Tag: Cal’s Coffee

Thoughts of Chair-man Moire

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“My apples and orange peels question, Sy,  isn’t that the same as Jeremy’s?  What’s the connection between heat capacity and counting?”

“You’re right, Anne.  Hmm.  Say, Al, all your coffee shop tables came with four chairs apiece, right?”

“Yup, four-tops every one, even in the back room.”

“You neaten them all up, four to a table, in the morning?”

“The night before.  There’s never time in the morning, customers demand coffee first thing.”

“But look, we’ve got six people seated at this table.  Where’d the extra chairs come from?”

“Other tables, of course.  Is this going somewhere?”

“Almost there.  So in fact the state of the room at any time will have some random distribution of chairs to tables.  You know on the average there’ll be four at a table, but you don’t know the actual distribution until you look, right?”

“Hey, we’re counting again.  You’re gonna say that’s about entropy ’cause the difference between four at a table and some other number is all random and there’s some formula to calculate entropy from that.”elephants and chairs

“True, Vinnie, but we’re about to take the next step.  How did these chairs wind up around this table?”

“We pulled them over, Mr. Moire.”

“My point is, Jeremy, we spent energy to get them here.  The more chairs that are out of position — ”

“The higher the entropy, but also the more energy went into the chairs.  It’s like that heat capacity thing we started with, the energy that got absorbed rather than driving the steam engine.”

“Awright, Anne!” from Jeremy <Jennie bristles a bit>, “and if all the chairs are in Al’s overnight position it’s like absolute zero.  Hey, temperature is average kinetic energy per particle so can we say that the more often a chair gets moved it’s like hotter?”

Jennie breaks in.  “Not a bit of it, Jeremy!  The whole metaphor’s daft.  We know temperature change times heat capacity equals the energy absorbed, right, and we’ve got a link between energy absorption and entropy, right, but what about if at the end of the day all the chairs accidentally wind up four at a table?  Entropy change is zero, right, but customers expended energy moving chairs about all day and Al’s got naught to set straight.”

“Science in action, I love it!  Anne and Jeremy, you two just bridged a gap it took Science a century to get across.  Carnot started us on entropy’s trail in 1824 but scientists in those days weren’t aware of matter’s atomic structure.  They knew that stuff can absorb heat but they had no inkling what did the absorbing or how that worked.  Thirty years later they understood simple gases better and figured out that average kinetic energy per particle bit.  But not until the 1920s did we have the quantum mechanics to show how parts of vibrating molecules can absorb heat energy stepwise like a table ‘absorbing’ chairs.  Only then could we do Vinnie’s state-counting to calculate entropies.”

“Yeah, more energy, spread across more steps, hiding more details we don’t know behind an average, more entropy.  But what about Jennie’s point?”

“Science is a stack of interconnected metaphors, Vinnie.  Some are better than others.  The trick is attending to the boundaries where they stop being valid.  Jennie’s absolutely correct that my four-chair argument is only a cartoon for illustrating stepwise energy accumulation.  If Al had a billion tables instead of a dozen or so, the odds on getting everything back to the zero state would disappear into rounding error.”

“How does black hole entropy play into this, Sy?”TSE classical vs BH

“Not very well, actually.  Oh, sure, the two systems have similar structures.  They’ve each got three inter-related central quantities constrained by three laws.  Here, I’ve charted them out on Old Reliable.”

“OK, their Second and Third Laws look pretty much the same, but their First Laws don’t match up.”

“Right, Al.  And even Bekenstein pointed out inconsistencies between classic thermodynamic temperature and what’s come to be called Hawking temperature.  Hawking didn’t agree.  The theoreticians are still arguing.  Here’s a funny one — if you dig deep enough, both versions of the First Law are the same, but the Universe doesn’t obey it.”

“That’s it, closing time.  Everybody out.”

~~ Rich Olcott

Taming The Elephant

On By rolcottIn Physics: Black Holes and Relativity, Physics: Entropy and Thermodynamics, UncategorizedLeave a comment

Suddenly they were all on the attack.  Anne got in the first lick.  “C’mon, Sy, you’re comparing apples and orange peel.  Your hydrogen sphere would be on the inside of the black hole’s event horizon, and Jeremy’s virtual particles are on the outside.”

[If you’ve not read my prior post, do that now and this’ll make more sense.  Go ahead, I’ll wait here.]white satin and 5 elephantsJennie’s turn — “Didn’t the chemists define away a whole lot of entropy when they said that pure elements have zero entropy at absolute zero temperature?”

Then Vinnie took a shot.  “If you’re counting maybe-particles per square whatever for the surface, shouldn’t you oughta count maybe-atoms or something per cubic whatever for the sphere?”

Jeremy posed the deepest questions. “But Mr Moire, aren’t those two different definitions for entropy?  What does heat capacity have to do with counting, anyhow?”

Al brought over mugs of coffee and a plate of scones.  “This I gotta hear.”

“Whew, but this is good ’cause we’re getting down to the nub.  First to Jennie’s point — Under the covers, Hawking’s evaluation is just as arbitrary as the chemists’.  Vinnie’s ‘whatever’ is the Planck length, lP=1.616×10-35 meter.  It’s the square root of such a simple combination of fundamental constants that many physicists think that lP2=2.611×10-70 m², is the ‘quantum of area.’  But that’s just a convenient assumption with no supporting evidence behind it.”

“Ah, so Hawking’s ABH=4πrs2 and SBH=ABH/4 formulation with rs measured in Planck-lengths, just counts the number of area-quanta on the event horizon’s surface.”

“Exactly, Jennie.  If there really is a least possible area, which a lot of physicists doubt, and if its size doesn’t happen to equal lP2, then the black hole entropy gets recalculated to match.”

“So what’s wrong with cubic those-things?”

“Nothing, Vinnie, except that volumes measured in lP3 don’t apply to a black hole because the interior’s really four-dimensional with time scrambled into the distance formulas.  Besides, Hawking proved that the entropy varies with half-diameter squared, not half-diameter cubed.”

“But you could still measure your hydrogen sphere with them and that’d get rid of that 1033 discrepancy between the two entropies.”

“Not really, Vinnie.  Old Reliable calculated solid hydrogen’s entropy for a certain mass, not a volume.”

“Hawking can make his arbitrary choice, Sy, he’s Hawking, but that doesn’t let the chemists off the scaffold.  How did they get away with arbitrarily defining a zero for entropy?”

“Because it worked, Jennie.  They were only concerned with changes — the difference between a system’s state at the end of a process, versus its state at the beginning.  It was only the entropy difference that counted, not its absolute value.”

“Hey, like altitude differences in potential energy.”

“Absolutely, Vinnie, and that’ll be important when we get to Jeremy’s question.  So, Jennie, if you’re only interested in chemical reactions and if it’s still in the 19th Century and the world doesn’t know about isotopes yet, is there a problem with defining zero entropy to be at a convenient set of conditions?”

“Well, but Vinnie’s Second Law says you can never get down to absolute zero so that’s not convenient.”

“Good point, but the Ideal Gas Law and other tools let scientists extrapolate experimentally measured properties down to extremely low temperatures.  In fact, the very notion of absolute zero temperature came from experiments where the volume of a  hydrogen or helium gas sample appears to decrease linearly towards zero at that temperature, at least until the sample condenses to a liquid.  With properly calibrated thermometers, physical chemists knocked themselves out measuring heat capacities and entropies at different temperatures for every substance they could lay hands on.”

“What about isotopes, Mr Moire?  Isn’t chlorine’s atomic weight something-and-a-half so there’s gotta be several of kinds of chlorine atoms so any sample you’ve got is a mixture and that’s random and that has to have a non-zero entropy even at absolute zero.”

“It’s 35.4, two stable isotopes, Jeremy, but we know how to account for entropy of mixing and anyway, the isotope mix rarely changes in chemical processes.”

“But my apples and orange peels, Sy — what does the entropy elephant do about them?”

~~ Rich Olcott

The Battle of The Entropies

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(the coffee-shop saga continues)  “Wait on, Sy, a black hole is a hollow sphere?”

I hadn’t noticed her arrival but there was Jennie, standing by Vinnie’s table and eyeing Jeremy who was sill eyeing Anne in her white satin.white satin and 2 elephants“That’s not quite what I said, Jennie.  Old Reliable’s software and and I worked up a hollow-shell model and to my surprise it’s consistent with one of Stephen Hawking’s results.  That’s a long way from saying that’s what a black hole is.”

“But you said some physicists say that.  Have they aught to stand on?”

“Sort of.  It’s a perfect case of ‘depends on where you’re standing.'”

Vinnie looked up.  “It’s frames again, ain’t it?”

“With black holes it’s always frames, Vinnie.  Hey, Jeremy, is a black hole something you could stand on?”

“Nosir, we said the hole’s event horizon is like Earth’s orbit, just a mathematical marker.  Except for the gravity and  the  three  Perils  Jennie and you and me talked about, I’d slide right through without feeling anything weird, right?”

“Good memory and just so.  In your frame of reference there’s nothing special about that surface — you wouldn’t experience scale changes in space or time when you encounter it.  In other frames, though, it’s special.  Suppose we’re standing a thousand miles away from a solar-size black hole and Jeremy throws a clock and a yardstick into it.  What would we see?”

“This is where those space compression and time dilation effects happen, innit?”

“You bet, Jennie.  Do you remember the formula?”

“I wrote it in my daybook … Ah, here it is —Schwarzchild factorMy notes say D is the black hole’s diameter and d is another object’s distance from its center.  One second in the falling object’s frame would look like f seconds to us.  But one mile would look like 1/f miles.  The event horizon is where d equals the half-diameter and f goes infinite.  The formula only works where the object stays outside the horizon.”

“And as your clock approaches the horizon, Jeremy…?”

“You’ll see my clock go slower and slower until it sto —.  Oh.  Oh!  That’s why those physicists think all the infalling mass is at the horizon, the stuff falls towards it forever and never makes it through.”

“Exactly.”

“Hey, waitaminute!  If all that mass never gets inside, how’d the black hole get started in the first place?”

“That’s why it’s only some physicists, Vinnie.  The rest don’t think we understand the formation process well enough to make guesses in public.”

“Wait, that formula’s crazy, Sy.  If something ever does get to where d is less than D/2, then what’s inside the square root becomes negative.  A clock would show imaginary time and a yardstick would go imaginary, too.  What’s that about?”

“Good eye, Anne, but no worries, the derivation of that formula explicitly assumes a weak gravitational field.  That’s not what we’ve got inside or even close to the event horizon.”

“Mmm, OK, but I want to get back to the entropy elephant.  Does black hole entropy have any connection to the other kinds?”

“Strutural, mostly.  The numbers certainly don’t play well together.  Here’s an example I ran up recently on Old Reliable.  Say we’ve got a black hole twice the mass of the Sun, and it’s at the Hawking temperature for its mass, 12 billionths of a Kelvin.  Just for grins, let’s say it’s made of solid hydrogen.  Old Reliable calculated two entropies for that thing, one based on classical thermodynamics and the other based on the Bekenstein-Hawking formulation.”Entropy calculations“Wow, Old Reliable looks up stuff and takes care of unit conversions automatically?”

“Slick, eh, Jeremy?  That calculation up top for Schem is classical chemical thermodynamics.  A pure sample of any element at absolute zero temperature is defined to have zero entropy.  Chemical entropy is cumulative heat capacity as the sample warms up.  The Hawking temperature is so close to zero I could treat heat capacity as a constant.

“In the middle section I calculated the object’s surface area in square Planck-lengths lP², and in the bottom section I used Hawking’s formula to convert area to B-H entropy, SBH.  They disagree by a factor of 1033.”

A moment of shocked silence, and then…

~~ Rich Olcott

Rockfall

On By rolcottIn Physics: Black Holes and Relativity, Physics: Entropy and Thermodynamics, Physics: Newton and Gravity, UncategorizedLeave a comment

<continued>  The coffee shop crowd had gotten rowdy in response to my sloppy physics, but everyone hushed when I reached for my holster and drew out Old Reliable.  All had heard of it, some had seen it in action — a maxed-out tablet with customized math apps on speed-dial.

“Let’s take this nice and slow.  Suppose we’ve got an non-charged, non-spinning solar-mass black hole.  Inside its event horizon the radius gets weird but let’s pretend we can treat the object like a simple sphere.  The horizon’s half-diameter, we’ll call it the radius, is rs=2G·M/c².  G is Newton’s gravitational constant, M is the object’s mass and c is the speed of light.  Old Reliable says … about 3 kilometers.  Question is, what happens when we throw a rock in there?  To keep things simple, I’m going to model dropping the rock gentle-like, dead-center and with negligible velocity relative to the hole, OK?”

<crickets>

“Say the rock has the mass of the Earth, almost exactly 3×10-6 the Sun’s mass.  The gravitational potential energy released when the rock hits the event horizon from far, far away would be E=G·M·m/rs, which works out to be … 2.6874×1041 joules.  What happens to that energy?”falling rock and black hole

“rs depends on mass, Mr Moire, so the object will expand.  Won’t that push on what’s around it?”

“You’re thinking it’d act like a spherical piston, Jeremy, pushing out in all directions?”

“Yeah, sorta.”

“After we throw in a rock with mass m, the radius expands from rs to rp=2G·(M+m)/c².  I set m to Earth’s mass and Old Reliable says the new radius is … 3.000009 kilometers.  Granted the event horizon is only an abstract math construct, but suppose it’s a solid membrane like a balloon’s skin.  When it expands by that 9 millimeters, what’s there to push against?  The accretion disk?  Those rings might look solid but they’re probably like Saturn’s rings — a collection of independent chunks of stuff with an occasional gas molecule in-between.  Their chaotic orbits don’t have a hard-edged boundary and wouldn’t notice the 9-millimeter difference.  Inward of the disk you’ve got vacuum.  A piston pushing on vacuum expends zero energy.  With no pressure-volume work getting done that can’t be where the infall energy goes.”

“How about lift-a-weight work against the hole’s own gravity?”

“That’s a possibility, Vinnie.  Some physicists maintain that a black hole’s mass is concentrated in a shell right at the event horizon.  Old Reliable here can figure how much energy it would take to expand the shell that extra 9 millimeters.  Imagine that simple Newtonian physics applies — no relativistic weirdness.  Newton proved that a uniform spherical shell’s gravitational attraction is the same as what you’d get from having the same mass sitting at the shell’s geometric center.  The gravitational pull the shell exerts on itself originally was E=G·M²/rs.  Lifting the new mass from rs to rp will cost ΔE=G·(M+m)²/rp – G·M²/rs.  When I plug in the numbers…  That’s interesting.”

Vinnie’s known me long enough to realize “That’s interesting” meant “Whoa, I certainly didn’t expect THAT!”

“So what didja expect and whatcha got?”

“What I expected was that lift-it-up work would also be just a small fraction of the infall energy and the rest would go to heat.  What I got for ΔE here was 2.6874×1041 joules, exactly 100% of the input.  I wonder what happens if I use a bigger planet.  Gimme a second … OK, let’s plot a range …  How ’bout that, it’s linear!”ep-es

“Alright, show us!”

“All the infall energy goes to move the shell’s combined mass outward to match the expanded size of the event horizon.  I’m amazed that such a simple classical model produces a reasonable result.”

“Like Miss Plenum says, Mr Moire, sometimes the best science comes from surprises.”

“I wouldn’t show it around, Jeremy, except that it’s consistent with Hawking’s quantum-physics result.”

“How’s that?”

“Remember, he showed that a black hole’s temperature varies as 1/M.  We know that temperature is ΔE/ΔS, where the entropy change ΔS varies as M².  We’ve just found that ΔE varies as M.  The ΔE/ΔS ratio varies as M/M²=1/M, just like Hawking said.”

Then Jennie got into the conversation.

~~ Rich Olcott

Red Harvest

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<continued> Al’s coffee shop was filling up as word got around about Anne in her white satin.  I saw a few selfie-takers in the physics crowd surreptitiously edge over to get her into their background.  She was busy thinking so she didn’t notice.  “The entropy-elephant picture is starting to come together, Sy.  We started out with entropy measuring accumulated heat capacity in a steam engine.”

“That’s where Carnot started, yes.”

“But when Jeremy threw that hot rock into the black hole” <several in the astronomy crew threw startled looks at Jeremy>, “its heat energy added to the black hole’s mass, but it should have added to the black hole’s entropy, too.  ‘Cause of Vinnie’s Second Law.”white satin and black hole 3

Vinnie looked up.  “Ain’t my Second Law, it’s thermodynamics’ Second Law.  Besides, my version was ‘energy’s always wasted.’  Sy’s the one who turned that into ‘entropy always increases.'”

“So anyway, black holes can’t have zero entropy like people used to think.  But if entropy also has to do with counting possibilities, than how does that apply to black holes?  They have only one state.”

“That’s where Hawking got subtle.  Jeremy, we’ve talked about how the black hole’s event horizon is a mathematical abstraction, infinitely thin and perfectly smooth and all that.”

“Yessir.”

“Hawking moved one step away from that abstraction.  In essence he said the  event horizon is surrounded by a thin shell of virtual particles.  Remember them, Jeremy?”

“Uh-huh, that was on my quest to the event horizon.  Pairs of equal and opposite virtual particles randomly appear and disappear everywhere in space and because they appear together they’re entangled and if one of them dips into the event horizon then it doesn’t annihilate its twin which — Oh!  Random!  So what’s inside the event horizon may have only one state, so far as we know, but right outside the horizon any point may or may not be hosting, can I call it an orphan particle?  I’ll bet that uncertainty give rise to the entropy, right?”

<finger-snaps of approval from the physics side of the room>

“Well done, Jeremy!  ‘Orphan’ isn’t the conventional term but it gets the idea across.”

“Wait, Sy.  You mentioned that surface area and entropy go together and now I see why.  The larger the area, the more room there is for those poor orphans.  When Jeremy’s rock hit the event horizon and increased the black hole’s mass, did the surface area increase enough to allow for the additional entropy?” <more finger-snapping>

“Sure did, Anne.  According to Hawking’s calculation, it grew by exactly the right amount.  Mass and area both grow as the square of the diameter.”

“How come not the radius?”

“Well , Vinnie, the word ‘radius‘ is tricky when you’re discussing black holes.  The event horizon is spherical and has a definite diameter — you could measure it from the outside.  But the sphere’s radius extends down to the singularity and is kind of infinite and isn’t even strictly speaking a distance.  Space-time is twisted in there, remember, and that radial vector is mostly time near its far end.  On the other hand, you could use ‘radius‘ to mean ‘half the diameter‘ and you’d be good for calculating effects outside the event horizon.”

“OK, that’s the entropy-area connection, but how does temperature tie in with surface gravity?”

“They’re both inversely dependent on the black hole’s mass.  Let’s take surface gravity first, and here when I say ‘r‘ I’m talking ‘half-diameter,‘ OK?”

“Sure.”

“Good.  Newton taught us that an object with mass M has a gravitational attraction proportional to M/r².  That still holds if you’re not inside the event horizon.  Now, the event horizon’s r is also proportional to the object’s mass so you’ve got M/M² which comes to 1/M.  With me?”

“Yeah.”

“Hawking used quantum physics to figure the temperature thing, but here’s a sloppy short-cut.  Anne, remember how we said that entropy is approximately heat capacity divided by temperature?”

“Mm-hmm.”

“The shell’s energy is mostly heat and proportional to M.  We’ve seen the shell’s entropy is proportional to M².  The temperature is heat divided by entropy.  That’s proportional to M/M² which is the same 1/M as surface gravity.” <boos from all sides>. “Hey, I said it was sloppy.”

~~ Rich Olcott

Rockin’ Round The Elephant

On By rolcottIn Physics: Black Holes and Relativity, Physics: Entropy and Thermodynamics, Uncategorized8 Comments

<continued…>  “That’s what who said?  And why’d he say that?”

“That’s what Hawking said, Al.  He’s the guy who first applied thermodynamic analysis to black holes.  Anyone happen to know the Three Laws of Thermodynamics?”

Vinnie pipes up from his table by the coffee shop door.  “You can’t win.  You can’t even break even.  But you’ll never go broke.”

“Well, that’s one version, Vinnie, but keep in mind all three of those focus on energy.  The First Law is Conservation of Energy—no process can create or destroy energy, only  transform it, so you can’t come out ahead.  The Second Law is really about entropy—”

“Ooo, the elephant!”white satin and black hole 2

“Right, Anne.  You usually see the Second Law stated in terms of energy efficiency—no process can convert energy to another form without wasting some of it. No breaking even.  But an equivalent statement of that same law is that any process must increase the entropy of the Universe.”

“The elephant always gets bigger.”

“Absolutely.  When Bekenstein and Hawking thought about what would happen if a black hole absorbed more matter, worst case another black hole, they realized that the black hole’s surface area had to follow the same ‘Never decrease‘ rule.”

“Oh, that Hawking!  Hawking radiation Hawking!  The part I didn’t understand, well one of the parts, in that “Black Holes” Wikipedia article!  It had to do with entangled particles, didn’t it?”

“Just caught up with us, eh, Jeremy?  Yes, Stephen Hawking.  He and Jacob Bekenstein found parallels between what we can know about black holes on the one hand and thermodynamic quantities on the other.  Surface area and entropy, like we said, and a black hole’s mass acts mathematically like energy in thermodynamics.  The correlations were provocative ”

“Mmm, provocative.”

“You like that word, eh, Anne?  Physicists knew that Bekenstein and Hawking had a good analogy going, but was there a tight linkage in there somewhere?  It seemed doubtful.”

“Nothin’ to count.”

“Wow, Vinnie.  You’ve been reading my posts?”

“Sure, and I remember the no-hair thing.  If the only things the Universe can know about a black hole are its mass, spin and charge, then there’s nothing to figure probabilities on.”

“Exactly.  The logic sequence went, ‘Entropy is proportional to the logarithm of state count, there’s only one state, log(1) equals zero,  so the entropy is zero.’  But that breaks the Third Law.  Vinnie’s energy-oriented Third Law says that no object can cool to absolute zero temperature.  But an equivalent statement is that no object can have zero entropy.”

“So there’s something wrong with black hole theory, huh?”

“Which is where our guys started, Vinnie.  Being physicists, they said, ‘Suppose you were to throw an object into a black hole.  What would change?’”

“Its mass, for one.”

“For sure, Jeremy.  Anything else?”

“It might not change the spin, if you throw right.”

“Spoken like a trained baseball pitcher.  Turns out its mass governs pretty much everything about a black hole, including its temperature but not spin or charge.  Once you know the mass you can calculate its entropy, diameter, surface area, surface gravity, maximum spin, all of that.  Weird, though, you can’t easily calculate its volume or density — spatial distortion gets in the way.”

“So what happens to all those things when the mass increases?”

“As you might expect, they change.  What’s interesting is how each of them change and how they’re linked together.  Temperature, for instance, is inversely proportional to the mass and vice-versa.  Suppose, Jeremy, that you threw two big rocks, both the same size, into a black hole.  The first rock is at room temperature and the other’s a really hot one, say at a million degrees.   What would each do?”

“The first one adds mass so from what you said it’d drop the temperature.  The second one has the same mass, so I don’t see, wait, temperature’s average kinetic energy so the hot rock has more energy than the other one and Einstein says that energy and mass are the same thing so the black hole gets more mass from the hot rock than from the cold one so its temperature goes down … more?  Really?”

“Yup.  Weird, huh?”

“How’s that work?”

“That’s what they asked.”

~~ Rich Olcott

Schrödinger’s Elephant

On By rolcottIn Gravitational astronomy, Physics: Black Holes and Relativity, Physics: Entropy and Thermodynamics, UncategorizedLeave a comment

Al’s coffee shop sits right between the Astronomy and Physics buildings, which is good because he’s a big Science fan.  He and Jeremy are in an excited discussion when Anne and I walk in.  “Two croissants, Al, and two coffees, black.”

“Comin’ up, Sy.  Hey, you see the news?  Big days for gravitational astronomy.”

Jeremy breaks in.  “There’s a Nobel Prize been announced —”

“Kip Thorne the theorist and Barry Barish the management guy —”

“and Rainer Weiss the instrumentation wizard —”

“shared the Physics prize for getting LIGO to work —”

“and it saw the first signal of a black hole collision in 2015 —”

“and two more since —”

“and confirmed more predictions from relativity theory —”

“and Italy’s got their Virgo gravitational wave detector up and running —”

“And Virgo and our two LIGOs, —”

“Well, they’re both aLIGOs now, being upgraded and all —”

“all three saw the same new wave —”

“and it’s another collision between black holes with weird masses that we can’t account for.  Who’s the lady?”

“Al, this is Anne.  Jeremy, close your mouth, you’ll catch a fly.”  (Jeremy blushes, Anne twinkles.)  “Anne and I are chasing an elephant.”

“Pleased to meetcha, Anne.  But no livestock in here, Sy, the Health Department would throw a fit!”

I grin.  “That’s exactly what Eddie said.  It’s an abstract elephant, Al.  We’ve been discussing entropy. Which is an elephant because it’s got so many aspects no-one can agree on what it is.  It’s got something to do with heat capacity, something to do with possibilities you can’t rule out, something to do with signals and information.  And Hawking showed that entropy also has something to do with black holes.”

“Which I don’t know much about, fellows, so someone will have to explain.”

Jeremy leaps in.  “I can help with that, Miss Anne, I just wrote a paper on them.”

“Just give us the short version, son, she can ask questions if she wants a detail.”

“Yessir.  OK, suppose you took all the Sun’s mass and squeezed it into a ball just a few miles across.  Its density would be so high that escape velocity is faster than the speed of light so an outbound photon just falls back inward and that’s why it’s black.  Is that a good summary, Mr Moire?”

“Well, it might be good enough for an Internet blog but it wouldn’t pass inspection for a respectable science journal.  Photons don’t have mass so the whole notion of escape velocity doesn’t apply.  You do have some essential elements right, though.  Black holes are regions of extreme mass density, we think more dense than anywhere else in the Universe.  A black hole’s mass bends space so tightly around itself that nearby light waves are forced to orbit its region or even spiral inward.  The orbiting happens right at the black hole’s event horizon, its thin shell that encloses the space where things get really weird.  And Anne, the elephant stands on that shell.”white satin and black hole“Wait, Mr Moire, we said that the event horizon’s just a mathematical construct, not something I could stand on.”

“And that’s true, Jeremy.  But the elephant’s an abstract construct, too.  So abstract we’re still trying to figure out what’s under the abstraction.”

“I’m trying to figure out why you said the elephant’s standing there.”

“Anne, it goes back to the event horizon’s being a mathematical object, not a real one.  Its spherical surface marks the boundary of the ultimate terra incognita.  Lightwaves can’t pass outward from it, nor can anything material, not even any kind of a signal.  For at least some kinds of black hole, physicists have proven that the only things we can know about one are its mass, spin and charge.  From those we can calculate some other things like its temperature, but black holes are actually pretty simple.”

“So?”

“So there’s a collision with Quantum Theory.  One of QT’s fundamental assumptions is that in principle we can use a particle’s current wave function to predict probabilities for its future.  But the wave function information disappears if the particle encounters an event horizon.  Things are even worse if the particle’s entangled with another one.”

“Information, entropy, elephant … it’s starting to come together.”

“That’s what he said.”

~~ Rich Olcott

Planetary Pastry, Third Course

On By rolcottIn Astronomy: Planetary Science, Uncategorized2 Comments

The Al’s Coffee Shop Astronomy gang is still discussing Jupiter’s Great Red Spot.  Cathleen‘s holding court, which is natural because she’s the only for-real Astronomer in the group…  “So here’s what we’ve got.  The rim of the Great Red Spot goes hundreds of miles an hour in the wrong direction compared to hurricanes on Earth.  An Earth hurricane’s eye is calm but the Jupiter Spot’s rim encloses a complex pattern of high winds.  Heat transport and cloud formation on Earth are dominated by water, but Jupiter’s atmospheric dynamic has two active players — water and ammonia.”

“Here’s your pastries, Cathleen.  I brought you a whole selection.  Don’t nobody sneeze on ’em, OK?”

“Oh, they’re perfect, Al.  Thanks.  Let’s start with this bear claw.  We’ll pretend it’s the base of the weather column.  On Earth that’d be mostly ocean, some land surface and some ice.  They’re all rough-ish and steer air currents, which is why there’s a rain shadow inland of coastal mountain ranges.”pastries 2

“Jupiter doesn’t have mountains?”

“We’re virtually certain it doesn’t, Sy.  The planet’s density is so low that it can’t have much heavy material.  It’s essentially an 88,000-mile-wide ball of helium-diluted liquid hydrogen topped by a 30-mile-high weather column.  Anything rocky sank to the core long ago.  The liquid doesn’t even have a real surface.”

<Al and Sy> “Huh?”

“Jovian temps are so low that even at moderate pressures there’s no boundary between gaseous and liquid phases.  Going downward you dive through clear ‘air,’ then progress through an increasingly opalescent haze until you realize you’re swimming.  Physicists just define the ‘surface’ to be the height where the pressure is one atmosphere.  That level’s far enough down that water and ammonia freeze to form overlying cloud layers but hydrogen and helium are still gases.  It could conceivably look like home there except the sky would be weird colors and you don’t see a floor.”

“If the boundary is that blurry, it’s probably pretty much frictionless — weather passes over it without slowing down or losing energy, right?”

“Yup.”

“So there’s way too much slivered almonds and stuff on that bear claw. On this scale it ought to have a mirror finish.”

“Good point.  But now we can start stacking weather onto it.  Here’s my doughnut, to represent the Great Red Spot or any of the other long-lived anticyclones.”

“Auntie who?”

“A-n-t-i-cyclone, Al.  Technical term for a storm that disobeys the Coriolis theory.”

“Uh-HUH. So why’s it do that?”

“Well, at this point we can only go up one level in the cause-and-effect chain.  <pulling out smartphone>  NASA’s Voyager 1 spacecraft sent back data for this this wonderful video

790106-0203_Voyager_58M_to_31M_reduced
Jupiter seen by Voyager 1 probe with blue filter in 1979. One image was taken every Jupiter day (approximately 10 hours).  Credit: NASA

“Basically, the Spot is trapped between two jet streams, one going westward at 135 mph and the other going eastward at 110 mph.  I’ll use these biscotti to represent them.pastries with arrows

“Hey, that’s like a rack-and-pinion gear setup, with two racks and an idler, except the idler gear’s four times as wide as the Earth.”

“A bit less than that these days, Sy.  The Spot’s been shrinking and getting rounder.  Every year since 1980 it’s lost about 300 miles east-west and about 60 miles north-south.  As of 2014 it was about 2.8 Earth-widths across.  And no, we don’t know why.  Theories abound, though.”

“What’s one of them?”

“Believe it or not, climate change.  On Jupiter, not Earth.  One group of scientists at Berkeley tackled a couple of observations

  • Unlike Earth, which is much hotter near the Equator than near the poles, Jupiter’s Equator is only a few degrees warmer than its poles.
  • Three persistent White Ovals near the Great Red Spot merged to form a single White Oval that recently turned red but only around the edges.

Their argument is long, technical and still controversial.  However, their proposal is that merging the three ovals disrupted the primary heat transport mechanism that had been evening out Jupiter’s temperature.  IF that’s true, and if it’s the case that Jupiter’s jet streams are powered by heat transport, then maybe disrupted heat patterns are interfering with  the Great Red Spot’s rack-and-pinion machine.  And maybe more.”

“Big changes ahead for the Big Planet.”

“Maybe.”

~~ Rich Olcott

Planetary Pastry, Second Course

On By rolcottIn Astronomy: Planetary Science, UncategorizedLeave a comment

We’re still sitting in Al’s coffee shop.  “OK, Cathleen, so Jupiter’s Great Red Spot acts like a hurricane turned inside-out.  Where’s the problem?”

“Just that it goes completely against all the computer models we’ve built to understand and predict hurricane activity.  It’ll take a whole new generation of even more complicated models for Jupiter-like planets.”

“Here’s the doughnuts you asked for, Cathleen.”

“Thanks, Al.  Perfect timing. <drawing on a paper napkin>  Let’s look at hurricanes first, OK, Sy?”

“Sure.”

“We’ll start with this doughnut that I’ve just taken a bite out of.  First thing that happens is that warm ocean water heats up the overlying air.  Warmed air rises, so we’ve got an updraft.”

“And then?”

“The rising air is humid (ocean air, remember?).  As it rises it cools and forces moisture to condense out.  Upward flow stops when the warmed air hits the top of the troposphere.  But there’s still more warm air pushing up the plume.  The cooled air has to go somewhere so it spreads out.  That’s where these red arrows on my paper napkin go horizontal.  The cooled air, loaded with water droplets, is heavy so it starts sinking which is why the red arrows turn downward.  They move back across that ocean water again ’cause they’re caught in the inflow.  Full cycle and that’s number 1 here, got it?”

“Yeah.”

“Hey, Cathleen,  are you gonna need more paper napkins?”Donuts 1
“A couple should be enough, Al, thanks.  Now we get to number 2, the Coriolis thing. That’s always tough to talk students through but let’s try.  The Earth rotates once every 24 hours, right, and its circumference at the Equator is 25,000 miles, so relative to the Sun anything at the Equator is flying eastward at about 1,000 miles per hour.  Any place north of the Equator has to be going slower than that, and further north, even slower.  With me, Sy?”

“Gimme a minute … OK, I suppose.”

“Good.  Now suppose a balloon is floating in the breeze somewhere south of that rising plume.  Relative to the plume, it’ll have eastward momentum.  Now the balloon’s caught in the plume’s inflow but it doesn’t go straight in because of that eastward momentum.  Instead it’s going to arc around the plume.  See how I’ve got it coming in off-center?  Al, would that be clockwise or counterclockwise if you’re looking down from a satellite or something?”

“Umm … counterclockwise, yeah?”

“Mm-hm.  What about a balloon that starts out north of the plume?”

“Uhh … It’ll be going slower than the plume, so the plume gets ahead of it and it’ll arc … hey, counterclockwise again!”

“How ’bout that?  Anywhere in the northern hemisphere, air flowing into a low-pressure region will turn it counterclockwise.  As the inflow draws from greater distances, there’s a greater speed difference to drive the counterclockwise spin.  So that’s number 2 here.  Add those two cycles together and you’ve got number 3, which spirals all around the doughnut.  And there’s your hurricane.”

“Cool.  So how does that model not account for the Great Red Spot?”

“To begin with, the Spot’s in Jupiter’s southern hemisphere so it ought to be going clockwise which it definitely is not.  And there’s no broad band of surrounding clouds — just a lot of structure inside the ring, not outside.  There’s something else going on that swamps Coriolis.”

“So how’s Jupiter different from Earth?  Besides being bigger, of course.”

“Lots of ways, Sy.  You know how labels on healthcare products divide the contents into active ingredients and inert ingredients?  The inert ones just carry or modify the effects of the active ones.  Atmospheres work the same way.  On Earth the inert ingredients are nitrogen and oxygen…”

“Hey, oxygen’s important!”

“Sure, Al, but not when you’re modeling air movement.  The important active ingredient is water — it transports a lot of heat when it evaporates from one place and condenses somewhere else.  The biggest outstanding problem in Earth meteorology is accounting for clouds.”

“You’re gonna tell us that Jupiter’s inactive ingredients are hydrogen and helium, I suppose.”

“Precisely, Sy.  Jupiter has two active ingredients, water and ammonia, plus smaller amounts of sulfur and phosphorus compounds.  Makes for a crazy complicated modeling problem.  I’m going to need more pastries.”

“Comin’ up.”

 

~~ Rich Olcott

Planetary Pastry, First Course

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

“Morning, Al.  What’s the scone of the day?”

“No scones today, Sy.  Cathleen and one of her Astronomy students used my oven to do a whole batch of these orange-and-apricot Danishes.  Something to do with Jupiter.  Try one.”Great Apricot Spot 1
Cathleen was standing behind me.  “They’re in honor of NASA’s Juno spacecraft.  She just completed a close-up survey of Jupiter’s famous cloud formation, the Great Red Spot.  Whaddaya think?”

“Not bad.  Nice bright color and a good balance of sweetness from the apricot against tartness from the orange.”

“You noticed that, hey?  We had to do a lot of balancing — flavors, colors, the right amount of liquid.  Too juicy and the pastry part comes out gummy, too dry and you break a tooth.  Notice something else?”

“The structure, right?  Like the Spot’s collar around a mushed-up center.”

“Close, but Juno showed us that center’s anything but mushed-up.  <pulls out her smartphone>  Here’s what she sent back.”

GRS 1 @400
Credits: NASA/JPL-Caltech/SwRI/MSSS/Jason Major

“See, it’s swirls within swirls. We tried stirring the filling to look like that but it mostly smoothed out in the baking.”

“Hey, is it true what I heard that the Great Red Spot has been there for 400 years?”

“We think so, Al, but nobody knows for sure.  When Galileo published his telescopic observations of Jupiter in 1610 he didn’t mention a spot.  But that could be because he’d already caught flak from the Church by describing mountains and craters on the supposedly perfect face of the Moon.   Besides, the Jovian moons he saw were much more exciting for the science of the time.  A planet with satellites was a direct contradiction to Aristotle’s Earth-centered Solar System.”

“OK, but what about after Galileo?”

“There are records of a spot between 1665 and 1713 but then no reports of a spot for more than a century.  Maybe it was there and nobody was looking for it, maybe it had disappeared.  But Jupiter’s got one now and it’s been growing and shrinking for the past 185 years.”

“So what is it, what’s it made of and why’s it been there so long?”

“Three questions, one of them easy.”

“Which is easy, Sy?”

“The middle one.  The answer is, no-one knows what it’s made of.  That’s part of Juno‘s mission, to do close-up spectroscopy and help us wheedle what kinds of molecules are in there.  We know that Jupiter’s mostly hydrogen and helium, just like the Sun, but both of those are colorless.  Why some of the planet’s clouds are blue and some are pink — that’s a puzzle, right, Cathleen?”

“Well, we know a little more than that, especially since the Galileo probe dove 100 miles into the clouds in 1995.  The white clouds are colder and made of ammonia ice particles.  The pink clouds are warmer and … ok, we’re still working on that.”

“What about my other two questions, Cathleen?”

“People often call it a hurricane, but that’s a misnomer.  On Earth, a typical hurricane is a broad, complex ring of rainstorms with wind speeds from 75 to 200 mph.  Inside the ring wall people say it’s eerily calm.  The whole thing goes counterclockwise in the northern hemisphere, clockwise in the southern one.”

“So how’s the Great Red Spot different?”

“Size, speed, complexity, even direction.  East-to-west, the Spot is eight times wider than the biggest hurricanes.  Its collar winds run about 350 mph and it rotates counterclockwise even though it’s in Jupiter’s southern hemisphere.  It’s like a hurricane inside-out.”

“It’s not calm inside?”

“Nope, take another look at that Juno image.  There’s at least three very busy bands wrapped around a central structure that looks like it holds three distinct swirls.  That’s the part that’s easiest to understand.” GRS core

“Why so?”

“Geometry.  Adjacent segments of separate swirls have to be moving in the same direction or they’ll cancel each other out.  <scribbles diagram on a paper napkin>  Suppose I’ve got just one inside another one.  If they go in the same direction the faster one speeds up the slower one and they merge.  If they go in opposite directions, one of them disappears.  If there’s more than one inner swirl, there has to be an odd number, see?”

“So if it’s not a hurricane, what is it?”

“Got any donuts, Al?”

~~ Rich Olcott