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

They Went That-away. But Why?

“It’s worse than that, Vinnie.”  I pull out Old Reliable, my math-monster tablet.  “Let me scan in that three-electron drawing of yours.”3 electrons in B-field

“Good enough to keep a record of it?”

“Nope, I want to exercise a new OVR app I just bought.”

“You mean OCR.”

“Uh-uh, this is Original Vector Reconstruction, not Optical Character Recognition.    OCR lets you read a document into a word processor so you can modify it.  OVR does the same thing but with graphics.  Give me a sec … there.  OK, look at this.”3 electrons in B-field revisited

“Cool, you turned my drawing 180°, sort of.  Nice app.  Oh, and you moved the red electron’s path so it’s going opposite to the blue electron instead of parallel to the magnetic field.  Why’d you bother?”

“See the difference between blue and red?”

“Well, yeah, one’s going up, one’s going down.  That’s what I came to you about and you shot down my theory.  Those B-arrows in the magnetic field are going in completely the wrong direction to push things that way.”

“Well, actually, they’re going in exactly the right direction for that, because a magnetic field pushes along perpendiculars.  Ever hear of The Right Hand Rule?”

“You mean like ‘lefty-loosey, righty-tighty’?”

“That works, too, but it’s not the rule I’m talking about.  If you point your thumb in the direction an electron is moving, and your index finger in the direction of the magnetic field, your third finger points in the deflection direction.  Try it.”

“Hurts my wrist when I do it for the blue one, but yeah, the rule works for that.  It’s easier for the red one.  OK, you got this rule, fine, but why does it work?”

“Part of it goes back to the vector math you don’t want me to throw at you.  Let’s just say that there are versions of a Right Hand Rule all over physics.  Many of them are essentially definitions, in the same way that Newton’s Laws of Motion defined force and mass.  Suppose you’re studying the movements directed by some new kind of force.  Typically, you try to define some underlying field in such a way that you can write equations that predict the movement.  You haven’t changed Nature, you’ve just improved our view of how things fit together.”

“So you’re telling me that whoever made that drawing I copied drew the direction those B-arrows pointed just to fit the rule?”

“Almost.  The intensity of the field is whatever it is and the lines minus their pointy parts are wherever they are.  The only thing we can set a rule for is which end of the line gets the arrowhead.  Make sense?”Spiraling electron

“I suppose.  But now I got two questions instead of the one I come in here with.  I can see the deflection twisting that electron’s path into a spiral.  But I don’t see why it spirals upward instead of downward, and I still don’t see how the whole thing works in the first place.”

“I’m afraid you’ve stumbled into a rabbit hole  we don’t generally talk about.  When Newton gave us his Law of Gravity, he didn’t really explain gravity, he just told us how to calculate it.  It took Einstein and General Relativity to get a deeper explanation.  See that really thick book on my shelf over there?  It’s loaded with tables of thermodynamic numbers I can use to calculate chemical reactions, but we didn’t start to understand those numbers until quantum mechanics came along.  Maxwell’s equations let us calculate electricity, magnetism and their interaction — but they don’t tell us why they work.”

“I get the drift.  You’re gonna tell me it goes up because it goes up.”

“That’s pretty much the story.  Electrons are among the simplest particles we know of.  Maxwell and his equations gave us a good handle on how they behave, nothing on why we have a Right Hand Rule instead of a Left Hand Rule.  The parity just falls out of the math.  Left-right asymmetry seems to have something to do with the geometry of the Universe, but we really don’t know.”

“Will string theory help?”

“Physicists have spent 50 years grinding on that without a testable result.  I’m not holding my breath.”

~~ Rich Olcott

Would the CIA want a LIGO?

So I was telling a friend about the LIGO announcement, going on about how this new “device” will lead to a whole new kind of astronomy.  He suddenly got a far-away look in his eyes and said, “I wonder how many of these the CIA has.”

The CIA has a forest of antennas, but none of them can do what LIGO does.  That’s because of the physics of how it works, and what it can and cannot detect.  (If you’re new to this topic, please read last week’s post so you’ll be up to speed on what follows.  Oh, and then come back here.)

There are remarkable parallels between electromagnetism and gravity.  The ancients knew about electrostatics — amber rubbed by a piece of cat fur will attract shreds of dry grass.  They certainly knew about gravity, too.  But it wasn’t until 100 years after Newton wrote his Principia that Priestly and then Coulomb found that the electrostatic force law, F = ke·q1·q2 / r2, has the same form as Newton’s Law of Gravity, F = G·m1·m2 / r2. (F is the force between two bodies whose centers are distance r apart, the q‘s are their charges and the m‘s are their masses.)

Jim and AlAlmost a century later, James Clerk Maxwell (the bearded fellow at left) wrote down his electromagnetism equations that explain how light works.  Half a century later, Einstein did the same for gravity.

But interesting as the parallels may be, there are some fundamental differences between the two forces — fundamental enough that not even Einstein was able to tie the two together.

One difference is in their magnitudes.  Consider, for instance, two protons.  Running the numbers, I found that the gravitational force pulling them together is a factor of 1036 smaller than the electrostatic force pushing them apart.  If a physicist wanted to add up all the forces affecting a particular proton, he’d have to get everything else (nuclear strong force, nuclear weak force, electromagnetic, etc.) nailed down to better than one part in 1036 before he could even detect gravity.

But it’s worse — electromagnetism and gravity don’t even have the same shape.

Electromagneticwave3D
Electric (red) and magnetic (blue) fields in a linearly polarized light wave
(graphic from WikiMedia Commons, posted by Lookang and Fu-Kwun Hwang)

A word first about words.  Electrostatics is about pure straight-line-between-centers (longitudinal) attraction and repulsion — that’s Coulomb’s Law.  Electrodynamics is about the cross-wise (transverse) forces exerted by one moving charged particle on the motion of another one.  Those forces are summarized by combining Maxwell’s Equations with the Lorenz Force Law.  A moving charge gives rise to two distinct forces, electric and magnetic, that operate at right angles to each other.  The combined effect is called electromagnetism.

The effect of the electric force is to vibrate a charge along one direction transverse to the wave.  The magnetic force only affects moving charges; it acts to twist their transverse motion to be perpendicular to the wave.  An EM antenna system works by sensing charge flow as electrons move back and forth under the influence of the electric field.

Gravitostatics uses Newton’s Law to calculate longitudinal gravitational interaction between masses.  That works despite gravity’s relative weakness because all the astronomical bodies we know of appear to be electrically neutral — no electrostatic forces get in the way.  A gravimeter senses the strength of the local gravitostatic field.

Maxwell and EinsteinGravitodynamics is completely unlike electrodynamics.  Gravity’s transverse “force” doesn’t act to move a whole mass up and down like Maxwell’s picture at left.  Instead, as shown by Einstein’s picture, gravitational waves stretch and compress while leaving the center of mass in place. I put “force” in quotes because what’s being stretched and compressed is space itself.  See this video for a helpful visualization of a gravitational wave.

LIGO is neither a telescope nor an electromagnetic antenna.  It operates by detecting sudden drastic changes in the disposition of matter within a “small” region.  In LIGO’s Sept 14 observation, 1031 kilograms of black hole suddenly ceased to exist, converted to gravitational waves that spread throughout the Universe.  By comparison, the Hiroshima explosion released the energy of 10-6 kilograms.

Seismometers do a fine job of detecting nuclear explosions.  Hey, CIA, they’re a lot cheaper than LIGO.

~~ Rich Olcott