Tuesday, June 30, 2015

Six Optical Miracles

Paul Peter Ewald (1888-1985) and Carl Wilhelm Oseen (1879-1944)
Exactly 100 years ago a remarkable paper appeared in Annalen der Physik, a prestigious German physics journal in which both Max Planck and Albert Einstein published their findings. This paper, by German physicist Paul Peter Ewald explained how light behaves when it strikes a sheet of glass. Ewald, in 1915, explained, in effect, how a window works. A few year later, Swedish physicist Carl Wilhelm Oseen extended these findings to explain how light behaves when it strikes a crystal. Together the work of these two men is known as the Ewald-Oseen Extinction Theorem.

(A new proof of the extinction theorem by Mansur Mansuripur has recently been published here,)

What's so mysterious about how a window works. Isn't a window merely a sheet of glass?

A light wave traveling through a sheet of glass
When light strikes a window some of it bounces off (about 10%) and the remainder is refracted (bent) into the glass at an angle that depends on a number "n" called the refractive index which is different for different materials. If n is greater than 1, the light bends deeper into the material; if n is less than 1, the light bends towards the surface. 

In a vacuum the speed of light is equal to a constant c. But in material media, the velocity v of light is equal to: v = c/n. For visible light in glass, the refractive index is about 1.5, so light travels at about 70% of its vacuum speed: inside glass, light travels SLOW. On the other hand, for X-rays in many materials, the refractive index is less than 1, so X-ray light travels FAST -- faster than light in a vacuum.

But those "in the know" realize that not only did Einstein prohibit anything from traveling faster than light, he also showed that light always travels at the same speed no matter who's looking at it. So both the notion of fast X-ray light and slow light in glass would seem to be outlawed by relativity. However this notion of fast and slow light in material media is being taught to high school students. It's called Snell's Law (and seems to have been discovered first by Arab physicist ibn Sahl during the Islamic Golden Age.

Snell's Law (Ibn Sahl's Law) does not violate relativity, because Einstein and Snell (ibn Sahl) are talking about two different ways of measuring velocity. Einstein's prohibition refers to group velocity, how fast a packet of light can move, while Snell's Law refers to phase velocity, how fast the peaks of a wavelet can move. The difference between group and phase velocity is often illustrated by the difference between how fast a caterpillar moves (group velocity) and how fast one of his humps moves (phase velocity). It is clear from this analogy that the phase velocity can be faster or slower than whatever speed limit the caterpillar must obey. Here's a nice animation showing the difference between group and phase velocity for deep ocean waves. (In this ocean wave case, phase velocity is faster than group velocity.)

To fully appreciate the miraculousness of the Ewald-Oseen Extinction Theorem, we must first realize that glass consists of a random arrangement of electrically-excitable molecules. And that light is a traveling electromagnetic wave that will excite each of the molecules it encounters. Each excited molecule will emit a omni-directional light wave (of the same frequency as the incident light) in somewhat the same manner as an ocean buoy will emit a scattered wave when struck by an incident wave train.

Incident ocean wave striking a buoy produces scattered wave.
But light approaching a sheet of glass is not just going to strike one buoy, but approximately 10^24 buoys or about 1 million billion billion buoys (electrical excitable molecules). And these buoys (in glass) are arranged in a random fashion. What is the first thing you would imagine happening if a wave of light impinged on a medium composed of zillions of randomly arranged excitable molecules? Total chaos. That's what I would guess. The window will turn into some sort of deeply frosted glass that will randomly scatter light in every direction.

If windows are made of zillions of randomly arranged excitable molecules, then windows can not be transparent. That's what I would predict.

The first optical miracle is that windows are transparent. But the second, third and fourth miracle are even better.

Ewald proves for random media like glass (and Oseen does the same for ordered media such as crystals), that the net result of all of those zillions of little excited light waves add up to zero in every direction but three.

Only three big waves survive the fierce destructive interference between zillions of little waves. The first surviving wave travels in the same direction as the incident wave but vibrates exactly 180 degrees out of phase with the incident wave. Thus the incident wave is extinguished as it passes into the glass over a length of a few tenths of a micron (the extinction length). This exceedingly unlikely mechanism for extincting the incident wave gives the extinction theorem its odd name.

Two more waves survive the Great Destruction -- the reflected wave that seems to bounce off the glass but in reality is created by zillions of tiny molecules all radiating with the proper timing to direct a beam only in the reflected direction (and no other) much in the manner of phased-array radar antennas which do not physically move but are aimed by changing the phase relation between separate fixed transmitters. The glass molecules (like the phased-radars) are radiating in all directions but in both radar and window pane destructive interference removes light from every direction except one.

The third wave that survives the Great Cancellation is the internally transmitted wave that travels into the glass at "Snell's angle" with a "slow" phase velocity of c/n. Everywhere inside the glass the little wavelets travel at velocity c, but the net product of all their activity is an effective slow-phase wave, produced, like the reflected wave, by a kind of internal phased-antenna array consisting of zillions of glass molecules.

Here then are four optical miracles:

1. That glass is transparent despite its consisting of zillions of randomly situated electrically-excitable molecules;

2. That the excitable medium, all by itself, completely extinguishes the incident wave;

3. That the excitable medium, all by itself, synthesizes a "reflected wave" traveling in exactly the right direction and no other.

4. That the excitable medium, all by itself, synthesizes an "internal wave" traveling in exactly the right direction (Snell's Law) and no other.

These four miracles apply not just to windows but to anything made of glass, or to anything transparent for that matter, such as the lenses in telescopes, the lenses in your cameras, your eyeglasses, your contact lenses, the living lens and the clear fluid that fills your eye. The inner operation of each of these optical devices is explained by the four-fold miraculous Ewald-Oseen Extinction Theorem. (Happy Hundreth Anniversary!)

But wait. There's more. The EOET was derived in 1915 before quantum mechanics was devised. And quantum mechanics has one final miracle to add to the wonder of classical window panes and lenses.

Classical physics considered all of its waves to be "real", that is, made of something actually vibrating at every location where the wave exists. Quantum physics, on the other hand, considers its waves to be "unreal", that is, made only of sheer possibility. A light wave, for instance, represents only the possibility for a "photon" (or quantum of light) to be observed.

Quantum waves only become real in the act of observation, in a still mysterious process called by some "the collapse of the wave function".

Now imagine the situation of a single photon striking a window pane. I remind you that a window pane consists of a million billion billion electrically excitable molecules. And photons like to excite molecules. 

What do you suppose the odds are for the photon to exit the window pane without collapsing its wave function? Because there seem to be a zillion ways for that photon to lose its phase, to shed its dignity, to become entangled with the randomly arrayed electrically-excitable mess that we call "a pane of glass", I would naively guess that a pane of glass must collapse the photon wave function with 100% certainty.

But this conclusion is wrong. For exactly the same reason that the window pane is transparent (namely the Ewald-Oseen Extinction Theorem), the window pane has a lot of fun with the photon but does not actually collapse its wave function.

This is the fifth optical miracle: Window panes do not collapse the photon wave function.

Lenses do not collapse the photon wave function. Your contact lens does not collapse the photon wave function The living lens in your eye does not collapse the photon wave function. Your aqueous and vitreous humours do not collapse the photon wave function.

But inside your retina the photon wave function does somehow finally collapse into an actual event.

Which gives rise to this marvelous visual experience.

The sixth optical miracle.

Thursday, June 25, 2015

The Philosopher's Bone

Nick Herbert aka Dr Jabir 'abd al-Khaliq


(for Kelly Evans)

I'd love to own the Philosopher's Bone
As big and hard as Allah's own
With Physics, Joy and Math inside It
And me be man enough to ride It
On my board that buggers the imagination
I'd surf the Curly Crimp of Creation
I'm strong and smart; I'm a quantum knave
But where can I go to catch Her Wave?

One hundred quantum billiard waves

Wednesday, June 17, 2015

Tom Herbert (1938 - 2015)

Tom Herbert was born on June 13, 1938 in Pittsburgh, PA and died on the same day in 2015 in Vienna, VA from complications following a stroke. He was the second-oldest of 5 children: Nick, Tom, Marilyn, Donald ("Duke") and Nancy who all grew up together in the Linden neighborhood of Columbus, OH, which was then populated mainly by immigrants from Italy, Ireland and Eastern Europe. Our Father spoke Ukrainian; Mom spoke Slovak. And both grew up in coal mining towns in Pennsylvania and Ohio, migrating North to Lorain, Ohio where some of the family found work in the steel mills along Lake Erie.

Thomas Anthony Herbert (1938 - 2015)
Tom was younger than Nick but stronger so we two were physically an even match to wrestle, box, sled, skate and explore the woods and creeks within easy reach of our neighborhood. Tom and I both went to grade school at St Augustine Catholic school (where Mom ran the cafeteria) and both completed high school at St Charles Borromeo Preparatory School. Tom was fond of animals and of water -- in our back yard he raised rabbits, chickens and ducks in addition to the obligatory dogs and cats. Not only did Tom work as a lifeguard at our local Morningside pool, but he also organized special events at the pool including water ballets. Tom also bought a kayak which he piloted on the Olentangy and Scioto rivers -- and he imagined that someday he would follow the route Huck Finn took down the Mississippi on his raft. The floor of our boy's bedroom was covered with a big linoleum map of the USA, so we could rehearse Tom's future trip down the big river using bottle caps for boats.

Tom, Nick and Duke Herbert at Betsy's Memorial Celebration
Both Tom and I obtained Bachelor's Degrees from Ohio State University, Tom in Electrical Engineering and Nick in Physics. For the next stage in his life, Nick made a move to California -- our parents gave me the family station wagon as a graduation present. Tom and I decided to use this opportunity to explore the country we had only seen printed on a floor mat. So we packed camping gear in the car and embarked on a long road trip. In those days (1960), the US was relatively uncrowded and on the few occasions we could not find a campground we just set up camp near the road and were never bothered. We explored Colorado, Utah, the Grand Canyon, Las Vegas and large parts of California together. Tom was a congenial companion and good camping buddy -- no matter what hardships we endured he would always see its humorous side. And, yes the two Ohio boys finally got to experience the mighty Mississippi (near St Louis) and to cool our feet in the Father of Waters.

Tom liked to eat and was especially fond of the Slovak food that Mom put on the table, which included stuffed peppers, stuffed cabbages (holubki), cabbage, nut and prune roll pastries. Tom enjoyed eating this kind of food so much that, unlike his brothers, he actually learned to duplicate Mom's recipes for himself. And in addition to cooking holubki, etc, Tom learned how to make Perfect Spaghetti Sauce which Mom probably learned from Leona Vanelli, her best friend. Mom used to say that Tom preferred a meal of her spaghetti and meatballs over steak.

Tom cooking Perfect Spaghetti Sauce
After our road trip, Tom flew back to Ohio State where he completed his degree, met and married his first wife Dawn and began an engineering career with the Air Force at Wright-Patterson in Dayton, Ohio. Tom and Dawn produced five children: Mark, Julie, Terri, Dan and Joe. After their divorce, Tom met a female physicist who had learned how to turn silicon into gold -- Gail Walters was a brilliant computer chip designer. Their combined careers took them to Colorado, to California's Livermore Valley and finally to their present home in Virginia near Washington, DC. Tom and Gail produced one child Meghan who, when asked what she wanted to do, answered: "Anything but what my parents do."

Tom Herbert and Gail Walters
Tom and Gail on a jet ski.
After leaving Wright-Patterson, Tom took on another government job that was so secret  he could not talk about it. Since this job often involved trips to exotic locations near the equator, I assumed it had something to do with the tracking of military spy satellites. Whatever the nature of his clandestine work, Tom always found time to explore the underwater beauties of these tropical locales in his SCUBA gear. Later Tom, Gail and Meghan would vacation in exotic places like the Caymen Islands that Tom had no doubt reconnoitered on his "business trips"

Tom Herbert in SCUBA gear
Tom Herbert worked hard, played hard (and often underwater) raised two fine families, was possessed of a contagious cheerfulness. I do not know whether he believed in reincarnation, but I'd like to think that in his next life Tom might come back as a smart, sexy, good-hearted dolphin.

Tom embraces his alter ego
Bon voyage, wonderful Tom. I will miss you, little brother.