Category: Physics

Trio for Rubber Ruler

On By rolcottIn Astronomy: Stellar Science, Astronomy: Techniques, Cosmology, Physics: Fundamentals, Physics: Quantum Mechanics, UncategorizedLeave a comment

“It’s all about how lightwaves get generated and then what happens.”

“Sy and me talked about that, Cathleen.  Lightwaves come from jiggling electrons, right?”

“Any kind of charged particles, Vinnie, but there’s different ways that can happen.  Each leads to its own kind of spectrum.”

“Different kinds of spectrum?  Do you mean like visible versus infrared and ultraviolet, Cathleen?”

“No, I don’t, Sy.  I’m referring to the thing’s overall appearance in every band.  A hundred and fifty years ago Kirchoff pointed out that light from a source can have lines of color, lines without color, or a smooth display without lines.”

“Like that poster that Al put up between the physicist and astronomer corners?”  (We’re still chatting at a table in Al’s coffee shop.  I’m on my fourth scone.)

Astroruler with solar spectrum
Based on N.A.Sharp, NOAO/NSO/Kitt Peak FTS/AURA/NSF

“Kind of.  That’s based on a famous image created at Kitt Peak Observatory.  In the background there you see a representation of what Kirchoff called a continuous or black-body spectrum, where all the colors fade smoothly into each other in classic rainbow order.  You’re supposed to ignore the horizontal dark lines.”

“And the vertical lines?”

“They form what Kirchoff called an absorption spectrum.  Each dark vertical represents an isolated color that we don’t get from the Sun.”

“You’re saying we get all the other colors but them, right?”

“Exactly, Vinnie.  The Sun’s chromosphere layer filters those specific wavelengths before they get from the deeper photosphere out into space.”

“Complicated filter.”

“Of course.  The Sun contains most of the elements lighter than nickel.  Each kind of atom absorbs its own collection of frequencies.”

“Ah, that’s the quantum thing that Sy and me talked about, right, Sy?”

“Mm-hm.  We only did the hydrogen atom, but the same principles apply.  An electromagnetic wave tickles an atom.  If the wave delivers exactly the right amount of energy, the atom’s chaotic storm of electrons resonates with the energy and goes a different-shaped storm.  But each kind of atom has a limited set of shapes.  If the energy doesn’t match the energy difference between a pair of levels, there’s no absorption and the wave just passes by.”

“But I’ll bet the atom can’t hold that extra energy forever.”

“Good bet, Vinnie.  The flip side of absorption is emission.  I expect that Cathleen has an emission spectrum somewhere on her laptop there.”Emission spectrum“You’re right, Sy.  It’s not a particularly pretty picture, but it shows that nice strong sodium doublet in the yellow and the broad iron and hydrogen lines down in the green and blue.  I’ll admit it, Vinnie, this is a faked image I made to show my students what the solar atmosphere would look like if you could turn off the photosphere’s continuous blast of light.  The point is that the atoms emit exactly the same sets of colors that they absorb.”

“You do what you gotta do, Cathleen.  But tell me, if each kind of atom does only certain colors, where’s that continuous rainbow come from?  Why aren’t we only getting hydrogen colors?”

“Kirchoff didn’t have a clue on that, Vinnie.  It took 50 years and Einstein to solve it.  Not just where the light comes from but also its energy-wavelength profile.”

“So where does the light come from?”

“Pure heat.  You can get a continuous spectrum from a hot wire, molten lava, a hole through the wall of a hot oven, even the primordial chaos of the Big Bang.  It doesn’t matter what kind of matter you’re looking at, the profile just depends on the temperature.  You know that temperature measures the kinetic energy stored in particle random motion, Vinnie?”

“Well, I wouldn’t have put it that way, but yeah.”

“Well, think about the Sun, just a big ball of really hot atoms and electrons and nuclei, all bouncing off each other in frantic motion.  Every time one of those changes direction it affects the electromagnetic field, jiggles it as you say.  The result of all that jiggling is the continuous spectrum.  Absorption and emission lines come from electrons that are confined to an atom, but heat motion is unconfined.”

“How about hot metal?”

“The atoms are locked in their lattice, but heat jiggles the whole lattice.”

~~ Rich Olcott

Étude for A Rubber Ruler

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

“93% redder?  How do you figure that, Sy, and what’s it even mean?”

“Simple arithmetic, Vinnie.  Cathleen said that most-distant galaxy is 13 billion lightyears away.  I primed Old Reliable with Hubble’s Constant to turn that distance into expansion velocity and compare it with lightspeed.  Here’s what came up on its screen.”Old Reliable z calculation“Whoa, Sy.  Do you read the final chapter of a mystery story before you begin the book?”

“Of course not, Cathleen.  That way you don’t know the players and you miss what the clues mean.”

“Which is the second of Vinnie’s questions.  Let’s take it a step at a time.  I’m sure that’ll make Vinnie happier.”

“It sure will.  First step — what’s a parsec?”

“Just another distance unit, like a mile or kilometer but much bigger.  You know that a lightyear is the distance light travels in an Earth year, right?”

“Right, it’s some huge number of miles.”

“About six trillion miles, 9½ trillion kilometers.  Multiply the kilometers by 3.26 to get parsecs.  And no, I’m not going to explain the term, you can look it up.  Astronomers like the unit, other people put it in the historical-interest category with roods and firkins.”

“Is that weird ‘km/sec/Mparsec’ mix another historical thing?”

“Uh-huh.  That’s the way Hubble wrote it in 1929.  It makes more sense if you look at it piecewise.  It says for every million parsecs away from us, the outward speed of things in general increases by 70 kilometers per second.”

“That helps, but it mixes old and new units like saying miles per hour per kilometer.  Ugly.  It’d be prettier if you kept all one system, like (pokes at smartphone screen) … about 2.27 km/sec per 1018 kilometers or … about 8 miles an hour per quadrillion miles.  Which ain’t much now that I look at it.”

“Not much, except it adds up over astronomical distances.  The Andromeda galaxy, for instance, is 15×1018 miles away from us, so by your numbers it’d be moving away from us at 120,000 miles per hour.”

“Wait, Cathleen, I thought Andromeda is going to collide with the Milky Way four billion years from now.”

Opposing motion in a starfield“It is, Sy, and that’s one of the reasons why Hubble’s original number was so far off.  He only looked at about 50 close-by galaxies, some of which are moving toward us and some away.  You only get a view of the general movement when you look at large numbers of galaxies at long distances.  It’s like looking through a window at a snowfall.  If you concentrate on individual flakes you often see one flying upward, even though the fall as a whole is downward.  Andromeda’s 250,000 mph march towards us is against the general expansion.”

“Like if I’m flying a plane and the airspeed indicator says I’m doing 200 but my ground-speed is about 140 then I must be fighting a 60-knot headwind.”

“Exactly, Vinnie.  For Andromeda the ‘headwind’ is the Hubble Flow, that general outward trend.  If Sy’s calculation were valid, which it’s not, then that galaxy 13 billion lightyears from here would indeed be moving further away at  93% of lightspeed.  Someone living in that galaxy could shine a 520-nanometer green laser at us.  At this end we see the beam stretched by 193% to 1000nm.  That’s outside the visible range, well into the near-infrared.  All four visible lines in the hydrogen spectrum would be out there, too.”

“So that’s why ‘old hydrogens’ look different — if they’re far enough away in the Hubble Flow they’re flying away from us so fast all their colors get stretched by the red-shift.”

“Right, Vinnie.”

“Wait, Cathleen, what’s wrong with my calculation?”

“Two things, Sy.  Because the velocities are close to lightspeed, you need to apply a relativistic correction factor.  That velocity ratio Old Reliable reported — call it b.  The proper stretch factor is z=√ [(1+b)/(1–b)].  Relativity takes your 93% stretch down to (taps on laptop keyboard) … about 86%.  The bluest wavelength on hydrogen’s second-down series would be just barely visible in the red at 680nm.”

“What’s the other thing?”Ruler in perspective

“The Hubble Constant can’t be constant.  Suppose you run the movie backwards.  The Universe shrinks steadily at 70 km/sec/Mparsec.  You hit zero hundreds of millions of years before the Big Bang.”

“The expansion must have started slow and then accelerated.”

“Vaster and faster, eh?”

“Funny, Sy.”

~~ Rich Olcott

Toccata for A Rubber Ruler

On By rolcottIn Astronomy: Stellar Science, Astronomy: Techniques, Cosmology, Physics: Fundamentals, UncategorizedLeave a comment

“How the heck do they know that?”

“Know what, Vinnie?”

“That the galaxy they saw with that gravitational lens is 13 billion years old?  I mean, does it come with a birth certificate, Cathleen?”

“Mm, it does, sort of — hydrogen atoms.  Really old hydrogen atoms.”

“Waitaminit.  Hydrogen’s hydrogen — one proton, one electron per atom.  They’re all the same, right?  How do you know one’s older than another one?”

“Because they look different.”

“How could they look different when they’re all the same?”

“Let me guess, Cathleen.  These old hydrogens, are they far far away?”

“On the button, Sy.”

“What where they’re at got to do with it?”

“It’s all about spectroscopy and the Hubble constant, Vinnie.  What do you know about Edwin Hubble?”

“Like in Hubble Space Telescope?  Not much.”

“Those old atoms were Hubble’s second big discovery.”

“Your gonna start with the other one, right?”

“Sorry, classroom habit.  His first big discovery was that there’s more to the Universe than just the Milky Way Galaxy.  That directly contradicted Astronomy’s Big Names.  They all believed that the cloudy bits they saw in the sky were nebulae within our galaxy.  Hubble’s edge was that he had access to Wilson Observatory’s 100-inch telescope that dwarfed the smaller instruments that everyone else was using.  Bigger scope, more light-gathering power, better resolution.”

“Hubble won.”

“Yeah, but how he won was the key to his other big discovery.  The crucial question was, how far away are those ‘nebulae’?  He needed a link between distance and something he could measure directly.  Stellar brightness was the obvious choice.  Not the brightness we see on Earth but the brightness we’d see if we were some standard distance away from it.  Fortunately, a dozen years earlier Henrietta Swan Leavitt found that link.  Some stars periodically swing bright, then dim, then bright again.  She showed that for one subgroup of those stars, there’s a simple relationship between the star’s intrinsic brightness and its peak-to-peak time.”Astroruler

“So Hubble found stars like that in those nebulas or galaxies or whatever?”

“Exactly.  With his best-of-breed telescope he could pick out individual variable stars in close-by galaxies.  Their fluctuation gave him intrinsic brightness.  The brightness he measured from Earth was a lot less.  The brightness ratios gave him distances.  They were a lot bigger than everyone thought.”

“Ah, so now he’s got a handle on distance.  Scientists love to plot everything against everything, just to see, so I’ll bet he plotted something against distance and hit jackpot.”

“Well, he was a bit less random than that, Sy.  There were some theoretical reasons to think that the Universe might be expanding.  The question was, how fast?  For that he tapped another astronomer’s results.  Vesto Slipher at Lowell Observatory was looking at the colors of light emitted by different galaxies.  None had light exactly like our Milky Way’s.  A few were a bit bluer, but most were distinctly red-shifted.”

“Like the Doppler effect in radar?  Things coming toward you blue-shift the radar beam, things going away red-shift it?”

“Similar to that, Vinnie, but it’s emitted light, not a reflected beam. To a good approximation, though, you can say that the red shift is proportional to the emitting object’s speed towards or away from us.  Hubble plotted his distance number for each galaxy he’d worked on, against Slipher’s red-shift speed number for the same galaxy.  It wasn’t the prettiest graph you’ve ever seen, but there was a pretty good correlation.  Hubble drew the best straight line he could through the points.  What’s important is that the line sloped upward.”

“Lemme think … If everything just sits there, there’d be no red-shift and no graph, right?  If everything is moving away from us at a steady speed, then the line would be flat — zero slope.  But he saw an upward slope, so the farther something is the faster it’s going further from us?”

“Bravo, Vinnie.  That’s the expansion of the Universe you’ve heard about.  Locally there are a few things coming toward us — that’s those blue-shifted galaxies, for instance — but the general trend is away.”

“So that’s why you say those far-away hydrogens look different.  By the time we see their light it’s been red-shifted.”

“93% redder.”

~~ Rich Olcott

The Biggest Telescope in The Universe

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

Vinnie rocks back in his chair.  “These gravitational lenses, Cathleen.  How do you figure their apertures and f-numbers, space being infinite and all?”

She takes a breath to answer, but I cut in.  “Whoa, I never got past a snapshot camera.  How about you explain Vinnie’s question before you answer it?”Bird and lenses

“You’re right, Sy, most people these days just use their cellphone camera and have no clue about what it does inside.  Apertures and f-numbers are all just simple geometry.  Everything scales with the lens’ focal length.”

“That’s how far away something is that you’re taking a picture of?”

“No, it’s a characteristic of the lens itself.  It’s the distance between the midpoint of the lens and its focal plane, which is where you’d want to put the sensor chip or film in a camera.  The aperture is the diameter of the light beam entering the lens.  The optimal aperture, the image size, even the weight of the lens, all scale to the lens focal length.”

“I can see image size thing — the further back the focal plane, the bigger the image by the the time it gets there.  It’s like a lever.”

“Sort of, Vinnie, but you’ve got the idea.”

“The aperture scales to focal length?  I’d think you could make a lens with any diameter you like.”

“Sure you could, Sy, but remember you’d be using a recording medium of some sort and it’s got an optimum input level.  Too much light and you over-expose, too little and you under-expose.  To get the right amount of light when you take the shot the aperture has to be right compared to the focal length.”

“Hey, so that’s the reason for the old ‘Sunny 16‘ rule.  Didn’t matter if I had a 35mm Olympus or a big ol’ Rollei, if it was a sunny day I got good pictures with an f/16 aperture.  ‘Course I had to balance the exposure time with the film’s speed rating but that was easy.”

“Exactly, Vinnie.  If I remember right, the Rollei’s images were about triple the size of the little guy’s.  Tripled focal length meant tripled lens size.  You could use the same speed-rated film in both cameras and use the same range of f-stops.  The rule still works with digital cameras but you need to know your sensor’s ISO rating.”

“Ya got this, Sy?  Can we move on to Cathleen’s gravity lenses?”

“Sure, go ahead.”

“Well, they’re completely different from … I’ll call them classical lenses. That kind has a focal plane and a focal length and an aperture and only operates along one axis.  Gravitational lenses have none of that, but they have an infinite number of focal lines and rings.”

Gravitational lens and galaxy“Infinite?”

“At least in principle.  Any observation point in the Universe has a focal line running to a massive object’s center of gravity.  At any point along the line, you could look toward an object and potentially see all or part of a ring composed of light from some bright object behind it.  Einstein showed that a completed ring’s  visual angle depends on the deflector’s mass and the three distances between the observer, the deflector and the bright object.”

“The way you said that, there could be a bunch of rings.”

“Sure, one for each bright object shining onto the lens.  For that matter, the deflector itself could be complex — the gravity of a whole cluster of galaxies rather than the single black hole we’ve been assuming as an example.”

“That diagram reminds me of Galileo’s telescope, just a three-foot tube with an objective lens at the far end and an eyepiece lens to look through.  But it was enough to show him the rings of Saturn and the moons of Jupiter.”

“Right, Sy.  His objective lens was maybe a couple of inches across.  If its focal point was halfway down the tube, his scope’s light-gathering power would match an f/9 camera lens.  Gravitational lenses don’t have apertures so not an issue.”

“So here we are like Galileo, with a brand new kind of telescope.”

“Poetic, Vinnie, and so right.  It’s already shown us maybe the youngest galaxy, born 13 billion years ago.  We’re just getting started.”

~~ Rich Olcott

On Gravity, Charge And Geese

On By rolcottIn Astronomy: Planetary Science, Astronomy: Stellar Science, Physics: Electromagnetism, Physics: Newton and Gravity, UncategorizedLeave a comment

A beautiful April day, far too nice to be inside working.  I’m on a brisk walk toward the lake when I hear puffing behind me.  “Hey, Moire, I got questions!”

“Of course you do, Mr Feder.  Ask away while we hike over to watch the geese.”

“Sure, but slow down , will ya?  I been reading this guy’s blog and he says some things I wanna check on.”

I know better but I ask anyhow.  “Like what?”

“Like maybe the planets have different electrical charges  so if we sent an astronaut they’d get killed by a ginormous lightning flash.”

“That’s unlikely for so many reasons, Mr Feder.  First, it’d be almost impossible for the Solar System to get built that way.  Next, it couldn’t stay that way if it had been.  Third, we know it’s not that way now.”

“One at a time.”

“OK.  We’re pretty sure that the Solar System started as a kink in a whirling cloud of galactic dust.  Gravity spanning the kink pulled that cloud into a swirling disk, then the swirls condensed to form planets.  Suppose dust particles in one of those swirls, for whatever reason, all had the same unbalanced electrical charge.”

“Right, and they came together because of gravity like you say.”

I pull Old Reliable from its holster.  “Think about just two particles, attracted to each other by gravity but repelled by their static charge.  Let’s see which force would win.  Typical interstellar dust particles run about 100 nanometers across.  We’re thinking planets so our particles are silicate.  Old Reliable says they’d weigh about 2×10 –18 kg each, so the force of gravity pulling them together would be …  oh, wait, that’d depend on how far apart they are.  But so would the electrostatic force, so let’s keep going.  How much charge do you want to put on each particle?”

“The minimum, one electron’s worth.”

“Loading the dice for gravity, aren’t you?  Only one extra electron per, umm, 22 million silicon atoms.    OK, one electron it is …  Take a look at Old Reliable’s calculation.gravity vs electrostatic calculation Those two electrons push their dust grains apart almost a quintillion times more strongly than gravity pulls them together.  And the distance makes no difference — close together or far apart, push wins.  You can’t use gravity to build a planet from charged particles.”

“Wait, Moire, couldn’t something else push those guys together — magnetic fields, say, or a shock wave?”

“Sure, which is why I said almost impossible.  Now for the second reason the astronaut won’t get lightning-shocked — the solar wind.  It’s been with us since the Sun lit up and it’s loaded with both positive- and negative-charged particles.  Suppose Venus, for instance, had been dealt more than its share of electrons back in the day.  Its net-negative charge would attract the wind’s protons and alpha particles to neutralize the charge imbalance.  By the same physics, a net-positive planet would attract electrons.  After a billion years of that, no problem.”

“All right, what’s the third reason?”

“Simple.  We’ve already sent out orbiters to all the planets.  Descent vehicles have made physical contact with many of them.  No lightning flashes, no fried electronics.  Blows my mind that our Cassini mission to Saturn did seven years of science there after a six-year flight, and everything worked perfectly with no side-trips to the shop.  Our astronauts can skip worrying about high-voltage landings.”

“Hey, I just noticed something.  Those F formulas look the same.”  He picks up a stick and starts scribbling on the dirt in front of us.  “You could add them up like F=(Gm1m2+k0q1q2)/r2.  See how the two pieces can trade off if you take away some mass but add back some charge?  How do we know we’ve got the mass-mass pull right and not mixed in with some charge-charge push?”

Geese and ducks“Good question.  If protons were more positive than electrons, electrostatic repulsion would always be proportional to mass.  We couldn’t separate that force from gravity.  Physicists have separately measured electron and proton charge.  They’re equal (except for sign) to 10 decimal places.  Unfortunately, we’d need another 25 digits of accuracy before we could test your hypothesis.”

“Aw, look, the geese got babies.”

“The small ones are ducks, Mr Feder.”

~~ Rich Olcott

The Speeds of Light

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

“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

They Went That-away. But Why?

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

“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

Three off The Plane

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

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

RIP, Dr Hawking

On By rolcottIn General: Serious Stuff, Physics: Black Holes and Relativity, Uncategorized1 Comment

Today I depart from my normal schedule and the current story line and science line.  A giant has left us and I want to pay proper tribute.

Dr Stephen Hawking enjoyed telling people of his fortunate birth date, exactly 300 years after Galileo Galilei passed away.  He liked a good joke, and I think he’d be tickled with this additional connection to the man whose work made Hawking’s work possible:
RIP Hawking

The equation in the center of this cut is Hawking’s favorite result, which he wanted to be carved on his gravestone.  It links a black hole’s entropy (S) to its surface area (A).  The other letters denote a collection of constants that have been central to the development of theoretical Physics over the past century and a half:

  • k is Boltzmann’s constant, which links temperature with kinetic energy
  • c is the speed of light, the invariance of which led Einstein to Relativity
  • G is Newton’s universal gravitational constant
  • h is Planck’s constant, the “quantum of action”

Hawking spent much of his career thinking deeply about the implications of Einstein’s concepts.  Newton’s equations support excellent descriptions of everyday physical motions, from the fall of raindrops to the orbits of solar systems.  Einstein’s equations led to insights about conditions at the most extreme — velocities near lightspeed, masses millions of times the Sun’s but packed into a volume only a few dozen miles wide.

But Hawking also pondered extremes of the ultimately large and the ultimately small — the edge of the Universe and distances far smaller than atomic nuclei.  Because his physical condition prohibited speech or quick jottings, he was forced to develop extraordinary powers of concentration and visualization that enabled him to encapsulate in a few phrases insights that would take others books to develop and communicate.

Hawking wrote books, too, of course, of a quality and clarity that turned his name and Science into watchwords for the general public as well as the physics community.  By his life and how he lived it he was an inspiration to many, abled and otherwise.  Science needs its popularizers, though some in the field deprecate them as hangers-on.  Hawking managed to bridge that gap with ease and grace, a giant with standing on either side.

Requiescat in pace, Dr Hawking.  Thank you.

~~ Rich Olcott

Three atop A Crosshatch

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

“Hey, Sy, what you said back there, ‘three and a fraction‘ ways to link atoms together…”

“Yeah, Vinnie?”

“What’s that about?  How do fractions come in when you’re counting?”

“Well, I was thinking about how atoms in separate molecules can interact short of reacting and forming new molecular orbitals.  I figure that as a fraction.”

“Charge sharing ain’t the whole story?”

“It would be except that sharing usually isn’t equal.  It depends on where the atoms are in the Periodic Table.”

“What’s it got to do with the Periodic Table?”

“The Table’s structure reflects atom structures — how many shells are active in a base-state atom of each element and how many units of charge are in its outermost shell.  Hydrogen and Helium are in Row 1 because the 1-node shell is the only active one in those atoms.  The atoms from Lithium to Neon in Row 2 have charge activating both the 1-node shell and the 2-node shell, and so on.”

“What’s that get us?”

“It gets us a feel for how the atoms behave.  You know I’m all about dimensions, right?”

“Ohhh, yeah.”

“OK, we’ve got a two-dimensional table here.  Going across, each atom’s nucleus has one more proton than its buddy to the left.  What’s that going to do to the electronic charge?”

“Gonna pull it in closer.”

“Wait, Vinnie, there’s an extra electron in there, too.  Won’t that cancel out the proton, Sy?”

“Good thinking, Eddie.  Yes, it does, but only partially.  The atoms do get smaller as you go across, but it’s irregular because negative-negative repulsion within a shell works to expand it almost as much as negative-positive attraction contracts it.”

“Bet things get bigger as you go down the Table, though.”

“Mostly, Vinnie, because each row down adds a shell that’s bigger than the shrinking inner shells.”

“Mostly?”

“The bigger shells with more nodes have more complex charge patterns than just balls and dumbbells.  Those two rows below the main table actually squinch into the lowest two boxes in the third column.  In those elements, some of the activated patterns barely shield the nucleus.  The atoms to their right in the main table are almost identical in size to the elements above them.”

“So I can guess an atom’s size.  So what?”

“So that and the charge give you a handle on the element’s properties and chemistry.  Up there in the top right corner you’ve got the atoms with the highest ratio of nuclear charge to size.  If given the opportunity to pull charge from atoms to their left and below them, what do you suppose happens?”

“You get lop-sided bonds, I guess.”

“Exactly.  In water, for instance, the Oxygen pulls charge towards itself and away from the Hydrogen atoms.  That makes each O-H bond a little dipole, positive-ish at the hydrogen end and negative-ish at the oxygen end.”

“Won’t the positive-ish ends pull on the negative-ish parts of next-door molecules?”

“You’ve just invented hydrogen bonding, Eddie.  That’s exactly what happens in liquid water.  Each molecule can link up like that with many adjacent ones and build a huge but floppy structure.  It’s floppy because hydrogen bonds are nowhere near as strong as orbital-sharing bonds.  Even so, the energy required to move through liquid H2O or to vaporize it is much greater than for liquid methane (CH4), ammonia (NH3) or any similar molecule.”

“Can that pull-away action go all the way?”

“You’ve just invented ionic bonding, Vinnie.  The elements in the Oxygen and Fluorine columns can extract charge completely away from many of those far to the left and below them.  Fluorine steals charge from Lithium, for instance.  Fluoride ions are net negative, lithium ions are net positive.  Opposites attract, same as always, but now it’s  entire ions that attract each other and you get crystals.”

“That’s your and-a-fraction?”

“Not quite, Vinnie.  There’s one more, Van der Waals forces.  They come from momentary polarizations as electron chaos sloshes back and forth in neighboring molecules.  They’re why solids are solid even without ionic or hydrogen bonding.”

“Geez, look at the time.  Rosalie’s got my dinner waiting.  Bye, guys, everybody out!”

~~ Rich Olcott