# 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.

Here 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

# 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.”

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