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

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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