Theory Update 29

A few years ago we looked at the triality of Sparling's twistor theory. Now the quark hexagon, formed from a length six path on the cube, defines the same twistor triality. Note that there are $9$ edges in the full diagram; one for each element of a CKM matrix.


This links each generation to one copy of $(x,t)$, namely spacetime coordinates in a three time picture.

Theory Update 28

The PeSla discusses how the six quarks fit onto a categorical cube, with charge represented by path length. The zero charge source stands for neutrinos and the charge $3$ target for the charged leptons. Edges are directed by the addition of one twisted ribbon piece to a three strand particle diagram.

Happy New Year.

Theory Update 27

For the CKM matrix
three phases of the complex matrix are given by
so that the new value $\sin 2 \beta = -0.649$ follows from the phase $- 0.7063$ radians. All phases are fixed by the three real parameters of the triple factors.

Theory Update 26

The mixing paper has been updated, yet again, to include the Standard Model CKM anomaly, using the simple $R$ factor ansatz from quantum information and triality. I ate too much pavlova and chocolate on the weekend, inducing a state of lethargy that has delayed further study of the D0 results.

Cool Conference

I may not be able to attend, but I can dream! Check out this short cosmology conference in Corsica in May 2011. Topics covered include cosmological parameters, neutrino cosmology, dark matter and large scale structure. Organised by Professor Triay and others.

Random Thoughts

One has to wonder why a leading journal should allow a paper to pass through its QC phase and onto a lengthy review process if the editor is going to then decide, on the basis of a personal reading of said paper, and demonstrating remarkably poor comprehension skills, to reject said paper as gibberish. Well, at least this provides more entertainment than the common practice of rejecting papers without forwarding them to reviewers. One wonders why such editors bother to write such lengthy email rejections, carefully outlining their total misunderstanding of every clear sentence in the paper. Surely they could not have obtained such a high rank in The Patriarchy without perfecting the skill of masking their ignorance, at least to themselves. Anyway, one must carry on.

Theory Update 25

Resonaances points us to an interesting new analysis of the CKM anomalies. The paper argues that the parameter $\sin 2 \beta$ is given by a non standard value, below the one obtained with an ordinary parameterisation. Previously here we have not bothered looking at this value, which is distinct from the $\beta_s$ case, but checking now the complex matrix we find a value of $\sin 2 \beta$ equal to $0.649$. This agrees with the non standard preferred value, measured at $0.668 \pm 0.023$. Recall that the arithmetic mixing matrix uses only three real parameters to determine the physical quantities of the CKM matrix.

Beyond Duality

After talking to kneemo recently, I noticed that the current trend in categorical physics had not swayed far from its roots a decade or two ago. A topological field theory is still a functor from a category of spaces to a category of algebraic objects, although these may now be higher dimensional categories with a rich structure. In noncommutative geometry, one uses an algebraic description of a space to generalise spaces beyond commutative ones. But even here, spaces are still spaces and algebras are algebras.

Descartes must be rolling in his grave, to say nothing of the modern algebraic geometers. How artificial, this distinction between algebra and space. Nice functors are endofunctors, so we should really start with a category that contains all algebras and spaces. Fortunately, we might be able to make them all look like matrices! Computer scientists like Vaughn Pratt have long taken this idea seriously, and they study just the kind of dualities that are used to define noncommutative geometry.

Of course, triality should also make its appearance, if physics has its fair say. So much to do.

Quote of the Month

From a 2008 astronomy paper, published in Nature:

If, as we have argued, galaxies come from at most a six parameter set, then for gaseous galaxies to appear as a one parameter set, as observed here, the theory of galaxy formation and evolution must supply five independent constraint equations to constrain the observations. This is such a stringent set of requirements that it is hard to imagine any theory, apart from the correct one, fulfilling them all ... a process of hierarchical merging, in which the present properties of any galaxy are determined by the necessarily haphazard details of its last major mergers, hardly seems consistent with the very high degree of organisation revealed in this analysis.

Dark Matter Update II

In summary, Louise Riofrio's density fractions for baryonic, dark matter and the remainder are given by

$\Omega_b = 1 - \frac{3}{\pi}$, $\Omega_d = \frac{3}{4 \pi}$, $\Omega_r = 3 \Omega_d = \frac{9}{4 \pi}$

and the total density is $\Omega = 1$. The number $\Omega_d = 3/(4 \pi)$ characterises all three densities, showing that Riofrio's law of pair creation and annihilation governs the mass energy content of our universe.

Dark Matter Update

A recent run of outstanding posts by leading cosmologist Louise Riofrio has resulted in renewed anonymous attacks on our technical arguments, along the lines of

what a bunch of crap

and

your behavior is a striking example of why you are considered to be crackpots.

No evidence that these critics actually know any physics has been forthcoming. Meanwhile Graham D discusses Louise's matter abundance fractions, which have now been confirmed by WMAP. We are familiar with the baryonic fraction $\Omega_b = 1 - 3/ \pi$. Graham D points out that the dark matter fraction is approximated by the simple volume ratio

$\frac{4/3 \pi R^3}{2 \pi^2 R^3} = \frac{2}{3 \pi} = 0.21221$

of an ordinary sphere to the volume of real spacetime. Louise's exact figure, however, is $0.23872$ which equals $3/(4 \pi)$. We obtain this fraction with the inverse volume rule

$\Omega_d = \frac{R^3}{4/3 \pi R^3} = \frac{3}{4 \pi}$

simply canceling the $R^3$. For each spherical piece of ordinary flat cosmos, the dark matter is taking up a cubical fraction. Even a child could predict future WMAP results.

SUSY Hiding

Predictably, Woit is ahead in announcing preliminary results from the CMS experiment. Below is the slide (from Schieferdecker) showing a new exclusion range for certain supersymmetric partners, although many stringers will argue that this merely reduces the parameter space in a helpful manner. Here is Mottle's optimistic spin.


Personally, I am looking forward to the good European wine that Tommaso promised me if he won his bet.

Theory Update 24

Recall that there were many ways to represent the tribimaximal neutrino mixing matrix. For instance, taking the Fourier transform of the complex matrix and then squaring, we obtain

where $x = 1.543$ and $y = - 2.524$. The analogue for the CKM mixing matrix is

Today's Links

$\bullet$ Louise Riofrio shows us how her prediction for the baryonic matter fraction was confirmed by the WMAP 7 year data.

$\bullet$ Dark Matter Awareness Week is now wrapped up, and there are some photos on Facebook.

$\bullet$ The LHC has begun to rule out popular ideas from string theory, and Tommaso reports on a new CDF result.

$\bullet$ Jeffrey Morton tells us about an upcoming conference on higher dimensional category theory and quantum gravity! As the blurb explains, all the pioneers in this field are men, although they did invite a token woman.

The Future

Many writers over the last week have expressed confusion at the support shown by feminists for the jailed leader of Wikileaks, accused of rape. I think Naomi Wolf summed it up pretty well when she thanked Interpol for suddenly initiating a new program to chase creepy guys around the world, several million of which every free woman has met.

But this is not about one man. It is about a barbaric world that would elevate heroes and abuse women, grant power to the greedy and make slaves, once again, of the poor. Our time will be remembered for its acceptance of all manner of deceit, as the once rich cling to the empty promises they made their children, letting the Earth die for hollow dogmas.

To those who would shoot down free speakers, for wanting to bring down the world they know, I ask you this: does your world even have a future? Is changing nothing even acceptable any more? Is the patriarchal 20th century, under any of its political systems, a fine model for all time to come? Will your children be happy when their city is filled with starving invalids and there are no more fish in the ocean? In a society with a ballooning complexity, the old system of strictly hierarchical reward is unsustainable. Unsustainable systems collapse.

Theory Update 23

Many thanks to kneemo for pointing me to this 2008 paper by Stanford's Zhang et al. They suggest that magnetic monopoles hide in topological insulators, like a mirror image of an electric charge sitting near the outside of the surface.

For reasons that we shall discuss later, we consider an adjustment of the Koide rule for the charged lepton masses, as follows. Instead of the usual eigenvalues, with parameters $r = \sqrt{2}$ and $\theta = 2/9$, we will consider eigenvalues

$\lambda_{i} = 1 + \sqrt{2} \cos (2/9 + \pi + \omega_i)$

for $\omega_i$ the usual cubed roots of unity. At the charged lepton mass scale, this gives us a candidate triplet of masses: $45.2$, $632.6$ and $1205$ MeV. This kind of monopole has not yet been well studied in the laboratory, but there is great interest in these materials.

Mercury and Gold

From Physics World today we learn that

The fission of mercury-180 was expected to be a symmetric reaction that would result in two equal fragments, but instead produced two nuclei with quite different masses, an asymmetric reaction that poses a significant challenge to theorists.

The ISOLDE experiment at CERN fired protons at a uranium target, expecting to observe two zirconium-90 nuclei. Instead, the favoured daughter nuclei were ruthenium-100 and krypton-80.

AES Encryption

The Advanced Encryption Standard uses a substitution permutation network. This performs two basic operations on a string: substitution of one block into another, or a permutation of bits. The key is used to define a sequence of such operations. Note that the length of the full string is preserved at each key step. This is one of the simplest ways to satisfy Shannon's 1949 measure of cryptographic strength, and is widely used today.

In category theory the definition of operad is based on substitution, which is usually depicted by tree graftings. This has generalisations that allow any number of inputs and outputs, like in the diagrams of modern M Theory. In this language, a combined AES operation of one key step and one substitution-permutation form an object for the 'operad'. Unlike the usual categorical definition, however, this gadget is terminated by the length of the key string.

Global Market

The international market moves. Arrested one day. A wide range of Free Assange online Christmas gifts the next.

Now That's A Challenge

From CNN:

Whatever you call the file Julian Assange has threatened to release if he's imprisoned or dies or WikiLeaks is destroyed, it's impossible to stop ... Assange specifically announced, on the Web, that there is a 256 bit key encryption code that only a few trusted associates know that will unleash the contents of the 1.4 gigabyte size file.

The widely available file, called insurance.aes256, has been around for months now and is analysed by geeks everywhere.

Quote of the Month

Elimination of wrong hypotheses - and indeed, elimination of people who only produce wrong hypotheses or results - is a key prerequisite for any science.

Lubos Motl

More Atiyah

Since somebody in a similar time zone likes to delete my comments at The Cafe, and since Alejandro was so keen on seeing Atiyah's newest slides, let us thank David Corfield for generously providing a link! One of Atiyah's slides is shown below. There are many photos and quotes (all of men), and not so many equations, but Atiyah does certainly seem very interested in quantum gravity.

Dark Matter Updates

New Scientist has been reporting on new ideas about Dark Matter. Apparently, the problems of Dark Matter and the antimatter abundance may be linked. A number of recent conferences discuss the positive results from direct detection experiments, which are seen as evidence for low mass dark matter WIMPs. Slides from a November Princeton workshop are now available online. In the slide below, Kathryn Zurek summarises her analysis with the simplest current explanation: a dark matter mass scale that is five times that of ordinary matter, assuming equal abundances of dark and ordinary particles.

The Glossary

Words in modern English, with which internet users should be familiar:

douche bag: You know the type. Nerdy guy with the sexist T-shirt who just loves telling strangers how much he knows about physics, which he is clearly an expert at since he was third in his science class at high school.
mansplain: The remarkable ability of a man to step into a group of women conversing on a subject with which they are quite familiar, and then to explain the subject to them as if they were five years old, without ever listening to anything they say.
bimbo: A derogatory term for any woman who acts and behaves precisely as she is expected and exhorted to do by most western societies.
feminist: Anyone, male or female, who believes that women have the right to equal opportunities and human rights.

Elliptical Dwarf

Universe Today reports on the latest exciting finding on elliptical galaxies. There are far more red dwarfs in these galaxies than in the spiral Milky Way.

No, this does not fix the dark matter problem. But it does even out the anomalous Dark to Light mass ratio, which was very high for dim galaxies, potentially bringing the galactic dark matter profiles closer to a totally universal one, as is suggested by empirical modified gravitational laws.

Don't forget Dark Matter Awareness Week next week!

Time For Change

Five years ago, when Time Magazine wrote that the geek will inherit the earth, they were just talking about boys and toys. With only a dim wiff of understanding did they muse that the geek may not be too fond of the status quo. When a slave with conscience realises that complacency and the blind eye are sometimes the greatest crimes, they change their ways. Life without adaption is extinction.

And the truth is not for sale. Go WikiLeaks!