Thursday, September 28, 2006

Look What They Done to my Song

Back in the 1960s graduate physics was about quantum mechanics, the Dirac equation, quantum field theory and Feynman diagrams. (General Relativity was over to the side since gravity was different.) I still have Feynman’s book Quantum Electrodynamics (second printing with corrections by Peter Cziffra, University of Rochester, 1962. I was in the physics department at Rochester from 1964 - 1971.) Every page is filled with Feynman’s squiggles showing photon propagation in processes such as two-photon pair annihilation or electron-positron scattering. We learned that positrons could be viewed as electrons moving backward in time and many other wonders of nature.

I kept a copy of a take home exam from Physics 503 (Melissinos) requiring:

The calculation in complete detail of the cross section for production of electron-positron pairs by photons incident on an infinitely heavy nucleus. Plot the yield of events as a function of angle and compare your results to Asbury et al, Phys Rev 161, 1344 (1967). Discuss the possibility that your results could be interpreted as a breakdown of QED (or not) at high energies. Work by yourself!

The calculations involved the Feynman slash notation, two Feynman diagrams in this first order approximation and conservation of 4-momentum. The scattering matrix elements were determined by inspection from the Feynman diagrams (plus a ton of matrix algebra). My calculated cross section was inversely dependent on the cube of the photon energy. It was a strong function of the angle between the outgoing electron and positron, going to zero at zero angle, then increasing to a peak at a small angle and going back to zero at 180 degrees.


My results agreed with Asbury et al who also measured the experimental cross section at high energy and showed that it agreed with QED to within 5%. This fancy theory we were learning was real. I got a B+ on the exam.

Those were the early days when the theory and the experiments were not yet as refined as they would become. But QED has been tested and tested over the years and is now known to be the most accurate theory in all of science. For example, the magnetic moment of the electron has been calculated to eighth order using over 900 Feynman diagrams (and years of computer time) to be 2.0023193044 with an uncertainty of 2 in the last digit (one part in a trillion). The experimental value agrees exactly with the theoretical value, with even less uncertainty.

QED was already 20 years old by 1969 when I took the PhD qualifying exam (and my son was born). Despite its remarkable successes we knew that QED was not a complete quantum theory since it did not account for protons and other strongly interacting particles. And the field of nuclear particles was a veritable zoo.

We learned that Hideki Yukawa had predicted that protons and neutrons interact via exchange of pi-minus mesons (pions) much like electrons and positrons interact by exchange of photons. Thus the nuclear force was said to be carried by pion exchange. Also by analogy to electrons and positrons, the neutron and proton were thought to have a spin parameter, called isospin, with a plus sign for protons and a minus sign for neutrons.

In addition to the nucleons and the pions, experimenters found several other strongly interacting particles such as the plus and minus K mesons and their antiparticles, the sigmas, deltas, lambdas, omegas, etc. A bright fellow named Murray Gell-Mann invented a property called strangeness that he used to explain the strange behavior of some new particles that had unusually long lifetimes and were always produced in pairs.

When Gell-Mann plotted the particles of a known family on a graph of isospin versus strangeness he found they formed a perfect hexagon with two particles at the center, for a sum of eight particles. He called his scheme the “Eightfold Way.” As I was moving into quantum optics, my friends doing particle physics were learning about the Lie group SU(3) that explained the symmetry of the Eightfold Way and even related the masses of the particles.

I did not know what they were talking about until a Scientific American article appeared in the 1970s. It turned out that Gell-Mann also noticed that the simplest multiplet of three particles predicted by the SU(3) theory was missing. He was convinced that they had to exist, he called them quarks, and named them Up, Down and Strange. He believed that they were right there under our noses but hidden inside the other “fundamental” particles. To make it work Gell-Mann predicted that Up, Down and Strange had to have partial electric charges (+2/3, -1/3, -1/3) and isospins (+1/2, -1/2, 0), respectively.

(Independently of Gell-Mann, George Zweig came up with the same idea, although he called his new particles aces rather than quarks.)

The quark model not only explained the observed properties of the strongly interacting particles in the zoo but it also provided a picture of their interactions via particle exchange. Evidence that quarks were real began showing up in experiments at the Stanford Linear Accelerator in the late 1960s. Today we know there are six types of quarks: Up, Down, Strange and Charm, Top and Bottom. Furthermore the quarks inside the protons and other strongly interacting particles interact through a new set of massless particles called gluons. Gell-Mann dubbed the whole theory of quarks and gluons and their interactions quantum chromo-dynamics or QCD.

Later on Feynman’s QED was unified with the theory of the weak interactions in the Electroweak theory which together with Gell-Mann’s QCD comprise the Standard Model of Particle Physics. Although I could not do a single calculation in the Standard Model, I can understand it, appreciate its beauty and marvel at its predictions and experimental accuracy. It’s truly “the theory of almost everything” (See the book by Robert Oerter, 2006) since all it lacks is a theory of quantum gravity.

Oerter calls the Standard Model of Particle Physics the “pinnacle of human intellectual achievement. It surpasses in precision, in universality and in its range of applicability, every scientific theory that has ever existed.” Yet it doesn’t get any respect -- It is the Rodney Dangerfield of scientific theories. Every new experiment validating another aspect of the Standard Model to unheard of precision is greeted with a ho-hum.

The public has been enticed by the vision of a crippled magician in a wheelchair talking about new concepts of time and by speculations of multiple universes. The string theories have captured the public imagination. But despite its mathematical obtuseness, its mind blowing concepts and its lack of verification at any level, string theory has been the hot thing in physics for two decades.

Now what is an old retired physicist to do if he wants to understand the new physics? Mahndisa sent me links to two papers that she said would "provide you with a balance in perspective and both are rigourous but well written:)" She’s such a dear. Here they are.

1.
Thiemann. T. The LQG -- String: Loop Quantum Gravity Quantization of String Theory I. Flat Target Space. 23 Jan 2004.

2.Helling, Robert C. Policastro, Guiseppe. String quantization: Fock vs. LQG Representations. 17 Sept 2004.

Thieman describes his 58 page paper as “a (relatively) non-technical summary of the status of the quantum dynamics in Loop Quantum Gravity (LQG).” One had hope. He explains that LQG is gaining in popularity relative to string theory because LQG has “put its cards on the table.” Encouraging.

Then the trouble starts, as this snippet from a random page in the paper will illustrate:

“If one wants to have a well posed initial value formulation (OK so far) then the metric fields g that live on M are such that (M, g) is globally hyperbolic which implies that M is diffeomorphic to the direct product R x S where S is an n-dimensional smooth manifold. Since the action is invariant under Diff(M), the diffeomorphisms Y: R x S --> M; (t, x) --> Y are a symmetry of the action. For each Y we obtain a foliation of M into a one parameter family of spacelike hypersurfaces.” …. and so on.

I’m sorry, but that doesn’t look like physics to me. In fact I had to go back to page 39 before finding mention of a physical thing. In the section called Physical Applications, I found the problem in an innocent little statement: “We have so far hardly mentioned matter.” Indeed. What follows is more unintelligible math and more new terms (complexifiers??).


Finally on page 42, I found a microscopic explanation of the Bekenstein Hawking black hole entropy: ln(N) = Ar/4L, as long as a factor that was cancelled out does not depend on “the hair of the black hole.” I give up!

Look what they done to my song, ma

Look what they done to my song,
The only thing I could do half right and now it's turning out all wrong,
Look what they done to my song



6 Comments:

Anonymous Anonymous said...

Hey, man--this is one great blog.Thank you..... I really appreciate your erudition and explanations.

One thing I learned that shocked me was that there was another way to generate a child--doing a Ph.D qualifying exam!

Burt

11:14 AM  
Blogger Mahndisa S. Rigmaiden said...

09 30 06

Hey Bill:
Wonderful post you have here. Sure, Mr. Thiemann's work is a bit mired in formalism and the physical significance gets lost. But to sum up the paper, he quantized the Nambu Goto string using the Polhmeyer state which (to me) looks like a normed Delta distribution; Y(x)={1 if x=0 and 0 otherwise. Now, when we try to define the position and momentum operators by going to the Weyl form of the CCR's, we cannot really define them at all! They aren't elements of that C* algebra. However, since the Polhmeyer state isn't weakly continuous, we haven't used the Stone von Neumann theorem. Instead, to resolve what in tarnation the quantization yields, Fell's theorem is invoked. Oh garbage, I need to go now. I will finish up later. Meanwhile, the author is JMG Fell and the paper - I forget the name of the paper! It has C* algegras in the title and it was published somewhere around 1964. I will do a post more on this because the philosophical implications of avoiding the SVN theorem are pretty intriguing!

5:21 PM  
Blogger Mahndisa S. Rigmaiden said...

10 01 06

Hey Bill:
Let me finish up what I started before I had to leave. In the Helling and Policastro paper, they use the Pohlmeyer state to quantize the harmonic oscillator. But the spectrum doesn't look anything like what we are used to seeing! You know how we are used to seeing V(x)=Kx^2, hence all states are bound states for the harmonic oscillator. However, the Pohlmeyer state quantization yielded only ONE bound state and the rest were scattering states!

So this quantization isn't in concert with our phenomenological expectations. HOWEVER that doesn't mean that it isn't representative of SOME physical system. And this is where the difficulty lies-in tying in the formalism to the physics of some type of process!!

And yes, the paper by JMG Fell was entitled: "The Dual Spaces of C* Algebras."

I will do a post about inequivalent reps of the Schroedinger Weyl forms within the week. I have been working on it for a while, but now your post has obligated me to do it! I hope you have a great week:)

1:20 AM  
Blogger Mark said...

I never really bought into 20th cent. quantum physics model. Carver Mead has done some interesting work on particle physics models; and astrophyics is a complete joke. It's been ignoring the entire dimension of plasma physics for, oh, about a hundred years now.

I don't trust anything that comes out of academia regarding physics when it is still using the Big Bang Theory as some sort of touchstone.

3:25 PM  
Anonymous Anonymous said...

Bill,
Thanks for this; it was delightful. It reminded of my undergraduate days at the Univ. of Chicago in the '50's. The professors were often late to class because they were discovering new particles almost every week; they brought in the cloud chamber photographs. I couldn't discern all that much in those little trails but I didn't know very much either.

About Thiemann, that was hilarious. In my last year of graduate work (math), I ran a seminar on "sheafs of manifolds". I can't help but get a little woozy thinking about it now. But people (maybe even me) were saying things like the Thiemann quote. I think it meant something at the time (at least I'm hoping it wasn't all pretend).

Roy S

10:02 PM  
Anonymous Anonymous said...

Well with ironics of idiocy in the theoretical application without the old fasihiioned experiments and proof there are those out there that will upset the standard and end with 58 pages of grabage......... great for Chem Waste and the environment.

John H.

9:30 PM  

Post a Comment

Subscribe to Post Comments [Atom]

<< Home