Category: Physics: Quantum Mechanics

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

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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

No-hair today, grown tomorrow

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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

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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

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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

LIGO and lambda and photons, oh my!

On By rolcottIn Astronomy: Multi-messenger, Gravitational astronomy, Physics: Black Holes and Relativity, Physics: Light and Relativity, Physics: Quantum Mechanics, UncategorizedLeave a comment

I was walking my daily constitutional when Al waved me into his coffee shop.  “Sy, he’s at it again with the paper napkins.  Do something!”

I looked over.  There was Vinnie at his table, barricaded behind a pile of crumpled-up paper.  I grabbed a chair.

“Morning, Vinnie.  Having fun?”

“Greek letters.  Why’d they have to use Greek letters?”

The question was both rhetorical and derivative so I ignored it.  There were opened books under the barricade — upper-level physics texts.  “How come you’re chasing through those books?”

“I wanted to follow up on how LIGO operates with photons after we talked about all that space shuttle stuff.  But geez, Sy!”

“You’re a brave man, Vinnie.  So,  which letters are giving you trouble?”

“These two, that look kinda like each other upside down.” He pointed to one equation, λ=c/ν.

“Ah, wavelength equals the speed of light divided by the frequency.”

“How do you do that?”

“Some of those symbols go way back.  You just get used to them.  Most of them make sense when you learn the names for the letters — lambda (λ) is the peak-to-peak length of a lightwave, and nu (ν) is the number of peaks per second.  If it makes you feel any better, I’ve yet to meet a physicist who can write a zeta (ζ) — they generally just draw a squiggle and move on.”

“And there’s this other equation,” pointing to E=h·ν.  “What’s that about?”

“Good eye.  You just picked two equations that are fundamental to LIGO’s operation.  If a lightwave has frequency ν, the equations tell us two things about it — its energy is h·ν (h is Planck’s constant, 6.6×10-34 Joule-seconds), and its wavelength is c/ν (c is the speed of light).  For instance, yellow light has a frequency near 520×1012/sec.  One photon carries 3.8×10-40 Joules of energy.  Not much, but it adds up when a light beam contains lots of photons.  The same photon has a wavelength near 580×10-9 meters traveling through free space.”

“So what happens when one of those photons is in a LIGO beam?  Won’t a gravitational wave’s stretch-and-squeeze action mess up its wave?”

paper-napkin-waveI smoothed out one of Vinnie’s crumpled napkins. As I folded it into pleats and scooted it along the table I said, “Doesn’t mess up the wave so much as change the way we think about it.  We’re used to graphing out a spatial wave as an up-and-down pattern like this that moves through time, right?”

“That’s a lousy-looking wave.”

time-and-space-and-napkin
As the napkin moves through space,
the upper graph shows the height of its edge
above the observation point.

“It’s a paper napkin, f’pitysake, and I’m making a point here. Watch close.  If you monitor a particular point along the wave’s path in space and track how that point moves in time, you get the same profile except we draw it along the t-axis instead of along a space-axis.  See?”

“Hey, the time profile is the space profile going backwards.  Oh, right, it’s goin’ into the past ’cause it’s a memory.”

“That’s one of those things that people miss.  If you only draw sine waves, they’re the same in either direction.  The important point is that although timewaves and spacewaves have the same shape, they’ve got different meanings.  The timewave is directly connected to the wave’s energy by that E equation.  The spacewave is indirectly connected, because your other equation there scales it by the local speed of light.”

“Come again?  Local speed of light?  I thought it was 186,000 miles per second everywhere.”

“It is, but some of those miles are shorter than others.  Near a heavy mass, for instance, or in the compression phase of a gravitational wave, or inside a transparent material.  If you’re traveling in the lightwave’s inertial frame, you see no variation.  But if you’re watching from an independent inertial frame, you see the lightwave hit a slow patch.  Distance per cycle gets shorter.  Like that lambda-nu equation says, when c gets smaller the wavelength decreases.”

Al walked over.  “Gotcha a present, Vinnie.  Here’s a pad of yellow writing paper.  No more napkins, OK?”

“Uhh, thanks.”

“Don’t mention it.”

~~ Rich Olcott

Reflections in Einstein’s bubble

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

There’s something peculiar in this earlier post where I embroidered on Einstein’s gambit in his epic battle with Bohr.  Here, I’ll self-plagiarize it for you…

Consider some nebula a million light-years away.  A million years ago an electron wobbled in the nebular cloud, generating a spherical electromagnetic wave that expanded at light-speed throughout the Universe.

Last night you got a glimpse of the nebula when that lightwave encountered a retinal cell in your eye.  Instantly, all of the wave’s energy, acting as a photon, energized a single electron in your retina.  That particular lightwave ceased to be active elsewhere in your eye or anywhere else on that million-light-year spherical shell.

Suppose that photon was yellow light, smack in the middle of the optical spectrum.  Its wavelength, about 580nm, says that the single far-away electron gave its spherical wave about 2.1eV (3.4×10-19 joules) of energy.  By the time it hit your eye that energy was spread over an area of a trillion square lightyears.  Your retinal cell’s cross-section is about 3 square micrometers so the cell can intercept only a teeny fraction of the wavefront.  Multiplying the wave’s energy by that fraction, I calculated that the cell should be able to collect only 10-75 joules.  You’d get that amount of energy from a 100W yellow light bulb that flashed for 10-73 seconds.  Like you’d notice.

But that microminiscule blink isn’t what you saw.  You saw one full photon-worth of yellow light, all 2.1eV of it, with no dilution by expansion.  Water waves sure don’t work that way, thank Heavens, or we’d be tsunami’d several times a day by earthquakes occurring near some ocean somewhere.

Feynman diagramHere we have a Feynman diagram, named for the Nobel-winning (1965) physicist who invented it and much else.  The diagram plots out the transaction we just discussed.  Not a conventional x-y plot, it shows Space, Time and particles.  To the left, that far-away electron emits a photon signified by the yellow wiggly line.  The photon has momentum so the electron must recoil away from it.

The photon proceeds on its million-lightyear journey across the diagram.  When it encounters that electron in your eye, the photon is immediately and completely converted to electron energy and momentum.

Here’s the thing.  This megayear Feynman diagram and the numbers behind it are identical to what you’d draw for the same kind of yellow-light electron-photon-electron interaction but across just a one-millimeter gap.

It’s an essential part of the quantum formalism — the amount of energy in a given transition is independent of the mechanical details (what the electrons were doing when the photon was emitted/absorbed, the photon’s route and trip time, which other atoms are in either neighborhood, etc.).  All that matters is the system’s starting and ending states.  (In fact, some complicated but legitimate Feynman diagrams let intermediate particles travel faster than lightspeed if they disappear before the process completes.  Hint.)

Because they don’t share a common history our nebular and retinal electrons are not entangled by the usual definition.  Nonetheless, like entanglement this transaction has Action-At-A-Distance stickers all over it.  First, and this was Einstein’s objection, the entire wave function disappears from everywhere in the Universe the instant its energy is delivered to a specific location.  Second, the Feynman calculation describes a time-independent, distance-independent connection between two permanently isolated particles.  Kinda romantic, maybe, but it’d be a boring movie plot.

As Einstein maintained, quantum mechanics is inherently non-local.  In QM change at one location is instantaneously reflected in change elsewhere as if two remote thingies are parts of one thingy whose left hand always knows what its right hand is doing.

Bohr didn’t care but Einstein did because relativity theory is based on geometry which is all about location. In relativity, change here can influence what happens there only by way of light or gravitational waves that travel at lightspeed.

In his book Spooky Action At A Distance, George Musser describes several non-quantum examples of non-locality.  In each case, there’s no signal transmission but somehow there’s a remote status change anyway.  We don’t (yet) know a good mechanism for making that happen.

It all suggests two speed limits, one for light and matter and the other for Einstein’s “deeper reality” beneath quantum mechanics.

~~ Rich Olcott

Is there stuff behind the stats?

On By rolcottIn Physics: Quantum Mechanics, UncategorizedLeave a comment

dragon plate 3It would have been awesome to watch Dragon Princes in battle (from a safe hiding place), but I’d almost rather have witnessed “The Tussles in Brussels,” the two most prominent confrontations between Albert Einstein and Niels Bohr.

The Tussles would be the Fifth (1927) and Seventh (1933) Solvay Conferences.  Each conference was to center on a particular Quantum Mechanics application (“Electrons and Photons” and “The Atomic Nucleus,” respectively).  However, the Einstein-Bohr discussions went right to the fundamentals — exactly what does a QM calculation tell us?

Einstein’s strength was in his physical intuition.  By all accounts he was a good mathematician but not a great one.  However, he was very good indeed at identifying important problems and guiding excellent mathematicians as he and they attacked those problems together.

Einstein 187Like Newton, Einstein was a particle guy.  He based his famous thought experiments on what his intuition told him about how particles would behave in a given situation.  That intuition and that orientation led him to paradoxes such as entanglement, the EPR Paradox, and the instantaneously collapsing spherical lightwave we discussed earlier.  Einstein was convinced that the particles QM workers think about (photons, electrons, etc.) must in fact be manifestations of some deeper, more fine-grained reality.

bohr 187Bohr was six years younger than Einstein.  Both Bohr and Einstein had attained Directorship of an Institute at age 35, but Bohr’s has his name on it.  He started out as a particle guy — his first splash was a trio of papers that treated the hydrogen atom like a one-planet solar system.  But that model ran into serious difficulties for many-electron atoms so Bohr switched his allegiance from particles to Schrödinger’s wave theory.  Solve a Schrödinger equation and you can calculate statistics like average value and estimated spread around the average for a given property (position, momentum, spin, etc).

wittgenstein 187Here’s where Ludwig Wittgenstein may have come into the picture.  Wittgenstein is famous for his telegraphically opaque writing style and for the fact that he spent much of his later life disagreeing with his earlier writings.  His 1921 book, Tractatus Logico-Philosophicus (in German despite the Latin title) was a primary impetus to the Logical Positivist school of philosophy.  I’m stripping out much detail here, but the book’s long-lasting impact on QM may have come from its Proposition 7: “Whereof one cannot speak, thereof one must be silent.“

I suspect that Bohr was deeply influenced by the LP movement, which was all the rage in the mid-1920s while he was developing the Copenhagen Interpretation of QM.

An enormous literature, including quite a lot of twaddle, has grown up around the question, “Once you’ve derived the Schrödinger wave function for a given system, how do you interpret what you have?”  Bohr’s Copenhagen Interpretation was that the function can only describe relative probabilities for the results of a measurement.  It might tell you, for instance, that there’s a 50% chance that a particle will show up between here and here but only a 5% chance of finding it beyond there.

Following Logical Positivism all the way to the bank, Bohr denounced as nonsensical or even dangerously misleading any attachment of further meaning to a QM result.  He went so far as to deny the very existence of a particle prior to a measurement that detects it.  That’s serious Proposition 7 there.

I’ve read several accounts of the Solvay Conference debates between Einstein and Bohr.  All of them agree that the conversation was inconclusive but decisive.  Einstein steadfastly maintained that QM could not be a complete description of reality whilst Bohr refused to even consider anything other than inscrutable randomness beneath the statistics.  The audience consensus went to Bohr.

None of the accounts, even the very complete one that I found in George Musser’s book Spooky Action at A Distance, provide a satisfactory explanation for why Bohr’s interpretation dominates today.  Einstein described multiple situations where QM’s logic appeared to contradict itself or firmly established experimental results.  However, at each challenge Bohr deflected the argument from Einstein’s central point to argue a subsidiary issue such as whether Einstein was denying the Heisenberg Uncertainty Principle.

Albert still stood at the end of the bouts, but Niels got the spectators’ decision on points.  Did the ref make the difference?

~~ Rich Olcott