A different kind of superposition

Pine Bluff has a lot of small churches that now occupy buildings where restaurants, retail stores and, in the above case, pawn shops where once located.  This church, at 1200 Main Street, had their sign installed a few months ago when I happened to passing by on my way home from work.  Since I only live a few blocks away, I got back with my camera before the pawn shop to church transition was complete.  The church's sign covers up the former Don's Trading Post sign.  Don is still in business as the Money Mart pawn shop in a different location (sorta like the McDonald's that used to be at 1300 Main now is on Olive Street).  Pawn Shops and day care centers (for both kids and senior citizens), along with the churches, are among the more prominent non-residential properties in Pine Bluff.

Back to Baym: polarization and superposition

There was a prominent family in Pine Bluff named Baim. Well, there still is, but the family's law firm is not quite as well known amongst the locals as the former Baim's department store on Main Street was.  I believe the original Baim patriarch in Pine Bluff was Samuel Baer Baim, based on his being the oldest grave among many Baims at Bellwood Cemetery.  (Born in 1875, died in 1956. His wife Sarah Baim was born in 1876 and died in 1951.)  Anyway, I brought up the Baim name because I'm wondering if it originally was Baym and was Americanized like so many other European names were when a family immigrated here.

Now back to Gordon Baym's 1969 book, Lectures on Quantum Mechanics, a title possibly chosen in homage to  Richard Feynman's Lectures on Physics, published in 1963, although Baym's book is a graduate-level textbook and Feynman's is taken from his lectures to freshman students at Cal Tech.

Baym was saying, as quoted in my earlier post, that it is "very weird" that about half the photons in a beam of light get through two polaroids with their axes turned 45 degrees relative to each other.  I very much like the fact that Baym even uses the word "weird," because this is in refreshing contrast to most stuffy graduate level texts, which are damn near unreadable--especially two that are widely used whose authors' last names are Goldstein and Jackson.  Baym's book is quite readable, and his choice of how to present the subject matter is particularly illuminating, rather like the great Arnold Sommerfeld.

And here's a good example of that, taking up just after his use of "weird," and describing photons of a single frequency when he says "all" :

"--classically we would say that if any photon gets through, then since all photons are identical and all see identical conditions at the polaroid they should all pass through. The only way we can interpret what happens at the polaroid is to say each photon has a probability one-half of passing through.  We are really forced into a probabilistic point of view by the fact that the energy of electromagnetic radiation is quantized!"

This is a sort of half-classical, half-quantum description.  Classically, a normal beam of light is made up of many individual waves each with its own polarization direction--you can say it has many polarization directions--and a horizontal polarizer, for example, filters out all the non-horizontal components of the beam.  In the quantum realm, however, it is hard to visualize how a particle, a photon, can have a polarization.  But this is where Baym's discussion is heading: toward a description of photon polarization.

 

 

 

He makes a couple of significant points in getting there, first that there will be fluctuations in the number of photons getting through these two polaroids--the number will not always be one-half, as it would classically, where probability isn't involved--and second that "the photon, if it passes through, emerges...polarized in the x direction!"  (The second polarizer in this case is oriented in the x-direction. The exclamation point is there because, if the photons are all identical as presumed, then they are somehow being forced to assume the x-direction polarization.)

Now, what I haven't discussed yet is circular polarization.  Yes, the polarization direction, which is the direction the electric field of the light wave is oscillating, can change as the wave travels, rotating as the wave travels, so that it's following a sort of corkscrew or helical path, although not exactly since the field strength is oscillating.  Circular polarization can be either clockwise or counter-clockwise (also known as right or left circular polarization, respectively).  Now we're ready to look at photon polarization.  Baym says

     Since all beams of light are superpositions of many beams consisting of one photon each, we shall turn our attention to the polarization properties of single photons.  As we have already seen, it will be easy to discover the probability rules for one photon from our knowledge of the behavior of classical beams.  The general laws of quantum mechanics are just generalizations of these rules.

After discussing mathematically the meaning of state vector, scalar product, orthogonality and bases (these are coordinate systems, such as the familiar x-y system), and then showing how a polarization state vector can be expressed in terms of a basis set like x and y or left and right circular polarization, Baym says, "These equations are examples of the superposition principle; we can regard any polarization as a coherent superposition of, e.g., x and y polarization states, or equivalently as a coherent superposition of right and left circularly polarized states."


The purpose of going through all this, remember, is to make some new discovery or interpretation of the physics of quantum superposition (photon polarization weirdness, Schroedinger's cat, EPR).  Still got a long way to go, but progress is being made.  Right?  Right!

More on measurements

I shouldn't have denigrated my digital bathroom scale for being precise but inaccurate.  Maybe I wasn't standing still, and my weight was slightly shifted during the consecutive measurements made by the scale earlier.  If I stand still and look straight ahead, then look down after the scale has had a moment to do the measurement (and calculation--it's digital, it calculates after doing an analog-to-digital conversion from whatever transducer, probably a strain gauge, used to make the physical part of the measurement), then I can get consistent consecutive readings to the 0.1 precision of the digital display.  Lately, they've been in the range of 144, 145, and 146 pounds on different days.  So I did approximately lose those ten pounds I said I needed to lose.  Summertime manual labor and walkin' with a little runnin' everyday is what did it presumably.  And more beer consumption seems not to have prevented the loss.  Smithwick's Irish Ale, to be specific.

Now for some more quantum superposition discussion.  Gary Zukav actually wanted to include three polarizers in the back of his book The Dancing Wu Li Masters, so that readers could do for themselves the experiment he describes--that's how important he considered the 3-polarizer mystery.  But the cost of the book would have been too much he thought so he didn't include the polarizers.  You can buy two pairs of cheap polarized sunglasses, though, and demonstrate the effect to your own satisfaction (well, I don't know how cheap you can get 'em, actually, not being a sunglasses buyer currently myself).

Gordon Baym, author of Lectures on Quantum Mechanics, published in 1969, when he was a professor at the U of Illinois, Urbana, also thought the polarization experiment or demonstration (not much to get out of it except to observe it) was important.  He starts his book off with a description of it, in well-written English as well as in mathematical detail.  He emphasizes how probability comes into the process once we consider a beam of light to be quantized, saying the total energy of the beam cannot be arbitrary, but must instead be an integral multiple of Planck's constant times the light's frequency. Another way of saying that is there are a certain number of photons in the beam.  (Is or are?  Never mind!)  Baym says, "Thus when the energy of the wave is halved by the polaroid what must happen is that half the photons pass through and half don't.  This is very weird--"

Gotta stop there for now, but we can think in the meantime of why that's weird.  If one of these identical photons gets throught, why should another not?

More from Zukav

Here’s what Gary Zukav has to say about superposition (p. 285) in The Dancing Wu Li Masters: “A ‘superposition’ is one thing (or more) imposed on another. A double exposure, the bane of careless photographers, is the superposition of one photograph on another.”

Well, some people intentionally make double exposures for the fun of it, but either way, intentional or not, it’s a good example of classical superposition.  Zukav next discusses quantum superposition, which he calls coherent superposition:  “A coherent superposition, however, is not simply the superposition of one thing on another.  A coherent superposition is a thing-in-itself which is as distinct from its components as its components are from each other.”

Now Zukav uses the example of polarized light—the same example I was talking about earlier: two polarizers, one “vertical” and one “horizontal”, allow no light to pass through, but when a third polarizer oriented at a 45 degree angle is placed in between these, light is able to pass through this triple combo of polarizers.  How?  Why?

Zukav says, referring to the 45° polarizer in the middle as producing diagonally polarized light:  “Diagonally polarized light is a coherent superposition of horizontally polarized light and vertically polarized light.  Quantum physics abounds with coherent superpositions. In fact, coherent super-positions are at the heart of the mathematics of quantum mechanics. Wave functions are coherent superpositions.”  Woowee, wave functions!  Now we’re getting somewhere!  "Coherent" comes up again also.

You may remember this discussion started with my interest in a new book I received in the mail earlier this year, called Introduction to the Theory of Coherence and Polarization of Light, by Emil Wolf.  I would not be interested at all except I'm trying to make a discovery.  Back in the mid-seventies, before I had any advanced physics training,  after reading a World Book encyclopedia article about some of the mysteries of quantum mechanics (I was in the back bedroom at my grandmother's house in Little Rock), I fell asleep and woke up with an idea: "diffuse retardations."  I wrote down those words even though they meant nothing to me at the time, but I later learned that a retarder in optics is a material like a birefringent crystal that changes the polarization of light passing through it.  The "diffuse" part is still mysterious and is something I'm still working on, but seems related to the 1980s idea of "decoherence" promoted by James Hartle and others.  Thus my interest in writing this--as a means of searching and researching--regardless of whether anyone else is reading it.

One more quote from Gary Zukav, then we will move on to Gordon Baym, J. J. Sakurai, and Arthur Fine.  Zukav mentions the “observed system,” which of course implies an observer.  An “observation” or measurement. In the Schrodinger’s cat experiment is what causes the cat to go from coherent superposition of “alive and dead” to either alive or dead.  The question for those who don’t simply dismiss it as a meaningless question is:  what in this case is the observation?  Now, go Gary:

“Every quantum mechanical experiment has an observed system.  Every observed system has an associated wave function. The wave function of a particular observed system (like a photon) is the coherent superposition of all the possible results of an interaction between the observed system and a measuring system (like a photographic plate).  The development in time of this coherent superposition of possibilities is described by Schrödinger’s wave equation.  Using this equation, we can calculate the form of this thing–in-itself, this coherent superposition of possibilities which we call a wave function, for any given time. Having done that, we then can calculate the probability of each possibility contained in the wave function at that particular time. …  In a nutshell, that is the mathematics of quantum physics.” 

Speaking of photos

Here are some recent ones from the Maui Minolta point and shoot-regular-35-mm-film camera.  I visited a restored Rosenwald School in Selma, Arkansas a couple of months ago, the purpose being a monthly meeting of Southeast Arkansas Economic Development District and its Regional Solid Waste District board, which administers Arkansas Department of Enviromental Quality recycling grants, which I depend on to keep the Recycling Center going.

I guess I'd heard of Rosenwald Schools, but don't recall when or where, and I'd never heard of Selma, except of course the one in Alabama.  Selma, Arkansas has about 150 residents and from the looks of the tiny town, it seemed more like ten. 

But it had a couple of old churches including this Methodist one (above) that dates to the 1880s.  The Rosenwald School building itself was built in the 1920s, and was restored, with the help of volunteer labor, a few years ago:

Edward Suber and Edward Suber Jr. were the most impressive people I met at the meeting.  Mr. Suber Sr. is a small man but he has I thought considerable charisma.  He's black, with somewhat graying but distinguished looking hair. He and his son were in the food line (a good lunch is always served at these meetings) in front of me. Earlier I'd seen him reading over a double-spaced manuscript, so I asked him if he was going to give a speech.  He pointed at his son--10 or 11 years old--and said, "No, he is."  And it was a super speech, about  the Rosenwald Schools.  And here's another story. On the backroads on my way to the meeting, I passed a cropduster just in the process of taking off parallel to the road.  The pilot was female, with a low-cut black blouse on!  I passed her, then she passed me as she took off.  Then she flew over me several times, disappearing over trees then coming back.  I was kind of worried about getting sprayed with herbicide, but there wasn't any spraying going on that I could see.  Then to top that off, on my way back to Pine Bluff, on different roads, I saw the same yellow plane again, and this time it seemed to be following me.  Why didn't I take a picture?  I was kind of afraid to.  I stopped once near a turn I was about to make, got out of the car with the camera, but didn't have the nerve or whatever to point it at the plane when it went by.  Then I got in the car and as the plane was coming back toward me, I turned on a road that was sheltered by trees on both sides.  I felt like I was being played around with, and it was sort of fun but sort of threatening, too.  The plane, a small yellow single engine plane, zoomed over me once while I was driving through the trees, then I didn't see it anymore.  Below, the inside of the Rosenwald School:

Speaking of Jews (Rosenwald), there are a lot of them buried in Pine Bluff's Bellwood Cemetery, where my ancestors and parents are buried (not in the large Jewish section, though) and where I take Jessie for a walk when I don't have time to go elsewhere.  Clouds and the entrance of the local Delta Kraft paper mill fill out this photo essay.

 

Stumbling upon The Dancing Wu Li Masters

There it was all along, in between Directions in Physics, by the taciturn "PAM" Dirac, and Art & Physics, by Leonard Schlain.  I was sitting at my dining room table, musing away about something after lunch on either Sunday or Monday, and I found it--I mean I realized I was looking at the book, the spine of the book, that I'd searched for earlier several times.

Wu Li translates as, among several other words and phrases mentioned by Zukav, "Patterns of Organic Energy," and "physics."  Yeh, how can that be?  Organic?  Later.

NYRB

The current issue of the New York Review of Books, dated July 14, is a good one.  Freeman Dyson's review of two books about Richard Feynman is enjoyable, thought provoking and, in one part, funny. Deborah Eisenberg's short story is quite amazing.  I think some friends of mine in Austin in particular would like this issue of the venerable NYRB. 

Making Waves

Yes, I've been writing, just not blogging away, until today.

A new thought on A Serious Man: the first words in English in the movie are “when the truth is found to be lies…”  This is what eventually happened to us, the innocent viewers, with the Coen Bros’ movie Fargo.   They billed it as a true story, but it wasn’t.  I was rather happy to hear that, however, and all the joy in me did not die.  Given all the suffering that goes on in the world, it was and is good to know that the particular suffering shown in that movie had not actually happened.  The trick of telling viewers it was a true story had the desired effect, at least in me.  It intensified the emotional experience of watching the movie. So I’m not pissed at the Bros for lying.  I can imagine the subterfuge of Fargo was on their minds while they were writing A Serious Man, which is itself a subterfuge on a more humorous level. 

Now, how is the three-polarizer experiment a demonstration of quantum superposition?  I wanted to talk about Gary Zukav’s description of the experiment, but I haven’t found The Dancing Wu Li Masters amongst my approximately 1,000 books.  I was reading from it earlier this year, so it’s around somewhere, but I’ll have to do without it for now. 

First of all, what the heck does “superposition” mean?   Sounds vaguely sexual to me, but then so does about everything else.  Classically, as opposed to quantumly, superposition means just what it sounds like, at least in the case of waves being superimposed.  As Frank Blatt, a physicist with a physical sounding last name, puts it in his first-year physics textbook, “when a transverse wave on a string is reflected at a fixed end, the incident and reflected waves superpose so as to create a standing wave.”

You can create this condition by tying one end a rope or cord to a doorknob (works best with the door closed) and shaking the other end up and down.  If you shake at the right rate, you can see a standing wave pattern: one hump, two humps, three humps, etc.   Under these conditions, waves traveling in opposite directions are combining with each other (linearly) to produce a standing wave.  It’s also called resonance.

If you yourself have taken a first-year physics course, you might have seen the demonstration of this standing wave phenomenon in the lab, where a mechanical vibrator is used (yeh, the sexual innuendos again).  I myself have done that experiment many times as a lab assistant or lab instructor.  With the rope on the doorknob, ya cain’t hardly get a good standing wave, but with a long piece of string in the lab, it looks very neat—big good vibrations, showing a larger and lower frequency version of what happens with stringed instruments as they are being played

In addition to standing waves on strings, there are acoustic standing waves (wind instruments and singing—in the shower especially), and electromagnetic standing waves, and water or other liquid standing waves. You know about the “rubbing the rim of the wine glass” sound, right?  You get standing waves in the wine and the glass then.   Also, waves combine with each other to produce the phenomena of interference and diffraction. 

Like waves on a string, electromagnetic waves are transverse.  For transverse waves (try the polarization hand waving thing again) the oscillatory motion is perpendicular to the direction the wave is traveling.  In contrast, sound in air is composed of longitudinal waves.  The oscillatory motion of the medium is along the same direction as the direction of travel of the wave.  If you and a friend stretch a Slinky along a flat surface, and then one of you pushes on the Slinky and pulls back, the compression travels to the other end as a longitudinal wave.  The same thing happens with air when it carries a sound wave: a back and forth motion along the direction the wave is traveling.

Going back to the cord tied to the door knob: you choose the direction of polarization of the wave by choosing whether to move your hand up and down or sideways, or in between.  So now do you think you’ve got the idea of the polarization thing?  Sure you do!  Congratulations!  So you can see that a longitudinal wave isn't subject to being polarized!  (Gettin’ out of the necessary range of the eventual quantum superposition discussion now.  But anyway, happy 4^th of July weekend.)