The book was written in 1884 by George F. Williams, an author with a very common name and possibly several other books. The book is a fictionalized memoir of the U.S. Civil War, 1861-1865, and follows the experiences of a young college graduate who enlists in the union side.

Since I’m writing this post with friends in mind from far away, I should explain some things. As I write this, the president of the US is Barrack Obama. He’s a member of the Democrat party. The previous president, George W. Bush, is a member of the Republican party. You may have noticed that the election of 2008 which replaced a Republican president with a Democrat president was widely reported, but didn’t result in any major changes in foreign policy. The reason for this stability (which for a world power is definitely a good thing, you don’t want to see the US alternating between Communist and Fascist governments) is that the US system of elections forces the political parties to compete over the center part of the population.

The change of power in the US in 2008 was peaceful, but that’s not how it always has been here. The election of 1860 split the nation into two sides with various names. The “U.S.A”, “North”, “Union”, or “United States of America” under Abraham Lincoln was Republican, while “South”, “Confederacy”, “CSA” or Confederate States of America was Democratic. The South included the slave states and slavery was probably the major issue of the war.

The war lasted 4 years and killed 620,000 people. Whether in terms of human life or destruction of property, it was the most expensive war the US has ever been involved in. The Civil war ended only after the larger and more industrialized North had produced enough munitions to kill or severely wound about half the adult males in the South. At that time the surviving Southerners agreed to rejoin the US.

Williams’ book was written in 1884, about 20 years after the Civil War. By that time, the two sides were on the road to reconciliation. Williams’ book was probably intended to help. It remains a reminder of the horrors of war. As with my other book reports, I’ll type in a few paragraphs to give a flavor of the book.

Late in the afternoon of the first day of July we [Republican soldiers] reached the picturesque town of Hanover. [Pennsylvania, a Republican stronghold] Near the cross-roads were lying the bloated carcasses of half a dozen cavalry horses, evidently slain in a brief skirmish between Pleasonton’s [a Republican general] and Stuart’s [a Democrat general] troops, a few hours before our arrival.

Close to the road, near the scene of the cavalry fight, stood a farmhouse, at the gate of which was an old-fashioned pump and horse-trough. The pump-handle was in constant motion, as the weary, foot-sore soldiers flocked around it to quench their thirst with the delicious water that flowed into the mossy trough.

Coming up and waiting for my turn to drink, I noticed a sunburnt, gray-haired man, leaning over his rude [primitive] gate, watching the troops. He was dressed in a faded, well-worn suit of homespun [home made cloth], having no doubt spent the day in the hayfield; and I could see that he was pleased that his pump was doing such good service.

“Good-evening, sir,” said I to him, removing my cap, and mopping the perspiration from my face. “It’s rather hot weather, this, for marching.”

“I ‘spose [suppose] it ’tis [it is], though I never did any marching,” was his brief response.

As the old farmer uttered the words he moved a little; and my eye was attracted by a new-made grave among a clump of rose-bushes, just inside the fence. Wondering at the sight, I ventured to ask the reason for its being there.

“Whose grave is that?” said I, pointing to the mound of fresh earth.

“A reb’s [Democrat's]” he replied laconically. “One that got killed in the fight the horsemen had here to-day.”

“Indeed! and so you buried him.”

“Yes: buried him myself. They left him lyin’ in the road, out thar, just as he fell. I could do no less, you know.”

“Of course! buy why did you make your rose-garden a graveyard?”

“Wa-al [Well], it was the wimmen [women] that wanted it so. Yer [you] see, stranger,” and the old man’s voice trembled and grew husky, “yer see, I had a boy once. He went out with the Pennsylvany [Pennsylvania] Researves [Reserves], and fou’t [fought] along with McClellan [a Republican general], down thar [there] among those Chicka-oming swamps [In Democrat territory]. And one day a letter come. It was writ [written] by a woman; and she told us as how a battle had bin [been] fou’t near her house, while she and another woman lay hid all day in the cellar. When the battle was o’er [over], them wimmen came out, and found our Johnny thar [there], his hair all bloody and tangled in the grass. So they digged [dug] a grave in the soft earth of their gardin [garden], for the sake of the mother who would never see him agin [again]. So when I saw that poor reb [Democrat] a-layin’ [lying] out thar, all dead and bloody in the dust of the road, I sed [said] I’d bury him. And the gals, they sed, ‘Yes father, bury him among the rose-trees.’ That’s why I did it, stranger.”

I screwed up some of the section titles (when I cut out the section on the mixing angles and inserted a section deriving spin-1/2) and so I fixed those things and clicked them into the online proof correction system. And this is the message you get:

Next thing is to finish up the 1st revision to the paper on unitary matrix parameterizations at Phys. Lett. B. I need some more calculations for the CKM and MNS matrices in magic form. I’m hoping this will finish up this week, I’ll get a week of feedback from my peeps, and then send it back to the reviewers there. And then Marni and I are working on improvements to our joint paper.

Marni Sheppeard has a new blog, Arcadian Pseudofunctor. She and I have submissions to the FFP10 conference proceedings. I still haven’t heard whether mine was accepted. I would think it’s getting kind of late. Of course Marni and I are writing papers; I expect to see another half dozen between the two of us by the end of the year. Right now I’ve got three more papers in the peer review process:

Spin Path Integrals and Generations

The Spin Path Integrals and Generations paper at Foundations of Physics got 2 of 3 reviews recommending publication with major revisions. I revised it on March 15th. Presumably the editor sent it out for review as it showed “under review” until March 27th. Since then it’s shown “Reviews Completed”. I imagine the editors are arguing over whether or not it should be published. I can understand this; the paper is radical in that it purports to give an explanation of the generation structure of the fermions from first principles. This is a major problem in elementary particles so it’s a serious step to publish it in your journal. It would be embarrassing, especially given the history Foundations of Physics has for publishing junk physics.

The third reviewer on “Spin Path Integrals and Generations” asked that I remove the sections on mixing angles and hadrons. This gave me more room in the paper so I added a section showing how spin-1/2 shows up in the long time limit.

Permutation Parameterizations of Unitary Matrices

After I removed the section on the mixing matrices from the Spin Path Integral paper, I sexed them up and sent them to Physical Review Letters. By “sexed them up” I mean that I rewrote it in terms of Lie Groups and Lie Algebras. Their editor responded, in about 48 hours, that the paper was too mathematical and not enough physical for that journal.

PRL is the top elementary particles journal but they charge you something like $750 for publishing there. Normally this is paid by the institution you work for but ITT Tech doesn’t play that game. So I took the mixing matrix paper and further sexed it up and added a bunch of applications to elementary particles. I sent the paper, Permutation Parameterizations for Unitary
Matrices” to the number 2 (we try harder) elementary particles journal, Phys. Lett. B. They have the advantage of being free. In addition, they are a “rapid publication” journal.

After 6 long weeks of waiting, I got back a very short bad review. Apparently the review was bad enough that the editor told me the paper was rejected. In an email, I pointed out to the editor that the comments by the reviewer were incorrect. I suppose that he agreed; in any case he and asked me to revise the paper, if necessary, and to respond to the reviewer. So the paper has passed, but barely, its first review at PLB.

The reviewer’s complaint was that the permutation I introduced was not any simpler than the standard permutation. In revising the paper, I will add a comparison on this; I thought it was obvious to anyone. Judge for yourself. Here’s the new parameterization:

Here’s the old one. Ooooops. It’s kind of hard to read. Click to get a bigger image:

Now these parameterizations are unitary matrices. With my parameterization this is obvious; it’s the exponential of a Hermitian matrix and so is automatically unitary. To show that the traditional parameterization is unitary requires a page of algebra. However, you can also write the traditional parameterization as a product of exponentials of Hermitian matrices (and therefore unitary). This form is: Ooooops. It doesn’t fit very nicely, click to get the full image:

I hadn’t included the old paramaterization in my paper because I thought it would be obvious to any moron that it was a lot simpler than the standard one. When I got back a review stating the opposite I was quite angry. Especially since it took 6 weeks to get here. PLB regularly publishes papers less than 2 weeks after submission. I’ll type up a revision that makes it obvious even that the new parameterization is far far superior to the standard. I’ll also add some stuff to show that the parameterization generalizes to nxn unitary matrices.

Zitterbewegung, Acceleration, and Gravity

At last year’s annual Gravity Research Essay Contest, I took an “honorable mention”. They give out money to the top few papers and honorable mentions to about two dozen more. This has been going on for a half century so most of 1000 papers have gotten awards. Last year I was the first amateur to get an honorable mention in at least the last 25 years, so this year I typed up a more aggressive attempt, Zitterbewegung, Acceleration, and Gravity.

The basic problem in unifying gravity with the other forces is that gravity is written in a completely different language. My approach to this is to force gravity into a form where it’s compatible with quantum mechanics rather than the other way around. In this I use Feynman’s path integrals as shown in the Spin Path Integrals paper. The usual way of graphically describing path integrals is through Feynman diagrams.

Now the standard model defines the masses of the elementary particles as what appears as interactions between the left and right handed chiral particles. The left and right handed states are completely distinct in how they behave, particularly with respect to the weak force. So it’s natural to treat them as distinct particles in their own right.

But when you split things up like this, the left and right handed particles have to travel at the speed of light. For example, to convert a spin-up electron to a right handed electron, one accelerates the electron in the +z direction. The close one gets to the speed of light, the more completely is the electron right handed. When one accelerates in the opposite direction, the electron becomes left handed. Now it’s quite bizarre, but the results of these accelerations are beasts of completely different behavior. The right handed electron does not interact weakly at all, while the left handed electron does.

Einstein got general relativity by making the assumption that acceleration is equivalent, as far as measurements go, to the action of a gravitational field. So my gravity paper analyzes gravity by looking at how an acceleration effects the interaction between left and right handed electrons. My assumption here is that gravity is due to gravitons that propagate faster than light, but otherwise obey the usual laws of quantum field theory.

Now the difference between gravity and electricity and magnetism is that gravity cannot be shielded. This implies that in modeling gravity, we cannot use a simple quantum field theory interactions such as the Feynman diagram for the E&M interaction between two electrons:

We’re concerned here with the interaction a particle has with gravitons emitted by matter. In that context, we only care about half the above Feynman diagram. So what we’re concerned with here is only:

In the above, a photon enters from the left and interacts with an electron coming up from the bottom. The electron absorbs the photon and its direction of motion is changed accordingly. But in this interaction, the photon is absorbed; thus it is possible to shield the electric force (with a conductor), or the magnetic force (with a superconductor).

Feynman diagrams are methods of computing matrix elements. You convert these matrix elements into probabilities by multiplying them by spinors. Even if you don’t know the structure of the Feynman diagram for some interaction, you can deduce facts about its Feynman diagram by determining how many spinors must multiply it. In essence, one can count the number of legs going into the Feynman diagram. In the above diagram, only one leg goes into the electromagnetic interaction.

Now my paper shows that if you assume that gravity is due to an interaction between gravitons and the right and left handed states, you conclude that the Feynman diagram it corresponds to has to be fairly complicated. If we look at the transition rate from left to right, we find that this rate has to be proportional to the cube of the left handed electrons and the square of the right handed ones. (It’s a little more complicated as I’m going to ignore the difference between “amplitudes” and “intensities” here, see the paper for the full story.)

A lot of chemistry is about computing the concentration of chemicals that are interacting with one another. If you know that a reaction rate depends on the cube of a concentration of one of the chemicals, then you know that that chemical enters into the reaction three times. This is called the “stochiometric coefficient”. Applying these ideas to the reaction rate derived in the paper, we find that the Feynman diagram for gravity has to be quite complicated:

Thus, from finding the rates at which the left and right handed electron states convert into one another we derive that they must be composite with three states contributing to each. Of course this is also the subject of the Spin Path Integrals paper. And since the diagram has at least 7 nodes, we obtain that gravity is naturally a force weaker than the others (which cat get by with a single node each).

An analysis of Wolfenstein parametrization for the Kobayashi-Maskawa matrix shows that it has a serious flaw: it depends on three independent parameters instead of four as it should be. Because this approximation is currently used in phenomenological analyzes from the quark sector, the reliability of almost all phenomenological results is called in question. Such an example is the latest PDG fit from \cite{CA}, p. 150. The parametrization cannot be fixed since even when it is brought to an exact form it has the same flaw and its use lead to many inconsistencies.

Among phenomenologists, this is a pretty serious accusation. There are hundreds of papers on arXiv alone that use the Wolfenstein parameterization. It’s the basis for the PDG estimates on the CKM matrix. If it’s true this is really big news in elementary particles.

The Dita paper claims that the Wolfenstein parameterization is defective because its apparent four real degrees of freedom are redundant; instead there are only three. Such a defect would prevent the parameterization from exploring “almost all” of the space of possible 3×3 unitary matrices. Instead of the whole 4-dimensional real manifold of 3×3 unitary matrices (up to multiplication of rows and columns by complex phases), one would obtain only a 3-dimensional submanifold.

In particular, the paper claims that it is impossible to use the Wolfenstein parameterization to obtain a unitary 3×3 matrix with the magnitude of all amplitudes the same (and equal to sqrt(1/3) ). This is the “democratic unitary 3×3 matrix”, a subject Marni Sheppeard and I have explored at length. It took me a few minutes to verify that it is possible to set these parameters (lambda, A, rho, and eta) to obtain a unitary matrix with all magnitudes equal.

So I wrote up a one page paper giving the solution and sent it up to arXiv: Comment on “On one parametrization of Kobayashi-Maskawa matrix.” Did they accept it? No. And as of 24 hours later, no explanation.

So here’s my view of the situation. ArXiv had no problem whatsoever with publishing a paper that accused hundreds of phenomenology papers of being based on a very basic error. But they refused to publish a paper showing that the standard view of the CKM matrix is correct.

This is not the case of an amateur writing an insane paper claiming that the majority view on physics is wrong. It’s the reverse; an amateur is correcting an obviously defective paper written by a professional. Clearly arXiv cares more about the institution of the authors who contribute papers than they care about the actual content.

I’ve given my first lecture on physics to students at ITT Technical Institute, so I suppose I’m technically again in academia and can no longer claim amateur status. Also, I’ve got the final proofs back from IJMPD on my gravity paper, and I’m now quite convinced it will appear this month, so soon I should have my first published, peer reviewed, paper. This is after spending 25 years in the “real world”.

When I posted the gravity paper to arXiv, the geniuses there put it into the “gen-ph” category instead of gr-qc, hep-th, or astro-ph like every one of the hundreds of other papers which won honorable mentions at the annual Gravity Essay contests. It will look kind of funny when I update the paper with the citation data in a couple weeks; about the only paper published in IJMPD that is stuck in gen-ph is mine. Compare, for example, to IJMPD papers on gr-qc. Has arXiv treated me like crap? Hell yes!

If these high and low redshift objects actually are related, this places doubt on the Hubble relation. In addition, when low and high redshift objects appear to be related, their redshifts are related by quantum values . From observations, Arp has proposed that quasars evolve from high to low redshift, and finally become regular galaxies.

Now for quasars to have redshifts that differ from their true distances implies that their redshifts are determined gravitationally; that is, what we are seeing is partly the redshift of light climbing out of a gravitational potential. And if these redshifts are quantized, this gives a clue that the structure inside the event horizon of a black hole is not a simple central singularity but instead there must be repetitive structure.

In a classical black hole, the region inside the event horizon can only be temporarily visited by regular matter. Even light cannot be directed so as to increase its radius in this region. Let’s refer to this region as the “forbidden region” of the black hole as it is near the central singularity. For the classical black hole, this includes everything inside the event horizon. We will be considering the possibility that the forbidden regions of a black hole occur as infinitesimally thin shells, and that between these shells, light can still propagate outwards:

Forbidden regions shown in red.

Event Horizons as Quantum amplitudes

If we were looking for a quantum mechanical definition of the inside of a black hole, we could define it as the region where particles have a zero probability of moving outwards. We could say that the transition probability for the particle moving outwards is zero. However, in quantum mechanics probabilities are defined as the squared magnitudes of complex amplitudes. The way we compute transition probabilities is from complex transition amplitudes. If the transition amplitude between two states is zero, we say that they are “orthogonal”. Zero transition amplitudes correspond to points where a sine wave is zero; at these points, deviations to either side give nonzero transition amplitudes:

How to get zero probabilities from nonzero in QM.

In quantum mechanics, it’s never the case that making steady changes to a state or pair of states causes their transition amplitude to become zero and then remain zero. Instead, upon obtaining zero transition amplitudes by arranging for a parameter to continuously change, we find that continuing to change the parameter causes the transition amplitude to become nonzero. For this reason, from basic quantum mechanical principles, it would be surprising that the forbidden regions of a black hole should have more than an infinitesimal thickness.

For the parameter that continuously changes, so as to create a forbidden region, we can propose the flux density of gravitons. This will be maximal at the central mass concentration, and then decrease, approximately following a 1/r^2 law, as one moves away from the center. Along this line, my paper that won an honorable mention at the annual gravity essay contest, provides calculations showing that this flux has to interact with itself in order to match tests of general relativity, see The force of gravity in Schwarzschild and Gullstrand-Painlevé coordinates, 0907.0660.

My paper on Spin Path Integrals

Now the paper I’m discussing at FFP10, Spin Path Integrals and Generations, proposes that the spin-1/2 elementary fermions have internal structure. The idea is that the left (or right) handed electron oriented with spin in the (1,1,1) direction, has three components, R, G, and B, which we will assume are oriented in the +x, +y, and +z directions. This behavior appears only at extremely short times; we don’t have sufficient energies in our experiments to observe it. However, the three degrees of freedom create three orthogonal particles which we do observe as the three generations. The paper discusses various examples of this. If you do all this, it turns out that spin and position end up with similar Feynman path integral behavior. This is a way of unifying the internal and external degrees of freedom of the elementary fermions.

I chose the +x, +y, and +z directions because they are taken from the three “mutually unbiased bases” of the spin-1/2 algebra, that is, the algebra of the Pauli spin matrices, the Hilbert space of two dimensions. Mutually unbiased bases are the finite dimensional version of complementary variables such as position and momentum. This is why they are used to make spin path integrals and position path integrals have similar behavior; we are taking the ideas behind position and momentum and applying it to spin.

Mutually unbiased bases are defined by requiring that transition probabilities be equal. Thus, if we are to include gravitation in this sort of theory we must assume that the effect of gravitons is to change the transition probabilities.

The paper is about the transition amplitudes and long term propagators for spin moving between orientation in the +x, +y, and +z direction (or any other three perpendicular directions). This is a model of the left or right handed electron; to get a complete model of the electron we have to allow for transitions between them. How can we modify these transition probabilities in order to model the effect of gravity?

From my paper, it’s clear that the (gravity modified) transition probabilities between +x, +y, and +z will have to stay the same. Thus we will assume that gravity modifies the transition probabilities between the states contributing to the left handed electron, say +x, +y, and +z, and the states contributing to the right handed electron, -x, -y, and -z.

If these transition probabilities are modified (but the ones among the + or – states remain unchanged), the requirement that we use a complete set of mutually unbiased bases amounts to our modifying the six states so that, for example, the +x, +y, and +z are moved closer together, and the -x, -y, and -z are moved farther apart.

Effect of gravity is to warp the MUBs.

The paper doesn’t discuss this, but the natural interpretation of the +x, +y, and +z states is that the particle is moving at some speed in these various directions. Since the maximum particle speed is c, that speed must be c sqrt(3). This result is similar to that of Feynman’s checkerboard model of the Dirac equation in 3+1 dimensions. See around equation (42) of Peter Plavchan’s informal paper Feynman’s Checkerboard, the Dirac equation, and spin.

With this interpretation, the effect of warping the mutually unbiased bases is to effect the maximum speeds of the particle in the +(1,1,1) and -(1,1,1) directions. For the illustration above, the particle speed in the -(1,1,1) direction has been slightly increased while the speed in the +(1,1,1) direction has slightly decreased. For a black hole, this would correspond to different speeds for the radial inward -(1,1,1) direction as opposed to the radial outward +(1,1,1) direction.

These calculations are easy to do with the particle’s spin oriented parallel or antiparallel to the gravitational force. To obtain more arbitrary directions, one uses linear superposition in a manner similar to how spin-1/2 can be written in terms of spin-up and spin-down.

Gravity as changes to velocity
These sorts of ideas about gravity, that it should be interpreted as a modification of the natural velocities of particles with differences between inbound and outbound particles, is used in the important paper by Andrew J. S. Hamilton and Jason P. Lisle, The River Model of Black Holes, Am.J.Phys.76:519-532,2008. This paper models rotating and non rotating black holes as a river of “space” that is sucked into the black hole. The river defines a velocity at each point in space and from this one can derive the various properties of black holes.

The non rotating coordinates used in Hamilton and Lisle’s papers are Gullstrand-Painleve, the same used in my paper on flux gravity. These coordinates, along with their rotating (and charged) generalizations, are unique in that they allow general relativity to be rewritten in terms of David Hestenes’ geometric algebra. This amounts to getting rid of the tensors general relativity is usually defined with, and replacing them with functions of Dirac’s gamma matrices. This is a particularly useful version of general relativity because Dirac’s gamma matrices are used to model the elementary fermions. The Cambridge geometry (geometric algebra) group has many papers giving calculations of electrons in black hole coordinates using these methods.

Redshifts are sort of multiplicative; to compare them we look at ratios of (1+z). For example, if an object has an intrinsic redshift (due to gravitation) of (1+y), and it is at a distance or moving with a velocity that gives a redshift of (1+x), then its total redshift is (1+x)(1+y).

The claim of the redshift quantization folks is that redshifts are quantized according to a factor of (1+z) = (1 + 0.23) . The factor 0.23 is suspiciously close to 2/9, the factor (prominent in my spin path integral paper above) which Marni Sheppeard and I call “that damned number”, which I’ve assumed comes from a sum over infrared divergences. These arise when considering particles with very small energies or very long distances.

Quasar redshift quantization

Quasar redshifts are observed by emission and absorption lines. In order for these to be gravitational rather than due to distance, the light we see, and the atoms responsible for the emission and absorption, have to originate deep inside event horizons of black holes. As far as arranging for the light to escape, this is not too difficult: Since the forbidden regions are thin, light need only tunnel through it in order to carry the imprint of the inner layer.

Inside the most central forbidden region, matter is not constrained to fall to the singularity so this region will consist of normal matter. Provided temperatures are sufficiently low, normal matter can exist in this region. This matter will emit light, providing emission lines, and imprint light with absorption lines. The light then works it way out of the quasar.

For all this to happen, the temperature of the black hole has to become sufficiently low that normal matter can exist deep with the forbidden regions. This can only happen if the black hole is sufficiently cool. Arp’s observation is that new quasars have high redshift so the implication is that they are cool as they are ejected, and then heat up as they age.

A black hole is heated by matter falling into it, so a cold black hole would be a good candidate for eventually heating up and running through the quasar sequence of quantized redshifts. When the black hole attracts sufficient matter to form a new galaxy, it has been sufficiently heated that its quantum structure becomes hidden.

As far as evidence, it might be possible to find a quasar with two sets of emission / absorption lines. This would happen when a black hole has cooled just sufficiently to expose two different forbidden regions. This would be observed as a single quasar with two different redshifts.

Cosmology

The cosmology implied by this model is one where the effects of the big bang and dark energy are due to changes in the background level of graviton flux. The effect of gravitons on matter is to change the probability amplitudes in such a way that, at low levels, the probability of a transition is increased. The transitions influenced (raised) are those that cause the particle to move in the direction from which the graviton flux arrived.

So over cosmological time, the internal clocks on particles is sped up. In a flat universe, the frequency of light is not changed with time; there is no stretching of space to redden it. However, the clocks of the observer do change and an observer will see ancient light reddened according to how much time has gone by.

It should be noted that when using Schwarzschild coordinates, the clocks of particles are slowed by the presence of a gravitating body. But in the velocity model, this is due to the velocity of those particles (near the speed of light) rather than the gravitons per se. To see particle clocks slowed by gravity, one can instead use Gullstrand-Painleve (GP) coordinates.

In GP coordinates, the particle speeds depend on the direction. For particles on a radial axis, the modified particle speeds are modified in such a way that the difference in velocity between an outgoing particle and an incoming one is still 2c (as in free space). In such a case, a particle moving back and forth between two points will be slowed down, relative to free space. The analogous example given in freshman physics classes is that when you travel one direction at 60+v mph, and travel back at 60-v, you will arrive later than someone who travelled at speed 60 both directions.

At the foundation of quantum mechanics particles with mass m have a de Broglie frequency proportional to its mass. If we are to increase the frequency over cosmological time, this is the same effect as increasing the mass. So a cosmological theory compatible with the evidence given in this post would be one where the masses of the elementary particles increase over time.

As it turns out, just such a cosmology theory is propounded by none other than Halton Arp. It’s called the “variable mass theory” and is mentioned in the paper I referenced above, Evolution of Quasars into Galaxies and its Implications for the Birth and Evolution of Matter.

The variable mass theory was originated by Jayant Narlikar. With Hoyle, he developed what is also called “Hoyle-Narlikar” theory. This was sufficiently long ago that it is difficult to find review articles on it. A more recent version is the quasi-steady state cosmological model (QSSC) Cosmology and Cosmogony in a Cyclic Universe, J.Astrophys.Astron.28:67-99,2007 (0801.2965), by Narlikar, Geoffrey Burbidge and R.G. Vishwakarma.

In theories where the internal clocks of particles changes with the background graviton flux, it is also the case that the speed of light (as measured by the particles for propagation between two fixed points) will decrease with time. This is the subject of Louise Riofrio’s cosmology.

Weird Gravitational effects

Finally, I would be remiss without mentioning that theories of gravity that involve graviton flux imply that when planets are aligned, gravity should be a little stronger. This effect, however, can be canceled by absorption of gravitons. It’s not clear what the net effect should be, however, strange behavior of pendulums and gravity measuring devices during total eclipses of the sun have been seen, and not seen. See my blog post, The Moon’s Subtle Influence.

I’m kind of surprised by this, given that the paper proposes a new theory of gravity. I was expecting to have that portion excised.

And to help make a week more perfect, my paper for Foundations of Physics, titled Spin Path Integrals and Generations, got a good review along with a nasty one (and much good advice from both), and the editor has asked for me to revise the manuscript and resubmit. So I suppose this paper will also eventually be published. I’m a little over half finished with the rewrite. This paper is, if anything, even more radical than the gravity paper.

Finally, the Frontiers of Fundamental and Computational Physics conference organizers have chosen my abstract (based on the Foundations of Physics paper) for a 15 minute talk. The title is Position, Momentum, and the Standard Model Fermions. Marni Sheppeard (my coauthor for a third paper, “The discrete Fourier transform and the particle mixing matrices” which so far is having some difficulty getting published), is giving a related talk, Ternary logic in lepton mass quantum numbers immediately following mine.

So all in all, I am a very lucky amateur physicist

If you’re unaware of this classic, I’ll type in a page. For context, Cu Chulainn is returning to his own village after killing three of the village’s enemies. Perhaps due to post-traumatic stress disorder, or maybe blood-lust, he’s now a bit berserk and needs psychiatric attention.

“There’s a man approaching us in a chariot,” cried the look-out in Emain Macha. “He’s got the bloody heads of his enemies in his chariot, and a flock of wild birds overhead, and a wild stag hitched behind. He’ll spill the blood of every soldier in the fort unless you act quickly and send the naked women out to meet him.”

Cu Chulainn turned the left board of his chariot towards Emain to show his disrespect, and he said:
“I swear by the god of Ulster, that unless a man is sent to fight me, I’ll spill the blood of everybody in the fort.”

“Bring on the naked women!” said Conchobar.

The women of Emain came out to meet him, led by Mugain, the wife of Conchobar Mac Nessa, and they bared their breasts at him.

“These are the warriors you must take on today,” said Mugain.

He hid his face. The warriors of Emain grabbed him and threw him into a barrel of cold water. The barrel burst to bits about him. They threw him into another barrel and the water boiled up till it seemed it was boiling with fists. By the the time they’d put him into a third barrel, he’d cooled down enough just to warm the water through. Then he got out and Mugain the queen wrapped him in a blue cloak with a silver broach in it, and a hooded tunic. She brought him to sit on Conchobar’s knee, and that was where he sat from then on.

“Is it any wonder,” said Fiacha Mac Fir Febe, “that someone [Cu Chulainn] who did all this when he was seven should triumph against all odds and beat all comers in fair fight, now that he’s reached seventeen?”

Some notes
Cu Chulainn is a national hero to both sides of the border in Ireland. The famous statue of his death appears on the 1966 10 shilling coin:

Chariots appear prominently in The Tain but there’s at least some argument about whether these existed in Ireland. I have little doubt, see this page for a discussion and illustration. For the wealthy, imagine a chariot hooded with expensive colorful cloth. For the very wealthy, imagine the cloth covered further with bird feathers. The warrior is right handed and stands on the right side of a chariot, so the left side is the unarmed side. Hence the disrespect. Perhaps this has something to do with why the British drive on the left side of the road; they’re showing respect from the days of chariots.

Among Cu Chulainn’s many many feats was destroying the Lia Fáil (Stone of destiny) by splitting it with his sword. Since then, the stone has failed to sing out in joy when a rightful king of Ireland places his feet on it, uh, with exceptions for Conn of the Hundred Battles and Brian Boru. The stone as it appears today:

An illustration of Cu Chulainn, in his chariot, from wikipedia, in his pretty, non-fighting, mode. Note the absence of beard:

His secret weapon is the Gáe Bulga, a sort of javelin that enters with a single wound but then spreads into barbs that fill the body. He uses this to kill his long time friend, Fer Diad.

A note in the book mentions the 1973 rock album by Horslips titled The Tain. Multiple bad copies of most of its songs are on you-tube, if you want to listen to them. My favorite cut is Dearg Doom, or Cu Chulainn’s lament. I’m not sure who did this version, it doesn’t quite sound like the original to me, but it’s not bad; a sweet sad song. Someone listening to you sing this will suppose that it is a song of lost love, rather than one suitable for use after you’ve just killed your best friend.

Life was a game.
Now I miss your name;
Your golden hair.
No more in your eyes is the blue of skies – Only shame.
A lonely soul, betrayed by love,
You walked into the stream.
With tears of love upon my cheeks
I heard your final scream.

More recently, The Decemberists cut an EP titled The Tain. And they put out a somewhat creepy music video for the track using silhouette crepe paper stop motion animation. A mild example of the creepiness is the aftermath of the final battle:

In the video, you will note that Cu Chulainn, when in fighting mode, has one of his eyes bulged out onto his cheek. This follows the original text and is actually fairly mild compared to the written description.

A quick google search for the lyrics found that the song is one that Cat Stevens wrote for the romantic comedy movie Harold and Maude. It was somewhat shocking to see in the theater because that part of the audience that is “in the know” bursts into laughter at the first few scenes, that of a suicide by hanging. The song wasn’t released on any Cat Stevens album until a greatest hits album in 1984. I almost never buy greatest hits albums for artists I like, so I don’t have a copy of the song. The above photo is Ruth Gordon age 29, over 50 years before she played Maude in 1971. If you want to hear it, it’s possible that google will find a version.

And I’ve got a solution for fixing my paper. There will have to be another in the series. Mother nature is a rhymes with witch. Now I understand the mathematical relation between quantum numbers and path integrals much better. Just because an object is primitive it doesn’t always mean that it has unit trace.

Heisenberg’s uncertainty principle states that certain pairs of physical observables (i.e. things that physicists can measure) cannot both be known exactly. The usual example is position and momentum. If you measure position accurately, then, by the uncertainty principle, the momentum will go all to Hell. That means that if you measure the position again, you’re likely to get a totally different result. Spin (or angular momentum), on the other hand, acts completely differently. If you measure the spin of a particle twice, you’re guaranteed that the second measurement will be the same as the first. It takes some time to learn quantum mechanics and by the time you know enough of it to question why spin and position act so differently you’ve become accustomed to these differences and it doesn’t bother you very much.

If you want to figure out where an electron goes between two consecutive measurements the modern method is to use Feynman’s path integrals. The idea is to consider all possible paths the particle could take to get from point A to point B. The amplitude for the particle is obtained by computing amplitudes for each of those paths and adding them up. The mathematical details are difficult and are typically the subject of first year graduate classes in physics. Spin, on the other hand, couldn’t be simpler. Spin-1/2 amounts to the simplest possible case for a quantum system that exhibits something like angular momentum.

The simplest possible case for something like Heisenberg’s uncertainty principle occurs in spin-1/2. This is a 2-dimensional Hilbert space so calculations are a lot simpler than the infinite dimensional case needed for position and momentum. In these finite dimensional Hilbert spaces the quantum information theorists refer to two observables as “mutually unbiased” if they are related the way that position and momentum are. That is, knowing one of the observables exactly means that you can know nothing at all about the other observable. In terms of quantum mechanics that means that the transition probabilities are all equal, or unbiased.

A paper by George Svetlichny describes Feynman’s path integrals using the concept of MUBs:

Feynman’s Integral is About Mutually Unbiased Bases, George Svetlichny, 2007:
The Feynman [position path] integral can be seen as an attempt to relate, under certain circumstances, the quantum-information-theoretic separateness of mutually unbiased bases to causal proximity of the measuring processes.

My two latest papers apply the idea of path integrals being about mutually unbiased bases to spin-1/2. Under this assumption, spin is no longer an observable that stays constant after you measure it. Instead, it jumps around just like position. So the papers are about applying the idea behind Heisenberg’s uncertainty principle to the simplest quantum mechanical system possible, the qubit (or spin-1/2). The two papers are for Foundations of Physics. The first is:

Spin Path Integrals and Generations, Carl Brannen, 2009:
Two consecutive measurements of the position of a non relativistic free particle will give entirely unrelated results. Recent quantum information research by G. Svetlichny, J. Tolar, and G. Chadzitaskos have explained this property of position observables as a result of a path in the Feynman integral being mathematically defined as a product of incompatible states; that is, as a product of mutually unbiased bases (MUBs). On the other hand, two consecutive measurements of a particle’s spin give identical results. This raises the question “what happens when spin path integrals are computed over products of MUBs?” We show that the usual Pauli spin is obtained in the long time limit along with three generations of particles. We propose applications to the masses and mixing matrices of the elementary fermions.

The above paper is in the “under review” stage at Foundations of Physics. This seems to be the middle stage for a paper, the first stage is “editor assigned” or something like that. The paper buries deeply into the shaky foundations of physics. Those who are working on the periphery of physics imagine that the foundations are more stable than they are and will find the paper a bit shocking. For laughs, I’ve linked in the copy that I uploaded to arXiv. Some moronic Cornell grad student moderated it off. Maybe I’ll resubmit it when the paper is accepted for publishing, maybe not. The second paper is:

Path Integrals and the Weak Force, Carl Brannen, 2009:
In a previous paper, we showed that spin-1/2 can arise from a more primitive form of spin called “tripled Pauli spin”, along with three generations of elementary fermions. This gave a possible explanation for various coincidences in the fermion masses and mixing matrices. In this paper we continue the analysis. We show that the weak hypercharge (t_0), and weak isospin (t_3) quantum numbers can be derived from the long term propagators of three tripled Pauli spin particles. This completes a derivation of the standard model elementary fermions.

The second paper should be ready to submit to Foundations of Physics around the end of the month. The above is a first draft. Of course I’d appreciate comments and corrections. Right now I’m thinking that my next paper will be about what all this says about the geometry of spacetime. Or maybe I’ll write an introduction to Clifford algebra.

The proton spin puzzle: where are we today?
Steven D. Bass Invited Brief Review for Modern Physics Letters A, 17 pages
The proton spin puzzle has challenged our understanding of QCD for the last 20 years. New measurements of polarized glue, valence and sea quark polarization, including strange quark polarization, are available. What is new and exciting in the data, and what might this tell us about the structure of the proton ? The proton spin puzzle seems to be telling us about the interplay of valence quarks with the complex vacuum structure of QCD.
http://arxiv.org/abs/0905.4619
Mod.Phys.Lett.A24:1087-1101,2009

The conclusion ends with the following (my emphasis):

“The spin puzzle appears to be a property of the valence quarks. Given that SU(3) works well, within 20%, in beta decays and the corresponding axial-charges, then the difference between and suggests a finite subtraction in the g1 spin dispersion relation. If there is a finite subtraction constant, polarized high-energy processes are not measuring the full singlet axial-charge: and the partonic contribution can be different. Since the topological subtraction constant term affects just the first moment of g1 and not the higher moments it behaves like polarization at zero energy and zero momentum. The proton spin puzzle seems to be telling us about the interplay of valence quarks with the complex vacuum structure of QCD.”

My theory for quarks involves analyzing the interaction between the valence quarks and the sea in the quantum information theory limit, that is, when position and momentum are ignored. I represent color bound states as 3×3 matrices. (See equation (41) of Spin Path Integrals and Generations). The diagonal entries on the matrix are propagators for color not being changed. For a proton, these are the valence quarks. The off diagonal entries are color changing, these correspond to the activity of gluons.

I end up with three solutions to the bound state problem. In terms of absolute values (i.e. ignoring colors), the solutions are 1-circulant; each row of the 3×3 matrix is the same as the one above. There are six off diagonal entries and three diagonal entries. So naively, the contribution from the valence quarks is about half the contribution from the sea. So as far as back of envelope calculations, I would have the spin contribution from the valence quarks at around 0.33 of the total proton spin.

Equation (6) from the review article:

In the parton model, this is “interpreted as the fraction of the proton’s spin which is carried by the intrinsic spin of its quark and antiquark constituents.” According to the paper, a puzzle is “Why is the quark spin content … so small?” But in my theory, 1/3 is a natural value for the percentage of the proton that is quark as opposed to sea.