Tag: Jeremy

Two Sharp Dice

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

<further along our story arc…>  “Want a refill?”

“No, I’ve had enough.  But I could go for some dessert.”

“Nothing here in the office, care for some gelato?”

We take the elevator down to Eddie’s on 2.  Things are slow.  Jeremy’s doing homework behind the gelato display.  Eddie’s at the checkout counter, rolling some dice.  He gives the eye to her white satin.  “You’ll fit right in when the theater crowd gets here, Miss.  Don’t know about you, Sy.”White satin and dice

“Fitting in’s not my thing, Eddie.  This is my client, Anne.  What’s with the bones?”

“Weirdest thing, Sy.  I’m getting set up for the game after closing (don’t tell nobody, OK?) but these dice gotta be bad somehow.  I roll just one, I get every number, but when I roll the two together I get nothin’ but snake-eyes and boxcars.”

I shoot Anne a look.  She shrugs.  I sing out, “Hey, Jeremy, my usual chocolate-hazelnut combo.  For the lady … I’d say vanilla and mint.”

She shoots me a look.  “How’d you know?”

I shrug.  “Lucky guess.  It’s a good evening for the elephant.”

“Hey, no livestock in here, Sy, the Health Department would throw a fit!”

“It’s an abstract elephant, Eddie.  Anne and I’ve been discussing entropy.  Which is an elephant because it’s got so many aspects no-one can agree on what it is.”

“So it’s got to do with luck?”

“With counting possibilities.  Suppose you know something happened, but there’s lots of ways it could have happened.  You don’t know which one it was.  Entropy is a way to measure what’s left to know.”

“Like what?”

“Those dice are an easy example.  You throw the pair, they land in any of 36 different ways, but you don’t know which until you look, right?”

Dice odds

“Yeah, sure.  So?”

“So your uncertainty number is 36.  Suppose they show 7.  There’s still half-a-dozen ways that can happen — first die shows 6, second shows 1, or maybe the first die has the 1 and the second has the 6, and so on.  You don’t know which way it happened.  Your uncertainty number’s gone down from 36 to 6.”

“Wait, but I do know something going in.  It’s a lot more likely they’ll show a 7 than snake-eyes.”

“Good point, but you’re talking probability, the ratio of uncertainty numbers.  Half-a-dozen ways to show a 7, divided by 36 ways total, means that 7 comes up seventeen throws out of a hundred.  Three times out of a hundred you’ll get snake-eyes.  Same odds for boxcars.”

“C’mon, Sy, in my neighborhood little babies know those odds.”

“But do the babies know how odds combine?  If you care about one event OR another you add the odds, like 6 times out of a hundred you get snake-eyes OR boxcars.  But if you’re looking at one event AND another one the odds multiply.  How often did you roll those dice just now?”

“Couple of dozen, I guess.”

“Let’s start with three.  Suppose you got snake-eyes AND you got snake-eyes AND you got snake-eyes.  Odds on that would be 3×3×3 out of 100×100×100 or 27 out of a million triple-throws.  Getting snake-eyes or boxcars 24 times in a row, that’s … ummm … less than one chance in a million trillion trillion sets of 24-throws.  Not likely.”

“Don’t know about the numbers, Sy, but there’s something goofy with these dice.”

Anne cuts in.  “Maybe not, Eddie.  Unusual things do happen.  Let me try.”  She gets half-a-dozen 7s in a row, each time a different way.  “Now you try,” and gives him back the dice.  Now he rolls an 8, 9, 10, 11 and 12 in order.  “They’re not loaded.  You’re just living in a low-probability world.”

“Aw, geez.”

“Anyway, Eddie, entropy is a measure of residual possibilities — alternate conditions (like those ways to 7) that give identical results.  Suppose a physicist is working on a system with a defined number of possible states.  If there’s some way to calculate their probabilities, they can be plugged into a well-known formula for calculating the system’s entropy.  The remarkable thing, Anne, is that what you calculate from the formula matches up with the heat capacity entropy.”

“Here’s your gelato, Mr Moire.   Sorry for the delay, but Jennie dropped by and we got to talking.”

Anne and I trade looks.  “That’s OK, Jeremy, I know how that works.”

~~ Rich Olcott

Three Perils for a Quest(ion), Part 3

On By rolcottIn Physics: Black Holes and Relativity, Physics: Quantum Mechanics, UncategorizedLeave a comment

“Things are finally slowing down.  You folks got an interesting talk going, mind if I join you?  I got biscotti.”

“Pull up a chair, Eddie.  You know everybody?”

“You and Jeremy, yeah, but the young lady’s new here.”

“I’m Jennie, visiting from England.”

“Pleased to meetcha.  So from what I overheard, we got Jeremy on some kinda Quest to a black hole’s crust.  He’s passed two Perils.  There’s a final one got something to do with a Firewall.”

“One minor correction, Eddie.  He’s not going to a crust, because a black hole doesn’t have one.  Nothing to stand on or crash into, anyway.  He’s headed to its Event Horizon, which is the next best thing.  If you’re headed inward, the Horizon marks the beginning of where it’s physically impossible to get out.”

“Hotel California, eh?”

“You could say that.  The first two Perils had to do with the black hole’s intense gravitational field.  The one ahead has to do with entangled virtual particles.”

“Entangled is the Lucy-and-Ethel thing you said where two particles coordinate instant-like no matter how far apart they are?”

“Good job of overhearing, there, Eddie.  Jeremy, tell him abut virtual particles.”

“Umm, Mr Moire and I talked about a virtual particle snapping into and out of existence in empty space so quickly that the long-time zero average energy isn’t affected.”

“What we didn’t mention then is that when a virtual pair is created, they’re entangled.  Furthermore, they’re anti-particles, which means that each is the opposite of the other — opposite charge, opposite spin, opposite several other things.  Usually they don’t last long — they just meet each other again and annihilate, which is how the average energy stays at zero.  Now think about creating a pair of virtual particles in the black hole’s intense gravitational field where the creation event sends them in opposite directions.”Astronaut and semi-biscotto
“Umm… if they’re on opposite paths then one’s probably headed into the Horizon and the other is outbound. Is the outbound one Hawking radiation?  Hey, if they’re entangled that means the inbound one still has a quantum connection with the one that escaped!”

“Wait on.  If they’re entangled and something happening to one instantaneously affects its twin, but the gravity difference gives each a different rate of time dilation, how does that work then?”

“Paradox, Jennie!  That’s part of what the Firewall is about.  But it gets worse.  You’d think that inbound particle would add mass to the black hole, right?”

“Surely.”

“But it doesn’t.  In fact, it reduces the object’s mass by exactly each particle’s mass.  That ‘long-time zero average energy‘ rule comes into play here.  If the two are separated and can’t annihilate, then one must have positive energy and the other must have negative energy.  Negative energy means negative mass, because of Einstein’s mass-energy equivalence.  The positive-mass twin escapes as Hawking radiation while the negative-mass twin joins the black hole, shrinks it, and by the way, increases its temperature.”

“Surely not, Sy.  Temperature is average kinetic energy.  Adding negative energy to something has to decrease its temperature.”

“Unless the something is a black hole, Jennie.  Hawking showed that a black hole’s temperature is inversely dependent on its mass.  Reduce the mass, raise the temperature, which is why a very small black hole radiates more intensely than a big one.  Chalk up another paradox.”

“Two paradoxes.  Negative mass makes no sense.  I can’t make a pizza with negative cheese.  People would laugh.”

“Right.  Here’s another.  Suppose you drop some highly-structured object, say a diamond, into a black hole.  Sooner or later, much later really, that diamond’s mass-energy will be radiated back out.  But there’s no relationship between the structure that went in and the randomized particles that come out.  Information loss, which is totally forbidden by thermodynamics.  Another paradox.”

“The Firewall resolves all these paradoxes then?”

“Not really, Jennie.  The notion is that there’s this thin layer of insanely intense energetic interactions, the Firewall, just outside of the Event Horizon.  That energy is supposed to break everything apart — entanglements, pre-existing structures, quantum propagators (don’t ask), everything, so what gets through the horizon is mush.  Many physicists think that’s bogus and a cop-out.”

“So no Firewall Peril?”

“Wanna take the chance?”

~~ Rich Olcott

Three Perils for a Quest(ion), Part 2

On By rolcottIn Physics: Black Holes and Relativity, Physics: Quantum Mechanics, UncategorizedLeave a comment

Eddie came over to our table.  “Either you folks order something else or I’ll have to charge you rent.”  Typical Eddie.

“Banana splits sound good to you two?”

[Jeremy and Jennie] “Sure.”

“OK, Eddie, two banana splits, plus a coffee, black, for me.  And an almond biscotti.”

“You want one, that’s a biscotto.”

“OK, a biscotto, Eddie.  The desserts are on my tab.”

“Thanks, Mr Moire.”

“Thanks, Sy.  I know you want to get on to the third Peril on Jeremy’s Quest for black hole evaporation, but how does he get past the Photon Sphere?”

“Yeah, how?”

“Frankly, Jeremy, the only way I can think of is to accept a little risk and go through it really fast.  At 2/3 lightspeed, for instance, you and your two-meter-tall suit would transit that zero-thickness boundary in about 10 nanoseconds.  In such a short time your atoms won’t get much out of position before the electromagnetic fields that hold your molecules together kick back in again.”

“OK, I’ve passed through.  On to the Firewall … but what is it?”

“An object of contention, for one thing.  A lot of physicists don’t believe it exists, but some claim there’s evidence for it in the 2015 LIGO observations.  It was proposed a few years ago as a way out of some paradoxes.”

“Ooo, Paradoxes — loverly.  What’re the paradoxes then?”

“Collisions between some of the fundamental principles of Physics-As-We-Know-It.  One goes back to the Greeks — the idea that the same thing can’t be in two places at once.”

“Tell me about it.  Here’s your desserts.”

“Thanks, Eddie.  The place keeping you busy, eh?”

“Oh, yeah.  Gotta be in the kitchen, gotta be runnin’ tables, all the time.”

“I could do wait-staff, Mr G.  I’m thinking of dropping track anyway, Mr Moire, 5K’s don’t have much in common with base running which is what I care about.  How about I show up for work on Monday, Mr G?”

“Kid calls me ‘Mr’ — already I like him.  You’re on, Jeremy.”

“Woo-hoo!  So what’s the link between the Firewall and the Greeks?”

“Link is the right word, though the technical term is entanglement.  If you create two particles in a single event they seem to be linked together in a way that really bothered Einstein.”

“For example?”Astronaut and biscotti
“Polarizing sunglasses.  They depend on a light wave’s crosswise electric field running either up-and-down or side-to-side.  Light bouncing off water or road surface is predominately side-to-side polarized, so sunglasses are designed to block that kind.  Imagine doing an experiment that creates a pair of photons named Lucy and Ethel.  Because of how the experiment is set up, the two must have complementary polarizations.  You confront Lucy with a side-to-side filter.  That photon gets through, therefore Ethel should be blocked by a side-to-side filter but should go through an up-and-down filter.  That’s what happens, no surprise.  But suppose your test let Lucy pass an up-and-down filter.  Ethel would pass a side-to-side filter.”

“But Sy, isn’t that because each photon has a specific polarization?”

“Yeah, Jennie, but here’s the weird part — they don’t.  Suppose you confront Lucy with a filter set at some random angle.  There’s only the one photon, no half-way passing, so either it passes or it doesn’t.  Whenever Lucy chooses to pass, Ethel usually passes a filter perpendicular to that one.  It’s like Ethel hears from Lucy what the deal was — and with zero delay, no matter how far away the second test is executed.  It’s as though Lucy and Ethel are a single particle that occupies two different locations.  In fact, that’s exactly how quantum mechanics models the situation.  Quite contrary to the Greeks’ thinking.”

“You said that Einstein didn’t like entanglement, either.  How come?”

“Einstein published the original entanglement mathematics in the 30s as a counterexample against Bohr’s quantum mechanics.  The root of his relativity theories is that the speed of light is a universal speed limit.  If nothing can go faster than light, instantaneous effects like this can’t happen.  Unfortunately, recent experiments proved him wrong.  Somehow, both Relativity and Quantum Mechanics are right, even though they seem to be incompatible.”

“And this collision is why there’s a problem with black hole evaporation?”

“It’s one of the collisions.”

“There’s more?  Loverly.”

~~ Rich Olcott

Three Perils for a Quest(ion), Part 1

On By rolcottIn Physics: Black Holes and Relativity, Physics: Quantum Mechanics, Uncategorized2 Comments

Eddie makes great pizzas but Jeremy thinks they stay in the oven just a little too long.  As he crunched an extra-crispy wedge-edge he mused, “Gravity aside, I wonder what it’d be like to land on a black hole.  I bet it’d be real slippery if it’s as smooth as Mr Moire says.”

Jennie cut in.  “Don’t be daft, lad.  Everyone’s read about the spaceman sliding through the event horizon unaware until it’s too late.  Someone far away sees the bloke’s spacetime getting all distorted but in his local frame of reference everything’s right as rain.  Right, Sy?”

“As rain, Jennie, if all you’re concerned about is relativity.  But Spaceman Jeremy has lots of other things to be concerned about on his way to the event horizon.  Which he couldn’t stand on anyway.”

“Why not, Mr Moire?  I mean, I said ‘gravity aside’ so I ought to be able to stand up.”

“Nothing to stand on, Jeremy.  It’d be like trying to stand on Earth’s orbit.”

“Pull the other one, Sy.  How can they be alike?”

“Both of them are mathematical constructs rather than physical objects.  An orbit is an imaginary line that depicts planet or satellite locations.  An event horizon is an imaginary figure enclosing a region with such intense spacetime curvature that time points inward.  They’re abstract objects, not  concrete ones.  But let’s get back to Jeremy’s black hole evaporation quest.  He’ll have to pass three perils.”

“Ooo, a Quest with Perils —  loverly.  What are the Perils then?”

“The Roche Radius, the Photon Sphere and the Firewall.  Got your armor on, Jeremy?”Astronaut and 3xBlack hole

“Ready, Mr Moire.”

“Stand up.  The Roche effect is all about gravitational discrepancy between two points.  The two meter distance between your head and feet isn’t enough for a perceptible difference in downward pull.  However, when we deal with astronomical distances the differences can get significant.  For instance, ocean water on the day side of Earth is closer to the Sun and experiences a stronger sunward pull than water on the night side.”

“Ah, so that’s why we get tides.”

“Right.  Sit, sit, sit.  So in 1849 Édouard Roche wondered how close two objects could get until tidal forces pulled one of them apart.  He supposed the two objects were both just balls of rocks or fluid held together by gravity.  Applying Newton’s Laws and some approximations he got a formula for threshold distance in terms of the big guy’s mass and the little guy’s density.  Suppose you’re held together only by gravity and you’re nearing the Sun feet-first.  Its mass is 2×1030 kg/m³.  Even including your space armor, your average density is about 1.5 kg/m³.  According to Roche’s formula, if you got closer than 8.6×106 kilometers your feet would break away and fall into the Sun before the rest of you would.  Oh, that distance is about 1/7 the radius of Mercury’s orbit so it’s pretty close in.”

“But we’re talking black holes here.  What if the Sun collapses to a black hole?”

“Surprisingly, it’s exactly the same distance.  The primary’s operative property is its mass, not its diameter.  Good thing Jeremy’s really held together by atomic and molecular electromagnetism, which is much stronger than gravity.  Which brings us to his second Peril, the dreaded Photon Sphere.”

“Should I shudder, Sy?”

“Go ahead, Jennie.  The Sphere is another mathematical object, not something physical you’d collide with, Jeremy.  It’s a zero-thickness shell representing where electromagnetic waves can orbit a massive object like a black hole or a neutron star.  Waves can penetrate the shell easily in either direction, but if one happens to fly in exactly along a tangent, it’s trapped on the Sphere.”

“That’s photons.  Why is it a peril to me?”

“Remember that electromagnetism that holds you together?  Photons carry that force.  Granted, in a molecule they’re standing waves rather than the free waves we see with.  The math is impossible, but here’s the Peril.  Suppose one of your particularly important molecules happens to lie tangent to the Sphere while you’re traversing it.  Suddenly, the forces holding that molecule together fly away from you at the speed of light.  And that disruption inexorably travels along your body as you proceed on your Quest.”

[both shudder]

~~ Rich Olcott

The Thin Edge of Infinity

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

Late in the day, project’s half done but it’s hungry time.  I could head home for a meal and drive back, but instead I board the elevator down to Eddie’s Pizza on the second floor.  The door opens on 8 and Jeremy gets on, with a girl.

“Oh, hi, Mr. Moire.  Didja see I hit a triple in the last game?  What if the Sun became a black hole?  This is that English girl I told you about.”

“Hello, Jennie.”

“Wotcha, Sy.”

“You know each other?”

“Ra-ther.  He wrote me into his blog a year ago.  You were going on about particles then, right, Sy?”

“Right, Jennie, but that was particles confined in atoms.  Jeremy’s interested in larger prey.”

“So I hear.”

The elevator lets us out at Eddie’s place.  We luck into a table, order and resume talking.  I open with, “What’s a particle?”

“Well, Sy, your post with Jeremy says it’s an abstract point with a minimal set of properties, like mass and charge, in a mathematical model of a real object with just that set of properties.”

“Ah, you’ve been reading my stuff.  That simplifies things.  So when can we treat a black hole like a particle?  Did you see anything about that in my archives, Jennie?”

“The nearest I can recall was Professor ‘t Hooft’s statement.  Ermm… if the Sun’s so far away that we can calculate planetary orbits accurately by treating it as a point, then we’re justified in doing so.”

“And if the Sun were to suddenly collapse to a black hole?”

“It’d be a lot smaller, even more like a point.  No change in gravity then.  But wouldn’t Earth be caught up in relativity effects like space compression?’

“Not unless you’re really close.  Space compression around a non-rotating (Schwarzchild) black hole scales by a factor that looks like Schwarzchild factor, where D is the object’s diameter and d is your distance from it.  Suppose the Sun suddenly collapsed without losing any mass to become a Schwarzchild object.  The object’s diameter would be a bit less than 4 miles.  Earth is 93 million miles from the Sun so the compression factor here would be [poking numbers into my smartphone] 1.000_000_04.  Nothing you’d notice.  It’d be 1.000_000_10 at Mercury.  You wouldn’t see even 1% compression until you got as close as 378 miles, 10% only inside of 43 miles.  Fifty percent of the effect shows up in the last 13 miles.  The edge of a black hole is sharper than this pizza knife.”Knife-edges

“How about if it’s spinning?  Ms Plenum referred me to a reading about frame-dragging.”

“Ah, Jeremy, you’re thinking of Gargantua, the Interstellar movie’s strangely lopsided black hole.  I just ran across this report by Robbie Gonzalez.  He goes into detail on why the image is that way, and why it should have looked more like this picture.  Check out the blueshift on the left and the shift into the infra-red on the right.”

better Gargantua
A more accurate depiction of Gargantua.  Image from
James, et al., Class. Quantum Grav. 32 (2015) 065001 (41pp),
licensed under CC BY-NC-ND 3.0

[both] “Awesome!”

“So it’s the spin making the weirdness then, Sy?”

“Yes, ma’am.  If Gargantua weren’t rotating, then the space around it would be perfectly spherical.  As Gonzalez explains, the movie’s plotline needed an even more extreme spacetime distortion than they could get from that.  Dr Kip Thorne, their physics guru, added more by spinning his mathematical model nearly up to the physical limit.”

“I’ll bite, Mr Moire.  What’s the limit?”

“Rotating so fast that points on the equator would be going at lightspeed.  Can’t do that.  Anyhow, extreme spin alters spacetime distortion, which goes from spherical to pumpkin-shaped with a twist.  The radial scaling changes form, too, from Schwarzchild factor to Kerr factor.  A is proportional to spin.  When A is small (not much spin) or the distance is large those A/d² terms essentially vanish relative to the others and the scaling looks just like the simple almost-a-point Schwarzchild case.  When A is large or the distance is small the A/d² terms dominate top and bottom, the factor equals 1 and there’s dragging but no compression.  In the middle, things get interesting and that’s where Dr Thorne played.”

“So no relativity jolt to Earth.”

“Yep.”

“Here’s your pizzas.”

“Thanks, Eddie.”

[sounds of disappearing pizza]

~~ Rich Olcott

No-hair today, grown tomorrow

On By rolcottIn Physics: Black Holes and Relativity, Physics: Quantum Mechanics, UncategorizedLeave a comment

It was a classic May day, perfect for some time by the lake in the park.  I was watching the geese when a squadron of runners stampeded by.   One of them broke stride, dashed my way and plopped down on the bench beside me.  “Hi, Mr Moire. <pant, pant>”

“Afternoon, Jeremy.  How are things?”

“Moving along, sir.  I’ve signed up for track, I think it’ll help my base-running,  I’ve met a new girl, she’s British, and that virtual particle stuff is cool but I’m having trouble fitting it into my black hole paper.”

“Here’s one angle.  Nobelist Gerard ‘t Hooft said, ‘A particle is fundamental when it’s useful to think of it as fundamental.‘  In that sense, a black hole is a fundamental particle.  Even more elementary than atoms, come to think of it.”

“Huh?”

“It has to do with the how few numbers you need to completely specify the particle.  You’d need a gazillion terabytes for just the temperatures in the interior and oceans and atmosphere of Earth.  But if you’re making a complete description of an isolated atom you just need about two dozen numbers — three for position, three for linear momentum, one for atomic number (to identify which element it represents), one for its atomic weight (which isotope), one for its net charge if it’s been ionized, four more for nuclear and electronic spin states, maybe three or four each for the energy levels of its nuclear and electronic configuration.  So an atom is simpler than the Earth”

“And for a black hole?”

“Even simpler.  A black hole’s event horizon is smooth, so smooth that you can’t distinguish one point from another.  Therefore, no geography numbers.  Furthermore, the physics we know about says whatever’s inside that horizon is completely sealed off from the rest of the universe.  We can’t have knowledge of the contents, so we can’t use any numbers to describe it.  It’s been proven (well, almost proven) that a black hole can be completely specified with only eleven numbers — one for its total mass-energy, one for its electric charge, and three each for position, linear momentum and angular momentum.  Leave out the location and orientation information and you’ve got three numbers — mass, charge, and spin.  That’s it.”

“How about its size or it temperature?”

“Depends how you measure size.  Event horizons are spherical or nearly so, but the equations say the distance from an event horizon to where you’d think its center should be is literally infinite.  You can’t quantify a horizon’s radius, but its diameter and surface area are both well-defined.  You can calculate both of them from the mass.  That goes for the temperature, too.”

“How about if it came from antimatter instead of matter?”

“Makes no difference because the gravitational stresses just tear atoms apart.”

“Wait, you said, ‘almost proven.’  What’s that about?”no hair 1

“Believe it or not, the proof is called The No-hair Theorem.  The ‘almost’ has to do with the proof’s starting assumptions.  In the simplest case, zero change and zero spin and nothing else in the Universe, you’ve got a Schwarzchild object.  The theorem’s been rigorously proven for that case — the event horizon must be perfectly spherical with no irregularities — ‘no hair’ as one balding physicist put it.”

“How about if the object spins and gets charged up, or how about if a planet or star or something falls into it?”

“Adding non-zero spin and charge makes it a Kerr-Newman object.  The theorem’s been rigorously proven for those, too.  Even an individual infalling mass has only a temporary effect.  The black hole might experience transient wrinkling but we’re guaranteed that the energy will either be radiated away as a gravitational pulse or else simply absorbed to make the object a little bigger.  Either way the event horizon goes smooth and hairless.”

“So where’s the ‘almost’ come in?”

“Reality.  The region near a real black hole is cluttered with other stuff.  You’ve seen artwork showing an accretion disk looking like Saturn’s rings around a black hole.  The material in the disk distorts what would otherwise be a spherical gravitational field.  That gnarly field’s too hairy for rigorous proofs, so far.  And then Hawking pointed out the particle fuzz…”

~~ Rich Olcott

Baseball And The Virtual Particle

On By rolcottIn Physics: Quantum Mechanics, UncategorizedLeave a comment

Al was pouring my mugful of his morning blend (“If it doesn’t wake you up we’ll call the doctor“) when Jeremy stepped into the counter.  “Hi, Mr Moire.  I’m still trying to get my head around that virtual particle thing.  Hi, Al, a large decaf, please, double sugar, three creamers.  It looks like the shorter amount of time you give a particle to happen, the bigger it can get, but that doesn’t make sense because I’d think the longer you wait the more likely it’s gonna happen.  Thanks, Al.”

“Take a breath to blow on that coffee, Jeremy, or you’ll burn your tongue.  Hmm…  Word is your batting average is running about 250 these days.  That right?”

“Yessir.  I didn’t know you’re keeping track.”

“Keeping my ears open is part of my job.  So you’re hitting about once every four at-bats.  That gives Coach an estimate of when you’ll get your next hit.  What’s your slugging average?”

“What’s a slugging average?”

“Your total number of batted-on bases, divided by your at-bats, times a thousand ’cause sports writers don’t do decimal points.  You get one count in the numerator for a single, two for a double and so on.”

“Lemme think.  If I’m doing 250 overall and about half are singles and the other half are doubles that’d give me an SA of … about 375.”

“Pretty good.  So does that number tell Coach anything about when to expect another double?”

“Mmm, no, but what does that have to do with my virtual particle question?”

“In each case you’ve got a pair of statistics that tell you some things and hide other things.  Batting averages and your wait-time notion are about when to expect an event of some sort to occur.  You could hit another single or you could tag a homer — all Coach knows is that you should be able to get on base about once every four at-bats.”

“What about the other statistics?”

“They’re the flip side, sort of.  You could think of the SA as batting potential.  If you hit homers all the time your SA would be 4000.  If you whiff every pitch your SA would be zero.  Anything between those extremes tells Coach something about your productivity but nothing about when you’re going to produce.  Energy uncertainty works the same way for virtual particles.  If you’re doing long-duration energy evaluations you can be pretty sure that any single measurement will be close to the long-term average.  You might possibly see a significant deviation from that average but only if you check just the right brief interval.”Virtual baseball

“And for the particles in that empty space?”

“If you’re looking long-term, no particles.  That’s what ’empty’ means.  When there’s definitely nothing in a volume of space it makes sense to say its energy is zero because particles have mass and therefore embody energy.  But a particle might show up and go away after a very brief interval without significantly affecting that long-term average.  Quantum theory doesn’t say it will show up, just that it might.”

“So does it?”

“Oh yes, in space, in the lab and in commerce.  One explanation for your cell phone’s NFC function hinges on virtual radio-frequency photons being exchanged between devices.”

“Wait.  If a virtual particle shows up in that empty space, then it’s not empty any more and its energy isn’t zero any more, is it?”

“You’ve just discovered one aspect of zero-point energy, the quantum prediction that every system, even empty space, contains a non-zero minimum amount of energy.  People have thought about tapping that energy to power perpetual motion machines.”

“That’d be cool — the ultimate renewable.”

“Wouldn’t it, though?  But no can do, for a couple of reasons.  Virtual particles, by their nature, are random phenomena.  You can’t depend upon what kind of particle might show up, or when, nor how long it might hang around.  It’s not like NFC where antennas generate the particles.  The other issue is that ‘minimum’ means minimum.  If you could pull energy out of that space you’d lower its energy content and drop it below the minimum…. What’s the grin about?”

“Just wondering how they’d score hitting a virtual ball that disappears before the fielder catches it.”

~~ Rich Olcott

Virtualosity

On By rolcottIn Physics: Quantum Mechanics, UncategorizedLeave a comment

No knock, the door just opened suddenly.

“Hello, Jeremy.  Rule of Three?”

“Huh?  No, I was down the hall just now when I saw you go into your office so I knew you hadn’t gotten busy with something yet.  Sir.  What’s the Rule of Three?”

“Never mind.  You’re up here about virtual particles, I guess.”

“Yessir.  You said they’re ‘now you might see them, now you probably don’t.’  What’s that about and what do they have to do with abstraction and Einstein’s ‘underlying reality’?”

“What have you heard about Heisenberg’s Uncertainty Principle?”

“Ms Plenum says you can’t know where you are and how fast you’re going.”

“Ms Plenum’s got part of the usual notion but she’s missing the idea of simultaneous precision and a few other things.  Turns out you CAN know approximately where you are AND approximately how fast you’re going at a particular moment, but you can’t know both things precisely.  There’s going to be some imprecision in both measurements.  Think about Coach using a radar gun to track a thrown baseball.  How does radar work?”

“It bounces a light beam off of something and measures the light’s round-trip travel time.  I suppose it multiplies by the speed of light to convert time to distance.”

“Good.  Now how does it get the ball’s speed?”

“Uhh… probably uses two light pulses a certain time apart and calculates the speed as distance difference divided by time difference.”

“Got it in one.  Now, suppose that a second after the ball’s thrown the radar says the ball is 61 feet away from the plate and traveling at 92 mph.  Air resistance acts to slow the ball’s flight so that 92 is really an average.   Maybe it was going 92.1 mph at the first radar pulse and 91.9 mph at the second pulse.  So that reported speed has an 0.2 mph range of uncertainty.”

“Oh, and neither of the two pulses caught the ball at exactly 61 feet so that’s uncertain, too, right?”

“There you go.  We know the two averages, but each of them has a range.  The Uncertainty Principle says that the product of those two ranges has to be greater than Planck’s constant, 10-34 Joule·second.  Plugging that Joule-fraction and the mass of an electron into Einstein’s E=mc², we restate the constant as about 10-21 of an electron-second.  Those are both teeny numbers — but they’re not zero.”

“So speed and location make an uncertainty pair.  Are there others?”Zebras“A few.  The most important for this discussion is energy and time.”

“Wait a minute, those two can’t be linked that way.”

“Why not?”

“Well, because … umm … speed is change of location so those two go together, but energy isn’t change of time.  Time just … goes, and adding energy won’t make it go faster.”

“As a matter of fact, there are situations where adding energy makes time go slower, but that’s a couple of stories for another day.  What we’re talking about here is uncertainty ranges and how they combine.  Quantum theory says that if a given particle has a certain energy, give or take an energy range, and it retains that energy for a certain duration, give or take a time range, then the product of the two ranges has to be larger than that same Planck constant.   Think about a 1-meter cube of empty space out there somewhere.  Got it?

“Sure.”

“Suppose a particle appeared and then vanished somewhere in that cube sometime during a 1-second interval.  What’s the longest time that particle could have existed?”

“Easy — one second.”

“How about the shortest time?”

“Zero.  Wait, it’d be the smallest possible non-zero time, wouldn’t it?”

“Good catch.  So what’s the time uncertainty?”

“One second minus that tiniest bit of time.”

“And what’s the corresponding energy range?”

“That constant number that I forget.”

“10-21 electron-second’s worth.  Now let’s pick a shorter interval.  What’s the mass range for a particle that appears and disappears sometime during the 10-19 second it takes a photon to cross a hydrogen atom?”

“That’s 10-21 electron-second divided by 10-19 second, so it’d be, like, 0.01 electron.”

“How about 1% of that 10-19 second?”

“Wow — that’d be a whole electron.”

“A whole electron’s worth of uncertainty.  But is the electron really there?”

“Probably not, huh?”

“Like I said, ‘Now you probably don’t’.”

~~ Rich Olcott

Abstract Horses

On By rolcottIn Physics: Einstein, Physics: Newton and Gravity, Physics: Quantum Mechanics, UncategorizedLeave a comment

It was a young man’s knock, eager and a bit less hesitant than his first visit.

“C’mon in, Jeremy, the door’s open.”

“Hi, Mr Moire, it’s me, Jerem…  How did ..?  Never mind.  Ready for my black hole questions?”

“I’ll do what I can, Jeremy, but mind you, even the cosmologists are still having a hard time understanding them.  What’s your first question?”

“I read where nothing can escape a black hole, not even light, but Hawking radiation does come out because of virtual particles and what’s that about?”

“That’s a very lumpy question.  Let’s unwrap it one layer at a time.  What’s a particle?”

“A little teeny bit of something that floats in the air and you don’t want to breathe it because it can give you cancer or something.”

“That, too, but we’re talking physics here.  The physics notion of a particle came from Newton.  He invented it on the way to his Law of Gravity and calculating the Moon’s orbit around the Earth.  He realized that he didn’t need to know what the Moon is made of or what color it is.  Same thing for the Earth — he didn’t need to account for the Earth’s temperature or the length of its day.  He didn’t even need to worry about whether either body was spherical.  His results showed he could make valid predictions by pretending that the Earth and the Moon were simply massive points floating in space.”

“Accio abstractify!  So that’s what a physics particle is?”

“Yup, just something that has mass and location and maybe a velocity.  That’s all you need to know to do motion calculations, unless the distance between the objects is comparable to their sizes, or they’ve got an electrical charge, or they move near lightspeed, or they’re so small that quantum effects come into play.  All other properties are irrelevant.”

“So that’s why he said that the Moon was attracted to Earth like the apple that fell on his head was — in his mind they were both just particles.”

“You got it, except that apple probably didn’t exist.”

“Whatever.  But what about virtual particles?  Do they have anything to do with VR goggles and like that?”

“Very little.  The Laws of Physics are optional inside a computer-controlled ‘reality.’  Virtual people can fly, flow of virtual time is arbitrary, virtual electrical forces can be made weaker or stronger than virtual gravity, whatever the programmers decide will further the narrative.  But virtual particles are much stranger than that.”

“Aw, they can’t be stranger than Minecraft.  Have you seen those zombie and skeleton horses?”Horses

“Yeah, actually, I have.  My niece plays Minecraft.  But at least those horses hang around.  Virtual particles are now you might see them, now you probably don’t.  They’re part of why quantum mechanics gave Einstein the willies.”

“Quantum mechanics comes into it?  Cool!  But what was Einstein’s problem?  Didn’t he invent quantum theory in the first place?”

“Oh, he was definitely one of the early leaders, along with Bohr, Heisenberg, Schrödinger and that lot.  But he was uncomfortable with how the community interpreted Schrödinger’s wave equation.  His row with Bohr was particularly intense, and there’s reason to believe that Bohr never properly understood the point that Einstein was trying to make.”

“Sounds like me and my Dad.  So what was Einstein’s point?”

“Basically, it’s that the quantum equations are about particles in Newton’s sense.  They lead to extremely accurate predictions of experimental results, but there’s a lot of abstraction on the way to those concrete results.  In the same way that Newton reduced Earth and Moon to mathematical objects, physicists reduced electrons and atomic nuclei to mathematical objects.”

“So they leave out stuff like what the Earth and Moon are made of.  Kinda.”

“Exactly.  Bohr’s interpretation was that quantum equations are statistical, that they give averages and relative probabilities –”

“– Like Schrödinger’s cat being alive AND dead –”

“– right, and Einstein’s question was, ‘Averages of what?‘  He felt that quantum theory’s statistical waves summarize underlying goings-on like ocean waves summarize what water molecules do.  Maybe quantum theory’s underlying layer is more particles.”

“Are those the virtual particles?”

“We’re almost there, but I’ve got an appointment.  Bye.”

“Sure.  Uhh… bye.”

~~ Rich Olcott

Wikipedia Skillz

On By rolcottIn General: Serious Stuff, UncategorizedLeave a comment

A young man’s knock, eager yet a bit hesitant.

“C’mon in, the door’s open.”

Tall kid, glasses, hoodie thrown back.

“Hi, Mr Moire, can I ask you some questions?  I’m doing a term paper on black holes and I’ve read up on in Wikipedia but there’s things I don’t understand and besides Ms Plenum said not to trust Wikipedia.”

“Hold on, son, let’s get acquainted first.  You are…?”

“My name’s Jeremy Yazzie, sir, and I’m like Richard Feynman’s archetypical intelligent high school student he wanted to explain things to except he gave up on particle spin.”

“Well, you have done your homework, though you’ve muddled a couple of his quotes.  But about Wikipedia — Ms Plenum’s mostly right but in my experience the technical articles are pretty dependable.  Those writers are usually more interested in explaining than convincing.  Have you checked Wikipedia’s Talk pages?”

“There’s, like, comments?”

“Sort of, except Talk pages lie behind articles and target what’s right or wrong and what should be changed to make the article better.  I often learn as much from the technical discussion as I do from the article itself.”

wikieyes
A riff on Wikipedia’s logo, original in Wikimedia Commons

“I’ve never seen those pages.  How do I get to them?”

“You need a desktop view.  That’s the standard view when you use a desktop or laptop computer, but you can only maybe get to it on a handheld device.  Depends on the device, the browser, and even their maintenance levels.  Do you have a handheld in that backpack?”

“Yeah, an iPad.”

“Safari, Firefox and Chrome can all show that other view.”

“I’ve got all three.”

“Great, pull up Chrome, get to Wikipedia and look up ‘Black hole.'”

… “Got it.  Uhh… don’t see anything about a Talk page.”

“You’re looking at ‘mobile mode.’  See that three-dots icon at the top right?  Tap on it and check the pop-up menu.”

“Hah, here’s one that says, Request Desktop Site.  I’ll tap on that.  Hey, now I’ve got tabs above the text, one says Article and another that says Talk.  Whoa, here’s one that says View Source.  Whups, now there’s a box that says I can start editing.  Better not, huh?  How do I get out of that?”

“Tap your browser’s backup button.  By the way, even though in principle anyone can edit any article, the Wikipedia moderators have locked down some of the most popular or controversial just to prevent update wars.  This article’s one of those.”

“Yeah, I just backed up then tried View Source again and it says I’m not an established registered user.  No duh, right?  OK, lessee what’s in the Talk page.  Umm, how-to stuff and then organization stuff and then, huh! ‘this article has been rated GA-class on the quality scale.’ People come around and, like, check your work?”

“Absolutely, which is why I think Ms Plenum’s advice is a little too pessimistic.  Trust but verify — if you see something you’d like to quote but you don’t want to look foolish, double-check with another source.  But on the whole I’ve found the science, math and other technical articles to be trustworthy.”

“Aha, the first set of comments is about my questions, Hawking radiation and how black holes evaporate and what are virtual particles and like that.”

“So many questions, so little time.  Let’s finish off with the browser issue before we dive into physics.  Bring up your Firefox browser on that iPad.”

“All right.  Mmm, I’m going to Wikipedia, and I’m searching for ‘Black hole’ … got it, but the display doesn’t have tabs or a three-dot icon.”

“Firefox has two ways to get to desktop mode.  One way is to tap the three-bar icon at the top right…”

“YESS! the pop-up menu has half-a-dozen options and there’s Request Desktop Site.  Hey, it toggles, I can flip modes back and forth.  Sweet!  What’s the other way?”

“Press-and-hold the reload circle-arrow in the address bar.”

“A-hah, that opens a Request Desktop Site button right under the arrow.  Cool, that’s a toggle, too.  How does Safari handle this stuff?”

“They use the reload circle-arrow ploy, same as Firefox, dunno who did it first.”

“Oops, late for class.  Seeya.”

“Don’t mention it.”

~~ Rich Olcott