What Are Quantum Birds Made Of?

“Do quantum thingies follow the same rules that birds do, Uncle Sy?”

“Mostly not, Teena.  Some quantum rules are simple, others are complicated and many are weird.”

“Tell me a simple one and a weird one.”

“Hm… the Principle of Correspondence is simple.  It says if you’ve got a lot of quantum things acting together, the whole mishmash acts by the same rules that a regular-sized thing that size would follow.  If all those birds flew in every direction there’s no flock to talk about, but if they fly by flock rules we can talk about how wind affects the flock’s motion.”

“It’s a murmuration, Uncle Sy.”

“Correction noted, Sweetie.”

“Now tell me a weird one.”

“There’s the rule that a quantum thing acts like it’s in a specific place when you look at it but it’s spread out when you’re not looking.”

“Kittie does that!  She’s never where you look for her.”

“Mm, that’s kind of in the other direction.  We see quantum particles in specific somewheres, not specific nowheres.  The rule is called wave-particle duality and people have been trying to figure out how it works for a hundred years.  Let’s try this.  Put your thumb and forefinger up to your eye and look between them at the blue sky.  Hold your fingers very close together but don’t let them touch.  What do you see?”

“Ooo, there’s stripes in between!  It looks like my finger’s going right into my thumb, but I can feel they’re not touching.  Hey, it works with my other fingers, too, but it hurts if I try it with my pinkie.”

“Then don’t do it with your pinkie, silly.  The stripes are called ‘interference’ and only waves do that.  You’ve watched how water waves go up and down, right?”

“Sure!”

“When the high part of one wave meets the low part of another wave, what happens?”

“I guess high and low make middle.”

“Good guess, that’s exactly right.  That little teeny space between your fingers lets through only certain waves.  You see light where the highs and lows are, dark where the waves middle out.”

“So light’s made out of waves, huh?”

“Well, except that scientists have done lots of experiments where light behaves like it’s made out of little particles called photons.  The funny thing is, light always acts like a wave when it’s traveling from one place to another, but at both ends of the trip it always acts like photons.  That’s the big mystery — how does it do that?”

“You know how it works, don’tcha, Uncle Sy?”

“Only kinda sorta, Teena.  I think it has to do with the idea of big things made out of little things made out of littler things.  Einstein — wait, you know who Einstein was, right?”

“He was the famous scientist with the big hair.”

“That’s right.  He and another scientist had a big debate over 80 years ago.  The other scientist said that when quantum things make patterns, like those stripes you’re looking at, the patterns are all we can know about them.  Einstein said that there has to be something deeper down that drives the patterns.”

“Who won the debate?”

“At the time most people thought that the other man had, but philosophies change.  Since that time lots of people have followed Einstein’s thinking.  Some of the theories are pretty silly, I think, but I’m betting on birds made out of birds.”

“That’s silly, too, Uncle Sy.”

“Maybe, maybe not, we’ll see some day.  It starts with what you might call ‘the smallness quantum,’ though it’s also called ‘the Planck length‘ after Mr Planck who helped invent quantum mechanics.  The Planck length is awesomely small.  It’s as much smaller than us as we are smaller than the whole universe.”

“But there’s lots of things bigger than we are.”

“Exactly.  We’re smaller than whales, they’re smaller than planets, planets are smaller than suns, and galaxies, and on up.  But we don’t know near as many size scales in the other direction – us and bacteria and atoms and protons and that’s about it.  I think there’s plenty of room down there for structures and chaos we’ve not thought of yet.”

“Like birds in murmurations.”

“Mm-hmm.”Bird made out of birds 1

~~ Rich Olcott

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Reflections in Einstein’s bubble

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

Oh, what an entangled wave we weave

“Here’s the poly bag wiff our meals, Johnny.  ‘S got two boxes innit, but no labels which is which.”
“I ordered the mutton pasty, Jennie, anna fish’n’chips for you.”
“You c’n have this box, Johnny.  I’ll take the other one t’ my place to watch telly.”

<ring>
” ‘Ullo, Jennie?  This is Johnny.  The box over ‘ere ‘as the fish.  You’ve got mine!”


In a sense their supper order arrived in an entangled state.  Our friends knew what was in both boxes together, but they didn’t know what was in either box separately.  Kind of a Schrödinger’s Cat situation — they had to treat each box as 50% baked pasty and 50% fried codfish.

But as soon as Johnny opened one box, he knew what was in the other one even though it was somewhere else.  Jennie could have been in the next room or the next town or the next planet — Johnnie would have known, instantly, which box had his meal no matter how far away that other box was.

By the way, Jennie was free to open her box on the way home but that’d make no difference to Johnnie — the box at his place would have stayed a mystery to him until either he opened it or he talked to her.

Entangled 2Information transfer at infinite speed?  Of course not, because neither hungry person knows what’s in either box until they open one or until they exchange information.  Even Skype operates at light-speed (or slower).

But that’s not quite quantum entanglement, because there’s definite content (meat pie or batter-fried cod) in each box.  In the quantum world, neither box holds something definite until at least one box is opened.  At that point, ambiguity flees from both boxes in an act of global correlation.

There’s strong experimental evidence that entangled particles literally don’t know which way is up until one of them is observed.  The paired particle instantaneously gets that message no matter how far away it is.

Niels Bohr’s Principle of Complementarity is involved here.  He held that because it’s impossible to measure both wave and particle properties at the same time, a quantized entity acts as a wave globally and only becomes local when it stops somewhere.

Here’s how extreme the wave/particle global/local thing can get.  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.

cats-eye nebula

The Cat’s Eye Nebula (NGC 6543)
courtesy of NASA’s Hubble Space Telescope

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.

Surely there was at least one other being, on Earth or somewhere else, that was looking towards the nebula when that wave passed by.  They wouldn’t have seen your photon nor could you have seen any of theirs.  Somehow your wave’s entire spherical shell, all 1012 square lightyears of it, instantaneously “knew” that your eye’s electron had extracted the wave’s energy.

But that directly contradicts a bedrock of Einstein’s Special Theory of Relativity.  His fundamental assumption was that nothing (energy, matter or information) can go faster than the speed of light in vacuum.  STR says it’s impossible for two distant points on that spherical wave to communicate in the way that quantum theory demands they must.

Want some irony?  Back in 1906, Einstein himself “invented” the photon in one of his four “Annus mirabilis” papers.  (The word “photon” didn’t come into use for another decade, but Einstein demonstrated the need for it.)  Building on Planck’s work, Einstein showed that light must be emitted and absorbed as quantized packets of energy.

It must have taken a lot of courage to write that paper, because Maxwell’s wave theory of light had been firmly established for forty years prior and there’s a lot of evidence for it.  Bottom line, though, is that Einstein is responsible for both sides of the wave/particle global/local puzzle that has bedeviled Physics for a century.

~~ Rich Olcott

Think globally, act locally. Electrons do.

“Watcha, Johnnie, you sure ‘at particle’s inna box?”
“O’course ’tis, Jennie!  Why wouldn’t it be?”
“Me Mam sez particles can tunnel outta boxes ’cause they’re waves.”

“Can’t be both, Jessie.”


Double slit experiment

The double-slit experiment.
An electron beam travels from the source at left to a display screen. In between there’s a barrier with two narrow slits.

Maybe it can.

Nobel-winning (1965) physicist Richard Feynman said the double-slit experiment (diagrammed here) embodies the “central mystery” of Quantum Mechanics.

When the bottom slit is covered the display screen shows just what you’d expect — a bright area  opposite the top slit.

When both slits are open, the screen shows a banded pattern you see with waves.  Where a peak in a top-slit wave meets a peak in the bottom-slit wave, the screen shines brightly.  Where a peak meets a trough the two waves cancel and the screen is dark.  Overall there’s a series of stripes.  So electrons are waves, right?

But wait.  If we throttle the beam current way down, the display shows individual speckles where each electron hits.  So the electrons are particles, right?

Now for the spooky part.  If both slits are open to a throttled beam those singleton speckles don’t cluster behind the slits as you’d expect particles to do.  A speckle may appear anywhere on the screen, even in an apparently blocked-off region.  What’s more, when you send out many electrons one-by-one their individual hits cluster exactly where the bright stripes were when the beam was running full-on.

It’s as though each electron becomes a wave that goes through both slits, interferes with itself, and then goes back to being a particle!

By the way, this experiment isn’t a freak observation.  It’s been repeated with the same results many times, not just with electrons but also with light (photons), atoms, and even massive molecules like buckyballs (fullerene spheres that contain 60 carbon atoms).  In each case, the results indicate that the whatevers have a dual character — as a localized particle AND as a wave that reacts to the global environment.

Physicists have been arguing the “Which is it?” question ever since Louis-Victor-Pierre-Raymond, the 7th Duc de Broglie, raised it in his 1924 PhD Thesis (for which he received a Nobel Prize in 1929 — not bad for a beginner).  He showed that any moving “particle” comes along with a “wave” whose peak-to-peak wavelength is inversely proportional to the particle’s mass times its velocity.  The longer the wavelength, the less well you know where the thing is.

I just had to put numbers to de Broglie’s equation.  With Newton in mind, I measured one of the apples in my kitchen.  To scale everything, I assumed each object moved by one of its diameters per second.  (OK, I cheated for the electron — modern physics says it’s just a point, so I used a not-really-valid classical calculation to get something to work with.)

“Particle” Mass, kilograms Diameter, meters Wavelength, meters Wavelength, diameters
Apple 0.2 0.07 7.1×10-33 1.0×10-31
Buckyball 1.2×10-24 1.0×10-9 0.083 8.3×10+7
Hydrogen atom 1.7×10-27 1.0×10-10 600 6.0×10+12
Electron 9.1×10-31 3.0×10-17 3.7×10+12 1.2×10+29

That apple has a wave far smaller than any of its hydrogen atoms so I’ll have no trouble grabbing it for a bite.  Anything tinier than a small virus is spread way out unless it’s moving pretty fast, as in a beam apparatus.  For instance, an electron going at 1% of light-speed has a wavelength only a nanometer wide.

Different physicists have taken different positions on the “particle or wave?” question.  Duc de Broglie claimed that both exist — particles are real and they travel where their waves tell them to.  Bohr and Heisenberg went the opposite route, saying that the wave’s not real, it’s only a mathematical device for calculating relative probabilities for measuring this or that value.  Furthermore, the particle doesn’t exist as such until a measurement determines its location or momentum.  Einstein and Schrödinger liked particles.  Feynman and Dirac just threw up their hands and calculated.

Which brings us to the other kind of quantum spookiness — “entanglement.”  In fact, Einstein actually used the word spukhafte (German for “spooky”) in a discussion of the notion.  He really didn’t like it and for good reason — entanglement rudely collides with his own Theory of Relativity.  But that’s another story.

~~ Rich Olcott