Footprints in The Glasses

I think he sometimes lies in wait for me like a cheetah crouching to ambush prey. No, more like a frog. Today I’m on my daily walk when suddenly — “Hey Moire, I got questions!”

Yeah, more like a frog. “Morning, Mr Feder. Out early today, aren’t you?”

“It’s gonna be hot today so I figured you’d walk the park early. I like it down here by the lake.”

Yup, definitely a frog. “Well, what can I do for you?”

“I’m wearing these new glasses, okay?”

“I can see that. Very … stylish.”

“So I read what you wrote about how light slows down when it goes through stuff and I wonder, does the light slow down enough going through these glasses that I might not see a bus in time? And how does stuff slow down light anyway?”

<drawing Old Reliable from its holster> “That first question is quantitative so let’s gather the numbers. The speed of light in vacuum is about 186 000 miles per second, that’s 300 megameters per second or 300 millimeters per nanosecond. Metric system conversions are kinda fun, aren’t they?”

“Hang on — megameters per second is meters per microsecond, take it down another thousand top and bottom…. I guess that’s okay.”

“Old Reliable doesn’t lie. Alright, your eyeglass lenses look like they’re a couple of millimeters thick. I’ll call it three millimeters to make the numbers pretty. If your lenses were vacuum space a short light pulse would pass through in 0.01 nanosecond, okay?”

“Not that thick, but go on.”

“The slow‑down factor is technically called the refractive index. Old Reliable says that eyeglass refractive indexes typically run about 1.5 so with the slow‑down our light pulse would take 0.015 nanosecond instead of 0.01. Is that enough increase to affect your rection time significantly? Let’s see … Says here that a typical nerve impulse travels at about 50 meters per second. Keeping the numbers pretty I’ll guess that between your eye and the vision centers in the back of your brain is about 2 inches or 5 centimeters. You good with that?”

“Not that short, but anything for pretty numbers. Go on.”

“Five centimeters is 0.05 meters, at 50 meters per second comes to 0.001 second. Slowing down that pulse lengthens your reaction time from 0.001 second to 0.001 000 000 015 second. Not enough of a difference to worry about.”

“But how come it slows at all seeing as I’ve heard it’s mostly empty space between the atoms?”

“There’s empty and there’s empty. You’re thinking of little solar‑system atoms, aren’t you, with particle electrons orbiting the nucleus and what space is left is vacuum. We’ve known for a century that it’s not that way. The electrons aren’t particles, they’re fuzzy blobs, and the volume around them is chock full of lumpy electric field. The incoming lightwave, really an electromagnetic wave, doesn’t see one electron here and another one way over there and free passage in between. Nope, it interacts with the whole field and that’s where the slow‑down happens.”

“Lots of quantum jumps and like that, huh?”

“No quantum jumps unless your glasses are tinted. Mmm… You ever run along the seashore?”

“I’m from Jersey. Of course I have.”

 Time periodicity at a point,
 space periodicity at a moment.

“Visualize running across hard sand and suddenly you hit a patch of soft sand. You keep your feet oscillating up and down at the same rate, but you make less progress along the beach. Your footprints get closer together, right?”

“Sometimes I fall down. So?”

“Something similar happens with a lightwave. It repeats in time like your foot going up and down and it repeats in space like your footprints in the sand. The wave’s energy changes with repeat time. When light passes through an electric field like the one inside clear, colorless glass, the field doesn’t absorb energy — no change in repeat time. What does happen is the field squeezes the peak‑to‑peak distance. The wave acts like your footprints getting closer together. Less distance divided by the same time means lower speed. The wave slows down inside the glass.”

“Does light ever fall down?”

“Only if its energy quantum matches an absorber’s gap.”

~~ Rich Olcott

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