The Moon’s Subtle Influence

Science or fiction, sometimes it is hard to tell. In 1997, a group of Chinese scientists hooked up a sensitive gravimeter, to automatically record the earth’s gravitational field (or more accurately, the local acceleration of the earth’s crust) in the obscure northeast China town of Mohe, Heilongjiang (Black Dragon River) province. They chose this town because it was near the center of the 1997 solar eclipse, achieving totality for about 2 minutes. They chose the most accurate unit available, it can detect the reduction in gravitation when it is raised 1cm.

After the eclipse they examined their data. They found the usual tidal effects and slow drifts but they also found an interesting signal at the beginning and end of the eclipse, a signal that indicated that the earth’s gravitation field weakened slightly, or that the location was lifted into the air a few cm, or, perhaps, the gravitational field of the sun or moon had increased slightly. Their data, published in Phys Rev D 62, 041101, in units of looked like this:

Mohe eclipse data

Let’s look at the data. Our first step will be to look at the elevation of the sun.

The Force of Gravity

Six weeks ago I submitted a paper, “The Force of Gravity in Schwarzschild and Gullstrand-Painleve Coordinates” to the annual Gravity Essay Contest at the Gravity Research Foundation.

The Gravity Research Foundation
The Gravity Research Foundation (see the informative wikipedia article) was started in 1948 by a wealthy businessman, Roger Babson, who also started Babson College, a private business college. Babson’s motivation was to help physicists discover antigravity. Physicists soon convinced him to instead fund new research into gravitation (and who knows, maybe the antigrav equipment will appear later). And so this has become a mainstream annual essay contest, with many winners with Nobel Prize winners recognizable in the list of winners.

The results are in today. I got an “honorable mention”. The email comes with a sentence: “Please expect an invitation from Dr. D. V. Ahluwalia regarding possible publication in a special issue of IJMPD.” This is the International Journal of Modern Physics D, a peer reviewed physics journal (impact factor of 1.87) which specializes in gravitation, astrophysics, and cosmology.

Matrix Decomposition by Discrete Fourier Transform

Given a 3-vector of complex numbers, (A,B,C), define its discrete Fourier transform as

where . That is, I’ll use lower case letters to denote the discrete Fourier transforms of UPPER case letters. The above leaves off a factor of but it will do.

Of interest today will be vectors (A,B,C) which happen to satisfy A+B+C = 0. These are eigenvectors of the Democratic D matrix

Democratic matrix with all entries D

that is, the matrix all of whose entries are equal to the complex number D. Of course their eigenvalues are zero. None of this is particularly interesting until we move from linearity to bilinearity and work with the discrete Fourier transforms of 3×3 matrices.

Define the Fourier transform of a 3×3 matrix U as where is the matrix:

Discrete Fourier transform matrix

where . With this definition, the discrete Fourier transform of the democratic matrix D, is:

Fourier transform of democratic matrix

This is a nice simplification.

Now let A+B+C=0 and compute some discrete Fourier transforms of four kinds of matrices, 1-circulant, 2-circulant, and two new types I will call “bra” and “ket” for obvious reasons. Untransformed matrices on the left, their transforms on the right, note that they fit together like the pieces of a jigsaw puzzle:

An Immorality Tale

She was born with given name Johanna Maria Magdalena and a last name of either Behrend or Ritschel, my sources disagree. Her parents were unmarried, did she receive the last name of her father, Oskar Ritschel, or her mother, Auguste Behrend? In either case it was November 11, 1901. She was one of the most fascinating personalities of her time.

Youth
Her mother worked as a servant in Berlin and her father was an engineer who worked in various places around Europe. Soon after her birth, they married, but only for 3 years. Until she was 5, she stayed with her mother. Then she went to Belgium to visit her father who, after a delay of two years and insistent requests from the mother, finally told her that he had sent their child to be educated by the nuns at a convent (Catholic) boarding school in Brussels.

Her mother met and married a Jewish businessman, Richard Friedländer. When, the couple saw the conditions at the convent her mother decided to transfer her daughter to another convent, one that was less strict, in Vilvoorde, Belgium. Her parents moved to Schaerbeek, near Brussels (Belgium), and now she was able to come home to visit. With the marriage, she became Johanna Maria Magdalena Friedländer, and from the age of 7 she was raised in a household that observed both Catholic and Jewish customs.

In 1914, the world descended into the horror of the first world war. As German aliens living in Belgium, overnight the Friedländers became refugees. Eventually they made it to the German border, probably feeling fortunate that there was space available on a cattle car for them. As the modern world is one of passenger jets, the railroad was the transportation mode of the first half of the 20th century. Transport by livestock car is not a pleasant thing. Later, in the second world war, many thousands would be transported this way to the concentration camp at Buchenwald, where Richard Friedländer died. But let us return to her story.

Survivors at Buchenwald, April 16, 1945

New Paper on Hadrons and Koide’s mass formula

I’ve got a paper on the hadrons ready to submit to Phys Math Central. This is a fairly new peer reviewed open access journal for which I have a “pass” that allows me to avoid having to pay the $1500 submission fee, so long as I submit before January 31. This is a big deal and I want to do it right, so I’m looking for advice from readers.

The paper as it stands is here:
Koide mass formulas for the hadrons, 49 pages, LaTeX.

The subject is the extension of Koide’s lepton mass formula to the neutrinos and then to the hadrons. I’ve written the background section so it should be accessible to typical grad students in physics.

I’ve put this together as an example of applying quantum information theory to the practical problem of the hadron masses. This all is fairly simple stuff and it uses very basic ideas in quantum mechanics.

More arXiv papers, Dec 15, 2008

Various papers which I may not yet have read, but want to take a look at:

Geodesic stability, Lyapunov exponents and quasinormal modes by Vitor Cardoso, Alex S. Miranda, Emanuele Berti, Helvi Witek, and Vilson T. Zanchin.

Categorical Foundation of Quantum Mechanics and String Theory by A. Nicolaidis.

A Finite Electroweak Model Without a Higgs Particle by J. W. Moffat and V. T. Toth.

A list of astrophysical paradoxes, and on the idea of “paradox” in general:Astrophysical Paradoxes by Dragoljub A. Cucic.

A particularly interesting paper for me:
Infinite Statistics, Symmetry Breaking and Combinatorial Hierarchy by V.Shevchenko:

The physics of symmetry breaking in theories with strongly interacting quanta obeying infinite (quantum Boltzmann) statistics known as quons is discussed. The picture of Bose/Fermi particles as low energy excitations over nontrivial quon condensate is advocated. Using induced gravity arguments it is demonstrated that the Planck mass in such low energy effective theory can be factorially (in number of degrees of freedom) larger than its true ultraviolet cutoff. Thus, the assumption that statistics of relevant high energy excitations is neither Bose nor Fermi but infinite can remove the hierarchy problem without necessity to introduce any artificially large numbers. Quantum mechanical model illustrating this scenario is presented.

This week’s arXiv haul (Dec 5, 2008)

More than the usual number of interesting articles at arXiv caught my eye this week. I’m thinking about making this a weekly habit.

Denis Kochan’s new arXiv article: Does path integral really need a Lagrangian/Hamiltonian?, 0812.0678

Path integral formulation of quantum mechanics is strongly dependent on a given Lagrangian and/or Hamiltonian function. In the paper a simple rearrangement of the path integral to a surface functional integral is proposed. It is shown that the surface integral formulation of a transition probability amplitude is free of any particular choices and requires just the underlying classical equations of motion. A simple example examining functionality of the proposed method is considered.

FQXi Nature of Time Voting Begins

December 1st was the last day to submit an essay on The Nature of Time to FQXi. The contest was open for essays way back on August 4th. I submitted an essay titled Density Operators and Time, back on September 2nd. As of today, there are 127 essays so far. There could be more. There are 48 entries dated December 1st or, interestingly, 2nd. Three of my favorite theoreticians (uh, other than myself) have submitted papers:

Marni Sheppeard wrote Measurement processes and cosmological emergence. This is the only essay that manages to get a mention in for mutually unbiased bases.

Louise Riofrio writes on The Riddle of Time: R = t. This is a revisit of her stuff on R=ct, but with c suppressed, I suppose, so that it doesn’t count as previously published.

David Hestenes writes on the electron Zitterbewegung, Electron time, mass and zitter. This is basically an abbreviation and rewrite of his arXiv article, which, somewhat hilariously, got classified by Cornell as “general physics”: 0802.3227.

Riofrio and Sheppeard got their papers in just before the deadline and may have been a bit rushed. Nevertheless, since these things basically amount to popularity contests, I’ve voted for them. Hopefully, having at least one restricted vote will distinguish them enough that people will read them.

The leading entry for restricted votes is that of Carlo Rovelli, “Forget time” . He argues that we should look for quantum gravity in a form where time plays no role at all.

The Battle of Campeche

Matt Springer, of Texas A&M, via his blog Built On Facts is sending me large numbers of visitors so I thought I would share a small part of the history of Texas, and the Texas navy.

Texas was a part of Mexico when the colony of Spain obtained independence as a result of the Mexican War of Independence, 1810-1821. There followed a brief empire under Agustín de Iturbide followed by the first Mexican Republic in 1824 with Guadalupe Victoria (an assumed name) as President. The election to succeed Guadalupe Victoria was one by the founder of the Partido Moderador (Moderate Party), Manuel Gómez Pedraza, however, before he could take office, the now infamous Antonio López de Santa Anna forced him out and annulled the election. Antonio López de Santa Anna installed the first arguably African-American president of a major North American country, Vicente Guerrero, into power. One of Vicente Guerrero’s most important acts of his brief (1 April 1829 – 17 December 1829) term in power was to ban slavery and emancipate all slaves. The Presidency of Vicente Guerrero ended when his Vice President, Anastasio Bustamante lead a coup against him (and had him executed). More unrest followed, but many must have thought that Mexico was slowly becoming a democracy.

Liberal changes may be good (especially applied to conditions of the early 19th century), but Valentín Gómez Farías changed things too much and too fast for the Catholic and military parts of Mexico which revolted against him. The resulting conflict saw Antonio López de Santa Anna in power as President with the followers of Valentín Gómez Farías forced to hide or leave (mostly to the United States). Enough with democracy; Antonio López de Santa Anna reformed Mexico into a Catholic dictatorship in 1836 and tore up the Constitution of 1824. The new Constitution of 1835 eliminated the loose confederation of states and created a powerful federal government.

New preprint on the weak quantum numbers

I’ve just submitted a paper, Density Matrices and the Weak Quantum Numbers to Foundations of Physics. There are things about the paper that I didn’t include, things that I didn’t think were appropriate to a journal submission and I thought I’d talk about them here, and explain what the paper is talking about to a more general (but still math/physics) audience.

The paper is on the subject of the weak quantum numbers of the left and right handed elementary fermions and anti-fermions. Ignoring color and generation, there are 16 of these quantum objects. I provide a method of defining these quantum numbers by an idempotency equation, that is, by solving an equation of the form . Since pure density matrices satisfy this equation, the calculation is a density matrix calculation based on the permutation group on 3 elements.

The usual method of elementary particles is to assume that a symmetry relates the quantum states. In this calculation, the quantum states themselves are assumed to be composed of group elements of the symmtry. This can be done in density matrix formalism because density matrices can operate on themselves. Also of interest are what happens when different density matrices operate on each other. Particularly when the density matrices are chosen from the basis states of a complete set of mutually unbiased bases. But that’s another paper (mostly written).

Lepton Jets and JACEE’s Anti Centauros

The recently announced results by the CDF Collaboration, Study of multi-muon events produced in p-pbar collisions at sqrt(s)=1.96 TeV has been seen before, by the cosmic ray emulsion experiment JACEE. Since few particle physicists follow cosmic ray stuff, I thought I’d describe the JACEE results in more detail.

Some JACEE papers are given at the University of Washington’s Particle Astrophysics Group Webpage. See Excessive production of electron pairs in low multiplicity interactions or Observation of early photon conversions in high-energy cosmic-ray interactions. But my favorite arXiv paper for a long description of emulsion cosmic ray experimental results is Are Centauros exotic signals of the QGP?, Ewa Gladysz-Dziadus, 150pp, (2001).

A “Centauro” is an event with an excess of hadrons relative to electromagnetics. The opposite event, the “anti-Centauro” is an excess of electromagnetics (muons) over hadrons. (For non particle people, I’ll put an explanation of what “electromagnetics” has to do with “muons” below the fold.)

For the particle people, it’s best to just quote the paper. This is section “3.3 JACEE Experiment”, around page 63:

The Japanese-American Cooperative Emulsion Chamber Experiment, JACEE, has flown emulsion chambers with baloons near the top of the atmosphere. Despite of a small area and short time of exposure, as compared to Chacaltaya/Pamir Experiment, a few events of anomalous γ/charged ratio have been observed by JACEE Collaboration. However, these events differ in some essential points from classical Centauros. The anomalies were noticed at incident energies lower than that estimated for “classical” Centauros and unusual γ/charged ratios were observed only in the limited (η − φ) phase space region. Besides that, an excess of photons (anti–Centauro), in contrary to the hadron excess observed in Centauros, was claimed. The examples are:

1.) 4L-II-27 event [74] of incident energy of 80 TeV, yielded 149 charged particles and 120 γ’s. Almost all γ–quanta were produced in a narrow jet in the extreme forward direction. The γ/charged ratio is 2.6 ± 1.1 in the region of pseudorapidity 5.5 ≤ η ≤ 7.5, what is a significant deviation from the expected ratio of ∼ 1. The analysis presented in [74] showed an anomaly at the 5-10% level among 41 studied events with E0 ≥ 40 TeV.

2.) The event, with ΣE = 15.4 TeV, described in [75, 76] was initiated by a singly charged primary. The collision occurred within the detector. Almost all leading particles were γ–quanta. Photons appear to cluster into two groups. The leading cluster consisted of about 32 γ’s with hpT i ≃ 200 MeV and only one accompanying charged particle. A possibly distinct cluster had three times as many photons as charged hadrons (about 54 photons versus 17 charged). This event is one out of a sample of about 70.

3.) The event presented in [77] is a peripheral collision of Fe nucleus (E ≃ 9 TeV/nucleon) in emulsion. There were found 27 γ–quanta with η ≤ 6. As they came from pair conversions at only 0.8 radiation lengths, one can expect that the total number of photons was about 50. At the same time, only 6 charged particles (out of 21 charged tracks detected in the whole angular region) falled in the same kinematical range.

In all these events there was observed a tendency to a group emission of mesons. Such groups, having similar directions and momenta, could be signs of a formation and a subsequent decay of the chiral condensates. It should be mentioned, however, that these events were found in emulsion by scanning for the leading photon showers, so there was a “trigger bias” in favour of a large neutral fraction. It would be interesting to hear something about anti-Centauros from the mountain-top emulsion chambers. Here, there is, however, even much more stronger “trigger bias” in favour of gamma families, and thus the interpretation of data, from this point of view, is a complicated exercise. It is rather difficult to identify anti–Centauros unambigously, with exception of unusual and rare events in which the interaction vertex is close to the top and clearly resolved in the chamber.

Centauros and CDF’s multi muon / lepton jets

An unexpected bump has the particle physics world busy tonight; (we’re too sedate to be “aflame”). The bump was discovered at Fermilab by the CDF collaboration: Study of multi-muon events produced in p-pbar collisions at sqrt(s)=1.96 TeV”, hep-ex/0810.5357. In short, they’ve discovered a particle that seems to produce jets of leptons.

CDF found that they have way too many events where there are a lot of muons going in the same direction. This sort of thing is called a jet. Normally jets are associated with the strong force, and consequently, they include hadrons as well as leptons. Getting jets without hadrons is very unusual behavior. This is quite exciting but some of the terminology may be a bit confusing in the original paper linked above. There are two types of particles, leptons which do not experience the strong force, and hadrons that do. Physics experiments can distinguish them because hadrons crash into matter and decay, while leptons do not. Leptons eventually end up as electrons and muons. Of these, the electrons are sufficiently light that they get stripped off leaving only the muons. Photons also get absorbed. What’s left is muons and these are detected in the outer parts of a detector. So “punch through” means hadrons that managed to survive all the matter in the inner part of the detector and survived to the part of the detector where muons are supposed to predominate.

Centauros
Cosmic ray data is pretty much ignored by particle theorists. When I go to conferences, I make sure to attend these lectures because cosmic rays have much greater energies than accelerators can produce, and consequently they are more likely to see new physics. Very few other theoreticians show up at these lectures. Partly for this reason, I haven’t stressed the cosmic ray data very much. But now that the same unusual behavior is being observed at an accelerator, it is time to revisit the cosmic ray data.

A similar set of events were discovered years ago in high energy cosmic ray experiments. They are called “anti-Centauros” (the Centauros are showers that have too many hadrons and not enough leptons, anti-centauros reverse the proportions). Typically, these experiments use photographic emulsion (film) to detect cosmic rays. The film is layered in between sheets of lead or air gaps. The lead breaks up the hadrons and the resulting showers are detected in the film. These events were called “Centauros”, see the article which discusses them: Are Centauros exotic signals of the QGP? by Ewa Gladysz-Dziadus (2001). A more recent update is Very High Energy Cosmic Rays and Their Interactions, Ralph Engel (2005).

The study of cosmic rays is largely ignored, other than the GZK measurement, but the emulsion cosmic ray researchers are still chasing after Centauros. CASTOR stands for “Centauro and Strange Object Research” and is the name for a calorimeter (to measure energy in particle tracks) at the Large Hadron Collider (LHC).

Cosmic ray experimentalists don’t get no respect. Consequently these observations are difficult to publish and when they are published, they are pretty much ignored. But unusual observations in cosmic rays have been piling up for years. Kopenkin and Fujimoto supposedly explained Centauros in 2006: Exotic models are no longer required to explain the Centauro events, but this hasn’t stopped the observations from lacking explanations.

Help Save Bou’s Brain!

Things are flying in the physics world and there’s amazing things going on economically. And I owe some posts on these subjects.

But right now, more important for the brotherhood of blogs, is one of our own; Boudicca needs us. Her brain is at stake. a natural math talent could go to mush. We need to get her to quit marathoning (at age 43) and start doing mathematics again. We should start with the complex numbers. Right now she’s spending too much time quilting, and not enough time doing math.

A New Parameterization for 3×3 Unitary Matrices

Given my final success in writing the CKM matrix as the sum of a real 1-circulant matrix and an imaginary 2-circulant matrix, the next step is to write down the parameterization that allows any 3×3 unitary matrix to be written in this elegant and natural form. Following the method used earlier to parameterize unitary 3×3 magic matrices, and correcting for a few typos (but the description of the method is correct).

We will use four real angles, , as parameters. First, define 6 real numbers I, J, K, R, G, and B as follows:

The the following matrix is unitary:

This is the sum of a real 1-circulant matrix and an imaginary 2-circulant matrix. Note that the sum of the 3 elements of any row or column is equal to the complex phase .

CKM in MNS form! Victory!

The MNS matrix (in tribimaximal form, which is compatible with all experimental measurements) can be written in elegant form as a unitary matrix which is the sum of a real 1-circulant matrix and an imaginary 2-circulant matrix. See Doubly Magic Matrices and the MNS. Now I’ve got the CKM matrix in the same form. And here it is:

The cool thing about the above is that it only involves 6 real numbers. Three reals define the 1-circulant matrix, +0.973313178, -0.008576543, and +0.000466480, while three more reals define the 2-circulant, +0.225761835, +0.040012680, and -0.004273188.

I’ve marked the larger contributions with red to help you see the symmetry. The real matrix has each of its rows shifted one to the right (i.e. 1-circulant), while the imaginary matrix has them shifted two to the right (i.e. 2-circulant). Note that the above matrix is unitary, which you will have to verify by taking dot products of its rows with the complex conjugatges of its rows, and the same for the columns. (You should get 1s and 0s.)

The experimental values I’m using for the CKM matrix come from hep-ph/0706.3588) and are:

If you square the elements of a row or column of the above, and add them up, you get 1, but it is not unitary. To put it into unitary form, we supplement each of the above real numbers by multiplying by a complex phase. The matrix is unitary when the resulting rows and columns are orthonormal.

The experimental measurement has 9 real numbers. Multiplying them by complex phases so as to make the matrix unitary is going to give you 18 real numbers. And yet I’ve been able to do this, put the experimental numbers into unitary form, and ended up with only 6 real numbers, and those are used in an elegant and symmetrical manner. This is by far the most elegant version of the CKM matrix around. It is the number crunched result of an observation by Marni Sheppeard that the CKM matrix is approximately the sum of a 1-circulant and a 2-circulant matrix. Well, now we have it exactly that way. Victory! But more to come.

To get an experimental measurement from the new magic form, compute the magnitude of the complex number. For instance, to get the top right value of 0.0042982, compute

|+0.000466480 – 0.004273188 i| = sqrt(0.000466480^2 + 0.004273188^2)
Uh, I get 0.0042986, which is within rounding errors on the experimental measurement number.

More generally, the nine elements of the experimental CKM matrix can be found by taking one element from the set {+0.973313178, -0.008576543, +0.000466480} along with one element from the set {+0.225761835, +0.040012680, -0.004273188} and computing the RMS value.

CKM as a magic unitary matrix II

It seems much longer but it was only two months ago that I wrote a post giving the CKM matrix in magic unitary form. With half the Nobel prize in physics going to Kobayashi and Maskawa, the K and M of the CKM matrix, I should include a quick update.

The CKM matrix is usually written in absolute magnitude form. Recent experimental measurements, after correcting to ensure compatibility with unitarity (from hep-ph/0706.3588), is:

If you square the elements of a row or column of the above, and add them up, you get 1, but it is not unitary. To put it into unitary form, we supplement each of the above real numbers by multiplying by a complex phase. The matrix is unitary when the resulting rows and columns are orthonormal.

There are a lot of ways we could choose the complex phases. However, there is only one way (except for the sign of the imaginary unit i) of writing the matrix as a unitary matrix whose rows and columns sum to unity. This is called the “magic” property. The MNS matrix is quite simple when written this way. So I wrote a computer program and found the magic unitary form for the CKM matrix, to see if it would also have a simple form. Here it is:

Note that each row and column sums to 1, the rows and columns are orthonormal, and the absolute value of each element is as given for the experimental measurements at the top of the page.

The above is a slight improvement from the data I gave before. This is due to an error in one of the digits of the input data, that is, in the experimental measurements. Of course it is not accurate to all its digits, but I’ve included them because it’s a complicated nonlinear relationship between the absolute values of a unitary matrix and its magic unitary form; I don’t know how to properly scale the errors. (I could get them by varying the input data to the computer program that finds the magic solution. If someone wants this data, ask for it in the comments.) Below the fold, I’ll include the data in LaTeX format so you can copy it more easily:

The X(3872) Files: Scanning for new mesons

New mesons! Let’s begin with a picture (from encarta) showing how new particles (states) were discovered back in the good old days:

Work on the big meson paper is continuing. I’m almost done with the isoscalar mesons. So in addition to describing just what these things are, I’m including a few lines on the new J/psi states, the X(3872), X(3940), X(3945), X(4260), and X(4360).

How to Find a New Hadron

Hadrons (mesons and baryons) are found by analyzing large numbers of particle interactions. When you plot the data, the graphs have little, uh, well the technical term is “bump” . Yes, hadrons, like children, begin as bumps. A hadron bump looks like this:

The above is from hep-ph/0510365. This bump happens to be one of the states, the X(3940), with which this post is concerned.

The Barbarous Relic Rises Again

There’s gold in them thar’ shops: the rush is on

Tucked away beside the ornate entrance of the Savoy hotel in London are the discreet premises of ATS Bullion. Over the last few days staff there have witnessed an unprecedented phenomenon: queues.
…
The US Mint, responsible for ensuring an adequate supply of American coinage since 1792, has been forced to halt sales of its American Buffalo solid 24 carat gold coin because it was running out of supplies. It is also limiting the availability of its 22 carat American Eagle alternative. [I don't believe this is a fact. The US makes money on sale of these coins and will mint however many the public wants. Any lack of them is just temporary. But I do believe that demand for gold bullion has gone way up.]

Demand for gold coin is undoubtedly higher outside the US than inside. The reason is that in panics, foreign investors tend to buy US dollars. This raises the value of the dollar, which drops the price of gold, as priced in US dollars. The effect is that the US consumer does not see a big drop in the value of the dollar. Hence they have no reason to hedge with gold. (This will change if the Fed gives up and begins using inflation to save the banking system.) Foreigners, on the other hand, see the price of gold going up, and worry about the financial headlines about the US. So they move into gold.

Scrap Metal and European Banks Collapse

More excitement in the markets: Three days ago we got quoted $0.60 per pound for stainless steel scrap. Today we dropped by with 10 thousand pounds. The manager was apologetic, but they were no longer buying at any price. Scrap metal prices collapsed about in half (at least here on the West Coast), probably due to a lack of buying in China.

And remember my post on the unusual activity at the Federal Reserve? “ For example, it must be noted that business cycles are world-wide” and therefore business cycles cannot be blamed on individuals, political parties, countries, or even continents. The bubbles always burst eventually, and when people in one country see the bubble burst in another, monkey see, monkey do. They act to avoid the consequences of a bubble bursting in their own country and that bursts their bubble. (Hence the famous stock trading advice: Avoid Panic. But, if you absolutely must panic, try to do it before everybody else does.)

Well, as expected, European financial companies are failing and for the same reason US financial companies have had trouble. They did the same thing that US financial companies did. And their equivalents to our Federal Reserve are doing equivalent things.

The human inclination to get over enthusiastic in markets, and to ignore risks, is universal. If you outlawed it one way, they’d find another way to do it. It’s like teenagers and sex. But even worse, humans imitate other humans so the European troubles are identical to our own. Too much debt, and, in this bubble, an inclination to create mortgage backed securities to theoretically decrease risks, part of which is due to physicists. The latest news from Europe:

Wall Street crisis spreads through Europe’s banks

PDG on road to fixing psi(3770) meson mass

The big paper on the mesons is coming along. Yesterday I was checking the mass formulas for heavy quarkonium, a subject which was discussed here a few months ago. While checking numbers for the paper, I found that the Particle Data Group has changed the values for psi(3770) in our favor! For us it was exciting so Kea says I have to blog it. And in fact I feel that I did an inadquate job the last posting on this.

So first, a little background. Mesons are made of a quark and an anti-quark, plus the color and electric force that binds them together. The usual method of modeling them is to simplify the color force and treat it as if it were just a scalar force like the electric force, and then calculate the binding energies (and therefore the masses of the mesons) by using the methods used to calculate atomic energies.

What I’ve been doing instead is looking at the problem from the point of view of quantum information theory. With this one ignores the spatial and momentum information and looks only at the information content of the particle states. When one does this to a spin-1/2 particle like the electron, one uses qubits. Since I want to model the color force but don’t care about spin, I use qutrits instead with the three states being red, green, and blue.

The usual method of modeling the mesons works best for lowest energy states of the heaviest quarkonium. This is because these states are the least relativistic (because the quarks are so heavy) and the color force isn’t as strong (since these quarks are so heavy, their deepest bound states are smaller than other mesons, and since the quarks are close to each other, the color force is reduced by asymptotic freedom). With my method, the reverse should be true; I should be more accurate at bigger states where color is more important. These states are either higher excitations or have lighter quarks. This is because I treat the color states correctly but don’t work on getting momentum modeled correctly.