Polymeric molecules, pure and mixed states

While it's still August, I'll quote again from friendly Frank J. Blatt's physics textbook, this time concerning one particular type of polarizer.  I bought the textbook at a yard sale at 4110 Avenue F in Austin, Texas in August 1997.  Or maybe it was 4112 Ave F.  Anyway, I like Blatt's writing:

The most common polarizer in use today is a synthetic dichroic material invented by E. H. Land. Polaroid is produced by stretching a sheet of polyvinyl alcohol, thereby aligning the long hydrocarbon chains of the polymeric molecules. The sheet is then impregnated with iodine, which attaches itself to the polymers and results in good electrical conduction along the chains, but allows little conduction perpendicular to them. Electromagnetic waves whose E vector is parallel to the polymers are then strongly absorbed by this material.

The E vector represents the electric field's direction and strength. 

Now a bit more from Gordon Baym on the mysteries of quantum mechanics:

There are really two levels of probability in quantum mechanics. The first, which is called the pure case, is when we have a system that is in a definite state (often called a pure state). Then the behavior of this system in a given experiment is governed by the probability amplitude rules we have been discussing. The second case is when the system can be in any of several states, with certain probabilities. This case is called the mixed case, and we say that the photon is in a mixed state. Then one must calculate the results one expects in a given experiment for each of the separate states that can be present, and take the weighted average of the result over these, as we have done ...   In averaging over the various states that can be present, one uses the ordinary classical probability rules; there is no possibility of interference occurring between these states.

Now, I'm not saying it makes any sense, yet.  But I learn stuff from copying it down, so by typing the quote, I will I hope remember its content.  I'll have more to say on pure and mixed states later.  To begin with, however, you can see that purity involves those delicate phase relationships and the possibility of interference, and mixed-ity involves only ordinary classical probabilities, with no chance of quantum mechanical interference.  Quantum superposition and interference are thus closely related.

And speaking of closely related:  what kicked off this whole polarization discussion was the mention by Emil Wolf of the close relationship of polarization and coherence (of light), and the fact that I had been thinking something similar myself before Wolfie wrote about it.

Those delicate phase relationships

Okay, to get back to the predicament of Schroedinger's cat, the reason we can't apply normal logic and say the cat is either alive or dead and we don't know which until we look is because quantum logic defies normal logic.  The cat is in a superposition of states of being alive and being dead.  In the state vector notation of quantum mechanics, this can be written

|Φ> = α|Ψ_alive> + β|Ψ_dead>,

where in this equally probable two-state example, α = β = 1⁄√2.  In Lectures on Quantum Mechanics, page 26, Gordon Baym discusses the difference between the classical either/or case and the quantum "unique superposition" case (which Gary Zukav noted the strangeness of by calling it a "thing in itself").  Instead of a cat Baym is talking about a single photon and how it's a superposition of polarization states:  

“It is very important to realize that the statement ‘the photon is either in state |Ψ₁> or |Ψ₂>, but we don’t know which,’ is not the same statement as ‘the photon is in a superposition of |Ψ₁> and |Ψ₂>.’ … The point is that when we say that a photon is in a state |Φ> that is a linear combination of states |Ψ₁> and |Ψ₂>,

|Φ> = α|Ψ₁> + β|Ψ₂>,

then we are implying that the relative phase of the coefficients α and β is certain.  For example, if |Ψ₁> = |x> and  |Ψ₂> = |y>, then if α = 1⁄√2 and β = i ⁄ √2, clearly |Φ> = |R>, but if if α = 1⁄√2 and  β = – i ⁄ √2, then |Φ> = |L>, which is a state completely different from |R>.  The relative phase must be fixed to specify the linear combination uniquely.  On the other hand, when we say that a photon is either in state |Ψ₁> or |Ψ₂>, but we don’t know which, then we are implying that there is no connection between the phases of these states, and hence no possibility of interference effects, which depend critically on delicate phase relations…”

The state |R> represents right circular polarization, |L> represents left circular polarization, and, of course, i is the square root of negative one.  Who would have thought this could be so much fun?!

Coherence, polarization, dog in the back seat

Definitions of coherence and polarization from the Encyclopedia Britannica:

coherence, a fixed relationship between the phase of waves in a beam of radiation of a single frequency. Two beams of light are coherent when the phase difference between their waves is constant; they are noncoherent if there is a random or changing phase relationship. Stable interference patterns are formed only by radiation emitted by coherent sources, ordinarily produced by splitting a single beam into two or more beams. A laser, unlike an incandescent source, produces a beam in which all the components bear a fixed relationship to each other.

polarization, property of electromagnetic radiations in which the direction and magnitude of the vibrating electric field are related in a specified way. Light waves are transverse: that is, the vibrating electric vector associated with each wave is perpendicular to the direction of propagation. A beam of unpolarized light consists of waves moving in the same direction with their electric vectors pointed in random orientations about the axis of propagation. Plane polarized light consists of waves in which the direction of vibration is the same for all waves. In circular polarization the electric vector rotates about the direction of propagation as the wave progresses. Light may be polarized by reflection or by passing it through filters, such as certain crystals, that transmit vibration in one plane but not in others.

 I've trained Jessie to wait in the backseat with the car door open until I say "okay!"  Other things I tell her to do, she has to think about for a little while before she does them. I give her credit for her contemplative ability.

Hiroshima

Hiroshima Remembrance Day.  I woke up remembering.  Resting in bed as long as I thought I could, and having to be at work at nine a.m. (first Saturday of the month), I finally sat up and looked at the clock, which said 8:15, the time the untested gun-type uranium-235 bomb went off in the summertime air above Hiroshima. 

My Trulock grandfather, circa 1900

My paternal grandfather, Walter Nichols Trulock, Jr, was born in 1898, in Pine Bluff.  When I was born, he was the age I am now. 

I don't know how old he is in this photo, but would guess two or three.

Just as I was writing this I realized I completed my master's thesis and got my master of science in physics at Southwest Texas State University (now Texas State University-San Marcos) one hundred years after my grandfather was born.  I'm still researching the subject of my thesis, which I called "The Binding Energy of the Classical Electron."  Now the "classical electron" is complete nonsense but there is much nonsense in physics!   So-called dark matter and dark energy currently are nonsense, or at least a groping in the dark.  Also the electron as a mathematical point, with no structure, is nonsense, but then so is an electron with a finite diameter.  Lots of room for improvement! 

The electron was discovered in 1897, which was when my grandfather was conceived (his birthday is February 7, 1898).  In my thesis, I say the electron was discovered "100 years ago."  Really, it was 101 as of 1998.  I could have called my thesis "Electron 101", not a bad name considering I was trying to take a new elementary look at the electron.  Why don't I just post the first and last paragraphs of the thesis?   First:

In the 100 years since the discovery of the electron, no one has produced a satisfactory answer to the most elementary questions about this first inhabitant of what has been called[1] the subatomic particle zoo.  Although it has been defined by precise measurements of its charge, charge-to-mass ratio, and magnetic moment, and even though the experimental value of magnetic moment fits very snugly into the calculational confines of quantum electrodynamics, the electron is still a mystery.  Why does it have the charge and mass it has?  Why is the charge precisely the same as the proton’s charge (but opposite in sign), and why do the electron and proton have the charge-to-mass ratios they have?  Until these conceptual questions are answered and the mass and charge of the electron are predicted by a theory, rather than inserted as parameters in quantum electrodynamics as they are now, we cannot say we understand what an electron is.

Last paragraph, not including the appendix:

There are two ways to look at the problems posed by the classical electron model.  Why not just say that an electron is given to us as a point charge and there is no sense in asking what its structure is?  That is the working assumption of quantum electrodynamics.  The answer to that question--the other way to look at the classical model of the electron--is contained in the questions about the electron’s (and proton’s) charge and mass posed in the Introduction.  An improved classical relativistic theory of the electron could lead to an improved quantum theory, and that could lead to a theory that explains and relates the charges and masses of the elementary particles.

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[1] Cindy Schwarz, A Tour of the Subatomic Zoo:  A Guide to Particle Physics , 2nd ed. (American Institute of Physics, New York, 1997).