Three-speed Transmission

“Have I got this straight, Sy? You’re saying that prisms throw rainbows because light goes slower through glass than in air and that bends the beam, but every frequency lightwave bends a different amount. Also you’re saying all the bending happens when speeds switch at the glass face, not inside the glass. Am I right so far?”

“Perfect, Vinnie, but you skipped an important detail.”

“Which one?”

“Snell’s ‘index of refraction‘, the ratio of wave speed in vacuum to wave speed in the medium. The higher the frequency, the higher the speed in the medium so the index decreases towards 1.0. The definition lets us calculate wave speed in the medium from that frequency’s refraction index. For most materials the index is usually greater than 1.0, meaning that the speed inside the material is usually slower than in space.”

“Still using those ‘most‘ and ‘usually‘ weasel‑words.”

“Guilty as charged, because we’ve finally gotten to the ‘multiple speeds of light‘ thing. Which means I need more precise wording. The wave speed we’ve been talking about so far applies to a specific part of the wave, say the peak or trough. Those are wave phases, so I’m going to call that speed the ‘phase speed‘, OK?”

“Fine with me.”

“Good, because the second speed is different. Among his many important contributions, Lord Rayleigh pointed out that you can’t have a pulse that’s one pure frequency. A single‑frequency wave never starts and never ends. Do you remember the time I combined waves to draw a camel?”

“You did, mostly, but there was funny stuff at his nose and butt.”

“Because I only included about a hundred component waves. It’d take many more to kill those boundary zig‑zags. Any finite wave has the same issue. Rayleigh said that an individual wave has a phase speed, but any ‘peculiarity,’ like a pulse rise or fall, could only be created by a group of waves. The peculiarity could travel at a different speed from the component waves, like a pair of scissors where the cutting point moves faster than either blade.”

“Sounds like carrier wave and sidebands on my ham radio. But if different frequencies have different speeds they’d get all out of sync with each other. How does a photon stay in one piece?”

“The vacuum is non-dispersive — the photon’s component waves all travel at the same speed and stay together. If a medium absorbs some frequency, that makes it dispersive and that changes things.”

“Ah, that’s why you hedged about transparency.”

“Exactly. Throw in a few absorbing atoms, like cobalt that absorbs red or gold that absorbs blue, and you get interesting effects from your sideband components interacting. Skipping some math, the bottom line is simple and cute. The group speed’s equation is just like the phase speed’s except there’s a positive or negative correction term in the denominator.”

“Sy, I don’t like equations, remember? I suppose f is frequency in your correction term but what’s slope?”

“That’s a measure of how rapidly the index changes as the frequency changes. For most frequencies and most media, the slope is very slightly negative because the index slowly descends towards 1.0 at high energies. The vg fraction’s denominator stays just less than nf so the group goes slightly faster than the phase. Near an absorption line, though, things get sloppy. Waves that are just a little off the absorber’s favorite frequency can still interact with it. That changes their speed and the ‘corrected’ refraction index.”

“Gimme a sec … guess I’m OK with the positive slopes but there’s that yellow part where the slope is negative. Wouldn’t that make the fraction’s bottom smaller and the group speed higher?”

“Certainly. In fact, under the right conditions the denominator can be less than 1.0. That pushes the group speed above c — faster than light in vacuum, even though the component waves all run slower than vacuum lightspeed. It’s only the between‑component out‑of‑syncness relationship that scissors along beyond c.”

“You said there’s a third speed?”

“Signals. In a dispersive medium those sideband waves get chaotic and can’t carry information. Wave theory and Einstein agree — chaos may be able to travel faster than light, but information can’t.”

~~ Rich Olcott

Through A Prism Brightly

Familiar footsteps outside my office. “C’mon in, Vinnie, the door’s open.”

“Hi, Sy, gotta minute?”

“Sure, Vinnie, business is slow. What’s up?”

“Business is slow for me, too. I was looking over some of your old posts—”

“That slow, eh?”

“You know it. Anyway, I’m hung up on that video where light’s got two different speeds.”

“Three, really.”

“That’s even worse. What’s the story?”

“Well, first thing, it depends on where the light is. If you’re out in the vacuum, far away from atoms, they’re all the same, c. Simple.”

“Matter messes things up, then.”

“Of course. Our familiar kind of matter, anyway, made of charges like quarks and electrons. Light’s whole job is to interact with charges. When it does, things happen.”

“Sure — photon bangs into a rock, it stops.”

“It’s not that simple. Remember the wave-particle craziness? Light’s a particle at either end of its trip but in between it’s a wave. The wave could reflect off the rock or diffract around it. Interstellar infra-red astronomy depends upon IR scooting around dust particles so we can see the stars behind the dust clouds. What gets interesting is when the light encounters a mostly transparent medium.”

“I get suspicious when you emphasize ‘mostly.’ Mostly how?”

“Transparent means no absorption. The only thing that’s completely transparent is empty space. Anything made of normal matter can’t be completely transparent, because every kind of atom absorbs certain frequencies.”

“Glass is transparent.”

“To visible light, but even that depends on the glass. Ever notice how cheap drinking glasses have a greenish tint when you look down at the rim? Some light absorption, just not very much. Even pure silica glass is opaque beyond the near ultraviolet. … Okay, bear with me on this. Why do you suppose Newton made such a fuss about prisms?”

“Because he saw it made a rainbow in sunlight and thought that was pretty?”

“Nothing so mild. We’re talking Newton here. No, it had to do with one of his famous ‘I’m right and everyone else is wrong‘ battles. Aristotle said that sunlight is pure white‑color, and that objects emit various kinds of darkness to overcome the white and produce colors for us. That was academic gospel for 2000 years until Newton decided it was wrong. He went to war with Aristotle using prisms as his primary weapons.”

“So that’s why he invented them?”

“No, no, they’d been around for millennia, ever since humans discovered that prismatic quartz crystals in a beam of sunlight throw rainbows. Newton’s innovation was to use multiple prisms arrayed with lenses and mirrors. His most direct attack on Aristotle used two prisms. He aimed the beam coming out of the first prism onto a reversed second prism. Except for some red and violet fringes at the edges, the light coming out of the second prism matched the original sunlight beam. That proved colors are in the light, not in Aristotle’s darknesses.”

“Newton won. End of story.”

“Not by a long shot. Aristotle had the strength of tradition behind him. A lot of Continental academics and churchmen had built their careers around his works. Newton’s earlier battles had won him many enemies and some grudging respect but few effective allies. Worse, Newton published his experiments and observations in a treatise which he wrote in English instead of the conventional scholarly Latin. Typical Newtonian belligerence, probably. The French academicians reacted by simply rejecting his claims out of hand. It took a generational turnover before his thinking was widely accepted.”

“Where do speeds come into this?”

“Through another experiment in Newton’s Optics treatise. If he used a card with a hole in it to isolate, say, green light in the space between the two prisms, the light beam coming from the second prism was the matching green. No evidence of any other colors. That was an important observation on its own, but Newton’s real genius move was to measure the diffraction angles. Every color had its own angle. No matter the conditions, any particular light color was always bent by the same number of degrees. Newton had put numbers to colors. That laid the groundwork for all of spectroscopic science.”

“And that ties to speed how?”

~~ Rich Olcott

The Sight And Sound of Snow

<ring> “Moire here.”

“Uncle Sy! Uncle Sy! It’s snowing! It’s snowing!”

“Yes, Teena, it started last night after you went to bed. But it’s real early now and I haven’t had breakfast yet. I’ll be over there in a little while and we can do snow stuff.”

“Yaaay! I’ll have breakfast, too. Mommie, can we have oatmeal with raisins?” <click>

<knock, knock> “Uncle Sy! You’re here! I wanna go sledding! Get my sled out, please?”

“G’morning, Sis. G’morning, Teena. Get your snowsuit and boots on, Sweetie. Want to come along, Sis? It’s a cold, dry snow, not much wind.”

“No, I’ll just stay warm and get the hot chocolate ready.”

“Bless you for that, Sis. OK, young’un, ready to go?”

“Ready! Pull me on the sled to the sledding hill, Uncle Sy!”

“Ooo, it’s so quiet. Why’s it always quiet when snow’s falling, Uncle Sy? Is the world holding its breath? And why is snow white? When I hold snow in my hand it melts and then it’s no-color.”

“Always the good questions. Actually, these two are related and they both have to do with the shape of snowflakes. Here, hold out your arm and let’s see if you can catch a few. No, don’t try to chase them, the breeze from your arm will blow them away. Just let them fall onto your arm. That’s right. Now look at them real close.”

“They’re all spiky, not flat and pretty like the ones in my picture book!”

“That’s because they grew fast in a really cold cloud and didn’t have time to develop evenly. You have to work slow to make something that’s really pretty.”

“But if they’re spiky like this they can’t lay down flat together and be cozy!”

“Ah, that’s the key. Fresh spiky snowflakes make fluffy snow, which is why skiers love it. See how the flakes puff into the air when I scuff my boot? Those tiny spikes break off easily and make it easy for a ski to glide over the surface. Your sled, too — you’ve grown so big I’d be hard-put to pull you over wet snow. That fluffiness is why <hushed voice> it’s so quiet now.”

“Shhh … <whispered> yeah … <back to full voice> Wait, how does fluffy make quiet?”

“Because sound waves … Have we talked about sound waves? I guess we haven’t. OK, clap your hands once.”


“Good. When your hands came together they pushed away the air molecules that were between them. Those molecules pushed on the next molecules and those pushed on the next ones on and on until they got to your ear and you heard the sound. Make sense?”

“Ye-aa-uh. Is the push-push-push the wave?”

“Exactly. OK, now imagine that a wave hits a wall or some packed-down icy snow. What will happen?”

“It’ll bounce off like my paddle-ball toy!”

“Smart girl. Now imagine that a wave hits fluffy snow.”

“Um … it’ll get all lost bouncing between all the spikes, right?”

“Perfect. That’s exactly what happens. Some of the wave is scattered by falling snowflakes and much of what’s left spreads into the snow on the ground. That doesn’t leave much sound energy for us to hear.”

“You said that snow’s white because of what snow does to sound, but look, it’s so bright I have to squint my eyes!”

“That’s not exactly what I said, I said they’re related. Hmm… ah! You know that ornament your Mommie has hanging in the kitchen window?”

“The fairy holding the glass jewel? Yeah, when the sunlight hits it there’s rainbows all over the room! I love that!”

A beam or white light passing through two prisms.  The first produces a spectrum and the second remixes the colors to white.

“I do, too. White light like sunlight has all colors in it and that jewel splits the colors apart so you can see them. Well, suppose that jewel is surrounded by other jewels that can put the colors together again. Here’s a picture on my cellphone for a clue.”

“White goes to rainbow and back to white again … I’ll bet the snowflakes act like little jewels and bounce all the colors around but the light doesn’t get trapped and it comes out and we see the WHITE again! Right?”

“So right that we’re going home for hot chocolate.”


~~ Rich Olcott

PS – A Deeper Look.