05 September 2011

Einstein's theory of invariants

Well, my 21st century writing about relativity finally did get published, on the "Voices" page of the Arkansas Democrat-Gazette, on November 3, 2007, almost exactly seven years after I started working on it and tried to interest the NY Times and Harper's magazine, without success.  Publication on the Voices page meant there was no payment involved.  It was really just a long letter to the editor labeled a "Guest Column."  Here it is, slightly edited for clarity that was lacking in the published version:


Once upon a time, in the fall of 1977, I had the perfect job. I was a night watchman at the Old State House, usually working the 4 p.m. to midnight shift. My job was to make rounds through the building every hour. The job was perfect because I was a full-time student at UALR, and making a round took only ten minutes. In theory, I had 50 minutes out of each hour for studying.

In practice, I tended to read whatever interested me and to put off working on my homework as long as possible. I also had the luxury of being able to explore the Old State House all by myself whenever I felt like it. Procrastination, of course, is not an uncommon activity among college students. My happy situation was that I was getting paid for it—with a portion of your Arkansas tax dollar.

Or maybe it was your parents’ or grandparents’ dollar. Whatever the case may be, I’d like to now offer a little in the way of a return on that 30-year investment. I’d like to pass along a little bit of scientific knowledge.

During the fall of 1977, I was taking a beginning class in relativity and quantum mechanics. A good deal of my extracurricular reading during the evenings at the Old State House involved those subjects. Among other things, I was trying to find out if relativity really should be associated with the saying “It’s all relative.” I’d read that statement in a newspaper article about the virtuoso violinist and former child prodigy Yehudi Menuhin, who was asked what he’d learned from his acquaintance with Albert Einstein. Menuhin claimed to have learned from Einstein the same thing everyone else had learned, namely that “everything is relative.”

What I’ve learned over the years is that Einstein’s theory means the opposite of what it sounds like it means. When I started teaching physics about ten years ago, I came up with a way of paraphrasing the usual textbook description of the two ideas Einstein used in creating his theory. The ideas, or postulates, can be stated as 1) the laws of physics are not relative, and 2) the speed of light is not relative.

Those are the requirements that went into relativity. In actually finding equations for laws that satisfy these ideas, Einstein rewrote Newton’s laws of motion, simplified the laws of electricity and magnetism, and discovered several new laws, the most well known of which is the equivalence of energy and mass, E = mc2.

Besides the laws themselves, other mathematical entities are invariant in relativity. In particular, space, time, and the speed of light combine together in a simple equation for an invariant quantity called “proper time.” (This is a mistranslation from the French word propre, meaning “own”.)  Proper time is the time you read on your own watch. Since you and your watch never move relative to each other, you never observe your own watch to speed up or slow down--contrary to the popular misconception of time slowing down the faster you travel. The slowing down of time is only valid when you compare your time to the time of the clocks in another rest frame, such as the one you left when you went moving off on your own.  "Moving on your own," however, is just like not moving at all.  That is the real message of relativity.

Relativity is not the name Einstein chose for his theory. He would have preferred it to be called the theory of invariants. This misnaming can be blamed on several of Einstein’s older contemporaries, including the French mathematician Henrí Poincaré and the German physicist Max Planck. Einstein unfortunately in his first relativity paper in 1905 used the accepted terminology of the time and called his first postulate "the principle of relativity". He later objected to his entire theory being called relativity, but he acquiesced to common usage among physicists in 1915 when he named his theory of gravity the general theory of relativity.

Gerald Holton, the grand old man of Einstein studies and an emeritus professor of physics at Harvard, wrote something of an off-the-beaten-path book published in 1996 called “Einstein, History and Other Passions.” Holton neatly summarizes the relative/relativity name confusion: “The cliché became, erroneously, ‘everything is relative’; whereas the point is that out of the vast flux one can distill the very opposite: ‘some things are invariant.’”

So, “everything is relative” may be a balm of hurt minds, but physicists are looking for those things in the universe that are invariant. Invariance, by the way, is related to symmetry, but you’ll have to look that up for yourself.

03 September 2011

Harper's query letter of a decade ago (rejected)

David W. Trulock
100 Riverbend Dr.
Apartment F9
West Columbia, SC
29169


Ann Gollin
Editor’s Assistant
Harper’s Magazine
666 Broadway, 11th Floor
New York, New York 10012

September 3, 2001
 
Dear Ms. Gollin:

I’m interested in writing an essay for Harper’s about the mistaken idea that relativism has legitimate roots in relativity. I am guessing there will be a lot of “relativistic” articles published between now and the 100th anniversary of Einstein’s relativity in 2005, and I would like to get the subject started off in the right direction for Harper’s readers.

I’ve enclosed some writing samples of mine, two of which are about relativity. The published piece, “Relativity is Not Relative And Einstein is Misunderstood,” appeared in Spectrum, a now-defunct alternative newspaper. “Displaying Little Regard for the Mysteries of Life” also appeared in Spectrum and was reprinted in A Spectrum Reader (August House, Little Rock, 1991). Spectrum was published bi-weekly in Little Rock from 1984 until 1990, when it became Spectrum Weekly. It may have weakened as a weekly, since it ceased publication in 1993. In any case, I moved from Little Rock to Austin in 1987 and didn’t write much for Spectrum after that. I wrote one full-length freelance article (enclosed) for the weekly Austin Chronicle, which is not defunct.

The short manuscript I’ve included in this query is my unsuccessful attempt to put the correct ideas about relativity on the New York Times Op-Ed page on April 18 of this year. In naming Albert Einstein “person of the century” a year and a half ago, Time magazine published some incorrect ideas about relativity. Walter Isaacson, for example, in his article “Who Mattered and Why,” implied that Einstein’s relativity destroyed the meaning or the existence of absolute laws. I hope from my enclosed writing samples you can see this is not true.

Why should I be the one to write this article? Because it’s likely no one else is going to bother to write it—many physicists accept the “two cultures” of relativity. Also, I’ve studied relativity for 25 years, independently and in graduate and undergraduate classes, and as a research project with Dr. John Safko here at the University of South Carolina, where I’m seeking a physics PhD. I have a master’s degree in physics from Southwest Texas State University, where I taught some physics classes, and a BA in physics from Hendrix College in Conway, Arkansas. I also attended Columbia University (Summer 1978) and the University of Texas at Austin (on and off as a non-degree-seeking student).

Sincerely yours,

01 September 2011

Turtle orgasm on Bayou Bartholomew trail

It happened two or three years ago.  I was carrying my Pentax K-1000, which hasn't had a working light meter in umpteen years, but I've still managed to get some good photos from it.  (This is one beauty of writing in a web-log,  especially a very private one, I don't worry much about correct grammar.)  I chanced, those several years ago, on the B.B. trail, upon these turtles.  The photo turned out discreetly dark. The male's mouth is widely open..."Oh, god!"


30 August 2011

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.




19 August 2011

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|Ψalive> + β|Ψdead>,

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  2> = |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?!

12 August 2011

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.

06 August 2011

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.