Sakurai complements (and compliments) Baym

Now back to our program.  We've looked at introducing quantum mechanics from the photon point of view, mainly as described in the first chapter of Gordon Baym's book Lectures on Quantum Mechanics.  Baym makes the point that once photons are introduced, things get weird.  Namely, in a linearly polarized beam of light, all the photons (we'd think) would be identical, so how come some get through a polarizer oriented at an angle different to that of the polarization plane of the beam, and some don't get through?

The reason is quantum superposition, which, even more than Heisenberg's uncertainty principle, is what makes quantum theory so different and inexplicable in terms of the classical ideas of continuity and unique identity.

Baym's discussion focuses on the concepts of the photon and quantum (or coherent) superposition.  He doesn't really emphasize the importance of how these concepts together lead to the fundamental formalism of quantum mechanics, which requires a complex vector space, as opposed to the "real"  vector space with which classical mechanics can be fully described. 

One of the other books I discussed earlier is Modern Quantum Mechanics, by J. J. Sakurai.  Whereas Baym takes the quantization of the electromagnetic field--the existence of the photon--as his starting point, Sakurai introduces quantum superposition as a way, the only way, of explaining certain experiments on the spin of the electron, and then points out how beams of light passing thru polarizers can be explained the same way without even invoking the concept of photons.

Sakurai opens his book by discussing an experiment involving the orientation of individual silver atoms after they pass through an inhomogeneous magnetic field. (Silver atoms ejected from an oven in gaseous form and collimated into a beam which passes thru the poles of a magnet is what we're talking about, y'all.) This famous experiment was first done in 1922 by Otto Stern and Walter Gerlach.  The inhomogeneous B field is used in order to exert a net force up-or-down on the atoms, due to the atoms having one unpaired outer electron.  The first non-classical aspect of this arrangement is that it shows the outer electrons of the silver atoms have only two orientations in space instead of a continuum of values.  Thus the demonstration of two discrete beams of silver atoms emerging from the Stern-Gerlach (SG) setup shows experimentally the quantized "spin" of the electron.

But the second non-classical effect that can be demonstrated with this experiment is the really strange one.  In a sequential setup that 1)  blocks one of the two up-or-down (z-direction) beams (say the downward oriented beam) emerging from the standard SG setup, then sends the one remaining beam thru 2) a B field in the x direction (horizontal; standard SG setup tilted 90 degrees), resulting in two horizontally deflected discrete beams, then 3) blocks one of these beams and sends the remaining single beam thru a final B field in the z direction (same as original SG setup), the result is that there are again two beams with z direction orientations, up and down.  The downward oriented beam that was blocked in 1) has come back in 3) without a fresh new group of downward-z-oriented atoms being used!  Yeh, I  had to study on it myself before I could wrap my mind around it for any length of time.

Then Sakurai shows how, in order to describe all possible orientations of the beams in relation to each other--the z, the x and the y orientations--complex numbers (a "complex vector space") must be used.  His introduction to the use of complex vector space is by way of polarized light.  The third orientation (the y direction) of the spinning electron is analogous to circularly polarized light, he says.  He also describes how th the 3-polarizer setup for light beams, is just like the three-SG setups in that coherent superposition is the only way to describe how a polarized beam can get thru the three consecutive, differently oriented polariods (polarizers).  Sakurai then mentions that he did not have to invoke the concept of photons in order to accurately describe the 3-polarizer effect.  Coherent superposition and complex vector space together are sufficient.

In a footnote, Sakurai says even though he didn't make use of the idea of photons, the reader can see Baym's book for an "extremely illuminating" discussion from the photon point of view (no pun intended, probably).  One reason Baym's description is illuminating is that he introduces the essential mystery of the 3-polarizer effect by commenting on the weirdness of one polarizer's effect on supposedly identical photons--some get thru and some don't. 

Tree frog on the ground



I took this with a disposable (recyclable, I would hope) camera in December, in Aunt Sue's yard at the farm.  It may not be her yard too much longer.  The high cost of heating and cooling her house (my Trulock grandparents' former home, built in 1926), plus maintenance costs, have caused her to start looking for a potential buyer.  I'm one of them, but not the primary one. I also now own a lot over on the Arkansas River in the Trulock Bay Estates area, developed by my grandfather in 1969.   Don't know what to do, but don't really want to do anything (typically!) and would actually be lonely living out in the country alone, even with my faithful dog Jessie.  I can easily live in the city without getting lonely.  Wonder why that is?

Sports Illustrated article on Drake's Landing: 55th anniversary today

DRAKES' LANDING: DUCKS BY THE MILLION

Farther south along the flyway, where the waters of the Arkansas and White rivers irrigate a triangle of rice-rich abundance, the Drakes' Landing Club nestles within a flooded forest. One of the oldest duck clubs in Arkansas, its 640 acres stretch into the heart of the famed Stuttgart hunting area. Twenty-five years ago, when the original nine members carted all facilities from Pine Bluff every weekend, tents were pitched and decoys set for each hunt. Today the club's caretaker sets out the decoys at the beginning of each season in a dozen permanent locations. The brick clubhouse sleeps 18, enabling each member to bring one guest. Only the ducks have been unchanged by progress. By the millions they cover the flood lands with a feathery blanket, luring the hunters into the early dawn.

Predawn breakfast is enjoyed by (left) member's son E. Russell Lambert Jr. of Chalmette Plantation; S. Ray West, partner, F. G. Smart Motors; Mrs. West and Dr. E. C. McMullen, for 26 years Drakes' Landing Club president. Walter Trulock Jr., cotton planter and ginner, sits with other hunters at rear table, as two club cooks dish out bacon and eggs in the little kitchen beyond.

MORNING COMES WITH MISTS AND MALLARDS

Fog mingles with the ends of night and fingers a procession of fiat-bottomed aluminum duck boats as hunters paddle silently away from the Drakes' Landing clubhouse. It is a half hour before sunrise. Anxious eyes search the blackened skies. Impatience makes the journey seem longer and shooting positions farther away. Tangled roots scratch against the bottoms of the boats, growling in the quiet. Like sentinels guarding a drowned land, the shadows of dead cypress trees cast somber reflections across the inky waters. Among them, pin oaks, rosewoods, overcups and pecan trees wait for another spring to sprout green leaves again. Clustered on branches everywhere, mistletoe drop waxen berries to the pools below and rustle gently with the wind. On the many lakes scattered throughout this watery woodland, decoys rock softly on the swells. Early morning filters pink through the trees, shifting the shadows as it comes, touching a hunter motionless beside a willow. Overhead, like dark specks in the dawn sky, a flock of ducks goes by. From the recesses of the woods the hunters begin their calls, coaxing the birds with loud, plaintive sounds. Down from the sky they fall, circling, dipping, circling again. The calls change, grow frenzied, more insistent and are answered. Back and forth ducks and hunters talk in excited, guttural conversation. In an ever-narrowing circle the ducks lose altitude, wingbeats audible above the chatter. Then, setting their wings, they push white bellies into the wind and drop toward the decoys below. The shots are loud, rapid. Three mallards plummet to the calm waters, spreading great rings from the places where they strike. In the distance, the remainder of the flight disappears into the sky. A hip-booted hunter walks through knee-deep water to the fallen birds. With twigs he props them up among the decoys and returns to wait beside his tree. At Hurricane Hole, Tin Can, Nine Oaks, or East Taylor other Drakes' Landing members wait, scanning the brightening skies. Some crouch in willow-covered blinds, others under large bushes, still others behind camouflaged boats, breathlessly, thigh-deep in water. By 7:30 almost any morning, the hunters usually have shot their limits and the day's hunt is over. An hour's drive away, in Pine Bluff, they will attend bank meetings, sell automobiles, negotiate cotton sales and treat patients at the opening of a regular business day.

Wading through the shallows of Hurricane Hole, Walter Trulock Jr. (right) heads homeward with sons Leo and Walter III after all three bagged limits within 45 minutes of legal shooting hour. Together they look skyward for one last glimpse of birds before returning to the city. In their wake, decoys bob up and down upon the rippled water, waiting for still another day.

"What Makes Theories Grow?"

"Scientific theories are invented and cared for by people, and so have the properties of any other human institution--vigorous growth when all factors are right; stagnation and decadence, even retrograde progress when they are not. And the factors that determine which it will be are seldom the ones (such as the state of experimental or mathematical techniques) that one might at first expect.  Among factors that have seemed, historically, to be more important are practical considerations, accidents of birth or personality of individual people; and above all, the general philosphical climate in which the scientist lives, which determines whether efforts in a certain direction will be approved or deprecated by the scientific community as a whole."

--Edwin T. Jaynes, from the opening paragraph of a talk given at one of the Delaware Seminars in the Foundations of Physics. The talk is titled "Foundations of Probability Theory and Statistical Mechanics."  The seminar took place and its proceedings were published (edited by Mario Bunge of the University of Delaware) in that Serious Man year of 1967.  Jaynes was at the time a physics professor at Washington University in St. Louis, and was a well respected contributor to the fields of statistical mechanics and quantum optics.  In 1980, I applied to Washington University because I'd read some of Jayne's papers.  They didn't want me.  Probably a wise decision on their part, given my desultory record of graduate work since then. 

Merton and Me

Me first.  From a journal entry March 22, 1987, related to quantum measurement:

The external world may be composed of entities that don’t have definite properties until an observation attaches the property or properties. Our senses, however, are not by themselves capable of detecting these entities.  So we probably should not talk about what exists and what doesn’t, since we must rely on second hand information from our measuring apparati.

We should only speak of how quantities or entities interact.  That would seem to be* all we can measure—the product of the interaction of our measuring instruments with the entities of nature.  It is the properties of the interaction that can be measured, that are in and of themselves the measurement.

The composite world definitely exists whether we observe** it or not.  The other world, the invisible world, is something we have created from our imagination, and perhaps there is no reason to expect it to show an existence independent of our imagination.

There is a problem with this view, however.  It doesn’t give us the fundamental physical entities from which the composite world is formed.  And of course we are habitually prone to ask what is interacting with us when we make a quantum measurement.

Now what is meant here (there, in second paragraph) by “the product of the interaction of our measuring instruments with the entities of nature”?  The joint product of the combined properties (at the moment of measurement) of the entity and the apparatus.  Modern physics has concocted virtual particles to explain interactions.  The particles are the media of interaction.  But I think there is a better way to explain these phenomena.  I don’t know what it is yet!  (That’s why I need some graduate physics classes.)      (end of quote. i took grad physics classes later, still don't know a better way than virtual particles, still working on it.)

*in my journal, instead of “would seem to be” I said “certainly is”.  So much for my open-minded attitude in 1987.

**I said “measure” not “observe” in my journal.  A measurement is a quantitative observation.

 

Now Thomas Merton, from chapter 30 (“Distractions”) in New Seeds of Contemplation, first published in 1961:

PRAYER and love are really learned in the hour when prayer becomes impossible and your heart turns to stone.

IF you have never had any distractions you don’t know how to pray.  For the secret of prayer is a hunger for God and for the vision of God, a hunger that lies far deeper than the level of language or affection.  And a man whose memory and imagination are persecuting him with a crowd of useless or even evil thoughts and images may sometimes be forced to pray far better, in the depths of his murdered heart, than one whose mind is swimming with clear concepts and brilliant purposes and easy acts of love.

That is why it is useless to get upset when you cannot shake off distractions. …  after a while, the doors of your subconscious mind fall ajar and all sorts of curious figures begin to come waltzing about on the scene.  If you are wise you will not pay any attention to these things: remain in simple attention to God and keep your will peacefully directed to Him in simple desire, while the intermittent shadows of this annoying movie go about in the remote background.  If you are aware of them at all it is only to realize that you refuse them.
 

The kind of distractions that holy people most fear are generally the most harmless of all. ….
 

If they ever had a sense of humor, they have now become so nervous that it has abandoned them altogether.  Yet humor is one of the things that would probably be most helpful at such a time.

I wonder if Thomas was thinking of vulgar humor when he wrote that.  I certainly enjoyed the vulgar humor in the movie Paul.  And Merton was certainly thinking of vulgar distractions ("the phantasms of a lewd and somewhat idiotic burlesuque" as he says in the paragraph I left out) as being what holy people most fear.