Moby Divergence

Stepping into Pizza Eddie’s I see Jeremy at his post behind the gelato stand, an impressively thick book in front of him.  “Hi, Jeremy, one chocolate-hazelnut combo, please.  What’re you reading there?”

“Hi, Mr Moire.  It’s Moby Dick, for English class.”

“Ah, one of my favorites.  Melville was a 19th-century techie, did for whaling what Tom Clancy did for submarines.”

“You’re here at just the right time, Mr Moire.  I’m reading the part where something called ‘the corpusants’ are making lights glow around the Pequod.  Sometimes he calls them lightning, but they don’t seem to come down from the sky like real lightning.  Umm, here it is, he says. ‘All the yard-arms were tipped with pallid fire, and touched at each tri-pointed lightning-rod-end with three tapering white flames, each of the three tall masts was silently burning in that sulphurous air, like three gigantic wax tapers before an altar.’  What’s that about?”St Elmos fire

“That glow is also called ‘St Elmo’s Fire‘ among other things.  It’s often associated with a lightning storm but it’s a completely different phenomenon.  Strictly speaking it’s a concentrated coronal discharge.”

“That doesn’t explain much, sir.”

“Take it one word at a time.  If you pump a lot of electrons into a confined space, they repel each other and sooner or later they’ll find ways to leak away.  That’s literally dis-charging.”

“How do you ‘pump electrons’?”

“Oh, lots of ways.  The ancient Greeks did it by rubbing amber with fur, Volta did it chemically with metals and acid,  Van de Graaff did it with a conveyor belt, Earth does it with winds that transport air between atmospheric layers.  You do it every time you shuffle across a carpet and get shocked when you put your finger near a water pipe or a light switch.”

“That only happens in the wintertime.”

“Actually, carpet-shuffle electron-pumping happens all the time.  In the summer you discharge as quickly as you gain charge because the air’s humidity gives the electrons an easy pathway away from you.  In the winter you’re better insulated and retain the charge until it’s too late.”

“Hm.  Next word.”

Corona, like ‘halo.’  A coronal discharge is the glow you see around an object that gets charged-up past a certain threshold.  In air the glow can be blue or purple, but you can get different colors from other gases.  Basically, the electric field is so intense that it overwhelms the electronic structure of the surrounding atoms and molecules.  The glow is electrons radiating as they return to their normal confined chaos after having been pulled into some stretched-out configuration.”

“But this picture of the corpusants has them just at the mast-heads and yard-arms, not all over the boat.”

“That’s where the ‘concentrated’ word come in.  I puzzled over that, too, when I first looked into the phenomenon.  Made no sense.”

“Yeah.  If the electrons are repelling each other they ought to spread out as much as possible.  So why do they seem pour out of the pointy parts?”

“That was a mystery until the 1880s when Heaviside cleaned up Maxwell’s original set of equations.  The clarified math showed that the key is the electric field’s spread-out-ness, technically known as divergence.”

DivergenceWith my finger I draw in the frost on his gelato cabinet.  “Imagine this is a brass ball, except I’ve pulled one side of it out to a cone.  Someone’s loaded it up with extra electrons so it’s carrying a high negative charge.”

“The electrons have spread themselves evenly over the metal surface, right, including at the pointy part?”

“Yup, that’s why I’m doing my best to make all these electric field arrows the same distance apart at their base.  They’re also supposed to be perpendicular to the surface.  What part of that field will put the most rip-apart stress on the local air molecules?”

“Oh, at the tip, where the field spreads out most abruptly.”

“Bingo.  What makes the glow isn’t the average field strength, it’s how drastically the field varies from one side of a molecule to the other.  That’s what rips them apart.  And you get the greatest divergence at the pointy parts like at the Pequod’s mast-head.”

“And Ahab’s harpoon.”

~~ Rich Olcott

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The Speeds of Light

“I don’t give up easy, Sy.”

“I know that, Vinnie.  Still musing about lightwaves and how they’re all an electron’s fault?”

“Yeah.  Hey, can your OVR app on Old Reliable grab a shot from this movie running on my smartphone?”

“We can try … got it.  Now what?”

“I wanna try mixing that with your magnetic field picture.”

“I’ll bring that up … Here, have at it.”

“Umm … Nice app, works very intuitive-like …  OK, see this?”Electrons and lightwave

“Ah.  It’s a bit busy, walk me through what’s in there.”

“OK. First we got the movie’s lightwave.  The ray’s running along that black arrow, see?  Some electron back behind the picture is going up and down to energize the ray and that makes the electric field that’s in red that makes other electrons go up and down, right?”

“That’s the red arrow, hmm?”

“Yeah, that electron got goosed ’cause it was standing in the way.  It follows the electric field’s direction.  Now help me out with the magnetic stuff.”

“Alright.  The blue lines represent the lightwave’s magnetic component.  A lightwave’s magnetic field lines are always perpendicular to its electric field.  Magnetism has no effect on uncharged particles or motionless charged particles.  If you’re a moving charged particle, say an electron, then the field deflects your trajectory.”

“This is what I’m still trying to wrap my head around.  You say that the field’s gonna push the particle perpendicular to the field and to the particle’s own vector.”

“That’s exactly what happens.  The green line, for instance, could represent an electron that crossed the magnetic field.  The field deflected the electron’s path upwards, crossways to the field and the electron’s path.  Then I suppose the electron encountered the reversed field from the lightwave’s following cycle and corrected course again.”

“And the grey line?”

“That’d be an electron crossing more-or-less along the field.  According to the Right Hand Rule it was deflected downward.”

“Wait.  We’ve got two electrons on the same side of the field and they’re deflected in opposite directions then correct back.  Doesn’t that average out to no change?”

“Not quite.  The key word is mostly.  Like gravity fields, electromagnetic fields get weaker with distance.  Each up or down deflection to an electron on an outbound path will be smaller than the previous one so the ‘course corrections’ get less correct.  Inbound electrons get deflected ever more strongly on the way in, of course, but eventually they become outbound electrons and get messed up even more.  All those deflections produce an expanding cone of disturbed electrons along the path of the ray.”

“Hey, but when any electron moves that changes the fields, right?  Wouldn’t there be a cone of disturbed field, too?”

“Absolutely.  The whole process leads to several kinds of dispersion.”

“Like what?”

“The obvious one is simple geometry.  What had been a simple straight-line ray is now an expanding cone of secondary emission.  Suppose you’re an astronomer looking at a planet that’s along that ray, for instance.  Light’s getting to you from throughout the cone, not just from the straight line.  You’re going to get a blurred picture.”

“What’s another kind?”

“Moving those electrons around extracts energy from the wave.  Some fraction of the ray’s original photons get converted to lower-energy ones with lower frequencies.  The net result is that the ray’s spectrum is spread and dispersed towards the red.”

“You said several kinds.”

“The last one’s a doozy — it affects the speeds of light.”

“‘Speeds,’ plural?”ripples in a wave

“There’s the speed of field’s ripples, and there’s the speed of the whole signal, say when a star goes nova.  Here’s a picture I built on Old Reliable.  The gold line is the electric field — see how the ripples make the red electron wobble?  The green dots on the axis give you comparison points that don’t move.  Watch how the ripples move left to right just like the signal does, but at their own speed.”

“Which one’s Einstein’s?”

“The signal.  Its speed is called the group velocity and in space always runs 186,000 mph.  The ripple speed, technically it’s the phase velocity, is slower because of that extracted-and-redistributed-energy process.  Different frequencies get different slowdowns, which gives astronomers clues about the interstellar medium.”

“Clues are good.”

~~ Rich Olcott

Three off The Plane

Rumpus in the hallway.  Vinnie dashes into my office, tablet in hand and trailing paper napkins.  “Sy! Sy! I figured it out!”

“Great!  What did you figure out?”

“You know they talk about light and radio being electromagnetic waves, but I got to wondering.  Radio antennas don’t got magnets so where does the magnetic part come in?”

“19th-Century physicists struggled with that question until Maxwell published his famous equations.  What’s your answer?”

“Well, you know me — I don’t do equations, I do pictures.  I saw a TV program about electricity.  Some Danish scientist named Hans Christian Anderson—”

“Ørsted.”

“Whoever.  Anyway, he found that magnetism happens when an electric current starts or stops.  That’s what gave me my idea.  We got electrons, right, but no magnetrons, right?”

“Mmm, your microwave oven has a vacuum tube called a magnetron in it.”

“C’mon, Sy, you know what I mean.  We got no whatchacallit, ‘fundamental particle’ of magnetism like we got with electrons and electricity.”

“I’ll give you that.  Physicists have searched hard for evidence of magnetic monopoles — no successes so far.  So why’s that important to you?”

3 electrons moving north“It told me that the magnetism stuff has to come from what electrons do.  And that’s when I came up with this drawing.”  <He shoves a paper napkin at me.>  “See, the three balls are electrons and they’re all negative-negative pushing against each other only I’m just paying attention to what the red one’s doing to the other two.  Got that?”

“Sure.  The arrow means the red electron is traveling upward?”

“Yeah.  Now what’s that moving gonna do to the other two?”

“Well, the red’s getting closer to the yellow.  That increases the repulsive force yellow feels so it’ll move upward to stay away.”

“Uh-huh.  And the force on blue gets less so that one’s free to move upward, too.  Now pretend that the red one starts moving downward.”

“Everything goes the other way, of course.  Where does the magnetism come in?”

3 electrons in B-field“Well, that was the puzzle.  Here’s a drawing I copied from some book.  The magnetic field is those B arrows and there’s three electrons moving  in the same flat space in different directions.  The red one’s moving along the field and stays that way.  The blue one’s moving slanty across the field and gets pushed upwards.  The green one’s going at right angles to B and gets bent way up.  I’m looking and looking — how come the field forces them to move up?”

“Good question.  To answer it those 19th Century physicists developed vector analysis—”

Electromagneticwave3D

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)

“Don’t give me equations, Sy, I do pictures.  Anyway, I figured it out, and I did it from a movie I got on my tablet here.  It’s a light wave, see, so it’s got both an electric field and a magnetic field and they’re all sync’ed up together.”

“I see that.”

“What the book’s picture skipped was, where does the B-field come from?  That’s what I figured out.  Actually, I started with where the the light wave came from.”

“Which is…?”

“Way back there into the page, some electron is going up and down, and that creates the electric field whose job is to make other electrons go up and down like in my first picture, right?”

“OK, and …?”

“Then I thought about some other electron coming in to meet the wave.  If it comes in crosswise, its path is gonna get bent upward by the E-field.  That’s what the blue and green electrons did.  So what I think is, the magnetic effect is really from the E-field acting on moving electrons.”

“Nice try, but it doesn’t explain a couple of things.  For instance, there’s the difference between the green and blue paths.  Why does the amount of deflection depend on the angle between the B direction and the incoming path?”

“Dunno.  What’s the other thing?”

“Experiment shows that the faster the electron moves, the greater the magnetic deflection.  Does your theory account for that?”

“Uhh … my idea says less deflection.”

“Sorry, another beautiful theory stumbles on ugly facts.”

~~ Rich Olcott