The Speeds of Light

(Look up top, just under the banner.  There’s a new item on the menu bar — Table of Contents.  Many of these multi-post stories have grown in the telling, so I’ve tried to impose some after-the-fact order to them for you.  Check it out.)

“I don’t give up easy, Sy.”

“I know that, Vinnie.  Still musing about lightwaves and how they’re all an electron’s fault?”

“Yeah.  Hey, can your OVR app on Old Reliable grab a shot from this movie running on my smartphone?”

“We can try … got it.  Now what?”

“I wanna try mixing that with your magnetic field picture.”

“I’ll bring that up … Here, have at it.”

“Umm … Nice app, works very intuitive-like …  OK, see this?”Electrons and lightwave

“Ah.  It’s a bit busy, walk me through what’s in there.”

“OK. First we got the movie’s lightwave.  The ray’s running along that black arrow, see?  Some electron back behind the picture is going up and down to energize the ray and that makes the electric field that’s in red that makes other electrons go up and down, right?”

“That’s the red arrow, hmm?”

“Yeah, that electron got goosed ’cause it was standing in the way.  It follows the electric field’s direction.  Now help me out with the magnetic stuff.”

“Alright.  The blue lines represent the lightwave’s magnetic component.  A lightwave’s magnetic field lines are always perpendicular to its electric field.  Magnetism has no effect on uncharged particles or motionless charged particles.  If you’re a moving charged particle, say an electron, then the field deflects your trajectory.”

“This is what I’m still trying to wrap my head around.  You say that the field’s gonna push the particle perpendicular to the field and to the particle’s own vector.”

“That’s exactly what happens.  The green line, for instance, could represent an electron that crossed the magnetic field.  The field deflected the electron’s path upwards, crossways to the field and the electron’s path.  Then I suppose the electron encountered the reversed field from the lightwave’s following cycle and corrected course again.”

“And the grey line?”

“That’d be an electron crossing more-or-less along the field.  According to the Right Hand Rule it was deflected downward.”

“Wait.  We’ve got two electrons on the same side of the field and they’re deflected in opposite directions then correct back.  Doesn’t that average out to no change?”

“Not quite.  The key word is mostly.  Like gravity fields, electromagnetic fields get weaker with distance.  Each up or down deflection to an electron on an outbound path will be smaller than the previous one so the ‘course corrections’ get less correct.  Inbound electrons get deflected ever more strongly on the way in, of course, but eventually they become outbound electrons and get messed up even more.  All those deflections produce an expanding cone of disturbed electrons along the path of the ray.”

“Hey, but when any electron moves that changes the fields, right?  Wouldn’t there be a cone of disturbed field, too?”

“Absolutely.  The whole process leads to several kinds of dispersion.”

“Like what?”

“The obvious one is simple geometry.  What had been a simple straight-line ray is now an expanding cone of secondary emission.  Suppose you’re an astronomer looking at a planet that’s along that ray, for instance.  Light’s getting to you from throughout the cone, not just from the straight line.  You’re going to get a blurred picture.”

“What’s another kind?”

“Moving those electrons around extracts energy from the wave.  Some fraction of the ray’s original photons get converted to lower-energy ones with lower frequencies.  The net result is that the ray’s spectrum is spread and dispersed towards the red.”

“You said several kinds.”

“The last one’s a doozy — it affects the speeds of light.”

“‘Speeds,’ plural?”ripples in a wave

“There’s the speed of field’s ripples, and there’s the speed of the whole signal, say when a star goes nova.  Here’s a picture I built on Old Reliable.  The gold line is the electric field — see how the ripples make the red electron wobble?  The green dots on the axis give you comparison points that don’t move.  Watch how the ripples move left to right just like the signal does, but at their own speed.”

“Which one’s Einstein’s?”

“The signal.  Its speed is called the group velocity and in space always runs 186,000 mph.  The ripple speed, technically it’s the phase velocity, is slower because of that extracted-and-redistributed-energy process.  Different frequencies get different slowdowns, which gives astronomers clues about the interstellar medium.”

“Clues are good.”

~~ Rich Olcott


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