s deepest unsolved questions is, ‘How does inertia work?’ Do you remember Newton’s First Law?”

<closes eyes> “In an inertial reference frame, an object either remains at rest or continues to move at a constant velocity, unless acted upon by a net force.“

“Right. In other words, every object resists change to its current steady motion along a geodesic. Why is that? There’s no coherent, well‑founded, well‑tested theory. Einstein liked Mach’s Principle, which says inertia exists because every object is attracted through space to all the mass in the Universe. Suppose there’s a Mach’s Principle for Time, saying that objects squirt up the Time axis because they’re repelled by all the mass in the Universe.”

Vinnie hoots, “Bo-o-o-ohh-GUS!”

~ Rich Olcott

A Carefully Plotted Tale

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

<chirp, chirp> “Moire here.”

“Hello, Mr Moire. Remember me?”

“Yes, I do, Walt. I hope your people were satisfied with what you brought them from our last meeting.”

“They were, which is why I’m calling. Buy you pizza at Eddie’s, fifteen minutes?”

“Make it twenty.”

We’re at the rear‑corner table, Walt facing both doors, naturally. “So, what’s the mysterious question this time?”

“Word on the street is that the CPT Law’s being violated. We want to know who’s involved, and what’s their connection with ChatGPT.”

Good thing I’ve just bit into my pizza so I can muffle my chuckle in my chewing. “What do you know about anti‑matter?”

“Inside‑out atoms — protons outside whizzing around electrons in the nucleus.”

“Common misconception. One proton has the mass of 1800 electrons. An atom built as you described would be unstable — the thing would fly apart. You’ve got anti‑matter’s charges arranged right but not the particles. Anti‑matter has negative anti‑protons in the nucleus and positrons, positive electrons, on the outside.”

<writing rapidly in his notebook> “You can do that? Just flip the sign on a particle?”

“No, positrons and such are respectable particles in their own right, distinct from their anti‑partners. Electric charge comes built into the identity. What’s important is, an anti‑atom behaves exactly like a normal atom does. Maxwell’s Equations and everything derived from them, including quantum mechanics, work equally well for either charge structure.”

“There’s a bit of Zen there — change but no‑change.”

“Nice. Physicists call that sort of thing a symmetry. In this case it’s charge symmetry, often written as C.”

“The C in CPT?”

“Exactly.”

“What about the P and T?”

“When someone says something is symmetrical, what do you think of first?”

“Right side’s a reflection of left side. Symmetrical faces look better but they’re usually less memorable.”

“Interesting choice of example. Anyway, reflection symmetry is important in common physical systems.”

“Classical Greek and Cambodian architecture; the Baroque aesthetic without the decorative frills.”

“I suppose so. Anyway, we call reflection symmetry Parity, or P for short.”

“And T?”

“Time.”

“Time’s not symmetrical. It’s always past‑to‑future.”

“Maybe, maybe not. In all our physical laws that deal with a small number of particles, you can replace t for time with –t and get the same results except for maybe a flipped sign. Newton’s Laws would run the Solar System in reverse just as well as they do forward.”

“But … Ah, ‘small number of particles,’ that’s your out. If your system has a large number of particles, you’re in chaos territory where randomness and entropy have to increase. Entropy increase is the arrow for one‑way time.”

“Good quote.”

“I’ve been in some interesting conversations. You’re not my only Physics source. So CPT is about Charge AND Parity AND Time symmetries. But you can’t simply add them together.”

“You multiply them. Technically, each of them is represented by a mathematical operator—”

“Step away from the technically.”

“Understood. This’ll be simpler. If a system’s atoms have positive nuclei, set C=1, otherwise set C=–1. If the system’s naturally‑driven motion is counterclockwise set P=1, otherwise P=–1. If time is increasing, set T=1, otherwise set T=–1. Okay?”

“Go on.”

“You can summarize any system’s CPT state by multiplying the prevailing symmetry values. The product will be either +1 or –1. The CPT Law says that in any universe where quantum mechanics and relativity work, one CPT state must hold universe‑wide.”

“Make it real for me.”

“You know the Right-hand Rule for electromagnetism?”

“Grab the wire with your right hand, thumb pointing along the current. Your fingers wrap in the direction of the spiraling magnetic field.”

“Perfect. Suppose C*P*T=+1 for this case. Now reverse the charge, making C=–1. What happens?”

“Ssss… The magnetic spin flips orientation. That’s a reflection operation so P=–1. The C*P*T calculation is (+1)*(–1)*(–1)=+1, no change.”

“The CPT Law in action. The CPT violation you’ve heard about is only observed in rare weak‑force‑mediated radioactive decays of a carefully prepared nucleus. That was a 1956 Nobel‑winning discovery, though the right person didn’t win it.”

“1956. Decades before A.I.”

“Yup, ChatGPT is off the hook. For that.”

“Bye.”

“Don’t mention it.”

~ Rich Olcott

  • Thanks to Caitlin, the hand model.

Why Those Curtains Ripple

On By rolcottIn Astronomy: Planetary Science, Physics: Electromagnetism, UncategorizedLeave a comment

I’m in the scone line at Cal’s Coffee when suddenly there’s a too‑familiar poke at my back, a bit right of the spine and just below the shoulder blade. I don’t look around. “Morning, Cathleen.”

“Morning, Sy. Your niece Teena certainly likes auroras, doesn’t she?”

“She likes everything. She’s the embodiment of ‘unquenchable enthusiasm.’ At that age she’s allowed.”

“It’s a gift at any age. Some of the kids in my classes, they just can’t see the wonders no matter how I try. I show them aurora photos and they say, ‘Oh yes, red and green in the sky‘ and go back to their phone screens. Of course there’s no way to get them outside late at night at a location with minimal light pollution.”

“I feel your pain.”

“Thanks. By the way, your aurora write-ups have been all about Earth’s end of the magnetic show. When you you going to do the rest of the story?”

“How do you mean?”

“Magnetism on the Sun, how a CME works, that sort of thing.”

“As a physicist I know a lot about magnetism, but you’re going to have to educate me on the astronomy.”

Plane‑polarized Lorentz (electromagnetic) wave
 Electric (E) component is red
 Magnetic (B) component is blue
(Image by Loo Kang Wee and Fu-Kwun Hwang from Wikimedia Commons)
Licensed under CC ASA3.0 Unported

“Deal. You go first.”

<displaying an animation on Old Reliable> “We’ll have to flip between microscopic and macroscopic a couple times. Here’s the ultimate micro — a single charged particle bouncing up and down somewhere far away has generated this Lorentz‑force wave traveling all alone in the Universe. The force has two components, electric and magnetic, that travel together. Neither component does a thing until the wave encounters another charged particle.”

“An electron, right?”

“Could be but doesn’t have to be. All the electric component cares about is how much charge the particle’s carrying. The magnetic component cares about that and also about its speed and direction. Say the Lorentz wave is traveling east. The magnetic component reaches out perpendicular, to the north and south. If the particle’s headed in exactly the same direction, there’s no interaction. Any other direction, though, the particle’s forced to swerve perpendicular to both the field and the original travel. Its path twists up- or downward.”

A charged particle traversing a Lorentz wave

“But if the particle swerves, won’t it keep swerving?”

“Absolutely. The particle follows a helical path until the wave gives out or a stronger field comes along.”

“Wait. If a Lorentz wave redirects charge motion and moving charges generate Lorentz waves, then a swerved particle ought to mess up the original wave.”

“True. It’s complicated. You can simplify the problem by stepping back far enough that you don’t see individual particles any more and the whole assembly looks like a simple fluid. We’ve known for centuries how to do Physics with water and such. Newton invented hydrodynamics while battling the ghost of Descartes to prove that the Solar System’s motion was governed by gravity, not vortices in an interplanetary fluid. People had tried using Newton‑style hydrodynamics math to understand plasma phenomena but it didn’t work.”

<grinning> “I don’t imagine it would — all that twistiness would have thrown things for a loop.”

“Haha. Well, in the early 1940s Swedish physicist Hannes Alfven started developing ideas and techniques, extending hydrodynamics to cover systems containing charged particles. Their micro‑level electromagnetic interactions have macro‑level effects.”

“Like what?”

“Those aurora curtains up there. Alfven showed that in a magnetic field plasmas can self‑organize into what he called ‘double layers’, pairs of wide, thin sheets with positive particles on one side against negative particles in the other. Neither sheet is stable on its own but the paired‑up structure can persist. Better yet, plasma magnetic fields can support coherent waves like the ones making that curtain ripple.”

“Any plasma?”

“Sure.”

“Most of the astronomical objects I show my students are associated with plasmas — the stars themselves, of course, but also the planetary nebulae that survive nova explosions, the interstellar medium in galactic star‑forming regions, the Solar wind, CMEs…”

“Alfven said we can’t understand the Universe unless we understand magnetic fields and electric currents.”

~ Rich Olcott