# Category Archives: particle physics

## Quantization of event horizon radius and Quasar Redshifts

I’m getting ready for the FFP10 meeting later this month. In reading the abstracts of those who will be giving talks or posters, I came upon “Analyses of the 2dF deep field” by Chris Fulton, Halton Arp and John G. Hartnett. The abstract is about the relationship between low redshift and high redshift astronomical objects. The claim is that some quasars have redshifts that do not give their true distance; instead, they are much closer. Looking on arXiv finds: The 2dF Redshift Survey II: UGC 8584 – Redshift Periodicity and Rings by Arp and Fulton.

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.

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Filed under gravity, particle physics, physics

## My Gravity paper accepted for publication

I’ve just got notice that my gravity paper, titled The force of gravity in Schwarzschild and Gullstrand-Painleve coordinates has been accepted for publication in the International Journal of Modern Physics D, with only a very minor modification.

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

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## Uncertain Spin

I’m releasing two papers that relate Heisenberg’s uncertainty principle, spin-1/2, the generations of elementary fermions, their masses and mixing matrices, and their weak quantum numbers. I haven’t blogged anything about these because I’ve been so busy writing, but I should give a quick introduction to them.

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.
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## The Proton Spin Puzzle

For 20 years QCD has been unable to guess the structure of the most common stable hadron, the proton. This is exemplified in the “Proton Spin Puzzle.” A recent review article:

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 $g_a^{(0)}|_{pDIS}$ and $g_a^{(8)}$ 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: $g_a^{(0)}$ and the partonic contribution $g_a^{(0)}|_{pDIS}= g_a^{(0)}-C_\infty$ 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:
$g_a^{(0)}|_{pDIS,Q^2\to\infty} = 0.33 \pm 0.03(stat.) \pm 0.05(syst.)$
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.

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Filed under anomaly, particle physics, physics

## Matrix Decomposition by Discrete Fourier Transform

Given a 3-vector of complex numbers, (A,B,C), define its discrete Fourier transform as
$(a,b,c) = (A+B+C,A+wB+w^*C,A+w^*B+wC)$
where $w = \exp(2i\pi/3)$. 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 $\sqrt{1/3}$ but it will do.

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

Democratic matrix with all entries D

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

Define the Fourier transform of a 3×3 matrix U as $u = F^{-1}UF/3$ where $F$ is the matrix:

Discrete Fourier transform matrix

where $w = \exp(2i\pi/3)$. With this definition, the discrete Fourier transform of the democratic matrix D, is:

Fourier transform of democratic matrix

This is a nice simplification.

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

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

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

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

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

Neutrinos are constantly being emitted by the sun in prodigious numbers. About 10^14 go through your body each second (maybe more if you supersize yourself like my old buddy Mario did). More technically, anti-neutrinos are created when neutrons decay into a proton + electron + anti-neutrino, and neutrinos are created when protons absorb electrons in the reverse process: proton+electron -> neutron + neutrino. These sorts of things happen to various atoms of the sun, depending on what sort of decay they are subject to, (beta decay or reverse beta decay, respectively), as well as proton-proton collisions that produce a positron a deuteron (PN), and a neutrino. However, not enough neutrinos seem to arrive on earth. This was known quite some time ago, see The Solar Neutrino Problem for the technical details as of 1998.

The explanation for the deficit in neutrinos is now called “neutrino oscillation.” In the theory of neutrino oscillation, these solar neutrinos are “electron neutrinos”, and in their passage to the earth, they change form and become “muon neutrinos” or “tau neutrinos.” For those students who take their physics on faith, this is not a problem. But every now and then someone learns their theory just a little too well and begins to have doubts about how it can be that a particle can transform itself into another particle in vacuum. Yes, neutrino oscillation is a little strange, but it can be explained much more clearly, and kept in context with the rest of particle physics, by analyzing the problem as neutrino interference. This way neutrino oscillation can be described in a way that doesn’t confuse students. And such is the topic of this post.
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