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.

Elevation of the Sun
If the Mohe anomaly is due to gravitons emitted from the sun and or moon, then we need to adjust for how far off the horizon these bodies are. The eclipse was observed at latitude 53°29′20″ N and longitude 122°20′30″ E, on March 9, 1997. Sunrise was at 06:20:00 local time, with first contact at 08:03:29, totality from 09:08:18 to 09:11:04, and fourth (last) contact at 10:19:50. The first anomaly peaked at around at around 7:30 while the second anomaly goes to at 10:20.

To see how far off the horizon the sun was at 7:30 and 10:20, we go to John Walker’s convenient applet Your Sky, and find the sky map for that spot on the earth at that time. Whoops, he doesn’t quite manage to get the numbers exactly right. Here’s his picture for the center of totality, showing the sun erroneously peeking out underneath the moon:

John Walker's eclipse image

Okay, so let’s go to Chris Obyrne’s Javacript eclipse calculator and select the 1997 data at the given longitude and latitude. We find that first contact has the sun 14 degrees of the horizon while fourth contact is 28 degrees. This is compatible with Walker’s program having the sun 21 degrees over the horizon at the center of totality.

Now, if the Mohe measurements are to be interpreted as modifications of the total gravity strength due to (a change in) the sun and moon, then, since the earth’s gravity dominates, we need to divide by the sine of the elevation of the sun. At first contact, this is a factor of 4.13, and at fourth contact 2.13; adjusting the anomaly peaks, this gives the first contact peak at around and the fourth contact goes to . These numbers are somewhat closer to symmetric than the originals.

Tides and Gravimeters

But we can’t interpret the data as measurements of the force of gravity. It is impossible, in a certain sense, to measure the force of gravity at a single point in space. What a gravimeter actually measures, at best, is an acceleration. Installed properly, this acceleration is the force applied to the base of the gravimeter. Consistent with Einstein’s Equivalence principle, a gravimeter in free-fall will measure no gravitational force.

Consequently, interpreting the anomaly peaks as corresponding to changes in the flux of gravitons is simplistic and wrong. But before we discuss what gravimeters actually do measure, let’s discuss the timing of the anomalies.

Gravitational Timing

A significant difference between Einstein’s theory of gravity and Newton’s is that in Newton’s theory, the force is instantaneous at a distance. For theories based on superluminal gravitons, the timing of the pulses needs to be adjusted.

It takes light from the sun about 8.3 minutes to reach the earth. Consequently, while we detect the center of the total eclipse at 09:09:41, the sun actually emitted that light at 09:01:23. This was the time at which the bodies were in alignment.

Thus, if gravitons travel at very high rates, we would expect that the eclipse’s modification of gravity would be symmetric not around the time of deepest eclipse, 09:09:41, but instead around the actual time of alignment, 09:01:23. Thus those who believe in faster than light gravitons expect the gravitonal eclipse effects to appear around 8 minutes before the photon eclipse effects.

Returning to the Mohe gravity data, we see that the first pulse is almost entirely over by the time of first contact, but that the second pulse is close to coincident with fourth contact. To make these two pulses symmetric with respect to the photon measurements of the time of the eclipse, we have to shift the gravity measurements later by around 7 or 8 minutes.

The Acceleration of the Sun and Moon
In preparation for discussing tides and gravimeters, it’s useful to calculate the acceleration, on the earth, of the sun and moon. Since I am a (hopefully soon to be published) general relativity theorist, I will make these calculations in the professional way, using units of centimeters only. To convert from cm to those ugly pedestrian units involving grams and seconds, we will be setting to unity, the gravitational constant G, and the speed of light c:

and so

Looking in wikipedia’s collection of Solar System values, the masses of the sun and moon, and their distances from the earth, are:

Mass Sun: ,
Distance: ,

Mass Moon: ,
Distance:

In theoretical general relativity, the formula for (Newtonian) acceleration is very simple; A = M/r^2. Applying this formula to the above, we get the force that the sun and moon apply to the earth, in units of 1/cm. We can convert these into cm/s^2 by multiplying by c^2. We find:

Sun accel: .
Moon accel: .

Tides

Sailors know that the moon makes stronger tides than the sun; so it is a little surprising that the gravitational acceleration of the sun is stronger in its effect on the earth. The tidal effects of the moon are stronger because the moon is so close.

Tidal forces are caused not by gravitational accelerations, but instead by differences in gravitational accelerations. The strong tides of the moon are caused by the difference in gravitational acceleration between the side of the earth closest to the moon and the side farthest away. As far as tides go, gravity is a 1/r^3 force, not a 1/r^2.

Gravimeters show tidal forces rather handily. They cannot measure actual gravitational forces. Consequently, when we use a gravimeter to look for gravitational anomalies, we need to interpret what we measure not as a gravitational force, but instead as a tidal force.

Since eclipses last several hours, the data for these sorts of experiments has to be corrected for the usual tidal forces. This means that there are lots of opportunities for getting the wrong answer. Later experiments, particularly with the European eclipse of 2003,

Like I said, I don’t know if this is significant. At least it is interesting. For a recent review of conventional explanations for these sorts of observations, see A review of conventional explanations of anomalous observations during solar eclipses by Chris P. Duif, and Review on Possible Gravitational Anomalies by Xavier E. Amador.

Corpuscular Gravity Shielding

The corpuscular graviton shielding theory is that gravity is a shielding effect; two masses are attracted to each other by their shielding of each other from the effect of an isotropic and universal sea of gravitons. This sort of theory expects to see a reduction in the effect of the combined sun and moon gravitational attraction during an eclipse.

Such a reduction would mean that the earth’s gravity field would become stronger. This is the opposite of the observation above, but there is evidence for a decrease in other gravimeter measurements. See Un Résultat Gravimétrique pour la Renaissance de la Théorie Corpusculaire “An Experimental Gravimetric Result for the Revival of Corpuscular Theory “, Maurice Duval, (in French). These are difficult measurements and difficult interpretation.

For how corpuscular theories of the graviton fit with these observations, see Un Résultat Gravimétrique pour la Renaissance de la Théorie Corpusculaire “An Experimental Gravimetric Result for the Revival of Corpuscular Theory “, Maurice Duval, (in French).

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.

My initial feeling was to submit the paper instead to Foundations of Physics as that is how I formatted the longer version of the paper originally. The essay contest paper has been cut down to approximate the 1500 word limit for the contest. But Foundations of Physics has an impact factor of 0.951, and is a more general journal, so overall, the paper belongs in IJMPD, if they are willing to publish it.

The Kepler Problem
My paper is about the orbits of test particles around the simplest sort of black holes (or “Schwarzschild metric” ; i.e. non rotating and uncharged. This is a fairly simple problem that was solved analytically a very long time ago, the wikipedia article is called the Kepler problem in general relativity. Of course the original Kepler problem was for Newton’s gravity.

The Kepler problem is to figure out the motion of very small (test) masses in the presence of a large mass. Newton’s gravitation is defined as a force and for this problem it is very simple:

where For simplicity, this uses units where the large mass M = 1, and the gravitational constant G=1. With the relativistic form, we will also put the speed of light c=1. Mathematically, the above is three coupled differential equations in t, one for x, one for y, and one for z.

I wanted to compare these differential equations with those for the corresponding problem in general relativity. This is not so easy to do. The motion of test masses in general relativity is written using geodesic equations. To make a long story short one ends up with four coupled differential equations in the “affine parameter” s, three for x, y, and z, and one (extra one) for t. So the problem is to convert these 4 differential equations to just 3 by eliminating s.

In converting general relativity geodesics into Newtonian forces, one must choose the coordinate system that one will assume to be equivalent to Newtonian. The usual method is to use Schwarzschild coordinates; but I had theoretical reasons (explained briefly in the paper) for preferring Gullstrand-Painleve (GP) coordinates. These coordinates are best explained by the paper, The River Model of Black Holes.

Post Newtonian Expansions
The usual technique for converting from geodesic equations to Newtonian force is to use the “post Newtonian expansion”. This is only an approximation. If one needs higher accuracy, one works with post post Newtonian, etc.

I didn’t want to deal with ugly approximations, and of course post^n Newtonian expansions in the literature are only for Schwarzschild coordinates so I decided to solve the problem exactly. Various people told me that it was impossible or unreasonable. In fact the calculation was horrendous, with hundreds and hundreds of terms. I used a symbolic calculus calculation engine, MAXIMA, which has the essential advantage over its competition that it is free.

Eventually I did manage to solve the geodesic problem exactly, both for Schwarzschild and Painleve coordinates. This is the first result in the paper; these are (6) and (7). The second result was that, in GP coordinates, the exact form can be written as only a few terms, each as powers of the radius.

At long distances r>>1, and low velocities v<<1, the Einstein result approximates the Newtonian. Writing Einstein’s result as a sum over powers of the radius is an invitation to figure out which of these terms have been tested by various tests of general relativity. So the next natural step is to figure out which terms are needed for compatibility with these experimental results. My paper does this, but only for the deflection of light. I’d have done more but I was only aware of the essay contest a few days before the deadline.

Gravity as a Flux of Gravitons
Finally, Newton’s gravity can be explained as being due to a flux of gravitons: Each massive object emits these in all directions and they shoot off in all various directions at an infinite speed. At a distance r, they are spread out over the surface , of the sphere with radius r. This accounts for the decrease in strength of the gravitational field proportional to 1/r^2. But Einstein’s theory gives a correction to this law; what does this say about how the flux of gravitons interacts with itself?

The first thing to note is that in Einstein’s theory, gravity waves move at speed c. In a graviton theory of Einstein’s gravity, one would naturally suppose that the speed of the gravitons is also c. But this is a local speed limit; in practice it will depend on the choice of coordinates. For GP coordinates, the (maximum) speed of light near the gravitating source is always higher than it is far away. (Note that for Schwarzschild coordinates, light slow down near the event horizon and never exceeds the speed of light far away.)

The reason the speed of the gravitons is important is that if the test body is moving with respect to the graviton flux, the speed of the graviton flux will change how much flux is seen by the test mass. For example, if the flux is moving at speed v, then the amount of flux seen by a test particle moving this speed in the same direction as the flux will be reduced to zero. A way to avoid the issue completely is to look at situations where the speed of the gravitons doesn’t matter. This happens if the test particle is not moving; the “gravitostatic” situation.

The fourth point of the paper is a computation of the gravitostatic attraction of gravity in Schwarzschild and GP coordinates. The result shows that if gravity is interpreted as due to a flux of gravitons, then that flux becomes stronger with distance. (That is, when integrated over the surface area of the sphere, the amount of flux increases with the radius.) So in the final part of the paper I showed that the amount of increase in flux is proportional to the square of the flux density. This is compatible with a theory of gravity where the graviton flux interacts with itself. Think “dark energy.”

Anyway, I had hopes that the paper would win a prize, but I guess I can understand why it has to go through peer review; it has a lot of calculations that need verifying.

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

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

Discrete Fourier transform matrix

Fourier transform of democratic matrix

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:

3x3 matrix by Discrete Fourier Transform jigsaw puzzle

The discrete Fourier transform for 3×3 matrices is 1-1 and onto, so the above gives a proof that we can always write a 3×3 matrix uniquely as the sum of a democratic, 1-circulant, 2-circulant, bra, and a ket matrix, each of which, other than the democratic, is subject to the constraint that A+B+C = 0. This gives a decomposition of a 3×3 matrix into five parts, with the democratic part giving one and the others two each degrees of freedom, for a total of nine (complex) degrees of freedom.

Unitary Matrices

Some time ago, I gave a parameterization that seems to be a complete parameterization of the magic unitary 3×3 matrices. This uses 4 real parameters. We can add five more parameters by multiplying rows and columns by arbitrary complex phases. This gives a total of nine parameters, just what are needed for an arbitrary unitary matrix. So I’m wondering how to prove that this parameterization is complete or not.

Of the five components of a 3×3 matrix as given above, three are magic, that is, three have rows and columns sum to the same value. The bra and ket forms have rows or columns that sum to the same value but not both. Consequently, we know that any magic matrix can be written uniquely as the sum of a democratic, a 1-circulant, and a 2-circulant and this must also apply to the magic unitary matrices. Because the decomposition is 1-1 and onto, we know that the magic matrices have 1+2+2 = 5 complex degrees of freedom.

The 1-circulant, 2-circulant, and democratic matrices are closed under multiplication and addition, thus the magic matrices are a subalgebra in the algebra of 3×3 matrices. The unitary matrices are also a subalgebra of the 3×3 matrices and so are the 3×3 magic unitary matrices. Now the 4 parameter parameterization I gave for them was under the additional restriction that the sum of the rows and columns, in addition to being equal, was required to be equal to 1. We can generalize with a 5th parameter to multiply the whole matrix with a complex phase and therefore make the sum of each row and column be an arbitrary complex phase. And this gives 5 parameters that define the magic unitary matrices completely.

This is kind of funny. Magic 3×3 matrices have five complex degrees of freedom, while magic 3×3 unitary matrices have five real degrees of freedom. Could there be a relationship between them?

All this discussion has to do with the democratic, 1-circulant, and 2-circulant portions of the matrices. What about the bra and ket portions?

The method I’ve been using to get a general unitary matrix into magic form is by multiplying the rows and columns by arbitrary complex constants. Ignoring the overall complex phase, we get to pick two rows and two columns for this treatment:

Multiplying rows and columns by phases

Comparing with the table of discrete Fourier transforms, the matrices of complex phases in the above equation can be seen to be the discrete Fourier transforms of 1-circulant matrices, that is, they are of the form

where, as before, the complex numbers A,B, and C are related by A+B+C = 0. This gives two complex degrees of freedom or four real degrees of freedom, again just twice what we need to arrange for multiplication by two complex phases.

So I think I’m getting fairly close to cobbling together a proof that the new parameterization does cover all the unitary matrices, when it is extended by multiplying columns and rows by complex phases.

The funny thing about all this is that it has the feeling of complete triviality, but I’ve never seen the unitary matrices parameterized so nicely.

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

After the family arrived in Berlin, she found a best friend in Lisa Arlosoroff, who recognized her as a fellow refugee from her French accent. She spent a great deal of time with the Arlosoroffs. The Arlosoroffs were Russian Jews who had been driven out of their home in the Ukraine by anti-Jewish pogroms in 1905. Lisa’s grandfather was a famous rabbi.

First love
Eventually she fell in love with Lisa’s brother Victor. Vitaly Viktor Haim Arlosoroff was an ardent Zionist, that is, he supported the emigration of Jews to Palestine, where they would one day (re)create a state, Israel. She spent a great deal of time with Zionists, but never quite felt at home with them as she was not racially Jewish and Victor eventually married in Palestine.

Vitaly Viktor (Victor) Haim Arlosoroff

Probably the most important contribution of Victor was the negotiation of the Ha’avara Agreement, an agreement between Nazi Germany, the Zionist Federation of Germany, and the Anglo-Palestine Bank, which allowed Jewish emigrants to put their money into an account that could be used outside the country, but only to purchase German goods.

Victor did not live to see the founding of Israel; instead, on the beach near Tel Aviv, on the 16th of June, 1933, he was mysteriously assassinated. His widow identified two members of the Revisionists, a more militant Zionist political organization. After the war, an alternative theory, which makes a certain amount of sense, appeared. The alternative is that he was assassinated, at least partly due to his early relationship with Johanna Maria Magdalena Friedländer. A few weeks before his death, after he had tried to meet her in Germany, she had written him to tell him that his life was in danger in there and that he must leave immediately. But let us return to her story.

Trains
During wartime, trains are destroyed by the enemy as they are used to transport troops. For example, as an American soldier, my grandfather was transported in a French cattle car to the battle at Belleau Wood in 1918. So the first world war destroyed a lot of trains, and in addition, in return for the cessation of hostilities, Germany was made to give up trains to the Allies.

The summer after the Armistice, she was 17, and had completed her schooling. Her biological father Ritschel paid for her tuition at a finishing school, as preparation for her future as a wife and mother. To get to the school near Goslar, Germany she used the train system but with the loss of trains getting a seat was almost impossible; most people were forced to stand.

One of the advantages of being very rich is that one can insulate oneself from some of the indignities suffered by the masses. For elegant railroad transportation, one reserves a car. One then has plenty of room. While standing at the railroad, waiting for her mother to find her a car with a seat, her striking beauty was noticed by Dr. Günther Quandt, who offered her a seat in his reserved car. For very elegant transportation, one would purchase a railroad car and fit it out as one would like. Eventually, she would tour the United States in just such a car.

As they introduced themselves, Quandt was shocked to hear that she was going to finishing school and was only 17. He was two decades older, but he was a wealthy industrialist, and his wife had died in the Spanish flu panepidemic of 1918. And he was taken by her beauty.

Her beauty still leaks through the photographs that remain but they do not tell the whole story. Apparently she had a certain poise, a calmness, that long preceded her time at finishing school. What else can I tell you? She was fluent in German and French, and could speak Italian and English as well. Her favorite book was Via Mala by the Swiss author was John Knittel. Perhaps like Kipling’s cat, all places were alike to her. Or maybe it was the slight French accent with which she spoke German.

In any case, as Quandt spent a few hours in the train car with her, he realized that her beauty was more than skin deep. Before she left his car, he memorized the address on her luggage with the intention of seeing her again. It wasn’t proper for a gentleman more than twice her age to visit a young lady at finishing school, so he wrote her asking if she would see him if he came calling on her as a “friend of her father’s”.

Quandt reminded her of her biological father Oskar Ritschel, and what with the attractions of wealth she wrote back “yes”. He arrived in a limousine with presents of choclates for the head mistress and for all the students. He was treated as visiting royalty. No questions were asked.

It is probably useful to note that the Armistice of November 11, 1918 was only an “armistice”, that is, a pause in the fighting. The war continued. The Allies did not lift the “Starvation Blockade” of Germany until the Treaty of Versailles was signed on June 28, 1919. By then three quarters of a million people had starved to death in Germany and the rest were very hungry. The fresh memory of starvation in the first world war contributed to the Nazi decision to kill off “undesirable” eaters when the second world war began in 1939. We will get to that part of the story, for now, let us note that in the hungry German summer of 1919, a little candy went a very very long way. In any case the relationship continued and they became engaged.

Marrying someone half your age doesn’t do too well in high society. That could not be fixed, but that she was Catholic and had a Jewish last name could. She converted to Protestant and became Johanna Maria Magdalena Ritschel, returning to her biological father’s name, just before marrying Günther Quandt on January 4, 1921.

First Marriage and Wealth
Quandt was quite wealthy. During the war he supplied the German Army with uniforms. After the war he acquired VARTA a company that sold batteries until the latter half of the century. He also had stakes in BMW and Daimler-Benz.

They had one child Harald Quandt, born November 1, 1921. This was not a good year to be born a German. During the second world war, he joined the Luftwaffe. He was injured and captured in Italy in 1944 and put into a prisoner of war camp in England. When his mother learned of his safety in November 1944 it must have been quite a relief. He was released in 1947 and went on to become one of postwar Germany’s wealthiest industrialists. With his brother Herbert, he ran the Quandt group of 200 industrial companies after their father died in 1954. He died in 1967, in the crash of one of his aircraft. He had a reputation as a “committed playboy”.

Harald Quandt (I believe)

A life of wealth is not necessarily a healthy experience for the human species. The Unabomber, in his manifesto, Industrial Society and its Future describes the problem as follows:

Consider the hypothetical case of a man who can have anything he wants just by wishing for it. Such a man has power, but he will develop serious psychological problems. At first he will have a lot of fun, but by and by he will become acutely bored and demoralized. Eventually he may become clinically depressed. History shows that leisured aristocracies tend to become decadent. This is not true of fighting aristocracies that have to struggle to maintain their power. But leisured, secure aristocracies that have no need to exert themselves usually become bored, hedonistic and demoralized, even though they have power. This shows that power is not enough. One must have goals toward which to exercise one’s power.

Perhaps this sort of thing effected Johanna Maria Magdalena Quandt. She became bored. She divorced Günther Quandt in 1929. Perhaps unfortunately for her, the divorce settlement was quite liberal. She had more money than she needed and suffered from boredom, and an absence of goals.

In 1930, she attended a speech by Joseph Goebbels. His extensive diaries have left us a view into the thinking of this man. I think the Unabomber would agree with Goebbel’s diary comment, “It doesn’t matter what you believe, the important thing is belief.”

Joesph Goebbels

It was love at first sight. She joined the Nazi party and volunteered at the local office. With her knowledge of foreign languages, she helped at the newspaper archives; she could assess articles about the Nazis in the foreign press.

Goebbels
“Nazi” is an abbreviation for “National Socialim”. They were a party formed from a combination of right wing or conservative, (nationalist), ideals and left wing or liberal, (socialist), ideals. Their right wing side is fairly well known; the insistence on a single, German, culture for Germany. Eventually they were to kill millions who did not belong. Less well known is their left wing side. Their left wing ambitions included abolition of unearned income, confiscation of war profits, nationalization of corporations, profit sharing, old age insurance, break up of large department stores, land for communal purposes, banning usury, and higher education at State expense for the gifted poor. These were included in the 25 points making up the Program of the NSDAP (Nazi) Party, February 24, 1920.

One of the odd features of the human species is that right wing parties tend to do best in the countryside, while left wing parties tend to be best in the cities. This pattern is seen in the United States where the right wing party, the Republicans, generally win the rural vote while the Democrats generally win the urban. But it is more general than just these two countries. The revolutionary history of France is replete with examples. An urban mob stormed the Bastille on July 14, 1789. Reaction to the revolution was concentrated in rural regions. Catholic rural peasants were executed as counter revolutionaries during the Terror. The Revolution of 1848 and the Communards of 1871 show similar splits, conservative peasants versus liberal workers. Whatever the explanation, the same pattern of rural conservatism and urban liberalism applied to inter-war Germany. Berlin was the most liberal part of the country.

In October 1926, Adolph Hitler gave Joseph Goebbels the title and task of Gaulitier or “regional leader” of Berlin. He was in charge of the Nazi party (or NSDAP) there. This was not an easy task; they were far behind the Socialist Democratic Party and likely the Communists in this most urban part of Germany. There were only a few hundred NSDAP members; this was not enough to pay much dues and it was the dues that Goebbels would take his pay from.

To raise the vote for the Nazis in Germany, Goebbels put the party into the news as much as possible. He chose sites for rallies specifically intended to pick fights with the Communists. For these fights he used the SturmAbteilung also called the SA. These were mostly young unemployed workers. They were also called “brownshirts” because their uniform were shirts left over from the war effort, intended for German troops in Africa (possibly manufactured by Quandt). I had always imagined these as a darker shade of brown, but it turns out that they are a light shade, one suitable for soldiers in a dusty land.

Pre 1936 SA brownshirt, NSKK (motor corp)

As the depression continued, the unemployed crowds in the streets of Berlin grew and Goebbels converted more and more of them to the Nazi party. In the party they were taken care of; for example there was an SA hospital.

By promoting fighting between the Communists and Nazis, Goebbels also increased the violence of the Communists. Faced with the threat of Communist violence, more and more members of the middle class began voting for the Nazis. (This technique is a classic method of insurgency; you use violence to make the government look impotent. The people will move in favor of those who show they can control the violence.) Within 18 months he had raised the Nazi vote to 50,000. He was elected to the Reichstag (Parliament) on May 28, 1928. Goebbels was a man increasing in prosperity and importance. But let us return to her story.

Second Marriage
In joining the Nazi party and volunteering, it was several weeks before she got any closer to the man who had so impressed her at the Nazi rally. However, eventually, they crossed paths in the stairway to the Nazi office. Goebbels was accompanied by his adjutant, Count Schimmelmann. The result is worth quoting:

They glanced into each other’s eyes for only a moment, and, ludicrous though it may sound, for that fraction of a second the spark ignited for both of them. Goebbels stopped dead in amazement while she walked to the exit. “Donnerwetter Schimmelmann,” he said, a trace of breathlessness in his voice, “Who was that? An amazing woman!” and then climbed the stairs to his bare study. Five minutes later Goebbels knew that this jewel was working in the gem-free setting of his office. The next morning he called her. “I need someone unimpeachably reliable, someone I can trust.” Not a word of sympathy, no compliments, barely a personal remark. Only his eyes seemed to embrace her. “I thought I would burst into flames beneath that purposeful gaze,” she told me much later. But by then she knew from his own lips that he had fallen in love with her at first sight. And the same was true of her.

Goebbel’s diary of February 15, 1931 provides as much of an explanation for why people shouldn’t keep diaries as anything I’ve ever seen: “She comes in the evening. And stays for a very long time. And blossoms with heady blonde sweetness. How can I describe you my queen? A lovely lovely woman! Whom I shall love very much. Today I am walking almost as though in a dream. So full of sated bliss. It is wonderful to love a beautiful woman, and to be loved by her.” By February 26th they had suffered their first fight, probably over another woman.

They married on December 19, 1931. In her divorce settlement, she had been given the right to use Quandt’s farm in Mecklenburg. Set in North Germany, it must have provided an austere place for a marriage ceremony. Hitler was the witness. She received a new name, the one she is known by in the history books. Going by Magda, short for Magdalena, she became Magda Goebbels, the infamous first lady of the third Reich. Anti-Nazi press carried headlines, “Nazi Chief Marries Jewess”.

Goebbels wedding, Hitler in back

The Goebbels Children
In terms of children produced, her marriage with Joseph Goebbels was very successful. They had six children, Helga Susanne (1932), Hildegard Traudel (1934), Helmut Christian (1935), Holdine Kathrin (1937), Hedwig Johanna (1938), and Heidrun Elisabeth (1940). They appeared in German newsreels three dozen times in 1941. One of the advantages of being married to the man in charge of the movie industry is that your home movies are of higher quality than usual, as this 42 minute movie clip of Magda and her children, from the summer of 1942 shows.

Magda Goebbels, children, and husband

In 1939, Goebbels used his children as an example to compare with handicapped children in a film. By 1941, about 5000 children were been killed as part of the total 70,273 killed in Action T4. Their deaths were recorded as pneumonia. Leaders of the Catholic church wrote private letters to the government protesting but these were ignored. In July 1941, a pastoral letter from the Bishops was read in all Catholic churches that it was wrong to kill, except in self defense or in a morally justified war. On August 24, 1941, Hitler ordered the program canceled, and further, that for the duration of the war, no further actions provoking the churches be undertaken.

The Death of the SA
Hitler first became aware of her through her son, Harald Quandt. When he was 10, she sewed up a uniform for him, one matching the brown (shirts) of the SA. She sent him upstairs to Hitler’s room in the luxurious Hotel Kaiserhof, which, in November 1943, was fated to be completely destroyed by British bombers. It is now the site of the North Korean embassy. Of course Hitler was charmed by the child in uniform. “Who made you this lovely uniform?” “My mother.” “And how do you feel in this uniform?” At this the boy stood up rather straighter and said, “Twice as strong!” … “Then give your mother a nice greeting from me, and do come and visit me again.”

Her relationship with Hitler was long and close. Years later, after a total of seven children, her marriage with Goebbels was strained by his going beyond sex with young German film actresses. He fell deeply in love with the Czech actress Lida Baarová.

Lida Baarová

Besides beating up Communists and others in the way of the Nazis, and terrorizing Jews, the SA were also useful to the Nazis in that they protected Nazi leaders. They tended towards the socialist end of the Nazi party, typically fighting on the side of workers in strikes and labor disputes, and this helped party membership. Like a substantial number of Nazi voters, they associated capitalism, particularly banking, with the Jews. One can see little echoes of this association in today’s news reports of the current banking panic; for some reason it seems to me that the religion or ethnicity of bankers are only mentioned when they happen to be Jewish. Interestingly, the website www.nazi.org is currently operated by a group promoting a combining National Socialism, with Green and Libertarian principles. They’ve updated Nazi flag replacing the red background with green.

So the Nazis were theoretically aligned against the people who controlled German industry and money. But then, at the infamous Secret Meeting of February 20, 1933, Hitler gained the financial support of two dozen of Germany’s most important industrial leaders. Günther Quandt was there. With their rising political power, the Nazis gained control over the police, military and industry, and the need for the SA to protect leaders, punish others, and to keep industry in line declined in importance. This was also the year that Hitler met with Ferdinand Porsche and had him design an inexpensive car. Originally called the “KdF Wagen”, it was a part of the Nazi’s leisure program, Strength Through Joy (KdF). The company producing the car was named Volkswagen, or “people’s car”, in 1937. Porche also designed several of Germany’s tanks such as the Tiger I and Tiger II.

Two Ferdinand Porsche designs

The German military was jealous of the attention given the 3 million members of the SA, and contemptuous of their amateur soldiering skills. And in terms of political power, pretty much the only person in Germany who would stand up to Hitler was the SA leader, Ernst Röhm. To top it all, Röhm, along with other SA leaders, was a homosexual and had apparently promoted others on the basis of sexual favors. In 1931, a socialist newspaper published letters by Röhm describing his numerous affairs.

Ernst Röhm

There was also conflict between the socialist branch of the Nazis and German aristocracy. Later, when aristocratic German officers attempted to assassinate Hitler in July 1944, Goebbels wrote in his diary, “When we have removed the last half-Jew, we must set about getting rid of the aristocracy … even without their titles these people are the same. They remain discontented, foreign bodies in the state … They only ever intermarry, and thus deepen their degeneration. Like the Jews, the aristocrats have foreign connections, and they never cease to form a caste of their own. They must be expunged entirely … leaving nothing, men, women and children must be eliminated.” Seven thousand were arrested, 4980 executed. But that was later, at the moment, the German military had plenty of aristocrats as officers and Hitler probably needed to improve his relations with them.

On June 30, 1933, on the pretext that The SA was planning a coup, Hitler had the SA leadership butchered an event known as the Night of the Long Knives. (As an aside, the Night of the Long Knives is the topic of a song, “Last Day of June, 1934″ by Al Stewart.) At the Reichstag, Hitler shouted “The supreme court of the German people during those twenty-four hours consisted of myself!” The deputies rose and cheered. German courts and the cabinet quickly set aside centuries old prohibitions against extra-judicial killings. That Christmas, she sent generous Christmas gifts to the widows of the SA leadership.

Prelude to the Second World War
The Holy Roman Empire, was a collection of Central European states founded in 962AD. A consequence of the peace Napoleon obtained at the 4th Peace of Pressburg on December 26, 1805, was that the last Holy Roman Emperor, Francis II, became Francis I, the first emperor of Austria. He dissolved the Holy Roman Empire in 1806.

The German states were partially reunited in 1871 by Otto von Bismark under William I. We call the result the German Empire. The last emperor, or kaiser, William II / Wilhelm II, was forced to abdicate on November 28, 1918 as a result of uprisings caused by the end of the first world war. His government was replaced by a Republic. Since the German word “Reich” is related to the English “region” but translates as “Realm” or “Domain” as well as “Empire”. The new, Democratic, state kept German Empire or Deutsche Reich as its official name until May 23, 1945. After a little confusion as a result of its status as a front line during the cold war, Germany was united again as the current Federal Republic of Germany or Bundesrepublik Deutschland.

The peace agreement at the end of the first world war increased the area of the winning countries at the expense of the losers. This left many German speakers now citizens of countries in which they were now ethnic minorities. In addition, the breakup of Austria left German speakers now subjects of successor states where German was no longer the primary language. Of the many bonds possible between people of different lands, the sharing of a common language is one of the most strong. Many Germans who had suddenly become minorities were unhappy with the change and saw Hitler as a method of reversing the situation.

Hitler, in violation of the world war one treaty, began (open) rearming of Germany on March 16, 1935. The former Allied powers realized that the treaty had been excessive and ignored this violation. On June 18, 1935, Britain and Germany signed the Anglo-German Naval Agreement which allowed Germany to build its navy beyond the limits of the world war one treaty, up to 35% of Britain’s navy. On March 7, 1936, Hitler moved troops into the demilitarized Rhineland, again ignoring the now dead treaty. Britain’s doing this was a partial repudiation of the Stresa Front an agreement between Britain, France, and Italy to resist German reunification, particularly the combining of Austria with Germany, in that it allowed Germany to exceed its treaty limitations.

The Empire of Japan and Germany had a common enemy in the Soviet Union. On November 25, 1936 they signed an agreement to fight on each other’s side if either were attacked by the Soviet Union. This was the Anti-Comintern (Communist International) Pact. On November 6, 1937, Italy joined the Pact, sealing the fate of the Stresa Front. Poland was offered membership in the Pact but, fearing status as a puppet state, instead stayed with Britain. Later, the Pact would grow to include Germany, Japan, Italy, Bulgaria, the Wang Jingwei government of China, Croatia, Denmark, Finland, Hungary, Manchuko, Romania, Slovakia, and Spain. With the failure of the Stresa Front, Germany was free to reunite with Austria.

In 1934, Austria was torn by a mild civil war. The result was that a group of conservatives ran the government. They banned the socialists, communists, and the Nazis. On February 12, 1938, Hitler demanded that the Austrian government end its ban on political parties, reinstate full party freedoms, release all imprisoned members of the Nazi party, and allow Nazis to hold government office. The government of Austria agreed. Hitler then demanded that Austria unite with Germany.

Partly as a result of Goebbels’ propaganda, many Austrians, Nazis or otherwise, were in favor of unification, or Anschluss with Germany. The Austrian government announced a referendum to be held on March 13, 1938. Since youth was strongly in favor of the Nazis, the government chose a minimum voting age of 24. In fact, the Anschluss was wildly popular in Austria. Small towns where the vote was held as planned on March 13 voted in favor of it by incredible margins of 95% to 5%. Seventy years later, and not speaking German, I can but marvel at the oratorical abilities of Goebbels and Hitler.

On March 12, 1938, one day before the referendum, Hitler accused the Austrian government of planning to steal the election and demanded that Austria immediately allow German troops to cross the border. With a military unwilling to fight at best, and at worst openly supportive of the Nazis, and with no realistic hope of assistance from abroad, Kurt Schuschnigg, the unpopular chancellor / dictator of Austria, resigned.

When German troops marched across the border on March 12, 1938, they were greeted by cheering crowds, flowers, Nazi flags, and Hitler style salutes. Hitler crossed the border that afternoon. Nazi leadership was stunned by the warmth of the reception. Hitler began a triumphal tour of Austria that ended in Vienna, on April 2, 1938 where a crowd of 200,000 heard him proclaim Germany and Austria as one nation. A plebiscite was held on April 10, 1938 with the Anschluss receiving a (non secret) vote of 99.73% in favor. About 10% of the population was not allowed to vote, mostly left wing and Jews.

Nazi party propaganda saw the regaining of lost German territories as a reunification and referred to their country, particularly after the Anschluss, as the “Das Dritte Reich” which is usually translated to English as “The Third Reich”. The first and second Reichs were the Holy Roman Empire, and the empire lost when Wilhelm II abdicated.

While Austria was an easy convert to Germany, more difficult were the German speaking regions of countries where Germans were a minority. In the breakup of Austria-Hungary, many Germans ended up in Czechoslovakia. In particular, they formed a majority in the Sudetenland, mountainous country bordering Austria.

Few of the countries on this planet do a good job of taking care of ethnic minorities and the young republic of Czechoslovakia was certainly no exception. From a position of peacefully demanding equal rights, the German regions were slowly pushed into seeing unification with Hitler’s Germany as a solution. After analyzing the problem, Britain, which had recently lost most of Ireland, agreed. Britain and France forced the Czechs to give the territory up between October 1, and 10th, 1938. The Czechs also had land populated by Poles and Hungarians and at the same time they gave these lands back to Poland and Hungary. Poland had been given land populated by Germans, particularly the city of Danzig which was 95% German.

Another ancient part of Germany, the Memel (German) territory or Klaipėda (Lithuania) region was made independent under French mandate at the end of the first world war. Lithuania ended up annexing it in 1923, as a result of the Klaipėda revolt. France did nothing to stop this and Germany formally recognized the loss on January 29, 1928. By ultimatum to the Lithuanian government, it was returned to Germany on March 23, 1939, in return for a 99 year lease on the port that Lithuania had built there. The return was confirmed by Lithuania, Britain, and France. This was the last peaceful return of German territory.

The Second World War
Somewhat arbitrarily, Neville Chamberlain’s government gave a war guarantee to Poland for its borders. With this guarantee, Poland refused to negotiate with Hitler. This guarantee would be the cause of the war. Pat Buchanan recently discussed the second world war as the unnecessary war as Churchhill called it.

Apparently Magda had word that Poland would be invaded as she told her mother to attend the Reichstag session for September 1, 1939, as a spectator, as it would be a historical event. Hitler announced that Poland had fired on German territory and that German troops were returning fire.

Magda had great faith in Hitler and was enthusiastic over the invasion of Poland, but her mother knew what war would entail. She was shaken by a violent weeping fit. Behind her, one of the Nazi women’s organization members told her to get a hold of herself, then clammed up when another member told her that the weeping woman was Frau Goebbel’s mother.

The Nazi leadership were not surprised when France and Britain gave them an ultimatum to cease. This had happened before with no effect. They were surprised when France and Britain declared war. Goebbels and his rival, the head of the Luftwaffe, Hermann Göring, had understood the risks before the invasion of Poland and thought that Hitler was taking too much of a risk of a war that Germany was not yet ready for.

As even with a commercial corporation, decisions are made from the top and those under the leader end up implementing policies, good or bad, as best they can, even when they had previously argued against the plan of action that brought them to that point. And though he was against it (for practical reasons, certainly not any moral doubts) Goebbels did his best to keep the German public in favor of the war. His extraordinarily voluminous diary recorded his daily thoughts on the progress of the war and make fascinating reading for those interested in what went on behind the scenes at the Nazi leadership.

The Bitter End
In a sense, wars balanced between equal enemies are far worse disasters than wars where one side quickly overcomes the other. Global wars can go on for decades. In the case of the second world war and Germany, the world is very lucky that Germany was quickly overcome, in less than 6 years, by an inadequacy of industrial production and an insufficient supply of oil.

Despite their early successes, that Germany would eventually, inevitably, lose the war was a fact that dawned on different people at different times. For those focused on control of territories, the turning point was 1942 and the Axis disasters in North Africa, Midway, and Stalingrad. For those focused on military strength, the turning point of the war would have been October or November 1941, by which time the USSR was fielding troops faster than the Germans were able to capture them, and steadily improving their strategies, tactics, and armaments. But for those focusing on industrial production it must have been obvious from the very first.

Her ex husband, Günther Quandt, was an industrialist and must have seen the end coming quite soon. His son, Harald, also understood and his pessimism is remarked upon in Goebbel’s diary. Churchill also understood the industrial situation and never wavered in the expectation that England and her allies would eventually win.

The war years were difficult for the German people. The extensive Allied bombing campaigns, which were substantially directed towards destroying as much civilian housing as possible, took a toll on the morale of the German people, as Goebbels diaries attest. Eventually Magda could see the end coming. A few months before the end of the war she had the opportunity to see the bombing campaign at one of its most terrible moments.

Magda’s sister in law, Ello Quandt, was staying in a sanatorium in the Elb hills close enough to see Dresden when it was firebombed in February 13-15, 1945, just 12 weeks before the end of the war. When Magda visited her a few weeks later, she told Ello, “We have nothing left Ello … total defeat is barely a matter of weeks away. – We’re all going to die, Ello … but by our own hands, not by the force of others!” She went on to explain, “In the longer or shorter term the whole of Europe will fall to Bolshevism. We were the last bulwark against the red deluge. As regards ourselves, we who were at the summit of the Third Reich, we must take the consequences. We have made unimaginable demands on the German people, we have treated other peoples harshly and relentlessly. The victors will take thorough revenge for that … and we cannot appear cowardly. Everyone else has the right to go on living, but we do not … We have failed.”

Dresden 1945, body pile awaiting cremation

“I was there. I believed in Hitler, and I believed in Joseph Goebbels for long enough. I am part of the Third Reich that is now being destroyed. You don’t understand my situation … What am I to do? If I stay alive I will be arrested immediately and interrogated about Joseph. If I were to tell the truth, I would have to portray him as he was … I would have to describe what went on behind the scenes. Then any respectable person would turn from me in revulsion. Everyone would think that, since my husband was dead or in prison, I was now most terribly traducing the father of my six children. As far as the outside world is concerned, I have lived by his side amidst brilliance and luxury, I have enjoyed all his power. As his wife I have stayed with him until the bitter end. No one would believe me if I said I had stopped loving him, and … perhaps I still do love him, against my reason, in the face of all my experiences with him. Regardless of what is behind me, Joseph is my husband and I owe him loyalty …, and comradeship beyond death. For that reason I could never say anything against him. After all this, after his plunge into the abyss, I could not do that!” She would also never be able to defend him, as it would go against her conscience.

Regarding her children, Magda said “We’ll take them with us, because they are too beautiful and good for the world’s that’s coming,” and she added that posterity would avenge the father’s crimes upon the children.” Ello violently disagreed.

USSR forces entered Berlin in April 1945. The Goebbels family moved into the same bunker where Hitler stayed, the Führerbunker.

Various people, especially including Hitler, tried to talk Magda into leaving Berlin, with her children, perhaps even to a neutral country, but she remained steadfast in her desires. There was a certain feeling among the Nazi leadership that with the German people losing the war, they did not deserve to live, but still one wonders why she stayed when no other wife of the leadership chose to do so. Perhaps she felt a stronger sense of guilt. But why take her children with her?

Her children provided entertainment to Hitler up until his suicide on April 30, 1945. On that day, he gave Magda his gold Nazi party pin. She wrote about these things on a final letter to her son Harald in a British PoW camp. In this letter she again states why she intended on following her husband to his death. On May 1, 1945, Magda and Joseph killed their six children inside the bunker and killed themselves just outside of it, having arranged to have their bodies set on fire. She was the only Nazi wife to go down with the party in this way, that is, to kill herself or her children others lived out their lives in poverty and /or embarrassment.

Magda’s belief that horrible retribution would be taken against the children of Nazi leadership, and that Europe would be conquered by the Soviet Union, were beliefs likely given to her by her husband. They turned out to be as fantastical as her idea of Germany as a superpower at the beginning of the war. These were themes that her husband gave out as propaganda. From his diaries, it appears that he sincerely believed in this. I’m sure they would have been surprised by events as they turned out.

The surviving children of the Nazi elite seem to have not been particularly badly abused, even the ones that supported Nazism after the war. And the USSR did not roll over Europe, though socialism might have. After seeing the punishment dished out to innocent civilians at Dresden, she could hardly have expected to receive better. But her husband was right that the conflict with the USSR would be the next problem of the western Allies. For that reason it was not possible to punish Germany; both postwar halves would be needed to supply the soldiers that faced off along the Fulda Gap.

Tribes
For hundreds of thousands of years, humans have lived in tribal societies. The human condition is one of an absence of absolute knowledge in every area. In facts, our ignorance and limitations force us to accept the opinions of those around us. We often follow these opinions blindly, as if they were edicts handed down from our dear leader. Inherently, genetically, we are believers to our innermost core.

In morality, our genes have long found that it is better to go along with the majority than to risk banishment or death. The mark of a highly moral human being, is not what they do in private, where no one can know what they’ve done. In the dark anyone can be moral, it’s a matter of choice unconstrained by the distorting opinions of our friends and relatives. Instead, the strength of our inner compass is indicated by what we do while the whole world is watching us; and egging us on.

Humans have a love of morality tales, simple histories with clear and obvious saints and sinners. By leaving things out, by stressing one fact or another, it is possible to slant a history in whatever way the author, consciously or otherwise, desires. Here I have tried to tell her sad story taking into account her point of view, as molded by her experience.

Book Review

Magda Goebbels
by Anja Klabunde
http://www.amazon.com/Magda-Goebbels-Anja-Klabunde/dp/075153448X

Normally I pick up books for $1 or $2 at the Half Price Book discount desk. This one I ordered by mail from Amazon, used, at a price of around $5, plus shipping. The book behind it, the one that influenced me to order this one, was the English translation of the final diary of Joseph Goebbels. These are the last 3 months or so of his diary. It deserves a book review on its own. The diary included Magda’s last letter to what would be her sole surviving child, Harald. You can read the letter in translation in various places; it is enough of an introduction to her that I decided to read a biography. The Nazi ideal of the perfect housewife and mother.

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.

Quantum information treats the information contained in quantum states. For a colored particle, that information is “red”, “green” or “blue”. But the usual method of modeling the color force is instead to approximate the color force as a modification to the Coulomb force.

On looking at the problem as a color force problem, we find that the excited states of a color bound state, in the quantum information approximation, must come in triplets and these triplets are related by the discrete Fourier transform on 3 variables.

So we apply the discrete Fourier transform to triplets of particles and what do we find. Well we get a simple equation relating the charged lepton masses which implies Koide’s mass equation. And we get an implication for a neutrino version. These two equations tell us how leptons look when they are excited, as if the leptons were composite particles.

The mesons and hadrons are composite particles and also have excitations. So, naturally, we plug those excitation mass numbers into the discrete Fourier transform and what do we get. Yes, we get more copies of the lepton mass equations.

The paper includes 33 mass equations that fit triplets of mesons, and 6 more that fit triplets of baryons.

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.

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.

The paper magnificently describes how I think of of Feynman diagrams. In the usual formalism, they are connected to a Largrangian / Hamiltonian, that is, a definition of the energy. To me, this is unfortunate because energy should not be the fundamental description of nature. Energy is just a symmetry, the fundamental description of nature has to be a differential equation, or the equations of motion. An interesting sentence from the first page:

It is a miraculous consequence (not requirement!) of the propagator definition that it satisfies an evolutionary chain rule (Chapman-Kolmogorov equation)

whose infinitesimal version is equivalent to the celebrated Schroedinger equation.

This is interesting to me because, as the alert reader will have noticed, it is an example of the idempotency equation . The reason for the similarity is that there is a relationship between pure density matrices and propagators. So in my version of “one past Feynman”, I look for interesting solutions to the idempotency equation. The Weak Quantum Numbers paper is an example of this type of idea.

Wonderfully amusing Cosmology article by Martin Lopez-Corredoira, Sociology of Modern Cosmology, 0812.0537.

Certain results of observational cosmology cast critical doubt on the foundations of standard cosmology but leave most cosmologists untroubled. Alternative cosmological models that differ from the Big Bang have been published and defended by heterodox scientists; however, most cosmologists do not heed these. This may be because standard theory is correct and all other ideas and criticisms are incorrect, but it is also to a great extent due to sociological phenomena such as the “snowball effect” or “groupthink”. We might wonder whether cosmology, the study of the Universe as a whole, is a science like other branches of physics or just a dominant ideology.

The same critique could be made of many other branches of physics. Right now, I’m busily typing up a paper on my version of quantum gravity and its cosmological consequences. Part of the paper will be a cleaned up and much improved version of the blog post on Louise Riofrio’s cosmology and the CMBR correlation anomaly.

The subject of ball lightning is a fascinating and so far unsolved problem. This might even be right (though I just quickly scanned it): Levan N. Tsintsadze: A New Concept of Ball Lightning, 0811.4640

We suggest that the ball lightning (BL) is a weakly ionized gas, in which the electromagnetic radiation can be accumulated through the Bose-Einstein condensation and/or the photon trapping in the plasma density well. We derive the set of equations describing the stability of BL, and show that the BL moving along charged surface becomes unstable. Eventually the instability leads to explosion of BL and release of energy of the trapped photons and/or the Bose-Einstein condensate.

A theorist fight is always entertaining and enlightening. This one is over the subject of 1/R gravity. This is a variation of general relativity that better explains inflation / cosmic acceleration observations (about which my new paper will address):
Solar system tests do not rule out 1/R gravity, and on the other hand,
Solar System tests DO rule out 1/R gravity.

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.

A jury decided on by FQXi is presumably busily reading the essays and will decide on “jury prizes”, up to 18 prizes as follows:

1st: $10,000
2nd: 2x $5,000
3rd: 5x $2,000
4th: 10x $1,000.

In addition, there will be up to 3 prizes determined by restricted votes:

1st: $5,000
2nd: 2x $2,500.

Each essay can win only one prize. Rules are here. Since my essay was turned in fairly early, I am listed at the top of the 5 entries with two restricted votes. (There are 8 essays with 1 restricted vote, and the remaining 100+ entries have none.) So if this keeps up, I could end up with a prize. Winners are to be announced on January 19, 2009, I suppose, unless FQXi was serious when they said that they would announce winners on January 19, 2008.

First, second, and third prize winners will be invited to join FQXi.

Members of the general public can also vote. Your votes are recorded and are shown publicly but they do not count towards the prizes, however, one supposes that they could influence people to read and vote on the essays.

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.

The Republics of The Rio Grande, Texas, and Yucatán
Those states of Mexico who disagreed with the new conservative government or wished to remain under the 1824 constitution revolted. Eventually 11 states went into revolt, among them Coahuila y Tejas, which included the colony of Texas. Three of the 11 revolting states declared themselves independent of Mexico. Of these new states, only Texas still remains free of Mexican control (more or less). The other two were eventually reabsorbed and are now mostly forgotten.

The Republic of the Rio Grande lasted from January 17 to November 6, 1840. It included territory south of the Rio Grande in what is now northeastern Mexico. Its president was Jesús de Cárdenas.

The revolt in Yucatán began in 1838 and the area declared its independence in 1840 as the Republic of Yucatán. Yucatán was well armed and Antonio López de Santa Anna negotiated its return to Mexico under a treaty that he then ignored. They revolted again. In 1843, Antonio López de Santa Anna ordered the blockade of Yucatán and they eventually agreed to another treaty. Again Antonio López de Santa Anna broke his promise and again the state declared its independence, this time on January 1, 1846.

As an interesting aside, Yucatán suffered a race or caste based civil war that began while it was independent, in 1847. It is known as the Caste War of Yucatán. A fascinating but long book on the subject is The Caste War of Yucatán. During the civil war, the Hispanics (or Yucatecos) of European descent asked for help from the US, Britain, and Spain, offering to sign the country over to whoever would send help against the Maya. Everybody turned them down and, in order to keep the Maya in place, Yucatán rejoined Mexico in 1848 where the state remains today. The Mayans had imported gunpowder over the border with British Honduras. This border was cloased in 1893, and the Mexican army finally marched into the Mayan capital, Chan Santa Cruz in 1901. The rest of the Mayan lands were mostly under Mexican control by May 5, 1915 when victory was declared but the last capture of a Mayan city by Mexican forces was in 1933. Now the area is relatively calm. One of the contributions to prosperity there is the export of chicle, or chewing gum. The introducer of chewing gum to the United States is said to be Antonio López de Santa Anna, who was living in exile in New York in 1848.

The Texas Navy
Antonio López de Santa Anna came north with an army to put down the revolt in Texas in 1836. Every professional knows that with an army, the most important thing is supply. In this case, the Mexican army could be supplied either by sea through the Gulf of Mexico, or by land through west Texas. At this time, supply by sea was far more efficient than supply by land (if it weren’t for rail it still would be), and knowing this, the government of Texas bought 4 small “ships” in early 1836 to protect the coast of Texas (as well as to harass Mexican shipping).

These ships are known as the “first Texas Navy” and they did their job well. The Mexicans were defeated at the Battle of San Jacinto, April 21, 1836. Antonio López de Santa Anna was captured and forced to sign documents giving Texas its independence. Of course these documents were repudiated by both the Mexican government and Antonio López de Santa Anna and the war would continue, but for now, the Texas government sold off its ships.

As another interesting aside, those who are not professionals look for alternative explanations to explain the fortunes of war than the boring topics of weapons and supplies, and a popular myth arose that the victory at San Jacinto was due to Antonio López de Santa Anna spending time with a woman. That woman was Emily D. West, and since she was mostly Caucasian, but partly black, and since she was quite beautiful, she was called “the Yellow Rose of Texas”. A song by that name is considered the unofficial state song of Texas. One of the (less offensive to the modern ear) stanzas is:
Where the Rio Grande is flowing, and the starry skies are bright,
She walks along the river in the quiet summer night;
She thinks if I remember, when we parted long ago,
I promis’d to come back again, and not to leave her so.
Over the years the song has morphed from a description of a yellow or high yellow woman, so much that the Elvis Presley version includes the lyrics has “Her eyes are even bluer than Texas skies above”.

By 1839, it had become clear that the Mexicans would still not acknowledge the independence of Texas and the Texas government, worried about another fight on Texas soil, particularly worried about an invasion of Galveston, commissioned the second Texas Navy. These ships harassed the Mexican coast and kept the Mexican navy busy defending their own coast instead of blockading Texas (which was very much dependant on sea for commerce and trade).

The Republic of Texas and the Republic of Yucatán were at opposite ends of Mexico but they both were on the Gulf of Mexico and it was natural that they assisted each other in naval affairs. Both states were blockaded by Mexico and both were invaded by Mexican troops that needed supplies from the Gulf. The existence of the Texas navy helped keep Yucatán from being blockaded and the government of Yucatán provided $8000 per month to help defray the costs of the Texas Navy.

The Battle of Campeche
The problems with the Texas navy on the Gulf coast drove the Mexican government to acquire one of the best warships of the time, the British built (and British manned) but Mexican owned 1100 ton ironclad steamer Guadalupe. This vessel, plus a wooden steam powered warship, the Moctezuma, blockaded the Yucatán port of Campeche. Two Yucatán warships, five gunboats, and two Texas Navy ships, the sloop Austin and the brig Wharton attempted to lift the blockade.

Two battles were fought, one on April 30, 1843, the other on May 16, 1843. The result was unusual in that this was the only naval battle which was arguably won by wooden sailing ships over steamships. “Won” in this case means that considerably more British and Mexicans were killed than Texans, but the Texas ships were badly knocked about and retreated to Galveston. British forces were suffering badly from yellow fever. The two Mexican steamers had British captains (Edward Phillip Charlwood or Charlewood captain of the Guadeloupe, and Cleaveland, captain of the Montezuma about whom I can find little information) and crews, so I suspect that this is the last time US and British sailors fought a significant sea battle against each other. At the start of the Mexican American war, the British steamers fled to Havana and were returned to the British.

The Guadeloupe was the world’s largest iron ship when it was built in 1836 by John Laird, who expected to sell it to the British Royal Navy. They weren’t interested because at that time, they hadn’t figured out how to correct compasses in iron ship; he sold it to the Mexicans instead. His business, John Laird Sons and Company, also built the Montezuma but is most famous for secretly building the Confederate commerce raider CSS Alabama (used by the Southern side in the US civil war from 1862-1864).

Other Texas conflicts with the Mexican Navy didn’t turn out so well, with several Texas ships ending this way. The remainder of the Texas Navy was absorbed into the US Navy in 1848 when Texas joined the United States.

And as yet one more interesting aside, Samuel Colt got one of his first contracts for his revolver from the Texas government. The company he founded, Colt, still makes weapons. When he created the Colt 1851 Naval Revolver for the US Navy he had a scene of the Battle of Campeche engraved on the barrel. These are very valuable collectibles nowadays. The engraving is just visible in this picture of this specimen (selling for $1975.00 ):

Youtube has a nice short video, History of the Texas Navy. A much more complete description of the battle, along with the minutes from the contemporary records, is at The Texas Navy’s website of the battle.

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).

Elementary particle physics, and quantum mechanics more generally, has been wedded to symmetry techniques almost since the founding of the subject. The elementary particles are described with symmetries and Einstein’s relativity is also a symmetry (space = time, more or less). In the case of the weak quantum numbers, the appropriate symmetry is U(1) x SU(2). One normally sees this written in reverse order, as SU(2) x U(1), but in the above paper I’ve listed the weak quantum numbers in the order (U(1), SU(2)), so it seems more appropriate to reverse them here.

Brief Description of Weak Isospin
The quantum numbers of a representation or “rep” of SU(2) can be zero, positive or negative, but they are always multiples of 1/2. With the weak quantum numbers, SU(2) provides the symmetry of weak isospin which is designated as . (By the way, the “3″ refers to the 3rd Pauli spin matrix, , the one oriented in the z direction. This is because, in the state vector treatment of spin-1/2 spinors, it is customary to use the basis defined by spin up/down. In this basis, the vector (1,0) represents spin up while (0,1) represents spin down. And this choice is from the fact that the 3rd Pauli spin matrix is diagonal.)

Getting back to SU(2) weak isospin, only two representations are used. The first of these two representations is the SU(2) “singlet”. It has only one quantum state with quantum number 0 so for these particles, weak isospin . Of the 16 left or right handed elementary fermions or anti fermions, 8 are weak isospin singlets. And of these 8, four are particles and four are antiparticles. The four particles are evenly split between leptons and quarks and the four antiparticles are also evenly split.

The other rep is the SU(2) “doublet”. This rep has two states with quantum number +1/2 and -1/2. The 8 left or right handed fermions or anti fermions that are SU(2) weak isospin doublets are grouped into four pairs of two each. Two of these pairs are particles and the other two are antiparticles. The two particle pairs include a pair of leptons and a pair of quarks. Similarly for the antiparticles. Still restricting ourselves to the first generation, the SU(2) doublet of leptons consists of a neutrino and an electron, while the SU(2) doublet of quarks has an up quark and a down quark.

The weak force is carried by the W and Z bosons. Of the handed elementary fermions, only the SU(2) doublets feel the weak force. That is, only they can absorb or emit a W or Z. The weak isospin singlets do not interact with the weak force at all. The W is a charged particle with charge +1 or -1. In order for a fermion to emit one of these, the charge on the fermion must change. When this happens, the fermion converts over to the other weak isospin doublet partner. Since the SU(2) partners are pairs of leptons or quarks, this means that a neutrino changes to an electron (or vice versa, or with the antiparticle pair), and similarly a down quark changes to an up quark or vice versa.

Brief Description of Weak Hypercharge
The U(1), or circle symmetry group has representations for all integers N, positive or negative. Unlike SU(2), all U(1) representations are singlets. These representations are homeomorphisms of the circle group: . The integer N is a “winding number”, it tells you how many times you wind around the circle in the map before you get back to the start. So one would think that the available quantum numbers for weak hypercharge would be all integers. Uh, well, that’s not how it turned out…

The left handed leptons have weak hypercharge quantum numbers of -1, so their transformation law is . Similarly, the right handed electron has quantum number -2 which gives . (Or is it +2, I forget.) In these transformations, is the “charge“, which means “the generator of a continuous symmetry.” In this phrase, the word “generator” means that you can make small (continuous) changes in the value while keeping your equations still satisfied.

Electrons and protons have the same (but opposite) electric charge and anything made from them has integer electric charge. Naturally people assumed that this would apply to any elementary particle and this assumption got frozen into the definitions. As a result, when it was found that it took three down quarks to equal the electron’s charge, the value of for weak hypercharge ended up taking it on the chin. The quarks ended up with fractional weak hypercharge. If we multiplied all weak hypercharges by 3, they would be all integers, leptons and quarks. So if this bothers you, you can think of them this way, or perhaps write a physics paper to correct the injustice in a manner more complicated than to simply multiply all the weak hypercharge quantum numbers by 3. By the way, I should mention that there is already a factor of 2 between weak hypercharge and electric charge. This suggests that the true unit of electric charge is 1/6 the charge of the electron.

Symmetry
The course of elementary particle physics over the last 50 years has been to assume that the fundamental laws of physics are symmetry laws. One then makes the assumption that the symmetry laws are simple. After finding that a symmetry is only approximate, one uses the technique of broken symmetries. Basically, this idea is to suppose that the underlying differential equations are perfectly symmetric, but that their low temperature realization breaks the symmetry. Of course, as in epicycles of early astronomy, you can approximate any old thing by postulating complicated enough symmetry breaking.

The alternative technique I would prefer to use is to suppose that the universe is organized around differential equations and that these differential equations are simple. Symmetry principles are frequently useful in solving differential equations, but in my view, one should being so married to symmetry that one is unable to solve a problem any other way.

The Foundations of Physics
In the case of the weak quantum numbers, the foundational problem is that of explaining why they happen to be what they are. From the symmetry point of view, this is an unanswerable question. One might take the anthropic point of view and try to show that other universes would be incompatible with intelligent life, but this is a rather difficult task.

A few years ago, I independently realized that there was an alternative way of writing special relativity, a way so that it was no longer a principle of symmetry, but instead was a description of a perfectly realizable manifold with normal material properties (except that we cannot fashion things using an extra dimension). This form of special relativity is called Euclidean Relativity. My version amounts to assuming a single hidden, cyclic, very small, dimension. I assume that this is the origin of the U(1) symmetry. With this idea, all classical objects then move at speed c. If they are massive and are stationary, then their velocity in the hidden dimension is c.

The primary attraction of this idea for me was not that it eliminated symmetry, but instead that it would allow a definition of quantum mechanics where quantum waves would not be dispersive. A non dispersive wave travels at the same speed regardless of its frequency. In normal quantum mechanics, particles with different energies travel at different speeds and this requires dispersion. Dispersion is difficult from a mathematical point of view; having a non dispersive quantum wave theory means that calculations are easier. And in fact, the Wick rotation commonly used in quantum mechanics amounts to a transform to Euclidean relativistic coordinates.

It turns out that no one wants to hear about this sort of foundational ideas. It’s clear that one can move back and forth between standard relativity and Euclidean relativity so there is little motivation for physicists to look at ideas that come from Euclidean relativity. And most of the people working on Euclidean relativity ideas are amateurs. It smells of crankdom. However, if the underlying structure of the universe is, in fact, Euclidean instead of Einsteinian, then one is likely to find insights into the structure of the elementary particles by rewriting elementary partices from a Euclidean point of view.

If all you do is switch from Einstein’s relativity to Euclidean relativity you will accomplish nothing. To get anywhere you have to take the principle that you used to prefer Euclidean relativity (that of avoiding symmetry in favor of geometry), and apply it to all of elementary particles. Since elementary particles is built from symmetries, this is a tough roe to hoe. And I’ve got the calluses to prove it.

Density Matrices
The other part of the title of the paper, “density matrices” describes how the calculation is set up. Density matrices are an alternative formulation of quantum mechanics that is not as commonly use as the usual state vector formulation. The advantage of density matrices is that they do not possess the arbitrary U(1) symmetry (which is more or less related to weak hypercharge) of the state vector formulation. Since my objective has been to rewrite elementary particle physics without recourse to using symmetry principles in the foundation, it is natural for me to prefer the density matrix formulation.

So finding the equations that define the weak quantum numbers was not a difficult task. This was done after I had used a very similar method to rewrite Koide’s wave equation as an eigenvalue equation and extended it from the charged leptons to the neutrinos. Knowing that the elementary fermions are composed of three identical preons, I was sure that the appropriate group would be the symmetry group on 3 elements. From the permutation group on 3 elements, it takes only a few minutes to write down the 6 coupled quadratic equations. Actually solving them took me 2 or 3 days of hard work. When you’re as slow as I am at calculations it helps to be able to restrict the problems you work on to the ones that will give useful results.

The calculation as submitted is not at all how I thought of it when I first began working on it. To me, the six elements I, J, K, R, G, and B are analogs of Feynman diagrams. Each represents a quantum amplitude. The requirement of idempotency is equivalent to requiring that the particle be in a stable state. This is all more completely described in the paper I wrote up when I had first made the calculation Density Operators, Spinors and the Particle Generations. Like the just submitted paper, this was intended for Foundations of Physics. But the length basically grew to infinity. The new calculation is improved in that it uses the principle of Hermiticity to separate the extra solutions of the idempotency equation from the 16 that represent the 16 handed elementary fermions or anti fermions.