Doing physics is fun. Writing papers is boring. Publishing them is quite painful. This year I’ve been concentrating on getting stuff published; I haven’t updated this blog. But with March madness receding into the past I’ve got some time and I’ll update what’s going on.
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).