Prelude to A Waltz

An excited knock, but one I recognize.  In comes Vinnie, waving his fresh copy of The New York Times.

LIGO‘s done it again!  They’ve seen another black hole collision!”

“Yeah, Vinnie, I’ve read the Abbott-and-a-thousand paper.  Three catastrophic collisions detected in less than two years.  The Universe is starting to look like a pretty busy place, isn’t it?”

“And they all involve really big black holes — 15, 20, even 30 times heavier than the Sun.  Didn’t you once say black holes that size couldn’t exist?”

“Well, apparently they do.  Of course the physicists are busily theorizing how that can happen.  What do you know about how stars work, Vinnie?”

“They get energy from fusing hydrogen atoms to make helium atoms.”

“So far, so good, but then what happens when the hydrogen’s used up?”

“They go out, I guess.”

“Oh, it’s a lot more exciting than that. Does the fusion reaction happen everywhere in the star?”

“I woulda said, ‘Yes,’ but since you’re asking I’ll bet the answer is,  ‘No.'”

“Properly suspicious, and you’re right.  It takes a lot of heat and pressure to force a couple of positive nuclei close enough to fuse together despite charge repulsion.  Pressures near the outer layers are way too low for that.  For our Sun, for instance, you need to be 70% of the way to the center before fusion really kicks in.  So you’ve got radiation pressure from the fusion pushing everything outward and gravity pulling everything toward the center.  But what’s down there?  Here’s a hint — hydrogen’s atomic weight is 1, helium’s is 4.”

“You’re telling me that the heavier atoms sink to the center?”

“I am.”

“So the center builds up a lot of helium.  Oh, wait, helium atoms got two protons in there so it’s got to be harder to mash them together than mashing hydrogens, right?”Star zones
“And that’s why that region’s marked ash zone in this sketch.  Wherever conditions are right for hydrogen fusion, helium’s basically inert.  Like ash in a campfire it just sinks out of the way.  Now the fire goes out.  What would you expect next?”

“Radiation pressure’s gone but gravity’s still there … everything must slam inwards.”

Slam is an excellent word choice, even though the star’s radius is measured in thousands of miles.  What’s the slam going to do to the helium atoms?”

“Is it strong enough to start helium fusion?”

“That’s where I’m going.  The star starts fusing helium at its core.  That’s a much hotter reaction than hydrogen’s.  When convective zone hydrogen that’s still falling inward meets fresh outbound radiation pressure, most of the hydrogen gets blasted away.”

“Fusing helium – that’s a new one on me.  What’s that make?”

“Carbon and oxygen, mostly.  They’re as inert during the helium-fusion phase as helium was when hydrogen was doing its thing.”

“So will the star do another nova cycle?”

“Maybe.  Depends on the core’s mass.  Its gravity may not be intense enough to fuse helium’s ashes.  In that case you wind up with a white dwarf, which just sits there cooling off for billions of years.  That’s what the Sun will do.”

“But suppose the star’s heavy enough to burn those ashes…”

“The core’s fresh light-up blows away infalling convective zone material.  The core makes even heavier atoms.  Given enough fuel, the sequence repeats, cycling faster and faster until it gets to iron.  At each stage the star has less mass than before its explosion but the residual core is more dense and its gravity field is more intense.  The process may stop at a neutron star, but if there was enough fuel to start with, you get a black hole.”

“That’s the theory that accounts for the Sun-size black holes?”

“Pretty much.  I’ve left out lots of details, of course.  But it doesn’t account for black holes the size of 30 Suns — really big stars go supernova and throw away so much of their mass they miss the black-hole sweet spot and terminate as a neutron star or white dwarf.  That’s where the new LIGO observation comes in.  It may have clued us in on how those big guys happen.”

“That sketch looks like a pizza slice.”

“You’re thinking dinner, right?”

“Yeah, and it’s your turn to buy.”

~~ Rich Olcott

Three Perils for a Quest(ion), Part 3

“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

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

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

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 scaling, 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 scaling to Kerr scalingA 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

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

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