The Top of the Tevatron

Today is the last day of Tevatron. Tevatron is a particle accelerator, and it started the physics measure in 1985, on the night of 13rd october. The story of Tevatron is reach of great events, and Tommaso Dorigo write a great summary of Tevatron's physics, in particular the first great physics result: the discover of the top quark!
In Standard Model we have 6 quarks, and they are the elementary particles that constitue barionic matter. They was introduced in physics with a parton model indipendetly developed by Murray Gell-Mann(1) and George Zweig(2, 3) in 1964. The original theory is constituted by three partons (up, down, strange), but in the subsequent years were provided also the others three quark. In particular in 1972 Makoto Kobayashi and Toshihide Maskawa(6) proposed the existence of a new quark, the well known top quark: they introduce in weak interaction theory, discovered by Weinberg in 1967(4) and 1971(5), the CP-violation. In particular they write the hadronic parts of the lagrangian in four terms: kinetics, massive, strong and $L'$. Following the Higgs mechanism(9), they supposed that the CP-violation it could be in massive term, because the spontaneous breaking of gauge symmetry.
Their calculations are group theory calculations: we can imagine the group that Kobayashi and Maskawa used like a space generated by two 4-dimensional spaces (the space of $SU (4)$ group). They pictured three possible partitions for every vector space:
  1. two 2-dimensional subspaces;
  2. one 2-dimensional subspace, and two mono-dimensional subspaces;
  3. four mono-dimensional subspaces.
They studied only the combination with a physical sense, and a consequence of the breaking of the symmetry is the existens of a new parton, quark top that was discovered in 1995 at Tevatron:

(from D0 paper)

(from CDF paper)
I conclude with the following video by Maria Scileppi with Rob Snihur, a Tevatron's researcher:

The universe and the flowers

Peeking the infinite increases the space, the breath, the brain of whoever is watching it.
Erri De Luca, italian writer
The universe is a perilous but also a beautiful place. But the beauty of the universe it's not only in galactic shots, but also in mathematics. For example the maps of the E8 group seems flowers, and if we follow Garrett Lisi and his preprint An exceptionally simple theory of everything(1), these maps are also a sort of universe's flowers!
The E8 maps in this post are extracted from Lisi's preprint and they represent the structure of the group (the first image is F4. E8 is a Lie group, most important in physics because all symmetries group of the physical systems are Lie groups. The Lie group is an analytical group: all functions that we can define in the group are continuous. A physical example is the Galilei's group, and studying it we can argue information about free particles, described by Schroedinger equation.

Waiting superluminal neutrinos: from Maxwell to Einstein

(CNGS device)
\[\vec \nabla \cdot \vec E = \frac{\rho}{\varepsilon_0}\] \[\vec \nabla \cdot \vec B = 0\] \[\vec \nabla \times \vec E = - \frac{\partial \vec B}{\partial t}\] \[\vec \nabla \times \vec B = \mu_0 \vec J + \mu_0 \varepsilon_0 \frac{\partial \vec E}{\partial t}\] In 1861 James Maxwell published the first (of four) part of the paper On Physical Lines of Force, in which he stated his famous equations on electromagnetic field. One of the most important thing about these equations is that they are not invariant under Galilei's transformations! But, if we search the symmetry transformation of the equations, we find Lorentz transformations: \[\begin{cases} t' &= \gamma \left( t - \frac{v x}{c^2} \right) \\ x' &= \gamma \left( x - v t \right)\\ y' &= y \\ z' &= z \end{cases}\] where $\gamma = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$.
From these transformations, discovered in 1887(1, 2), we can extract the physics of special relativity, thanks to Albert Einstein. So, if we want tosubstitute c with the alleged OPERA's neutrinos speed, we must conclude that the new boson particle of electromagnetic field is the neutrino! In this sense I say that special relativity is right: our universe and our observations are based on electromagnetic field, so if OPERA results will be verified, we probably think to:
  1. change the weak interaction(3);
  2. study an eventually quantum interaction between neutrinos and space time(4);
  3. imagine a new field exclusively for neutrinos(5);
  4. other way that in this moment I cannot imagine(6)!
This is the science, people: we find data, we search interpretation, we quest for confirmation, we calculate mathematical explenation, and only at this point we write text books. But, and this is the most important idea, we don't reject the old theories: Newton and Galilei's theories are today right, but we must substitute them in quantum world and to a cosmo's schale. And the destiny of model standard and Einstein's relativity is the same, and our task is find their limits.

Waiting the superluminal neutrinos (if they exist!)

It seems that Opera experiment observed some superluminal neutrinos.
First of all we must see the scientific data: at 4pm on 23rd september (Geneva time) we can connect to the Cern seminar (also on webcast), but probably a preprint will be puiblished on arXiv in the next hours. In every case I think that it's very important say some worlds about the news.
There's a lot of comments about the question, and some people say that special relativity and also standard model will be falsified by the results if they will be confirmed. Instead I think that we simply speak about an extension of standard model, and there're no really consequence about special relativity.
First of all we must remember that special relativity and standard model are first of all electromagnetic theories, where the boson is the photon and the speed of light is important for the photon and for the em interaction. And neutrinos don't interact with electromagnetic field, and the results is simply the confirmation of this situation!
At the other hand the results, if confirmed, say us simply that neutrinos are the most elusive particles in the universe: in this case they escape from the control of special relativity, which would not be the correct theory to describe them at highest energy. In the same way, we must modify standard model in order to include these new superneutrinos. In this last case the changes will be at the high orders of the theory: we must remember that, if the effect it's really important at the energy of standard model, the theory would never have been tested with a high degree of accuracy.
Another hypothesis is that the introduction of superluminal neutrinos in model standard could resolve some mathematical problems of the model, or explain some physical question (like the matter-antimatter asymmetry, for example). But we can continue playing with the assumptions: the superneutrinos could be the trace of a new fifth interaction between neutrinos and dark matter. This hypothesis is included in some dark matter theories: so model standard and special relativity could be remain unmodified.
In every case, if the results will be confirmed, the first step for model standard theorists is propose changes at the highest orders of the theory. And for the future search an extension of the theory.

Thanks to Marco Delmastro, Tommaso Dorigo, Peppe Liberti, Annarita Ruberto for sharing the news.

Riemann hypothesis

The Rieman hypethesis was stated following the 1859 Riemann's paper On the Number of Primes Less Than a Given Magnitude. This is the begin of the paper(1):
For this investigation my point of departure is provided by the observation of Euler that the product \[\prod \frac{1}{1-\frac{1}{p^s}} = \sum \frac{1}{n^s}\] if one substitutes for $p$ all prime numbers, and for $n$ all whole numbers. The function of the complex variable $s$ which is represented by these two expressions, wherever they converge, I denote by $\zeta (s)$. Both expressions converge only when the real part of $s$ is greater than 1; at the same time an expression for the function can easily be found which always remains valid.
The Riemann zeta function is connected to the prime numbers distribution, in particular Riemann argued that all of its non trivial zeros(2) have the form $z = \frac{1}{2} + bi$, where $z$ is complex, $b$real,$i = \sqrt{-1}$. There's also a general form of the zeros: $z = \sigma + bi$, where $\sigma$ belong to the critical strip (see below and the image at the right).
In the story of the search of the zeta-zeros, Hugh Montgomery has an important part(4): in 1972 he investigated the distance between two zeta-zeros, finding a function of this difference. After this paper, in 1979, with Norman Levinson(5) he established some others zeta properties, investigating in particular the zeros of zeta derivatives. Obviosly he first of all proofed an equivalence relation between the zeros of Riemann zeta function and the zeros of the derivatives: in particular also these zeros belong to the critical strip, $0 < \sigma < \frac{1}{2}$.
The analitical research around zeta-zeros is not the only way: the first was Lehmer (1956 and 1957) who performed the first computational attempt in order to proof the hypothesis. An example of this kind of researches is given by Richard Brent(6): in his work he try to evaluate Riemann zeta using the Gram points, that are the points in which the zeta change its sign(3). Brent focused his research on the first 70000000 Gram blocks, veryfing the hypothesis.
But there's another approach to the problem: physics. In the end of 90s Alain Connes(7) proofed the link of Rieman hypotesis with quantum chaos.
Quantum chaos studies chaotic classical dynamical systems using quantum laws. In particular Connes found a particular chaotic system in which quantum numbers are prime numbers and the energy levels of the system correspond to the zeta-zeros on the critical line $\sigma = \frac{1}{2}$. In physics it could be the better (but not only) suspect to resolve the hypothesis
Others connection with physics are in the review Physics of the Riemann Hypothesis by Daniel Schumayer and David A. W. Hutchinson, but we can speak about the stories in the paper in another moment.

One planet, two stars

When we are going to approach to the binary system Kepler-16 (image source) we'll see two different stars: the largest of the couple, the star A, is a K dwarf with a mass of about 0.69 solar mass and about 0.65 Sun's radius, and a little red dwarf, the stra B, with a mass of about 0.2 solar mass and about 0.23 Sun's radius. But when we'll arrive at about 0.5 au from the gravitational centre of the binary system we'll see a great surprise: a little planet with a mass of 0.333 ± 0.016 and a radius of 0.7538 ± 0.0025 those of Jupiter(1).
In this momenti is very difficult to suppose the properties(2) (like composition and surface temperature) of Kepler-16b, but the most important thing is that Kepler can discover, using the transit technique, also a planet around a binary system! I think that this is the principle reason becuase the paper was accepted by Science. And it's clear that all nerd and sci-fi fan think about Skywalker family's planet, Tatooine:

Earlth and Moonch

This beautiful shot (via Universe Today) is the Cygnus Constellation. The photographer is Marco T., italian, and you can see others great photos on his flickr account.
But this beautiful shot is the better introduction to Earlth and Moonch, a animated short by Dei Gaztelumendi I see the short in Italy, during the Milano Film Festival, and in the worlds of Gaztelumendi is a reflession about Earth, ecology and our future.

Nuclear accidents: abstract about Fukushima and video from France

At the end
And now the video news about France accident: