Oscar Chacaltana, Yuji Tachikawa and I are deep in the weeds of nilpotent orbits. One of the things we had to study were the nilpotent orbits of ${𝔤}_2$, and how they sit in $\mathrm{𝔰𝔬}(8)$. Understanding the answer involves an explicit description of $\mathrm{Spin}(8)$ triality, which I thought was kinda cute. Few people will care about the nilpotent orbits, but the bit about triality and $G_2$ might be of some independent interest. So here it is.

Under this decomposition, the action of triality is easy to describe: pick one of the $\mathrm{𝔰𝔩}(2)$ subalgebras to hold fixed, and consider all permutations of the other three (supplemented by the obvious action on the $(2,2,2,2)$).

That’s triality. Looked at this way, it seems absurdly simple. The above description gives a perfectly concrete action of triality, as permutations of the generators. And we can push a little harder, and really understand ${𝔤}_2$, this way.

The subalgebra, invariant under the $S_3$ permutations, is ${𝔤}_2\subset \mathrm{𝔰𝔬}(8)$, under which

where $V$ is the 2-dimensional irreducible representation of $S_3$. In terms of our previous decomposition,

where the first $\mathrm{SU}(2)$ is the one you kept fixed, and ${\mathrm{SU}(2)}_D$ is the diagonal $\mathrm{SU}(2)$ of the three which are permuted by triality. Under this embedding,

An explicit basis of antisymmetric $8\times 8$ matrices which give this ${𝔤}_2$ subalgebra is as follows. First, we embed ${\mathrm{𝔰𝔩}(2)}^4$, by taking the $8\times 8$ matrix to be block-diagonal, with $4\times 4$ blocks containing ${\mathrm{𝔰𝔩}(2)}^2$, as

where we’ve chosen the normalization conventions

We pick one of these (the ${\mathrm{𝔰𝔩}(2)}_L$ in the upper left-hand block) to hold fixed, and embed our second $\mathrm{𝔰𝔩}(2)$ diagonally in the other three:

The highest weight of the $(2,4)$ is

The remaining ones, e.g., $S_{-1,3}=[Y_1,S_{1,3}]$, are obtained by acting with the lowering operators, $Y_{1,2}$. With this choice of Cartan, the simple roots of ${𝔤}_2$ correspond to $X_2$ (short root) and $S_{1,-3}$ (long root).

This 8-dimensional representation of $G_2$, as it’s reducible, is not the most convenient one for studying the representation theory of $G_2$. But it’s tailor-made for our purpose, which is understanding the embedding in $\mathrm{Spin}(8)$. With an explicit embedding in hand, we can manufacture a distinguished triple, $(H,X,Y)$ for each nilpotent orbit of ${𝔤}_2$, and see how it sits in $\mathrm{𝔰𝔬}(8)$. But that, probably, holds little interest for the general reader, so I’ll end here.

Sitting in the office at the end of a long week, and looking forward to going to an interesting-sounding concert at St David’s Hall later on. I may get the chance to review it over the weekend, but in the meantime I thought I’d put up this version of one of the pieces I’m going to hear later. I think it’s great but I’ve never heard it live…

The European Commission is reportedly close to admitting that imports of biodiesel made from crops such as palm oil, soybean and rapeseed cause more greenhouse gas pollution than fossil diesel.

According to the website EurActiv, which tracks European political news, numbers in a leaked Commission impact assessment suggest these biofuels’ effect on climate could be as bad as oil from Canadian tar sands.

Once officially recognized, this inconvenient truth would set politicians at loggerheads with a biodiesel industry that their own renewable fuel directives helped to create.

Scientists and non-governmental organizations have repeatedly pointed out that Europe underestimates biofuel carbon emissions. Calculations don’t take account of the fact that when biodiesel crops are planted on agricultural land, forests and wetlands elsewhere are cleared in order to produce the food crops that the biodiesel edged out.

The effect of this ‘indirect land use change’ (ILUC) is tricky to calculate, but scientists now think it wipes out any carbon emissions savings made by avoiding fossil fuels, as reports from the commission’s Joint Research Center in Ispra, Italy, and at the International Food Policy Research Institute (IFPRI) in Washington DC, have pointed out.

The chart below, from an October 2011 article in Nature Climate Change, illustrates this: ‘direct’ emissions come from the EU’s 2009 Renewable Energy Directive, and the added ‘ILUC’ emissions from an IFPRI draft report. (The orange and grey dashed lines show the threshold for a 50% and 35% emissions saving compared with fossil fuels – at the moment, biofuels have to certifiably deliver a 35% saving under EU law, but this is set to increase by 2018).

“]

[Source: Nature Climate Change 1, 389–390 (2011)

That’s not to mention the other ethical and environmental harms of biofuels, such as displacement of indigenous peoples, and destruction of the rainforest, as pointed out by the London-based Nuffield Council on Bioethics last April.

Now what? “Politicians are trying to find an impossible compromise of maintaining the biodiesel industry that they created, while taking account of indirect emissions,” says Robbie Blake, a spokesperson for Friends of the Earth. According to Nature Climate Change, one middle-ground solution might be not to penalise biodiesel, but to reward producers for practices that mitigate ILUC (by using biofuel by-products as animal feed, or by encouraging better-integrated farming systems).

ENDSEurope reported on 26 January that the issue, which has created a rift between the EU’s energy and climate departments, has gone up to the office of Commission president José Manuel Barroso.

I was going to write something about the politics of scientific publishing, but instead, I want to focus on what's really important in modern publishing:

That's right, I got a couple of early copies of How to Teach Relativity to Your Dog in the mail this morning. It's a real book, with pages and everything... You can see it above, next to How to Teach Physics to Your Dog, and various clutter on my desk, for scale.

There's not much else to say, other than "Woo-hoo!" They're printing lots more, of course, and it will be available wherever books are sold starting Feb. 28th.

If you live nearly anywhere on Earth — those of you north of 73° you’re out of luck, but I’m guessing there aren’t many of you! — and look to the southeast shortly after sunset, you’ll see the figure of Orion. Follow the three belt stars to the east, and you’ll see a bright star: Sirius, the brightest star in the night sky. If it’s near the horizon, you may see it twinkling madly: flickering, dancing, perhaps even changing color.

This gave astronomer David Lynch an idea: take a time exposure of Sirius with a camera and telephoto, and purposely wiggle the mount. He tried it on January 4, 2012, and the result he got is actually quite lovely:

Isn’t that cool? As the vibrating camera caused the star to trail around, the changing colors got recorded along the track. The changing brightness of Sirius can be seen as well, as parts of the loop-de-loop fade and intensify.

The reason stars twinkle is because of our atmosphere: little blobs of air are constantly in motion. These air parcels act like lenses, and as light passes through them, the path of the ray gets bent a little bit. That’s what causes the dancing motion, the actual twinkling. Different colors get bent by different amounts (which is why prisms break up white light into separate colors).

While it’s beautiful to our eyes, twinkling is a major pain to astronomers. It blurs our images! That’s why we launch telescopes into space, or design fancy optics for ground-based telescopes to remove it. Twinkling is free, but correcting it sure ain’t.

Lynch has several websites loaded with interesting pictures he’s taken of nature, including Thule Scientific, Color and Light in Nature, and San Andreas Fault.

Image credit: David Lynch (used by permssion). Tip o’ the Snell’s Law to Earth Science Picture of the Day.

Today NASA’s Kepler mission announced the discovery of 26 new planets (above, green). The new worlds, comparable to the giant planets of our solar system (blue), nearly double the number of planets previously discovered by the probe (red), but it’s probably only a small taste of what’s to come.

Kepler looks at 150,000 distant stars and searches for tiny changes in brightness as a planet passes by. So far, the probe has turned up 2,300 planet candidates. Confirming a planet is far more difficult, but Kepler has managed to verify the new worlds announced today by measuring slight changes in their orbits due to the gravitational influence of other, nearby planets. NASA has also released a very cool video showing the different systems in action (below).

Kepler’s ultimate goal is to discover another earth orbiting a distant star. That goal is still some years off, but it’s already contributing quite a lot towards our understanding of exoplanetary systems. An abundance of mid-sized planets has forced astronomers to rethink their theories of planetary formation, and the mission’s precise measurements of star brightness has shown that some stars are far more turbulent than are sun.

Credit: NASA Ames/D. Fabrycky, UC Santa Cruz/J. Steffen, Fermilab Center for Particle Astrophysics

Fun post for everyone today. In response to last week’s post on describing KEK Laboratory’s discovery of additional exotic hadrons, I got an absolutely terrific question from a QD reader:

Surprisingly, the answer to “How does an electron-positron collider produce quarks if neither particle contains any?” all begins with the inconspicuous photon.

No Firefox, I Swear “Hadronization” is a Real Word.

As far as the history of quantum physics is concerned, the discovery that all light is fundamentally composed of very small particles called photons is a pretty big deal. The discovery allows us to have a very real and tangible description of how light and electrons actually interact, i.e., through the absorption or emission of photon by electrons.

Figure 1: Feynman diagrams demonstrating how electrons (denoted by e^-) can accelerate (change direction of motion) by (a) absorbing or (b) emitting a photon (denoted by the Greek letter gamma: γ).

The usefulness of recognizing light as being made up many, many photons is kicked up a few notches with the discovery of anti-particles during the 1930s, and in particular the anti-electron, or positron as it is popularly called. In summary, a particle’s anti-particle partner is an identical copy of the particle but all of its charges (like electric, weak, & color!) are the opposite. Consequentially, since positrons (e⁺) are so similar to electrons (e^-) their interactions with light are described just as easily.

Figure 2: Feynman diagrams demonstrating how positrons (e⁺) can accelerate (change direction of motion) by (a) absorbing or (b) emitting a photon (γ). Note: positrons are moving from left to right; the arrow’s direction simply implies that the positron is an anti-particle.

Then came Quantum Electrodynamics, a.k.a. QED, which gives us the rules for flipping, twisting, and combining these diagrams in order to describe all kinds of other real, physical phenomena. Instead of electrons interacting with photons (or positrons with photons), what if we wanted to describe electrons interacting with positrons? Well, one way is if an electron exchanges a photon with a positron.

Figure 3: A Feynman diagram demonstrating the exchange of a photon (γ) between an electrons (e^-)  and a positron (e⁺). Both the electron and positron are traveling from the left to the right. Additionally, not explicitly distinguishing between whether the electron is emitting or absorbing is intentional.

And now for the grand process that is the basis of all particle colliders throughout the entire brief* history of the Universe. According to electrodynamics, there is another way electrons and positrons can both interact with a photon. Namely, an electron and positron can annihilate into a photon and the photon can then pair-produce into a new electron and positron pair!

Figure 4: A Feynman diagram demonstrating  an annihilation of an electrons (e^-)  and a positron (e⁺) into a photon (γ) that then produces an e⁺e^- pair. Note: All particles depicted travel from left to right.

However, electrons and positrons is not the only particle-anti-particle pair that can annihilate into photons, and hence be pair-produced by photons. You also have muons, which are identical to electrons in every way except that it is 200 times heavier than the electron. Given enough energy, a photon can pair-produce a muon and anti-muon just as easily as it can an electron and positron.

Figure 5: A Feynman diagram demonstrating  an annihilation of an electrons (e^-)  and a positron (e⁺) into a photon (γ) that then produces a muon (μ^-) and anti-muon(μ⁺) pair.

But there is no reason why we need to limit ourselves only to particles that have no color charge, i.e., not charged under the Strong nuclear force. Take a bottom-type quark for example. A bottom quark has an electric charge of -1/3 elementary units; a weak (isospin) charge of -1/2; and its color charge can be red, blue, or green. The anti-bottom quark therefore has an electric charge of +1/3 elementary units; a weak (isospin) charge of +1/2; and its color charge can be anti-red, anti-blue, or anti-green. Since the two have non-zero electric charges, it can be pair-produced by a photon, too.

Figure 6: A Feynman diagram demonstrating  an annihilation of an electrons (e^-)  and a positron (e⁺) into a photon (γ) that then produces a bottom quark (b) and anti-bottom quark (b) pair.

On top of that, since the Strong nuclear force is, well, really strong, either the bottom quark or the anti-bottom quark can very easily emit or absorb a gluon!

Figure 7: A Feynman diagram demonstrating  an annihilation of an electrons (e^-)  and a positron (e⁺) into a photon (γ) that produces a bottom quark (b) and anti-bottom quark (b) pair, which then radiate gluons (blue).

In electrodynamics, photons (γ) are emitted or absorbed whenever an electrically charged particle changes it direction of motion. And since the gluon in chromodynamics plays the same role as the photon in electrodynamics, a gluon is emitted or absorbed whenever  a “colorfully” charged particle changes its direction of motion. We can absolutely take this analogy a step further: gluons are able to pair-produce, just like photons.

Figure 8: A Feynman diagram demonstrating  an annihilation of an electrons (e^-)  and a positron (e⁺) into a photon (γ) that produces a bottom quark (b) and anti-bottom quark (b) pair. These quarks then radiate gluons (blue), which finally pair-produce into quarks.

At the end of the day, however, we have to include the effects of the Weak nuclear force. This is because electrons and quarks have what are called “weak (isospin) charges”. Firstly, there is the massive Z boson (Z), which acts and behaves much like the photon; that is to say, an electron and positron can annihilate into a Z boson. Secondly, there is the slightly lighter but still very massive W boson (W), which can be radiated from quarks much like gluons, just to a lesser extent. Phenomenally, both Weak bosons can decay into quarks and form semi-stable, multi-quark systems called hadrons. The formation of hadrons is, unsurprisingly, called hadronization. Two such examples are the the π meson (pronounced: pie mez-on)  or the J/ψ meson (pronounced: jay-sigh mezon). (See this other QD article for more about hadrons.)

Figure 9: A Feynman diagram demonstrating  an annihilation of an electrons (e^-)  and a positron (e⁺) into a photon (γ) or a Z boson (Z) that produces a bottom quark (b) and anti-bottom quark (b) pair. These quarks then radiate gluons (blue) and a W boson (W), both of which finally pair-produce into semi-stable multi-quark systems known as hadrons (J/ψ and π).

In summary, when electrons and positrons annihilate, they will produce a photon or a Z boson. In either case, the resultant particle is allowed to decay into quarks, which can radiate additional gluons and W bosons. The gluons and W boson will then form hadrons. My friend Geoffry, that is how how you can produce quarks and hadrons from electron-positron colliders.

Now go! Discuss and ask questions.

Happy Colliding

- richard (@bravelittlemuon)

* The Universe’s age is measured to be about 13.69 billion years. The mean life of a proton is longer than 2.1 x 10²⁹ years, which is more than 15,000,000,000,000,000,000 times the age of the Universe. Yeah, I know it sounds absurd but it is true.

If you were wondering where I got yesterday’s piece from, the answer is that I fired up my old laptop and found it among a lot of old papers there. And by “old laptop”, I mean really old laptop: I bought it in 1995! Anyway, since I haven’t got time to write anything today here is another piece I wrote a long time ago but have only recently unearthed. This one is about Galaxies. It’s a lot longer than yesterday’s effort, but like that one I can’t remember what it was for. Still, some of you might find it interesting. The piece ends with a reference to galaxies observed as they were in the distant past, rather like the article itself!

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A galaxy is a collection of stars, held together by their mutual gravitational attraction and orbiting around their common centre.  Galaxies range in size from dwarf systems of perhaps a few million stars, to giants containing up to a thousand billion. The Sun and all the stars visible in the night sky to the naked eye belong to one such galaxy, our own Galaxy the Milky Way. Although principally recognized through the light given off by their component stars, galaxies also contain other material such as clouds of gas and dust, and significant quantities of dark matter whose nature is not yet understood.

Only stars inside our Galaxy can be resolved with the naked eye; these stars have been studied and catalogued since antiquity. Ancient astronomers  also knew of the existence of a diffuse band of light crossing the sky they could not resolve into individual stars; we now call this the Milky Way. The word galaxy is derived from the Greek galaktos, meaning “milk”. The existence of galaxies other than our own is a much more recent discovery. While even relatively nearby stars appear as point sources of light, the light from other galaxies appears as cloudy and diffuse much like small fragments of the Milky Way. The generic term for a such sources is nebula, the latin word for “mist”.

A Persian astronomer, al-Sufi, in the 10^th century AD described such a faint patch of light in the constellation Andromeda which is now known to be another galaxy, but it was only in the 18^th Century that a systematic catalogue of  nebulae was compiled, by the French astronomer Charles Messier. Not all the objects he found were other galaxies – some were clouds of dust and gas inside our own – but the Messier catalogue contained 32 objects that we now know to be galaxies, including al-Sufi’s object, which was number 31 in his list. The Andromeda nebula is known to this day as M31. With the increasing power of astronomical telescopes, the list of known nebulae grew to thousands even before the use of astronomical photography became widespread. William and Caroline Herschel and, later, their son John played a leading role in identifying and cataloguing such objects in the early 19^th century.

While the existence of large numbers of these nebulae was well established by the start of the 20^th Century, their nature remained controversial. Since their distances could not be directly measured, it was possible that they could be inside our own galaxy. Many astronomers believed that the spiral structure seen in some of them, for example M31, suggested that they represented the formative stages of planetary systems like our own Solar System inside the Milky Way. Others argued that the nebulae were very much more distant than that, and were “island universes” on a much larger scale. This debate was only resolved in the 1920s, when Edwin Hubble was able to measure the distances to some nebulae using variable stars called Cepheids. He found them to be far too distant to be inside the Milky Way. This discovery established galaxies as the basic building-blocks of the Universe and gave rise to the field of extragalactic astronomy. Astronomers now estimate that there are as many galaxies in our observable Universe as there are individual stars in our own galaxy, i.e. around a hundred billion.

Galaxies come in a rich variety of shapes and sizes, but there are three basic types: Galaxies come in three basic types: spiral (or disk), elliptical and irregular. Hubble proposed a morphological classification, or taxonomy, for galaxies in which he envisaged the three basic types (spiral, elliptical and irregular) as forming a sequence which in the past was often assumed to represent various evolutionary stages of a galaxy . Although it is now not thought the interpretation as an evolutionary sequence is correct, Hubble’s nomenclature is still commonly used.

Spiral galaxies account for more than half the galaxies observed  in our neighbourhood.  These contain a bright central nucleus surrounded by a flattened disk that sometimes contains beautiful spiral arms. Hubble divided these galaxies into classes labelled as normal (S) or barred (SB) depending on whether the prominent spiral arms emerge directly the nucleus, or originate at the ends of a luminous bar projecting symmetrically through it . Spirals often contain copious amounts of dust, and the spiral arms containing many young stars givin them a noticeably blue colour.  The normal and barred spirals S and SB are further subdivided into a, b or c depending on how tightly the spiral arms are wound up.

The elliptical galaxies (E), which account for only around 10% of observed bright galaxies, are elliptical in shape and have no discernible spiral structure. They are usually red in colour, have very little dust and show no signs of active star formation. The further classification of elliptical galaxies into En depends on the degree of elongation of the galaxy: E0 is nearly spherical; E7 is cigar-shaped. Ellipticals tend to occur in regions of space where there are many other galaxies, giving rise to the idea that they might originally have been spiral galaxies but have lost their spiral structure through mergers or interactions with other galaxies.

The shapes and colours of elliptical galaxies resemble the corresponding properties of spiral nuclei. Elliptical galaxies cover a broad range in mass, from a few hundred thousand to a thousand billion times the mass of the Sun. Spiral galaxies seem to have a smaller spread in mass, typically weighing in at about a hundred billion times the mass of the Sun.

Lenticular, or S0 galaxies, were added later by Hubble to bridge the gap between normal spirals and ellipticals. Around 20% of galaxies we see have this morphology. They are more elongated than elliptical galaxies but have neither bars nor spiral structure.

Irregular galaxies have no apparent structure. They are relatively rare, and are often faint and small so are consequently very hard to see. Their irregularity may stem from the fact that they are have such small masses that the material within them is relatively loosely bound and may have been disturbed by the environment in which they sit.

The classification of galaxies proposed by Hubble applies to “normal” galaxies whose light output is dominated by radiation their constituent population of stars. Stars predominantly emit visible light, which occupies a relatively narrow part of the spectrum of electromagnetic radiation. Spiral galaxies also contain dust which is heated by starlight and radiates in the infra-red. Active galaxies are characterized by the prodigious amounts of energy they emit in regions of the spectrum normal galaxies cannot reach, particularly in radio and X-rays. Much of the energy broadcast by active galaxies is associated with the relatively small nucleus of the galaxy, so the term Active Galactic Nuclei (AGN) is often used to describe these regions. Sometimes the central nucleus is accompanied by a jet of material being ejected at high velocity into the surrounding intergalactic medium. The different types of active galaxy include Seyfert galaxies, radio galaxies, BL Lac objects, and quasars.

Seyfert galaxies are usually spiral galaxies with no radio emission and no evidence of jets. They do, however, emit radiation over a continuous range of frequencies from infra-red to X-rays. Splitting their optical light up into its characteristic spectrum reveals the presence of strong and variable emission lines.  One can see such lines in ordinary stellar spectra and consequently in the spectra of normal galaxies, but they are much more prominent in active galaxies. Radio galaxies, on the other hand, are more commonly elliptical galaxies. These objects are extremely dramatic in their appearance, frequently having two lobes of  radio-emitting material extending far away from the central compact nucleus. There is also sometimes the appearance of a jet of material, extending from the core into the radio lobes. It appears that material is ejected from the nucleus along the jet, eventually being slowed  down by its interaction with the intergalactic medium and forming the radio lobes. The central parts of radio galaxies seem to have properties similar to those of Seyfert galaxies.

BL Lac objects have spectra with no emission lines, but they emit strongly in all wavebands from radio to X-ray frequencies. Their main characteristic, however, is their extremely strong and rapid variability. It is thought that a possible explanation for these objects is that the observer is seeing a jet of material travelling head-on at close to the velocity of light.

The first quasars to be found were detected by their strong radio emission, but they were found to be so small that, like stars but unlike other galaxies, they could not be resolved with optical telescopes. For this reason they became known as quasi-stellar radio sources, or quasars for short. Later on, other such objects were found which did not emit radio waves at all, so the name was changed to quasi-stellar object or QSO, but the name quasar has in any case stuck. It seems that only one in about two hundred quasars is actually radio-loud, but the quasars are still the most powerful of all the active galaxy types.

These different kinds of objects were discovered at different times by different people and were originally thought to be entirely different phenomena. Now, however, there is a unified model in which these structures are all interpreted as having basically similar structure but a different orientation to the observer’s line-of-sight. The engine which powers the activity is thought to be a supermassive black hole, with a mass up to about 100 million solar masses. This seems very large, but is actually just a small fraction of the mass of the host galaxy, which may be a thousand times larger. Material surrounding the black hole is attracted towards it and undergoes a process of accretion, gradually spiralling in and being swallowed. As it spirals in, it forms an accretion disk around the black hole. This disk can be very hot, producing the X-ray radiation frequently seen in AGN, but its presence prevents radiation being transmitted through it. Radiation tends therefore to be beamed out of the poles of the nucleus and does not appear from the equatorial regions which are obscured by the disk. When the beamed radiation interacts with material inside the host galaxy or in the surrounding medium, it forms jets or radio lobes. Depending on the thickness of the disk, the size of the `host’ galaxy ,the amount of gas and dust surrounding the nucleus and the orientation at which the whole system is viewed one can, at least qualitatively, account for the variety of properties listed above.

It is not known what fraction of normal galaxies undergoes activity at some stage in their careers. Although active galaxies are relatively uncommon in our neighbourhood, this may simply be because the active phase lasts for a very short time compared to the total life of a galaxy. For example, if activity only lasts only one-thousandth of the total lifetime, we would expect only to see one in a thousand galaxies at any one time displaying the symptoms. It is perfectly possible, therefore, that the kind of extreme activity displayed by these galaxies is merely a phase through which all galaxies pass. If so, this would suggest that all galaxies should possess a massive black hole at their centre, which is no longer powering an accretion disk because there is insufficient gas left in the surrounding regions. Recent studies using the ultra-high resolution available on the Hubble Space Telescope suggest that most normal galaxies may indeed have black holes in their centres.

A somewhat milder form of activity is displayed by starburst galaxies which, as their name suggests are galaxies undergoing a vigorous period of star formation. Such activity is not thought to involve an active galactic nucleus, but is probably triggered by a tidal interaction between two galaxies moving closely past each other.

The stars in a galaxy exert gravitational forces on each other. This not only holds the galaxy together, it also causes the stars to move. The internal dynamical properties of galaxies are extremely important because they allow astronomers to work out how much matter is there.

In spiral galaxies, the component stars orbit roughly in a plane about the central nucleus. It is this bulk rotation that is responsible for the flattened shape of these systems. Much the same state of affairs applies in the Solar System, with all the planets moving in roughly circular orbits about the Sun. In the case of a disk galaxy that lies edge-on to the observer, stars on one side will be approaching while those on the other will be receding. These motions cause a Doppler shift in the light from different parts of the disk: one side will have a spectrum that is shifted towards blue colours, while the other side will be shifted to the red. One can therefore use spectroscopic methods to plot a graph showing how the rotation speed of material  varies with distance from the centre of rotation. Such a curve is called a rotation curve.  These curves show that the matter in spiral galaxies has a roughly constant velocity out to tens of thousands of light years from the centre. This is surprising because the planets of the Solar System have orbital speeds that fall off quite rapidly with distance from the Sun. Most of the mass of the Solar System lies in the Sun, which is near the centre of motion. Most of the light produced in a galaxy is likewise produced in the central regions. If all the mass in a galaxy were where the stars are, i.e. in the middle, the rotation speed should fall off the further out from the centre one looked. The simplest interpretation of this strange behaviour is that galaxies contain a large amount of material that does not produce starlight and which is not as concentrated in the centre of the galaxy as the stars. To make this work requires galaxies to be embedded in a diffuse halo of dark matter that is about ten times as large as the luminous part of the disk and containing perhaps ten times as much matter.

Dynamical studies of elliptical galaxies are more complicated because the stellar motions within them are not those of simple rotation. Nevertheless, these objects too reveal evidence for dark matter in similar quantity to that in spiral galaxies.

It is thought that less than 10 per cent of the total mass of a galaxy is in visible stars, but the form of the mysterious dark matter is not at all understood. The best candidate at the moment is some form of exotic particle left over from the Big Bang, usually called a WIMP (Weakly Interacting Massive Particle), although no such particle has yet been directly detected.

Galaxies are the basic building blocks of the Universe. They are not, however, the largest structures one can see. They tend not to be isolated, but cluster together. The distribution of nebulae on the sky was thought to be non-uniform even in the days of the Herschels, but it is only in the 20^th century that it has become possible to map their three-dimensional positions in a systematic fashion.

The technique used to explore the large-scale distribution of galaxies is based on the discovery of the expanding universe usually attributed to Edwin Hubble, who built  on earlier work by Vesto Slipher. Slipher had discovered that lines in the optical spectra of galaxies were systematically shifted towards the longer wavelength, red end of the electromagnetic spectrum. Hubble extended this study by looking at these redshifts in tandem with the distances he had estimated for the galaxies. He found, to his surprise, that the redshift of a galaxy came out to be proportional to its distance. Contrary to popular belief, Hubble never really interpreted this himself as the result of cosmic expansion but the empirical correlation between redshift and distance now known as Hubble’s Law is the cornerstone of the big-bang cosmology. It is now accepted that the redshift of the galaxies arises from their motion away from the observer, similar to the Doppler shift that causes a change of pitch in a receding police siren. While the accurate determination of extragalactic distances remains difficult, measuring redshifts is rather straightforward. Hubble’s law has been used to chart the pattern traced out by millions of individual galaxies from their spectral shifts.

The general term used to describe a physical  aggregation of many galaxies is a cluster of galaxies, or galaxy cluster. Clusters can be systems of greatly varying size and richness. Our galaxy, the Milky Way,  is a member of the Local Group of galaxies which is a rather small cluster of galaxies of which the only other large member is the Andromeda galaxy (M31). On the other extreme, there are the so-called rich clusters of galaxies, also known as Abell clusters, which contain many hundreds or even thousands of galaxies in a region just few million light years across: prominent nearby examples of such entities are the Virgo and Coma clusters. In between these two extremes, galaxies appear to be distributed in systems of varying density.

Individual galaxy clusters are not the largest structures in the Universe. The distribution of galaxies on scales larger than around 30 million light years also reveals a wealth of complexity. Galaxies are not simply distributed in blobs, like the Abell clusters, but often lie in extended linear structures called filaments, such as the Perseus-Pisces chain, or flattened sheet-like structures like the Great Wall. The latter object is roughly two-dimensional concentration of galaxies, discovered in 1988 by astronomers from the Harvard-Smithsonian Center for Astrophysics. This structure is at least 200 million light years by 600 million light years in size, but is less than 20 million light years thick. It contains many thousands of galaxies and has a mass of at least 10¹⁶ solar masses.  The interconnecting network of filaments and sheets is aptly called the “cosmic web”, with rich clusters appearing where the parts of the web join together.

Rich clusters are clustered into enormous loosely-bound agglomerations called superclusters, containing anything from around ten rich clusters to more than 50. The most prominent known supercluster is called the Shapley concentration, while the most nearby is the Local Supercluster, a flattened structure in the plane of which the Local Group is moving. Superclustering is known to exist on scales up to 300 million light years, and superclusters may contain as much as 10¹⁷ solar masses of material or more.

These overdense structures are complemented by vast underdense regions known as voids, many of which appear to be roughly spherical.  These regions containing very many fewer galaxies than average, or even no galaxies at all. Voids with density less than 10% of the average density on scales of up to 200 million light years have been found in large-scale redshift surveys.

The existence of galaxies, clusters of galaxies and the overall complexity of large-scale structure in the Universe around us must be contrasted with the extreme simplicity of the very early Universe. Observations of the cosmic microwave background, relic radiation left over from the early stages of the Big Bang, suggest that the initial state of the Universe was almost featureless, with variations in density from place to place of less than one part in a hundred thousand.

The process that is thought to have transformed these smooth beginnings into the clumpiness we see today is called gravitational instability. If the universe were initially exactly smooth, it would have remained so as it expanded and cooled. But if there were small initial variations in density, these would become amplified. A small patch of the Universe that was more dense than average would exert a slightly greater gravitational pull on its surroundings than an average patch. This would cause material to flow in, making it even denser. This, in turn, would make it pull even more than average. This starts a runaway process by which small initial ripples can turn into dense clumps.

This basic idea has been around since it was first suggested by Sir James Jeans more than a hundred years ago, but it is only in the last ten years or so that a convincing picture has been put together explaining how it works in the expanding Universe. According the modern theories, most of the matter in the Universe is in the form of exotic particles left over from the primordial fireball phase that was the Big Bang. These particles are thought to be very slow-moving and are consequently called Cold Dark Matter (CDM). These particles cluster together via the process of gravitational instability, first forming small objects with the mass of a very small dwarf galaxy (around one hundred thousand solar masses). These small seed objects then progressively merge into larger objects in a hierarchical fashion, eventually forming galaxy-sized and cluster-sized dark matter clumps. These form gravitational wells into which gaseous matter falls and becomes trapped. Stars  form as gas clouds cool and fragment in the dark matter clumps. All this happens within a continuous sequence of interaction, disruption and merging. The whole process is extremely complicated, but extensive computer simulations show that the structure produced is very similar to the cosmic web revealed by observations, at least in the essential details.

Further support for these theoretical ideas is provided by observations of galaxies so distant that it has taken their light a large fraction of the age of the Universe to reach us. Looking at such objects allows astronomers to see galaxies in the process of formation.

Yesterday was the weekly live video Space Roundup, run by Fraser Cain from Universe Today. This week we had Pamela Gay, Alan Boyle, Nicole Gugliucci, and Ian O’Neill. We talked about the solar storm, black holes, arsenic life, Newt Gingrich, Phobos-Grunt, and answered some questions from the listeners. Here’s the video:

We do these every week on Google+ at 18:00 UTC on Thursday. Come join us!

2012 may well turn out to be The Year of The Higgs.  Right now we have very little knowledge about this particle, but that may change dramatically over the year. As I described in my previous post, we’re coming toward the end of Phase 1 of the Higgs search (where the ATLAS and CMS experiments at the Large Hadron Collider [LHC] search for the simplest possible form of the Higgs particle, the Standard Model Higgs, or SM Higgs for short.) And we’re also starting up Phase 2 of the Higgs search. As discussed in my Cosmic Variance guest post, and in more detail in my most recent post, if a particle resembling the SM Higgs is found, Phase 2 involves checking its details and determining as well as possible whether it is or isn’t precisely what is predicted by the Standard Model. If no such particle is found, Phase 2 involves searching widely for the many other types of Higgs particles that nature might or might not possess. Fortunately, despite these apparently divergent aims, the two possible branches of Phase 2 involve asking some of the same experimental questions (see Figure 3 of the most recent post), and so we can start on Phase 2 before even finishing Phase 1. And that is happening now.

One of the things that has to be done in Phase 2 is to search for decays of the Higgs particle that are not among the decays predicted to occur in the Standard Model.  ["Decay" = "a disintegration of one particle into two or more". Click here for an introduction.]  Such “exotic” decays are thought of as particularly plausible, because a lightweight Higgs (below about 150 GeV/c² or so) is a very sensitive creature. It is very easy for new particles and/or forces to alter the Higgs’ properties, perhaps causing changes in how (or how often) it is produced, and to what (and with what probability) it may decay.  As shown in a large number of papers, written by  quite a variety of particle physics theorists, there are many, many types of possible exotic decays, and they can arise for many reasons.  If you’re curious what kind of exotic decays might occur, I gave a few examples in my now somewhat out-of-date analysis of what the summer’s Higgs searches imply. The basic logic of how unusual Higgs decays might arise is still correct in the cases described, but there are many, many more possibilities too. I’ll have to write a long article about the options in the coming month or so.

Another thing I could recommend, especially to graduate students and to those laypersons who are willing to sit through a certain amount of technical mumbo-jumbo enclosed within a largely non-technical discussion, is the first 8 (or even 20.5) minutes of a lecture I gave in 2010 to graduate students who were not Large Hadron Collider [LHC] experts.  (If it loads too slowly you can download it from this page; it is my June 18th lecture.)

You might ask,“but if there were new particles and forces that could affect Higgs production or its decays, wouldn’t we have seen signs of them already at other experiments or at least at the LHC itself?” The answer is “no!” Because a lightweight Higgs is so sensitive, the new particles and forces required to alter it may easily be so weakly interacting with ordinary matter, or so heavy, that they can evade detection at all previous experiments and so far at the LHC. The first place they will be discovered is in the properties of the Higgs particle. And so it is very important to measure how the Higgs particle behaves as carefully and precisely as possible!

There are three good reasons why one of the most important strategies to be used in Phase 2 will be to check whether the Higgs has exotic decays — perhaps common, or perhaps rare.

• If we don’t find an SM-like Higgs in Phase 1, it might well be that although there is a Higgs there with SM or near-SM production rates, its decays are not those expected in the Standard Model, but are somehow “exotic.”
• Conversely, if we do find an SM-like Higgs in Phase 1, we know now that it can only lie above 600 GeV/c² (but this is disfavored) or in the 115-127 GeV/c² range, in which case (being lightweight) it may very easily have rare or even common exotic decays.
• And if current hints of an SM-like Higgs at 125 GeV/c² turn out to be the real thing, we still only know from current data that it roughly looks like an SM-Higgs. If it decays as expected only, say, 85% of the time, and decays exotically, say, 15% of the time, we wouldn’t know that yet. Our data sets are still far too small, and the hints far too uncertain, to be able to rule that out.

At the very least, then, we should be prepared to look for exotic Higgs decays that are perhaps common, or perhaps somewhat rare. These searches might very well be the first to reveal a breakdown of the Standard Model! So we should be preparing for them, and designing them to be as powerful as possible.

“But slow down,” you might say. “We’re not even sure yet that the Higgs particle is there at all; we’re still arguing over whether what’s been seen near 125 GeV/c² is a mirage. In 2012 that mirage may take solid form, but even if it does, there will be just barely enough data for confidence in its reality. At such an early stage, how could we ever hope to detect something that the Higgs particle does only rarely?”

Ah. We need to remember that the Phase 1 searches for the SM Higgs particle themselves rely on things that a Higgs particle does only very rarely. The most important search strategies for the Higgs in 2011 and 2012 will be to look for its decays to two photons and its decays to “four leptons” (shorthand for two lepton/anti-lepton pairs.) If the Higgs has a mass of 125 GeV/c², it decays to two photons only 0.2% of the time. It decays to four leptons only 0.01% of the time. Even its decay to a lepton, anti-lepton, neutrino and anti-neutrino, which is also somewhat useful, is only a few percent effect. All of the decays of the SM Higgs that we can hope to actually measure are rare. The common ones, such as the decay to a bottom quark/anti-quark pair or to a tau lepton/anti-lepton pair, are almost completely drowned in huge backgrounds.  (More accurately, there are in fact clever ways to measure decays to  bottom quarks or to taus, but only by using rare production processes, so these are rare too,  for a different reason.)

It’s well worth going through these numbers a bit more carefully. If indeed there is an SM-like Higgs at 125 GeV/c², produced at the rates expected in the Standard Model, then the number of Higgs bosons produced so far at ATLAS and CMS (separately!) is

the probability of making a Higgs in a 7 TeV proton-proton collision:

• 0.000,000,000,16

times the number of proton-proton collisions in 2011 at ATLAS or CMS:

• 570,000,000,000,000

equals the number of Higgs particles produced at ATLAS and at CMS

• 90,000

Let me say that again.  If nature sports a SM-like Higgs particle with a mass of  125 GeV/c², the number produced so far at ATLAS and CMS is already approaching one hundred thousand in each experiment.

Most of these Higgs particles were not noticed; they disappeared under huge backgrounds, as the planet Venus disappears in bright sunlight.   A few thousand or so decayed (via two W particles) to a lepton, an anti-lepton, a neutrino and an antineutrino; those can be detected, but the backgrounds are large and the measurement is hard. The number of Higgs particles that decay to two photons is something like a few hundred in each experiment, though not all are detected. The number that decay to four leptons is a handful, and some are lost. It’s the last two very rare processes that give the most striking information in the search for the SM Higgs.

But maybe this new Higgs particle is not a Standard Model Higgs particle after all, but just looks similar at first glance. Maybe a few dozen, or a few hundred, or a few thousand of the 90,000 Higgs bosons produced in 2011 decayed in an unexpected way, or in one of several unexpected ways. And maybe one of those types of decays gives an experimental signature that we can discover rather easily, giving a signal that stands out above background. All the experimenters might need to do … is look. Maybe they don’t even need more data; just searching through the 2011 data might be enough. All the focus last year was on pushing Phase 1 of the Higgs search as far as possible. But Phase 2 can start with this year’s questions about last year’s data.  It could even lead to a striking discovery before we get far into 2012.  [I hope some of the experimenters at ATLAS and CMS are reading this.]

Of course we should also get as much information about the Higgs as possible from the new 2012 data, starting in March or April, which with some good fortune might bring 3 to 4 times as many collisions as in 2011. These may occur at a slightly higher energy per collision (8 TeV versus 7 last year) which would give slightly higher Higgs production rates. If there are some exotic decays happening, we obviously want the LHC experiments to collect as many of them as possible in order to maximize the chances that they can be identified when the data is analyzed. But this is where the trouble starts.

The trigger. Remember the trigger?

Read about the trigger here. You can’t deeply understand the Large Hadron Collider and how science is done there if you don’t understand the trigger. It all starts from there.

The trigger involves the real-time trashing of 99.9999% of the data that the LHC is collecting.  As quickly as the data comes in, all but 1 in a million collisions is discarded irretrievably.  There’s no choice.  Let’s go through these numbers too.

Last year, 20,000,000 times a second, two bunches of about 100,000,000,000 protons crossed through each other at the center of CMS and at the center of ATLAS; and in each bunch crossing the number of proton-proton collisions which occurred simultaneously was between an average of 5 or so (at the beginning of the year) and an average of 15 (at the end of the year.)

As an aside, note that this means that every time a potentially interesting proton-proton collision occurred at ATLAS or CMS in 2011, the detector was measuring the debris from not just this possibly interesting collision but from as many as 20 others that happened all at the same time. Almost always those other collisions were very boring — just glancing blows that make small sprays of particles — but they do clutter up the detector with uninteresting particles that have to be removed later, to the extent possible, in the data analysis stage. These multiple proton-proton collisions in the same bunch crossing are called “pile-up”.  [In addition, there are also particles, of rather low energy, still running around from collisions that occurred during previous bunch-crossings, and they're actually even worse, I'm told.]  Pile-up makes measurements harder — not so much harder that one should avoid pile-up at the expense of fewer collisions, but one has to actively deal with it. The effect of pile-up is a little like electronic static on a video screen (or “snow” on an old-style TV) making it harder to see the image; you can still see it, but some of your ability to see detail is lost, and you may want to use special image processing techniques to clean it up.

Given this amount of pile-up, the total number of collisions toward the end of 2011 was about 300,000,000 per second, of which it is possible to store a few hundred per second, for a total of a few billion (1,000,000,000) collisions stored in 2011 for data analysis. The rest of the half a million billion collisions (570,000,000,000,000) may as well never have happened; they’re gone, forever.  All of these numbers apply for ATLAS and CMS separately.

This year, the LHC is going to collect more data — probably not by having more frequent bunch crossings (the only other practical option would be 40,000,000 crossings per second), but probably by arranging for an average of 30 – 40 proton-proton collisions in each bunch crossing. In other words, the pile-up may double. On top of that, the energy per collision may be slightly higher, meaning the probability of any particular interesting-looking proton-proton collision will be higher. That’s good because the things you want to discover happen more often; but it’s still a problem for the trigger, because the rate for interesting-looking-but-actually-boring stuff goes up too… and since that stuff is so vastly more common, it’s what determines how aggressive the trigger’s decisions have to be.

So both the higher energy and the higher pileup will cause new challenges for the trigger. That means that the trigger will have to throw out collisions in 2012 that it would have kept in 2011. (Stated more accurately, the trigger is constantly being adjusted for changing conditions: the more interesting-looking collisions there are, and the more “noise” there is from pile-up, the tighter are the criteria that a collision has to satisfy for the trigger system to decide to keep it.)

Now, for some types of searches for new phenomena, this does not matter much. But the Higgs is a lightweight particle, so its decays typically produce a rather small amount of energy and momentum in particles moving perpendicular to the beam. And that isn’t very distinctive. [Specifically, if you add up the ``scalar transverse momentum'' (take each particle, measure the amount of its momentum perpendicular to the beam --- just the magnitude, not the direction --- and add the numbers up) for all the particles that are produced in a Higgs event, you will get only about 100 -- 200 GeV or so. Unfortunately, a proton-proton collision can in many other ways generate that much transverse momentum --- not easily... the probability is in the 1/20,000-1/200,000 range... but that's far too often. Remember only 1/1,000,000 events can be stored, and not all of them can be aimed at studying the Higgs -- the LHC needs to look for other new phenomena too, and make precise measurements of known particles, like the top quark.)]

What this means is that collisions that make a Higgs particle tend to sit in a dangerous place — right about where the trigger’s long knives do their slicing.  So if you don’t think about the trigger carefully… ouch!

Even in 2011, the trigger threw quite a few of those 90,000  or so Higgs particles away.  That was ok for Phase 1, the search for the SM Higgs.  The SM Higgs can be produced in several ways, and then can decay in several ways.  But not all combinations of production and decay have any hope of being discovered; for some combinations, backgrounds are far too large. Over the years there have been many studies that tell us which combinations are promising, and for each of them, there are logical pathways built into the current trigger strategies at ATLAS and CMS that allow for them to be studied.

But what about exotic decays? There are perhaps two dozen possibilities that we have to consider, maybe more. The theoretical studies of how to discover them have in some cases never been performed, and in other cases were performed in a context that is slightly but importantly different from the context of 2012. [One of the most important common differences is that many studies were done to examine what would happen if the Higgs were not found in Phase 1 because the probability of a certain exotic decay is near 100%. In this case the exotic decay would be common, but the Higgs mass would be unknown. But in fact we find ourselves in a different situation, with a Higgs that may be in the process of being found in Phase 1, with a mass that (if it is there) is known to be close to 125 GeV/c², and for which any exotic decay (given that the decays expected in the SM must be common, to make the discovery of this SM-like Higgs possible) must be rare --- at most, say, 10-15% of all Higgs decays, and perhaps much, much smaller! Knowing the Higgs' mass makes the search easier, but the smaller maximum probability for the decay makes it harder; together they certainly make the search different, different enough that the previous studies may not apply.]  So we find ourselves in the unfortunate position of not yet knowing precisely how to look for large classes of exotic decays.

But we certainly want to know this information in advance! Otherwise, how can we be sure how best to adjust the trigger strategies? How can we try to collect the right fraction of the data starting in March 2012, if we don’t know what strategies we’re going to want to use at the time of the data analyses, some of which won’t be done until 2013?!

I personally believe that we need to act quickly — that a number of theory studies of how to detect exotic Higgs decays are needed, now. [I hope some of my theorist colleagues are reading this.]

Certain things have to be done faster than others. The most urgent (which is what I have been working on for the past month, in consultation with some members of CMS and separately with some members of ATLAS — the two detectors have trigger systems which are different in crucial ways, and the strategies they will use may end up being quite different) is to understand which types of exotic decays are most likely to cause a problem for the trigger systems, such that collisions that make a Higgs with this type of decay would often be discarded under present trigger strategies. Conversely, for these problematic cases, it is urgent to understand what types of tricks can be used to make sure that more of these collisions pass the trigger. The good news is that the number of dangerous cases isn’t quite as large as I initially feared, and in the cases that worry me, it appears tentatively that there might be some tricks that can be played. But the jury is still out.

Moreover, adjusting the trigger is very complicated and controversial, because any time you choose to play some tricks that allow the trigger to keep a class of events that you were going to throw away, you have to choose to throw away other events that you were planning to keep. It’s close to a zero-sum game. So this is not something to be done lightly; you have to find the right compromise, and long arguments ensue within the experimental collaborations as to how best to do that.

Fortunately, even if in 2012 ATLAS and CMS don’t trigger on Higgs exotic decays as well as they possibly could, there is a safety net, a fall-back position. As various people often remind me, the production of a Higgs from a collision of a quark and anti-quark that makes a Higgs along with a W or Z particle (see the third row of Figure 2 of my article on Higgs production) offers a guarantee: no matter how the Higgs decays, the ~22% of the time that the W decays to a lepton or a neutrino, and the ~25% of the time that the Z decays to a neutrino/anti/neutrino or to a lepton/anti-lepton pair, offer up something that the trigger system can easily recognize — a lepton and/or anti-lepton, or “missing energy” (actually “missing transverse momentum”, or, more intuitively, a sign that something you can detect must be recoiling against something you have failed to detect — the neutrinos in this case.) But unfortunately the production of a Higgs in association with a W or Z is only about 5% of Higgs production (for an SM Higgs of 125 GeV; it’s a bit less for a heavier one and a bit more for a lighter one.) So if we have to rely on the safety net, only about 1% (and probably somewhat less when all is said and done) of Higgs bosons produced at the LHC will be triggered in this way. That means that although we’d have something like 400,000 Higgs bosons produced at each experiment in 2012, and perhaps as many as 40,000 or so decaying exotically, we’d only have 400 exotic decays stored permanently for later data analysis. Clearly, anything we can do to increase that 400 toward 4000  is worth doing!  Especially since the fraction of exotic decays might be much smaller than 10%, making that 400 in the safety net more like 40 or 4.  So yes, there’s a fall-back position, but we shouldn’t fall back until we’re beaten. And my own studies suggest we’re nowhere near beaten yet — though the time constraints of getting ready for the start of the 2012 data-taking mean we do have to work very fast.

[It is a pleasure to thank especially Oliver Buchmueller, Alex Tapper, Yuri Gershtein, Eva Halkiadakis, Andy Haas, Kyle Cranmer, Elliot Lipeles, Henry Lubatti, Dan Ventura, Guido Ciapetti, Barbara Mele, Stefano Giagu, Kathryn Zurek, Scott Thomas, David Shih,  Jared Evans, Yevgeny Kats, Neal Weiner, Nima Arkani-Hamed, Josh Ruderman, Tomer Volansky, Itay Yavin, and others for many useful discussions on this and closely related topics.]

Philosophy of science is about as useful to scientists as ornithology is to birds.

12月26日(月)から28日(水)の3日間、KEKにおいてBelle Plus(ベル・プリュス)2011が開催され、全国各地から22人の高校生が集まりました。

Belle PlusはKEK、奈良女子大学、奈良教育大学理数教育研究センターが共催している、高校生を対象とした研究体験型のサイエンスキャンプです。研究者に直接指導を受けながら素粒子物理学に関する実習や解析を行い、最終的に研究発表を行うもので、実際に研究者が行っている研究活動の流れを体験することができます。平成18年度よりBelle実験グループが中心となって実施しており、今年度で5回目の開催となります。

今回は、「B-Lab班」、「ワイヤーチェンバー班」、「霧箱班」、「理論班」の４つの班に分かれて実習を行いました。その他にもKEKの施設の見学や素粒子に関する講義、放射線についてのサイエンスカフェが開かれるなど盛りだくさんの内容となりました。最後の日には研究発表会が行われ、高校生同士で活発に質疑応答する様子が見られました。

高校生からは「将来研究者になりたい」「自分が興味を持っている事柄を、同じく興味を持つ他の人と共有できたので、とても良かった」といった感想が聞かれました。Belle Plusでの経験や共に議論した仲間達との繋がりを大切にしながら、素粒子物理学に対する興味関心がさらに高まればいいなと思います。

Belle Plus2011についての詳しい活動内容は以下をご覧ください。

Belle PlusのHP 活動報告　http://belle.kek.jp/b-camp/report.html

高エネルギー加速器研究機構 トピックス記事 http://www.kek.jp/ja/NewsRoom/Release/20120127130000/

McKinsey & Company is a management consulting firm. In 2010 they released this ‘carbon abatement cost curve’ for the whole world:

Click it to see a nice big version. So, they’re claiming:

• By 2030 we can cut CO₂ emissions about 15 gigatonnes per year while saving lots of money.

• By 2030 can cut CO₂ emissions by up to 37 gigatonnes per year before the total cost—that is, cost minus savings—becomes positive.

The graph is cute. The vertical axis of the graph says how many euros per tonne it would cost to cut CO₂ emissions by 2030 using various measures. The horizontal axis says how many gigatonnes per year we could reduce CO₂ emissions using these measures.

So, we get lots of blue rectangles. If a rectangle is below the horizontal axis, its area says how many euros per year we’d save by implementing that measure. If it’s above the axis, its area says how much that measure would cost.

I believe the total blue area below the axis equals the total blue area above the axis. So if we do all these things, the total cost is zero.

37 gigatonnes of CO₂ is roughly 10 gigatonnes of carbon: remember, there’s a crucial factor of here. In 2004, Pacala and Socolow argued that the world needs to find ways to cut carbon emissions by about 7 gigatonnes/year by 2054 to keep emissions flat until this time. By now we’d need 9 gigatonnes/year.

If so, it seems the measures shown here could keep carbon emissions flat worldwide at no net cost!

But as usual, there are at least a few problems.

Problem 1

Is McKinsey’s analysis correct? I don’t know. Here’s their report, along with some others:

• McKinsey & Company, Impact of the financial crisis on carbon economics: Version 2.1 of the global greenhouse gas abatement cost curve, 2010.

For more details it’s good to read version 2.0:

• McKinsey & Company, Pathways to a low carbon economy: Version 2 of the global greenhouse gas abatement cost curve, 2009.

They’re free if you fill out some forms. But it’s not easy to check these things. Does anyone know papers that try to check McKinsey’s work? I find it’s more fun to study a problem like this after you see two sides of the same story.

Problem 2

I said ‘no net cost’. But if you need to spend a lot of money, the fact that I’m saving a lot doesn’t compensate you. So there’s the nontrivial problem of taking money that’s saved on some measures and making sure it gets spent on others. Here’s where ‘big government’ might be required—which makes some people decide global warming is just a political conspiracy, nyeh-heh-heh.

Is there another way to make the money transfer happen, without top-down authority?

We could still get the job about half-done at a huge savings, of course. McKinsey says we could cut CO₂ emissions by 15 gigatonnes per year doing things that only save money. That’s about 4 gigatonnes of carbon per year! We could at least do that.

Problem 3

Keeping carbon emissions flat is not enough. Carbon dioxide, once put in the atmosphere, stays there a long time—though individual molecules come and go. As the saying goes, carbon is forever. (Click that link for more precise information.)

So, even Pacala and Socolow say keeping carbon emissions flat is a mere stopgap before we actually reduce carbon emissions, starting in 2054. But some more recent papers seem to suggest Pacala and Socolow were being overly optimistic.

Of course it depends on how much global warming you’re willing to tolerate! It also depends on lots of other things.

Anyway, this paper claims that if we cut global greenhouse gas emissions in half by 2050 (as compared to what they were in 1990), there’s a 12–45% probability that the world will get at least 2 °C warmer than its temperature before the industrial revolution:

• Malte Meinshausen et al, Greenhouse-gas emission targets for limiting global warming to 2 °C, Nature 458 (2009), 1158–1163.

Abstract: More than 100 countries have adopted a global warming limit of 2 °C or below (relative to pre-industrial levels) as a guiding principle for mitigation efforts to reduce climate change risks, impacts and damages. However, the greenhouse gas (GHG) emissions corresponding to a specified maximum warming are poorly known owing to uncertainties in the carbon cycle and the climate response. Here we provide a comprehensive probabilistic analysis aimed at quantifying GHG emission budgets for the 2000–50 period that would limit warming throughout the twenty-first century to below 2 °C, based on a combination of published distributions of climate system properties and observational constraints. We show that, for the chosen class of emission scenarios, both cumulative emissions up to 2050 and emission levels in 2050 are robust indicators of the probability that twenty-first century warming will not exceed 2 °C relative to pre-industrial temperatures.

Limiting cumulative CO₂ emissions over 2000–50 to 1,000 Gt CO₂ yields a 25% probability of warming exceeding 2 °C—and a limit of 1,440 Gt CO2 yields a 50% probability—given a representative estimate of the distribution of climate system properties. As known 2000–06 CO₂ emissions were 234 Gt CO₂, less than half the proven economically recoverable oil, gas and coal reserves can still be emitted up to 2050 to achieve such a goal. Recent G8 Communiques envisage halved global GHG emissions by 2050, for which we estimate a 12–45% probability of exceeding 2 °C—assuming 1990 as emission base year and a range of published climate sensitivity distributions. Emissions levels in 2020 are a less robust indicator, but for the scenarios considered, the probability of exceeding 2 °C rises to 53–87% if global GHG emissions are still more than 25% above 2000 levels in 2020.

This paper says we’re basically doomed to suffer unless we revamp society:

• Ted Trainer, Can renewables etc. solve the greenhouse problem? The negative case, Energy Policy 38 (2010), 4107–4114.

Abstract: Virtually all current discussion of climate change and energy problems proceeds on the assumption that technical solutions are possible within basically affluent-consumer societies. There is however a substantial case that this assumption is mistaken. This case derives from a consideration of the scale of the tasks and of the limits of non-carbon energy sources, focusing especially on the need for redundant capacity in winter. The first line of argument is to do with the extremely high capital cost of the supply system that would be required, and the second is to do with the problems set by the intermittency of renewable sources. It is concluded that the general climate change and energy problem cannot be solved without large scale reductions in rates of economic production and consumption, and therefore without transition to fundamentally different social structures and systems.

It’s worth reading because it uses actual numbers, not just hand-waving. But it seeks much more than keeping carbon emissions flat until 2050; that’s one reason for the dire conclusions.

It’s worth noting this rebuttal, which says that everything about Trainer’s paper is fine except a premature dismissal of nuclear power:

• Barry Brook, Could nuclear fission energy, etc., solve the greenhouse problem? The affirmative case, Energy Policy, available online 16 December 2011.

To get your hands on Brook’s paper you either need a subscription or you need to email him. You can do that starting from his blog article about the paper… which is definitely worth reading:

• Barry Brook, Could nuclear fission energy, etc., solve the greenhouse problem? The affirmative case, BraveNewClimate, 14 January 2012.

According to Brook, we can keep global warming from getting too bad if we get really serious about nuclear power.

Of course, these three papers are just a few of many. I’m still trying to sift through the information and figure out what’s really going on. It’s hard. It may be impossible. But McKinsey’s list of ways to cut carbon emissions and save money points to some things we start doing right now.

Following news that Pac-Man is NP-Hard, theorists determine the computational complexity of Scrabble.

Having been invented in the US in the mid-20th century, Scrabble is now available in dozens of languages and sells in numbers measured in hundreds of millions. That makes it one of the most popular games in the world.  

That has naturally piqued the interest of game theorists. "Since Scrabble is such a successful game, it becomes a natural question to determine the computational complexity of finding an optimal play," say Michael Lampis at the KTH Royal Institute of Technology in Sweden and a few pals. 

The same question has been successfully asked of many board games, such as chess, Go and Othello, which tend to be PSPACE or EXPTIME-complete. But Scrabble is trickier because players do not know the order in which the tiles will be drawn meaning that chance plays a greater role.

The question that Lampis and co attempt to answer is this: given a Scrabble position how hard is it to determine the best playing strategy? 

They point out that in any given round, a Scrabble player is confronted with two tasks: deciding which word to form and deciding where to place it on the board. These tasks are related because the words that can be formed depend on the position of letters on the board. 

But which of these task is it that makes Scrabble hard? What Lampis and co show is that both are hard and give a proofs of each to back up their claim. That's impressive because it allow us to 'see' why Scrabble is hard. 

"We establish that during the course of a game, Scrabble players need to perform not one, but two computationally hard tasks, which is probably the reason why Scrabble is so much fun to play," they write.

That's not to say computational complexity theorists are done and dusted with Scrabble. Their next task is to discover whether there is a polynomial-time algorithm to determine the move that would maximize the score achieved in this round.

Now that would be handy! 

Ref: arxiv.org/abs/1201.5298: Scrabble is PSPACE-Complete

The workshop in Warwick yesterday went on very quickly! The room was packed. The three first talks were by myself, Christophe and Pierre, so less about GPUs and more about simulation techniques which could benefit from or even require implementation on GPUS. (I did manage to have complete slides this time… More seriously, Christophe’s talk set me thinking on the issue of estimating the likelihood function in ways different (?) from the one used in ABC.) The second half was more novel for me, in that the three talks went into the computing and computer aspects of GPUS, with Chris Holmes doing sparse [Lasso-like] regression on a scale otherwise [i.e. w/o GPUs] impossible, Chris [fourth Chris in the list of speakers!] Barnes explaining ABC for molecular biology and design (a point I plan to discuss on a later post), with even more details about the architecture and programming of GPUs, and Michael Stumpf delivering a grand finale, with essentially three talks into one: network analysis (incl. terrific movie bits incorporated within the beamer slides!), GPUs vs. CPUs and older alternatives, and random generators on GPU, commenting on a recent paper by Salmon et al. (SC, 2011) and showing that true gains in efficiency from using GPUs involved a heavy involvement into the hardware structure… A very exciting day followed by Stilton cheese degustation and haggis (if not poems) to celebrate Burns’ night!

Some hae meat and canna eat,
And some wad eat that want it;
But we hae meat, and we can eat,
And sae let the Lord be thankit.

When the US National Science Board nixed plans for an underground lab in 2010, multiple potential experiments were left homeless, and the US physics community was in a kerfuffle. Now, 40 leading theoretical physicists, including three Nobel Prize winners, have written to the US Department of Energy (DOE) urging it build an underground facility to study subatomic neutrinos that would compensate to some degree for the lab’s absence.

“We … are writing this letter to note the pressing scientific need for having a large underground detector, linked to a long baseline intense neutrino beam,” say the signatories, who include Nobelists Steven Weinberg of the University of Texas at Austin, Sheldon Glashow of Boston University in Massachusetts and Frank Wilczek of the Massachusetts Institute of Technology in Cambridge.

Their letter, dated 19 January, is a boost for the Long Baseline Neutrino Experiment (LBNE), an estimated US$1.3-billion complex with detectors housed in the Homestake mine in South Dakota and, 1,300 kilometres away, at Fermilab in Batavia, Illinois, where particle accelerators would generate beams of neutrinos and antineutrinos (see graphic). The letter argues that an underground facility is needed to search for matter–antimatter asymmetry using neutrinos and for proton decay, a process that, if seen, would confirm the theoretical unification of the forces of nature at scales beyond that which could be probed by the Large Hadron Collider at CERN, Europe’s particle-physics laboratory near Geneva, Switzerland.

The letter is a welcome boost at a difficult time for LBNE, which faces a Go/No-Go decision from DOE later this year, probably between May and September.  Budget constraints have recently forced the collaboration to choose between two detection technologies: a liquid-argon detector, in which neutrinos would be detected as they interact with argon nuclei, and a Cerenkov detector, in which neutrinos would be seen as they pass through water. It had previously been hoped that both might be built. Whereas an external review committee convened by DOE favoured liquid argon, a later committee comprising many members of the collaboration settled on the Cerenkov option. “We thought it was less expensive and less risky,” says LBNE co-spokesman Robert Svoboda of the University of California, Davis. But project manager James Strait of Fermilab went with the liquid argon. That leaves about 70 people who had been working on the water–Cerenkov option at a loose end. Svoboda says that he’s encouraging them to take three months to make a decision about how to proceed — presumably by either leaving the experiment or switching to the liquid-argon effort. He expects that the majority will decide that they will be able to do the physics they want to do in liquid argon and stay. In their letter to the DOE, the theoretical physicists say that either technology should be able to fulfill the physics goals, with liquid argon being slightly more sensitive to proton decay.

Pran Nath, a physicist at Northeastern University in Boston who co-signed the letter, says that the signatories worked on it for several months following the decision not to build the underground lab, experiments in which were strongly endorsed in a 2011 report from the US National Academy of Sciences. Nath says that the theorists’ hope is that once an underground facility is up and running, it might be able to house other experiments as well.

In addition, the closure of the Tevatron, Fermilab’s particle collider, in 2011, means that the United States risks being left without a large-scale particle-physics experiment, and young experimentalists will have to go to Europe to work on the Large Hadron Collider. “A country as large as the US needs a large experiment to be at the forefront of physics,” says Nath.

Image: LBNE/Symmetry Magazine

A recently approved cancer drug that was hailed as a miracle worker for some patients with advanced melanoma has mysteriously failed in early clinical trials against colon cancers. But work published today in Nature clarifies how colon cancers dodge the drug, called vemurafenib, and what can be done to overcome this resistance.

Vemurafenib (once known as PLX4032) was approved last year for the treatment of advanced melanomas that bear a mutation in a protein called BRAF  (see ‘Melanoma drug gets speedy approval’). Its dramatic — although admittedly short-lived (see ‘The roots of resistance‘) — success against melanoma raised hopes that the drug could be used against other cancers that harbor the same mutation (see ‘Rare victory in fight against melanoma’ and ‘Melanoma drugs slow disease, boost hopes for combination therapy’) . But colon cancers with BRAF mutations proved surprisingly wily, and early trials were disappointing. “No one would have expected that five years ago,” says oncologist Keith Flaherty of Harvard Medical School in Boston, Massachusetts. “Melanoma was historically the intractable one, not colon cancer.”

Cancer researcher René Bernards of the Netherlands Cancer Institute in Amsterdam and his colleagues decided to tackle this question using a large genetic screen based on RNA-interference, a technique that can be used to systematically reduce the expression of individual genes.

They found that colon cells with the BRAF mutation became sensitive to vemurafenib when expression of another cancer-associated protein, EGFR, was knocked down. In fact, treatment with vemurafenib activated EGFR in colon tumours, but not in melanoma, where EGFR is expressed only at low levels.

This finding is cause for renewed optimism: there are EGFR-inhibiting drugs already approved for the treatment of cancer. Bernards and his colleagues found that coupling these drugs with vemurafenib shut down the EGFR escape route, suggesting that the 8–10% of colon cancers that carry the BRAF mutation may be once again in the cross hairs. “This observation is so readily translatable, this could be done tomorrow,” says Flaherty, who was not involved with the study but has spearheaded trails of vemurafenib. The drug is also being tested against lung and thyroid cancers with the BRAF mutation.

I have nothing to add to this, except to say it’s great, and I saw it because Brian Cox mentioned it on Twitter.

Oh yeah: one more thing; watch it in HD and full screen. Coooool.

Impressive winning Famelab talk on the importance of nothing:

The new atomic x-ray laser won't replace the LCLS and other accelerator-based systems. In fact, to make the atomic laser work, researchers blasted neon atoms with x-rays from the LCLS itself. Still, the results mark a conceptual triumph, fulfilling a 45-year-old prediction that such an atomic x-ray laser is possible. "Nobody had done this before, and everybody knew that somebody had to go out and do this," says Philip Bucksbaum, director of SLAC's PULSE Institute for Ultrafast Energy Science in Menlo Park, California, who was not involved in the work. "So this is great."

A few years ago I was asked to provide a short description of the history of cosmology, from the dawn of civilisation up to the establishment of the Big Bang model, in less than 1200 words. This is what I came up with. Who and what have I left out that you would have included?

–0–

 Is the Universe infinite? What is it made of? Has it been around forever?  Will it all come to an end? Since prehistoric times, humans have sought to build some kind of conceptual framework for answering questions such as these. The first such theories were myths. But however naïve or meaningless they may seem to us now, these speculations demonstrate the importance that we as a species have always attached to thinking about life, the Universe and everything.

Cosmology began to emerge as a recognisable scientific discipline with the Greeks, notably Thales (625-547 BC) and Anaximander (610-540 BC). The word itself is derived from the Greek “cosmos”, meaning the world as an ordered system or whole. In Greek, the opposite of “cosmos” is “chaos”. The Pythagoreans of the 6^th century BC regarded numbers and geometry as the basis of all natural things. The advent of mathematical reasoning, and the idea that one can learn about the physical world using logic and reason marked the beginning of the scientific era. Plato (427-348 BC) expounded a complete account of the creation of the Universe, in which a divine Demiurge creates, in the physical world, imperfect representations of the structures of pure being that exist only in the world of ideas. The physical world is subject to change, whereas the world of ideas is eternal and immutable. Aristotle (384-322 BC), a pupil of Plato, built on these ideas to present a picture of the world in which the distant stars and planets execute perfect circular motions, circles being a manifestation of “divine” geometry. Aristotle’s Universe is a sphere centred on the Earth. The part of this sphere that extends as far as the Moon is the domain of change, the imperfect reality of Plato, but beyond this the heavenly bodies execute their idealised circular motions. This view of the Universe was to dominate western European thought throughout the Middle Ages, but its perfect circular motions did not match the growing quantities of astronomical data being gathered by the Greeks from the astronomical archives made by the Babylonians and Egyptians. Although Aristotle had emphasised the possibility of learning about the Universe by observation as well as pure thought, it was not until Ptolemy’s Almagest, compiled in the 2^nd Century AD, that a complete mathematical model for the Universe was assembled that agreed with all the data available.

Much of the knowledge acquired by the Greeks was lost to Christian culture during the dark ages, but it survived in the Islamic world. As a result, cosmological thinking during the Middle Ages of Europe was rather backward. Thomas Aquinas (1225-74) seized on Aristotle’s ideas, which were available in Latin translation at the time while the Almagest was not, to forge a synthesis of pagan cosmology with Christian theology which was to dominated Western thought until the 16^th and 17^th centuries.

The dismantling of the Aristotelian world view is usually credited to Nicolaus Copernicus (1473-1543).  Ptolemy’s Almagest  was a complete theory, but it involved applying a different mathematical formula for the motion of each planet and therefore did not really represent an overall unifying system. In a sense, it described the phenomena of heavenly motion but did not explain them. Copernicus wanted to derive a single universal theory that treated everything on the same footing. He achieved this only partially, but did succeed in displacing the Earth from the centre of the scheme of things. It was not until Johannes Kepler (1571-1630) that a completely successful demolition of the Aristotelian system was achieved. Driven by the need to explain the highly accurate observations of planetary motion made by Tycho Brahe (1546-1601), Kepler replaced Aristotle’s divine circular orbits with more mundane ellipses.

The next great development on the road to modern cosmological thinking was the arrival on the scene of Isaac Newton (1642-1727). Newton was able to show, in his monumental Principia (1687), that the elliptical motions devised by Kepler were the natural outcome of a universal law of gravitation. Newton therefore re-established a kind of Platonic level on reality, the idealised world of universal laws of motion. The Universe, in Newton’s picture, behaves as a giant machine, enacting the regular motions demanded by the divine Creator and both time and space are absolute manifestations of an internal and omnipresent God.

Newton’s ideas dominated scientific thinking until the beginning of the 20^th century, but by the 19^th century the cosmic machine had developed imperfections. The mechanistic world-view had emerged alongside the first stirrings of technology. During the subsequent Industrial Revolution scientists had become preoccupied with the theory of engines and heat. These laws of thermodynamics had shown that no engine could work perfectly forever without running down. In this time there arose a widespread belief in the “Heat Death of the Universe”, the idea that the cosmos as a whole would eventually fizzle out just as a bouncing ball gradually dissipates its energy and comes to rest.

Another spanner was thrown into the works of Newton’s cosmic engine by Heinrich Olbers (1758-1840), who formulated in 1826 a paradox that still bears his name, although it was discussed by many before him, including Kepler. Olbers’ Paradox emerges from considering why the night sky is dark. In an infinite and unchanging Universe, every line of sight from an observer should hit a star, in much the same way as a line of sight through an infinite forest will eventually hit a tree. The consequence of this is that the night sky should be as bright as a typical star. The observed darkness at night is sufficient to prove the Universe cannot both infinite and eternal.

Whether the Universe is infinite or not, the part of it accessible to rational explanation has steadily increased. For Aristotle, the Moon’s orbit (a mere 400,000 km) marked a fundamental barrier, to Copernicus and Kepler the limit was the edge of the Solar System (billions of kilometres away). In the 18^th and 19^th centuries, it was being suggested that the Milky Way (a structure now known to be at least a billion times larger than the Solar System) to be was the entire Universe. Now it is known, thanks largely to Edwin Hubble (1889-1953), that the Milky Way is only one among hundreds of billions of similar galaxies.

The modern era of cosmology began in the early years of the 20^th century, with a complete re-write of the laws of Nature. Albert Einstein (1879-1955) introduced the principle of relativity in 1905 and thus demolished Newton’s conception of space and time. Later, his general theory of relativity, also supplanted Newton’s law of universal gravitation. The first great works on relativistic cosmology by Alexander Friedmann (1888-1925), George Lemaître (1894-1966) and Wilhem de Sitter (1872-1934) formulated a new and complex language for the mathematical description of the Universe.

But while these conceptual developments paved the way, the final steps towards the modern era were taken by observers, not theorists. In 1929, Edwin Hubble, who had only recently shown that the Universe contained many galaxies like the Milky way, published the observations that led to the realisation that our Universe is expanding. That left the field open for two rival theories, one (“The Steady State”, with no beginning and no end)  in which matter is continuously created to fill in the gaps caused by the cosmic expansion and the other in which the whole shebang was created, in one go, in a primordial fireball we now call the Big Bang.

Eventually, in 1965, Arno Penzias and Robert  Wilson discovered the cosmic microwave background radiation, proof (or as near to proof as you’re likely to see) that our Universe began in a  Big Bang…

By James Dacey

A new report released earlier this week concluded that physical scientists use and access information in very different ways depending on the precise field they work in. Based on interviews and focus groups with a range of physical scientists, Collaborative Yet Independent reports that researchers have started to use online tools such as social networking sites in relation to their work. It found, however, that when it comes to disseminating new scientific results, publication in a traditional scientific journal remains the “gold standard” for researchers.

We want to know whether you think this will remain the case looking to the future of science. In this week’s Facebook poll we are asking the question:

Do you believe that researchers will always view the scientific paper as the gold standard for sharing new results?

Yes
No, it will be replaced by other forms of communication

To cast your vote, please visit our Facebook page. And, as always, please feel free to explain your response by posting a comment on the poll.

In last week’s poll you may have clocked that we addressed the timely issue of timekeeping. It was the topic of the hour because last Thursday delegates were debating whether or not we should scrap the “leap second”, at a meeting of the International Telecommunication Union in Geneva. This is a second that is added to or taken away from Co-ordinated Universal Time (UTC) every few years to take account of the slight speeding up or slowing down in the rotation of the Earth.

Since the first leap second was inserted in 1972, people have deliberated whether this is the most effective way of dealing with time. Some have suggested swapping the leap second in favour of the addition of a larger chunk of time after a longer period – such as a leap hour roughly every millennium. Others have suggested abandoning astronomical time altogether, replacing it with an Earth-based reference such as an atomic clock. To do so would decouple time from the Earth’s rotation, allowing traditional night hours to gradually become day hours, and over millions of years the seasons would shift from their traditional months.

We asked for your opinion on this issue and 72% of respondents believe that we should define time using an atomic clock. The remaining 28% would prefer to maintain our connection with the heavens by keeping astronomical time.

One commenter, Robert Minchin, believes that we should keep the leap second to save a stitch in time. “Getting rid of them would simply be storing up problems for the future, when a larger leap-something will need to be introduced before the night becomes the day,” he wrote. Another respondent, who goes by the name of Strum Cat, feels strongly that we should ditch astronomical time. He wrote: “Are you kidding? Defining time by the rotation of Earth is fine for getting to work on time, but useless for precise science.”

It appears, however, that the debate is set to continue for some time yet. Last Thursday – after our poll went live – officials at the ITU announced that they have sent the issue back to a panel of experts for further assessment. They say a revised proposal will be introduced no earlier than 2015.

Thank you for all of your votes and comments, and we look forward to hearing from you again in this week’s poll.

For a few years now, Famelab has grown into an international competition for young scientists aged 18-35 eager to share their passion.

Here is an unusual contest: participants are asked to communicate their work or interest in a 3-minute speech delivered to a general audience. In return, they get training from professionals (science communicators and media people), get invited to a Masterclass and can even make it to the finals at the Cheltenham Science Festival in the United Kingdom. The contestants are judged by professional scientists on their content, clarity and charisma. The goal is to detect the new voices for science and to find communicators able to captivate their audience.

It started in 2005 at the Cheltenham Science Festival. In 2007, the British Council adopted this competition as one of its flagship science engagement projects first in South East Europe for a pilot project, then expanding in 2010 to include 14 countries from Europe, Asia and Africa. Check out if there is a competition near you. You can also get help to host your own event.

On February 4, CERN will be hosting the Swiss semi-finals, with the finals to be held in Zurich on March 30. Anybody working or studying in Switzerland can participate. You can register up to the day of the event itself. Every one is also invited to attend the competition, which will start at 15:00 in CERN Globe of Innovation.

Don’t miss Tom Whyntie’s winning performance at the 2009 finals. Tom is a Ph.D student working on the CMS experiment at CERN. This is the most convincing speech you might ever heard about the importance of nothing.

Pauline Gagnon

To be alerted of new postings, follow me on Twitter: @GagnonPauline or sign-up on this mailing list to receive and e-mail notification.

The Globe of Innovation, CERN expositions and visitors center

Depuis quelques années déjà, Famelab est devenu une compétition internationale pour les jeunes de 18 à 35 ans intéressé-e-s à partager leur passion pour les sciences.

Cette compétition est assez inhabituelle: les participant-e-s ont trois minutes pour décrire leur recherche ou un sujet qui les intéresse devant une audience tout-public. En retour, ils et elles  reçoivent une formation donnée par des professionnel-le-s en communication et sont invité-es à participer à une « Masterclass ». Les finalistes iront au Cheltenham Science Festival au Royaume-Uni. Le jury est composé de scientifiques et gens des médias.

Les participant-e-s seront jugés sur leur clarté, le contenu et leur charisme. Le but est de repérer ceux et celles qui sauront captiver leur auditoire et qui pourraient devenir les nouvelles voix de la science.

L’idée est née au Festival des Sciences de Cheltenham en 2005 et grâce à l’implication du British Council, l’événement a vite évolué d’un premier projet pilote dans le sud ouest de l’Europe pour atteindre 14 pays d’Europe, d’Asie et d’Afrique. Vérifiez pour voir si une compétition se tient près de chez vous. Vous pouvez même obtenir de l’aide pour lancer votre propre compétition.

Le 4 février, le CERN accueillera les demi-finales suisses. La finale aura lieu à Zurich le 30 mars. Toute personne travaillant ou étudiant en Suisse peut participer. On peut s’inscrire jusqu’au 4 février. Le public est aussi invité à assister à la compétition dès 15:00 au Globe de l’Innovation du CERN.

Ne manquez pas la performance du grand gagnant de 2009, Tom Whyntie. Tom est étudiant au doctorat et fait sa recherche au CERN sur l’expérience CMS. Vous ne trouverez pas discours plus convaincant sur l’importance de rien.

Pauline Gagnon

Pour être averti-e lors de la parution de nouveaux blogs, suivez-moi sur Twitter: @GagnonPauline ou par e-mail en ajoutant votre nom à cette liste de distribution

Le Globe de l’Innovation du CERN, centre d’expositions et de visites

• slacktivist » Mark Driscoll, John Woolman, Zacchaeus and grace

  That [Quaker abolitionist John] Woolman was so miraculously persuasive suggests to me that he likely wasn't as monomaniacally focused on a single subject as the old preacher in the story I shared in the previous post. And the more I think about that story and Woolman's, the more I want to qualify my commendation of such a single-minded relentlessness. Woolman certainly was single-minded and relentless. He did one thing for decades, obsessively. Yet he also convinced people to change -- he convinced hundreds of people to change radically. I don't think he could have been so convincing unless all those people who encountered Woolman were convinced that he cared about them. And I don't think that they could have been convinced of that unless he took a real interest in more than just the one issue he had come to discuss with them -- as vitally important as that one issue was.

• Learning Before Class Strategies Part 2: Types of Resources to Provide Your Students « Science Learnification

  [T]he purpose of most of the resources that I discuss below is to deliver some initial content to the students so that class time can be spent building on the ideas presented by that initial content. With this in mind, I don't think that getting them to read the textbook is the most effective use of their time and can actually do some damage to any sort of buy-in that you have managed to generate toward the learning before class process. I say this because at their best textbooks attempt to be all of the following: (A) a resource to students on their first encounter with a topic, (B) a resource for students when working on their homework or studying for exams, and (C) a reference for students after they have completed a course. I have yet to see a textbook that is structured in such a way that use (A) is clearly and consistently delineated from uses (B) and (C) so that it can be truly useful for use (A). I'm not saying it is not possible, but it would require a very targeted effort.

• Compensation - Ta-Nehisi Coates - National - The Atlantic

  A great post taking a close look at dubious arguments about alternatives to ending slavery in the US that would've avoided the Civil War. And, being the kind of nerd I am, I just look at the graph and wonder what happened in 1839.

• Mike Vaccaro on NFL's northeast corridor of power with Patriots and Giants - NYPOST.com

  THIRTY THOUSAND FEET ABOVE AMERICA -- To all of you down there, to the flyover country I'm currently flying over? Sorry. To the fine sporting folk of Northern California, to all of your West Coast brethren, to those of you down South and up North and everywhere else south of South Amboy, N.J., and north of Northampton, Mass., and west of Eastchester, N.Y.? Yeah. Sorry to all of you, too. Because these next 12 days? They belong to us again, to New York and New England, to Gotham and Olde Towne, to New York and New Jersey, to Massachusetts and Maine, to that great DMZ of Connecticut that finds itself betwixt and between.

By Hamish Johnston

Anyone who has trained as a scientist has learned about the "scientific method" – but the concept remains ill-defined and its origins are a topic of debate among philosophers and historians.

In this week's instalment of In Our Time on BBC Radio 4, Melvyn Bragg and his cabal of intellectuals discuss the role of the English polymath Francis Bacon (1561–1626) in the development of the method. Through writings such as Novum Organum Scientiarum, Bacon (right) championed the use of inductive reasoning in science. Indeed, Bacon had a very important influence on a future generation of scientists who founded the Royal Society in 1660.

Another character associated with the development of the scientific method is Isaac Newton. According to historian Simon Shaffer of Cambridge University, Newton first developed his rules of scientific enquiry to study a very non-scientific subject: the Bible's Book of Revelation. Newton then further developed his ideas by applying them to what we would think of as science.

Rounding off Bragg's panel are the philosophers John Worrall of the London School of Economics and Michela Massimi of University College London. The quartet go on to discuss how Charles Darwin's 1859 On the Origin of Species was first received by Victorian scientists. Not very well it seems – Darwin's arguments seemed to fly in the face of the scientific method because the processes of evolution could not be observed in laboratory experiments.

The team also looks at how the overthrow of Newtonian physics in the early 20th century by relativity and quantum mechanics led to a rethinking of the scientific method. Leading the way was philosopher Karl Popper with his idea of falsifiability and Thomas Kuhn with his theory of paradigm shifts.

You can listen to the programme here.

This week the Earth has seen some increased magnetic activity in the upper atmosphere, and that means we got to see aurore! Across Northern Europe and the Northern USA people looked to the skies to see the northern lights. An aurora is one of the most beautiful sights in the natural world, and a phenomenon that actually tells us a lot about the Earth and how it interacts with its environment.

Those who followed me on Twitter (@aidanatcern) may have already seen some of the wonderful images of aurorae. There are dedicated webcams that capture the night sky, and you can see some sample images at the Aurora Webcam archive.

Aurora over Alaska (wikimedia)

When charged particles accelerate or decelerate, they emit electromagnetic radiation, and it is this radiation that we see in the aurora. The color of the light depends on the wavelength of the radiation, and the intensity of the light depends on how much radiation is emitted. That means that there is always an aurora above us, but if the energy of the radiation is too low, or the intensity is too weak, we won’t see anything. Once we know how to interpret the light we can learn something about the radiation that is emitted. Usually we see a variety of colors in an aurora and each color corresponds to a different wavelength, so if we can see a region of the sky that is all one color, we know that the wavelength (and hence the energy, ignoring the effects of aberration) must be the same. That means we can “map” the sky and find contours of wavelength.

Since the particles are accelerating, there must be something that causes the acceleration. The Earth’s core is made of (among other materials) molten iron. The rotation of the Earth means that this core is also rotating, and a rotating fluid magnetic medium creates a magnetic dipole, giving the Earth magnetic North and South poles. These poles are aligned near the geographic North and South poles of the Earth, but not exactly. (In fact, magnetic North and South keep moving and from time to time they even swap places. The exact mechanism behind this is not yet fully understood, but geological records show it happens every few hundred thousand years. Simulations suggest that the rotating magnetic fluid is a chaotic system, so the reversals occur at stochastic, or random, intervals of time.)

The sun produces a stream of charged particles, known as the solar wind, and they create their own electromagnetic field. The two fields, from the Earth and the sun, interact and they force the charged particles along curved paths. As they particles move along these paths they accelerate and decelerate, and that is what produces the aurorae. The most recent increase in magnetic activity can be traced back to a huge coronal mass ejection that arrived from the sun. This video shows the arrival of the flare:

The effect looks impressive, but don’t be scared, solar winds like this are perfectly harmless. Far bigger winds have hit the Earth in the past few billions years and life has continued to flourish in spite of them. Life has adapted to the Earth’s magnetic field and this field protects us from the high energy particles.

It turns out that while looking up at the night sky is a beautiful and moving experience in itself, it is also important to particle physicists. Some of the most important discoveries in the last century came from a different phenomena, cosmic rays. Cosmic rays are very high energy particles (usually protons) that travel huge interstellar distances and rain down on the Earth in much the same way that the solar wind does. They interact with the upper atmosphere to create cascades of particles, and usually the muons are the only detectable particles that reach sea level. Interactions of these cosmic rays gave rise to the discovery of the muon (“Who ordered that?!”), the pion and the kaon, the lightest forms of mesonic matter. It was around this time that large scale accelerators were developed, and we found hundreds of new mesons and baryons. Cosmic rays gave us a very small glimpse into a rich “zoo” of particles that has occupied physicists ever since.

Eventually, when we have exhausted our ability to accelerate particles to higher energies we might need to rely on cosmic rays again. There are proposals to develop ground based detectors to study the interactions of extremely high energy particles from outer space. Those particles have the potential to reach energy regimes we can only dream of at the moment. (Incidentally, this is one of the ways that we know for sure that the LHC cannot destroy the world. The universe creates much more energetic particles than we could ever hope to create in our accelerators, and since the universe seems to be in one piece we can conclude that the LHC is safe on Earth!)

An aurora from above (Expedition 28 on board the International Space Station)

If you’re fortunate enough to see an aurora then take a few moments to think about the huge forces at work, the vast distances involved, and how the colors tell us so much about how the Earth and solar wind behave. It really is one of the most beautiful phenomena in the universe.

There are places available in the forthcoming Safety courses. For updates and registrations, please refer to the Safety Training Catalogue.

FEBRUARY 2012
(alphabetical order)

Conduite de Plates-Formes Elevatrices Mobiles de Personnel (PEMP) / Cherry-picker driving :
09-FEB-12 au 10-FEB-12, 08.00 – 17.30, in French (with possibility to have handouts in English)

Magnetic Fields :
03-FEB-12, 9.30 – 12.00, in French

Self-rescue mask :
02-FEB-12, 8.30 – 10.00, in French
02-FEB-12, 10.30 – 12.00, in English
07-FEB-12, 8.30 – 10.00, in French
07-FEB-12, 10.30 – 12.00, in English
14-FEB-12, 8.30 – 10.00, in French
14-FEB-12, 10.30 – 12.00, in English
16-FEB-12, 8.30 – 10.00, in French
16-FEB-12, 10.30 – 12.00, in English
21-FEB-12, 8.30 – 10.00, in French
21-FEB-12, 10.30 – 12.00, in English
28-FEB-12, 8.30 – 10.00, in French
28-FEB-12, 10.30 – 12.00, in English

Radiological Protection :
03-FEB-12, 13.30 – 17.30, in English
07-FEB-12, 08.30 – 12.30, in English
07-FEB-12, 13.30 – 17.30, in French
10-FEB-12, 13.30 – 17.30, in English
24-FEB-12, 08.30 – 12.30, in English
24-FEB-12, 13.30 – 17.30, in French
28-FEB-12, 13.30 – 17.30, in English

Risques liés aux interventions en espace confiné / Confined spaces :
10-FEB-12, 09.00 – 17.30, in French

The classic '80s arcade game turns out to be equivalent to the travelling salesman problem, according a new analysis of the computational complexity of video games

In the last few years, a few dedicated mathematicians have begun to study the computational complexity of video games. Their goal is to determine the inherent difficulty of the games and how they might be related to each other and other problems.

Today, Giovanni Viglietta at the University if Pisa in Italy reveals a body of Herculean work in this area in which he classifies a large number of games from the 1980s and 90s including Pac-Man, Doom, Tron and many others.

Viglietta's work involves several steps. The first is to determine the class of computational complexity to which the game belongs. Next, he works out whether knowing how to solve the game also allows you to solve many other problems in the same class, a property that complexity theorists call 'hardness'. Finally, he determines whether the game is complete, meaning that it is one of the 'hardest' in its class. 

His approach is relatively straightforward. He first works through a number of proofs showing that any video game with specific game-playing properties falls into a certain complexity class. 

He then classifies the games according to game-playing properties they have. 

For instance, one type of game involves a player moving through a  landscape visiting a number of locations. He calls this 'location traversal' and an example would be a game in which certain items are strewn around a landscape and the goal is to collect them all. 

Some location traversal games allow each location to be visited only once. So-called single use path games might include downhill races. 

He then uses graph theory to prove that any game exhibiting both location traversal and single-use paths is NP-hard, that's the same class of complexity as the travelling salesman problem. 

It turns out that Pac-Man falls into this category (the proof involves distributing power pills around the maze in a way that enforces single use paths).

He shows how games fall into other complexity categories too. For example, games that feature pressure pads to open and close doors are PSPACE-hard if each door is controlled by two pressure plates. Doom falls into this category.

And so on.

The resulting list is impressive. Here are a few of his results:

Boulder Dash (First Star Software, 1984) is NP-hard.

Deflektor (Vortex Software, 1987) is in L.

Prince of Persia (Brøderbund, 1989) is PSPACE-complete.

Tron (Bally Midway, 1982) is NP-hard.

For the full list and reasoning, see the paper below.

That's clearly been a labour of love for Viglietta, given the title of his paper: "Gaming Is A Hard Job, But Someone Has To Do It!"

Interestingly, he says this kind of analysis is unnecessary for modern games. "Most recent commercial games incorporate Turing-equivalent scripting languages that easily allow the design of undecidable puzzles as part of the gameplay," he says.

In a way, that makes these older games all the more charming still.

Ref: arxiv.org/abs/1201.4995 :Gaming Is A Hard Job, But Someone Has To Do It!

Like as the waves make towards the pebbled shore,
So do our minutes hasten to their end;
Each changing place with that which goes before,
In sequent toil all forwards do contend.
Nativity, once in the main of light,
Crawls to maturity, wherewith being crown’d,
Crooked eclipses ‘gainst his glory fight,
And Time that gave doth now his gift confound.
Time doth transfix the flourish set on youth
And delves the parallels in beauty’s brow,
Feeds on the rarities of nature’s truth,
And nothing stands but for his scythe to mow:
And yet to times in hope my verse shall stand,
Praising thy worth, despite his cruel hand.

Sonnet No. 60, by William Shakespeare (1564-1616)

Please take the pledge not to do business with Elsevier. 404 scientists have done it so far:

• The cost of knowledge.

You can separately say you

1) won’t publish with them,
2) won’t referee for them, and/or
3) won’t do editorial work for them.

At least do number 2): how often can you do something good by doing less work? When a huge corporation relies so heavily on nasty monopolistic practices and unpaid volunteer labor, they leave themselves open to this.

This pledge website is the brainchild of Tim Gowers, a Fields medalist and prominent math blogger:

• Tim Gowers, Elsevier: my part in its downfall and http://thecostofknowledge.com.

In case you’re not familiar with the Elsevier problem, here’s something excerpted from my website. This does not yet mention Elsevier’s recent support of the Research Works Act, which would try to roll back the US government’s requirement that taxpayer-funded medical research be made freely available online. Nor does it mention the fake medical journals created by Elsevier, where what looked like peer-reviewed papers were secretly advertisements paid for by drug companies! Nor does it mention the Chaos, Solitons and Fractals fiasco. Indeed, it’s hard keeping up with Elsevier’s dirty deeds!

The problem and the solutions

The problem of highly priced science journals is well-known. A wave of mergers in the publishing business has created giant firms with the power to extract ever higher journal prices from university libraries. As a result, libraries are continually being forced to cough up more money or cut their journal subscriptions. It’s really become a crisis.

Luckily, there are also two counter-trends at work. In mathematics and physics, more and more papers are available from a free electronic database called the arXiv, and journals are beginning to let papers stay on this database even after they are published. In the life sciences, PubMed Central plays a similar role.

There are also a growing number of free journals. Many of these are peer-reviewed, and most are run by academics instead of large corporations.

The situation is worst in biology and medicine: the extremely profitable spinoffs of research in these subjects has made it easy for journals to charge outrageous prices and limit the free nature of discourse. A non-profit organization called the Public Library of Science was formed to fight this, and circulated an open letter calling on publishers to adopt reasonable policies. 30,000 scientists signed this and pledged to:

publish in, edit or review for, and personally subscribe to only those scholarly and scientific journals that have agreed to grant unrestricted free distribution rights to any and all original research reports that they have published, through PubMed Central and similar online public resources, within 6 months of their initial publication date.

Unsurprisingly, the response from publishers was chilly. As a result, the Public Library of Science started its own free journals in biology and medicine, with the help of a 9 million dollar grant from the Gordon and Betty Moore Foundation.

A number of other organizations are also pushing for free access to scholarly journals, such as Create Change, the Scholarly Publishing and Academic Resources Coalition, and the Budapest Open Access Initiative, funded by George Soros.

Editorial boards are beginning to wise up, too. On August 10, 2006, all the editors of the math journal Topology resigned to protest the outrageous prices of the publisher, Reed Elsevier. In August of this year, the editorial board of the Springer journal K-Theory followed suit. The Ecole Normale Superieure has also stopped having Elsevier publish the journal Annales Scientifiques de l’École Normale Supérieure.

So, we may just win this war! But only if we all do our part.

What we can do

What can we do to keep academic discourse freely available to all? Here are some things:

1. Don’t publish in overpriced journals.

2. Don’t do free work for overpriced journals (like refereeing and editing).

3. Put your articles on the arXiv or a similar site before publishing them.

4. Only publish in journals that let you keep your articles on the arXiv or a similar site.

5. Support free journals by publishing in them, refereeing for them, editing them… even starting your own!

6. Help make sure free journals and the arXiv stay free.

7. Help start a system of independent ‘referee boards‘ for arXiv papers. These can referee papers and help hiring, tenure and promotion committees to assess the worth of papers, eliminating the last remaining reasons for the existence of traditional for-profit journals.

The nice thing is that most of these are easy to do! Only items 5 through 7 require serious work. As for item 4, a lot of math and physics journals not only let you keep your article on the arXiv, but let you submit it by telling them its arXiv number! In math it’s easy to find these journals, because there’s a public list of them.

Of course, you should read the copyright agreement that you’ll be forced to sign before submitting to a journal or publishing a book. Check to see if you can keep your work on the arXiv, on your own website, etcetera. You can pretty much assume that any rights you don’t explicitly keep, your publisher will get. Eric Weisstein didn’t do this, and look what happened to him: he got sued and spent over a year in legal hell!

Luckily it’s not hard to read these copyright agreements: you can get them off the web. An extensive list is available from Sherpa, an organization devoted to free electronic archives.

If you think maybe you want to start your own journal, or move an existing journal to a cheaper publisher, read Joan Birman’s article about this. Go to the Create Change website and learn what other people are doing. Also check out SPARC—the Scholarly Publishing and Academic Resources Coalition. They can help. And try the Budapest Open Access Initiative—they give out grants.

You can also support the Public Library of Science or join the Open Archives Initiative.

Also: if you like mathematics, tell your librarian about Mathematical Sciences Publishers, a nonprofit organization run by mathematicians for the purpose of publishing low-cost, high-quality math journals.

Which journals are overpriced?

In 1997 Robion Kirby urged mathematicians not to submit papers to, nor edit for, nor referee for overpriced journals. I think this suggestion is great, and it applies not just to mathematics but all disciplines. There is really no good reason for us to donate our work to profit-making corporations who sell it back to us at exorbitant prices! Indeed in climate science this has a terrible effect: crackpot bloggers distribute their misinformation free of charge, while lots of important serious climate science papers are hidden, available only to people who work at institutions with expensive subscriptions.

But how can you tell if a journal is overpriced? In mathematics, Up-to-date information on the rise of journal prices is available from the American Mathematical Society. They even include an Excel spreadsheet that lets you do your own calculations with this data! Some of this information is nicely summarized on a webpage by Ulf Rehmann. Using these tools you can make up your own mind which journals are too expensive to be worth supporting with your free volunteer labor.

What about other subjects? I don’t know. Maybe you do?

When I first learned how bad the situation was, I started by boycotting all journals published by Reed Elsevier. This juggernaut was formed by merger of Reed Publishing and Elsevier Scientific Press in 1993. In August 2001 it bought Harcourt Press—which in turn owned Academic Press, which ran a journal I helped edit, Advances in Mathematics. I don’t work for that journal anymore! The reason is that Reed Elsevier is a particularly bad culprit when it comes to charging high prices. You can see this from the above lists of journal prices, and you can also see it in the business news. In 2002, Forbes magazine wrote:

If you are not a scientist or a lawyer, you might never guess which company is one of the world’s biggest in online revenue. Ebay will haul in only $1 billion this year. Amazon has $3.5 billion in revenue but is still, famously, losing money. Outperforming them both is Reed Elsevier, the London-based publishing company. Of its $8 billion in likely sales this year, $1.5 billion will come from online delivery of data, and its operating margin on the internet is a fabulous 22%.

Credit this accomplishment to two things. One is that Reed primarily sells not advertising or entertainment but the dry data used by lawyers, doctors, nurses, scientists and teachers. The other is its newfound marketing hustle: Its CEO since 1999 has been Crispin Davis, formerly a soap salesman.

But Davis will have to keep hustling to stay out of trouble. Reed Elsevier has fat margins and high prices in a business based on information—a commodity, and one that is cheaper than ever in the internet era. New technologies and increasingly universal access to free information make it vulnerable to attack from below. Today pirated music downloaded from the web ravages corporate profits in the music industry. Tomorrow could be the publishing industry’s turn.

Some customers accuse Reed Elsevier of price gouging. Daniel DeVito, a patent lawyer with Skadden, Arps, Slate, Meagher & Flom, is a fan of Reed’s legal-search service, but he himself does free science searches on the Google site before paying for something like Reed’s ScienceDirect—and often finds what he’s looking for at no cost. Reed can ill afford to rest.

Why should we slave away unpaid to keep Crispin Davis and his ilk rolling in dough? There’s really no good reason.

Sneaky tricks

To fight against the free journals and the arXiv, publishing companies are playing sneaky tricks like these:

• Proprietary Preprint Archives. Examples included ChemWeb and something they called "The Mathematics Preprint Server". The latter was especially devious, because mathematicians used to call the arXiv "the mathematics preprint server".

However, the Mathematics Preprint Server didn’t fool many smart people, so lots of the papers they got were crap, like a supposed proof of Goldbach’s conjecture, and a claim that the rotation of a galactic supercluster is due to a "topological defect" in spacetime. Eventually Elsevier gave up and stopped accepting new papers on their preprint server. Now it’s a laughable shadow of its former self. Similarly, ChemWeb was sold off.

• Web Spamming. More recently, publishers have tried a new trick: “web spamming”, also known as “search engine spamming” or “cloaking”. The company gives search engine crawlers access to full-text articles — but when you try to read these articles, you get a "doorway page" demanding a subscription or payment. Sometimes you’ll even be taken to a page that has nothing to do with the paper you thought you were about to see!

Culprits include Springer, Reed Elsevier, and the Institute of Electrical and Electronic Engineers. The last one seems to have quit — but check out their powerpoint presentation on this subject, courtesy of Carl Willis.

If you see pages like this, report them to Google or your favorite search engine.

• Journal Bundling. Worse still is the strategy of "bundling" subscriptions into huge all-or-nothing packages, so libraries can’t save money by ceasing to subscribe to a single journal. It’s a clever trap, especially because these bundled subscriptions look like a good deal at first. The cost becomes apparent only later. Now universities libraries are being bankrupted as the prices of these bundles keep soaring. The library of my own university, U.C. Riverside, barely has money for any books anymore!

Luckily, people are catching on. In 2003, Cornell University bravely dropped their subscription to 930 Elsevier journals. Four North Carolina universities have joined the revolt, and the University of California has also been battling Elsevier. For other actions universities have taken, read Peter Suber’s list.

• Legal bullying. Large corporations like to scare people by means of threats of legal action backed up by deep pockets. A classic example is the lawsuit launched by Gordon and Breach against the American Physical Society for publishing lists of journal prices. Luckily they lost this suit.

• Hiring a Dr. Evil lookalike as their PR consultant.

Click either of the pictures for an explanation.

Please take the pledge not to do business with Elsevier. 402 scientists have done it so far:

• The cost of knowledge.

You can separately say you 1) won’t publish with them, 2) won’t referee for them, and/or 3) won’t do editorial work. At least do number 2): activism is rarely so little work, but when a huge corporation relies so heavily on nasty monopolistic practices and unpaid volunteer labor, they leave themselves open to this.

This pledge website got started thanks to Tim Gowers:

• Tim Gowers, Elsevier: my part in its downfall and http://thecostofknowledge.com.

For more, see:

• Journal publishing reform, Polymath.
• John Baez, What we can do about science journals.

… and the many links therein!

In a campaign stop today along Florida’s Space Coast, Republican presidential candidate Newt Gingrich unveiled his vision for US goals in space: by 2020, he says, he wants a permanent base on the Moon. By then, he also wants constant near-Earth-orbit commercial activity supporting science, tourism and manufacturing — and he also wants a propulsion system in place by then that would allow a manned trip to Mars by 2030. He even suggests that he would devote 10% of NASA’s budget to support entrepreneurial prizes of the kind that spurred Lindbergh’s flight across the Atlantic.

The campaign stop in Cocoa came as Gingrich looked ahead to the 31 January primary election in Florida, a crucial state that could propel either Gingrich or his chief rival, Mitt Romney, to the Republican nomination.

Romney has made fun of Gingrich’s tendency to romanticize space — ‘Newt Skywalker’ is one of Gingrich’s self-acknowledged nicknames. But Gingrich is unabashed in his enthusiasm. “I have a deep passion about this because I’m old enough that I used to read Missiles and Rockets magazine,” he told supporters.  Yet even as he exhorted NASA to reach higher, he denigrated a bureaucratic culture that he says spends more time studying things than doing things. “It’s tragic to see what’s happened to our space programme over the last 30 years,” he says. “I’m sick of being told we have to be timid.”

How would Gingrich change NASA’s culture? He had several prescriptions. In addition to supporting tax-free prizes, he says that NASA should be attempting “five or eight” launches a day. NASA and the military should be working to make their rockets interchangeable, and extra space on rocket flights should not be wasted. Finally, he says that NASA should just be doing more things, and taking more risks: “1% of the studies and 10 times as many experiments”. Overall, it sounds a lot like the earlier NASA culture of “faster, better, cheaper” under former administrator Dan Goldin. “We want to become lean and aggressive,” Gingrich says.

Image credit: Gage Skidmore

As mentioned in the latest post on ABC, I am giving a short doctoral course on ABC methods and convergence at CREST next week. I have now made a preliminary collection of my slides (plus a few from Jean-Michel Marin’s), available on slideshare (as ABC in Roma, because I am also giving the course in Roma, next month, with an R lab on top of it!):

and I did manage to go over the book by Gouriéroux and Monfort on indirect inference over the weekend. I still need to beef up the slides before the course starts next Thursday! (The core version of the slides is actually from the course I gave in Wharton more than a year ago.)

The toy model of statistical entropy that I talked about the other day is the sort of thing that, were I a good computational physicist, I would've banged out very quickly. I'm not a good computational physicist, but by cargo-culting my way through some of the VPython examples, I managed to get something that mostly works:

The graph at the bottom of that window is the entropy versus "time" for a lattice of 20 sites with a 25% hopping probability (either left or right). The window with the colored balls at the upper left is a graphical representation-- red dots are "occupied" sites, white "unoccupied." The VPython code to do this is here: entropytestN2.py, from which you can see that I'm not much of a computational physicist, let alone a programmer (there are some really kludgey initialization steps that exist because it kept throwing strange errors when I did simpler things that should've worked, and I didn't have the patience to figure out the underlying problem).

It is, as I expected, kind of fun to play around with. I think there might be some bias built in that ends up pushing things to the right, but I'm not sure whether that's real or just my inability to recognize randomness. As expected, for small numbers of sites, you see frequent fluctuations down to zero, and as you increase the number of sites, significant decreases in entropy become much rarer.

I haven't attempted to do anything quantitative with this, because I don't know how to write data out from VPython into a form that any of my other analysis programs might use. If I think of a good way to do it, I might try to quantify this a little more, but for now, I'm happy just to have a working toy.

1. Minimal SUSY without fine-tuning predicts the Higgs mass close to the Z boson mass, that is about 90 GeV.
2. Minimal SUSY ignoring fine-tuning predicts the Higgs boson lighter than 160 GeV.
3. Non-minimal SUSY in general makes no predictions about the Higgs mass.
   

"[In the 1960s], I read many referee reports on my papers and discussed the matter with every theoretical physicist who was willing to listen; nobody that I contacted recognized the connection with the Planck proposal, and few took seriously the idea of [the Planck length] as a possible fundamental length. The view was nearly unanimous, not just that I had failed to prove my result, but that the Planck length could never play a fundamental role in physics. A minority held that there could be no fundamental length at all, but most were then convinced that a [different] fundamental length..., of the order of the proton Compton wavelength, was the wave of the future. Moreover, the people I contacted seemed to treat this much longer fundamental length as established fact, not speculation, despite the lack of actual evidence for it."

The first supernova of the year was spotted a couple of weeks ago: Supernova 2012A, in the galaxy NGC 3239 in the constellation of Leo. Adam Block of the Mount Lemmon SkyCenter took a phenomenal image of it:

[Click to corecollapsenate.]

Funny, the supernova isn’t what you’d expect; it’s not that really bright star (which is probably a star in our own galaxy that happens to be superposed on the galaxy) but instead the fainter one indicated. Images taken years ago show no sign of the new star.

The galaxy is called NGC 3239 (or Arp 263), and is a weird galaxy technically classified as irregular. Its distance isn’t well known, but it’s something like 25 million light years away or so. I imagine we’ll get a better distance determination very soon, since that’s important in understanding how much energy a supernova puts out.

The shape of the galaxy is probably the result of the collision of two separate galaxies which are still in the process of merging. The odd shape is a consequence of that. The pinkish glow is from gas clouds actively forming stars, and the overall blue tinge is from massive, hot, young stars, again probably triggered by the galaxy collisions. In fact, SN 2012A is the type of supernova formed when a massive star explodes, and these are short-lived stars.

The supernova is bright enough to be spotted in amateur-astronomy sized telescopes, so it’s getting some attention, like here and here and here. Adam Block has access to a telescope nearly a meter across which is equipped with an excellent camera, so his image is spectacular. I love all the background galaxies as well; we’re looking well away from the obscuring dust and junk floating around in our own galaxy, as well as toward a part of the Universe littered with distant galaxies.

It used to be that only a few dozen supernovae were discovered in a year, so the first one of a new year may not have been found for some time. Supernova 1987A — which I studied for my PhD — was the first one in 1987 and it was seen in the third week of February! Now, with robotic telescopes sweeping the skies with exquisite sensitivity, it’s rare to go a whole week in the new year without discovering one. And this is a numbers game: the more supernovae we find, the better we can understand them.

Image credit: Adam Block/Mount Lemmon SkyCenter/University of Arizona, used with permission.

A particularly long and mostly if locally coherent discourse by a single drunkard in the Paris métro this morning. Excerpts:

- Je préfére complet blanc, complet noir. Quand tu te regardes tout nu dans le miroir le matin, t’as pas de problème!

…

- Là-bas, y mange avec les macaques, y mange avec les rats, y nage avec les morts, y vit,  y tombe malade, c’est pas comme ici… Y peut pas tenir longtemps, y meurt au bout du compte, y peut pas fonder une famille, c´est pour cela que j’ai laissé tomber la mère…, c’est pas possible!

…

- Ici, c’est la Sibérie, essaie de dormir dehors, là, dans la voiture, tu peux pas dormir, tu deviens dingue. Y faut s’habituer, quand tu as l’habitude…., c’est plus facile.

There is a very good reason why I was silent in the past days. The reason is that I was involved in one of the most difficult article to write down since I do research (and are more than twenty years now!).  This paper arose during a very successful collaboration with two colleagues of mine: Alfonso Farina and Matteo Sedehi. Alfonso is a recognized worldwide authority in radar technology and last year has got a paper published here about the ubiquitous Tartaglia-Pascal triangle and its applications in several areas of mathematics and engineering. What was making Alfonso unsatisfied was the way the question of Tartaglia-Pascal triangle fits quantum mechanics. It appeared like this is somewhat an unsettled matter. Tartaglia-Pascal triangle gives, in the proper limit, the solution of the heat equation typical of Brownian motion, the most fundamental of all stochastic processes. But when one comes to the Schroedinger equation, notwithstanding the formal resemblance between these two equations, the presence of the imaginary term changes things dramatically. So, a wave packet of a free particle is seen to spread like the square of time rather than linearly. Then, Alfonso asked to me to try to clarify the situation and see what is the role of Tartaglia-Pascal triangle in quantum mechanics. This question is old almost as quantum mechanics itself. Several people tried to explain the probabilistic nature of quantum mechanics through some kind of Brownian motion of space and the most famous of these attempts is due to Edward Nelson. Nelson was able to show that there exists a stochastic process producing hydrodynamic equations from which the Schroedinger equation can be derived. This idea turns out to be a description of quantum mechanics similar to the way David Bohm devised it. So, this approach was exposed to criticisms that can be summed up in a paper by Peter Hänggi, Hermann Grabert and Peter Talkner (see here) denying any possible representation of quantum mechanics as a classical stochastic process.

So, it is clear that the situation appears rather difficult to clarify with such notable works. With Alfonso and Matteo, we have had several discussions and the conclusion was striking: Tartaglia-Pascal triangle appears in quantum mechanics rather with its square root! It appeared like quantum mechanics is not itself a classical stochastic process but the square root of it. This could explain why several excellent people could have escaped the link.

At this point, it became quite difficult to clarify the question of what a square root of a stochastic process as Brownian motion should be. There is nothing in literature and so I tried to ask to trained mathematicians to see if something in advanced research was known (see here). MathOverflow is a forum of discussion for advanced research managed by the community of mathematicians. It met a very great success and this is testified by the fact that practically all the most famous mathematicians give regular contributions to it. Posting my question resulted in a couple of favorable comments that informed me that this question was not known to have an answer. So, I spent a lot of time trying to clarify this idea using a lot of very good books that are available about stochastic processes. So, last few days I was able to get a finite answer: The square of Brownian motion is computable in a standard way with Itō integral reducing to a Brownian motion multiplied by a Bernoulli process. The striking fact is that the Bernoulli process is that of tossing a coin! The imaginary factor emerges naturally out of this mathematical procedure and now the diffusion equation is the Schroedinger equation. The identification of the Bernoulli process came out thanks to the help of Oleksandr Pavlyk after I asking this question at MathStackexchange. This forum is also for well-trained mathematicians but the kind of questions one can put there can also be at a student level. Oleksandr’s answer was instrumental for a complete understanding of what I was doing.

Finally, I decided to verify with the community of mathematicians if all this was nonsense or not and I posted again on MathStackexchange a derivation of the square root of a stochastic process (see here).  But, with my great surprise, I discovered that some concepts I used for the Itō calculus were not understandable at all. I gave them for granted but these were not defined in literature! So, after some discussions, I added important clarifications there and in my paper making clear what I was doing from a mathematical standpoint. Now, you can find all this in my article. Itō calculus must be extended to include all the ideas I was exploiting.

The link between quantum mechanics and stochastic processes is a fundamental one. The reason is that, if one get such a link, an understanding of the fundamental behavior of space-time is obtained. This appears a fluctuating entity but in an unexpected way. This entails a new reformulation of quantum mechanics with the language of stochastic processes. Given this link, any future theory of quantum gravity should recover it.

I take this chance to give publicly a great thank to all these people that helped me to reach this important understanding and that I have cited here. Also mathematicians that appeared anonymously were extremely useful to improve my work. Thank you very much, folks!

Update: After an interesting discussion here with Didier Piau and George Lowther, we reached the conclusion that the definitions I give in my paper to extend the definition of the Ito integral are not mathematically consistent. Rather, when one performs the corresponding Riemann sums one gets diverging results for the interesting values of the exponent and the absolute value. Presently, I cannot see any way to get a sensible definition for this and so this paper should be considered mathematically not consistent. Of course, the idea of quantum mechanics as the square root of a stochastic process is there to stay and to be eventually verified, possibly with different approaches and better mathematics.

Marco Frasca (2012). Quantum mechanics is the square root of a stochastic process arXiv arXiv: 1201.5091v1

Farina, A., Giompapa, S., Graziano, A., Liburdi, A., Ravanelli, M., & Zirilli, F. (2011). Tartaglia-Pascal’s triangle: a historical perspective with applications Signal, Image and Video Processing DOI: 10.1007/s11760-011-0228-6

Grabert, H., Hänggi, P., & Talkner, P. (1979). Is quantum mechanics equivalent to a classical stochastic process? Physical Review A, 19 (6), 2440-2445 DOI: 10.1103/PhysRevA.19.2440

I forgot to mention on this blog some important news about the Planck mission which many people here in the School of Physics & Astronomy at Cardiff University are heavily involved in.

Here is the official announcement from The Planck Science Team home page:

The High Frequency Instrument (HFI) on ESA’s Planck mission has completed its survey of the remnant light from the Big Bang. The sensor ran out of coolant on January 14 2012 as expected, ending its ability to detect this faint energy. Planck was launched in May 2009, and the minimum requirement for success was for the spacecraft to complete two whole surveys of the sky. In the end, Planck worked perfectly for 30 months, about twice the span originally required, and completed five full-sky surveys with both instruments. Able to work at slightly higher temperatures than HFI, the Low Frequency Instrument (LFI) will continue surveying the sky for a large part of 2012, providing even more data to improve the Planck final results.

For more details, see here. Basically, the HFI instrument consists of bolometers contained in a cryogenic system to keep them cool and thus suppress thermal noise in order to enable them to detect the very weak signals coming from the cosmic microwave background radiation. The helium required to maintain the low temperature is gradually lost as Planck operates, and has now run out. The HFI bolometers consequently warmed up, which makes them useless for cosmological work, so the instrument has been switched off. I’m sure you all understand how uncomfortable it is when your bolometers get too hot…

You can find a host of public information about Planck here but the scientific work is under strict embargo until early next year. However, as a Telescoper exclusive I am able to offer you a sneak preview of the top secret Planck data well in advance of official release. If you want to see what Planck scientists have been looking at for the last couple of years, just click here.

In almost any project, the path between “a good idea” and the “final exciting result” contained a proposal. It may have been a proposal to obtain access to scarce resources (like telescopes or accelerator beams), or it may be have been a proposal to obtain other more prosaic resources (i.e., money, to pay for the needed personnel and supplies). Whatever the nature of the proposal, however, I guarantee that the competition was ridiculously stiff, and that the odds of having any given proposal accepted were quite low (for reference, in most astronomy contexts, over-subscription rates tend to be factors of 5-10). These unfavorable odds can be incredibly demoralizing. They also can have profoundly negative impacts on a talented scientist’s career, if the odds never manage to tip in their favor.

Given the inspiration of the looming Hubble Space Telescope deadline, I thought I would share some of my “big picture” views on crafting successful proposals, expanding significantly on the more succinct advice given in an earlier post. While I’ve developed these opinions based on my experience in astronomy, I suspect they’d apply to many other fields, both within and beyond science. So here goes…

A Proposal is a Highly Structured Rigorous Argument

In its most abstract form, a proposal is a piece of persuasive writing that lays out a convincing case that the proposed research is:

1. important
2. feasible
3. efficient

By “important”, I mean that the project must rise above the level of “good to do”, and instead be seen as “must be done”, even by people who don’t work in the field. By “feasible”, I mean that there must be a clear path to a definitive scientific result. By “efficient”, I mean that the particular approach you’ve taken is the optimal one for reaching the important goals you’re targeting (i.e. aim for “Studying X provides the cleanest test of Important Science Y” and avoid building a proposal to study X when studying Z is clearly a more direct approach to Important Science Y — even if you worked on X for your thesis.)

You should lay out your arguments for Every. Single. One. of these cases before you write a single word of latex. Why? Because proposals live or die not on the beauty of your prose, but on the structure of your argument. If the reviewer does not believe that you’ve made the case for importance, feasibility, and efficiency, you’re done.

Here’s how I do this. Although I’m sure it will seem remedial to many of you, and reveal me as the anal geek that I am, I start a stupid ASCII file with two sections:

1. Selling Points
2. Potential Weaknesses to Shore Up

I then start filling out each with short bullet points listing every possible argument for or against what I’m proposing.

The selling points should be fairly easy, since you’re likely to write proposals for things you are inclined to think are awesome. Do, however, avoid the pitfall of conflating “important to me” with “important to Science”. Just because you would really like to know more about some property of something you’re interested in, doesn’t mean that other people will naturally share your enthusiasm. Keep your eye on the big picture.

The “Potential Weaknesses” section can be a bit trickier, since you need to channel your inner crabby reviewer. Think of every nit-picky, outside the box criticism one could throw at your idea, and every area where a reviewer could get confused. (As an example, here’s a list of some of the self-criticisms I came up with for an HST proposal for NIR observations of nearby galaxies a few years back: “What about AO from the ground?” “Why this many targets — how many do you actually need?” “What about dust (i.e. is 1 NIR filter OK)?” “Are the models really in need of improvement?” “How can we claim to do galaxy science while simultaneously arguing that the models aren’t yet up to it?” “Are the results confused depending on fraction of O-rich vs C-rich AGB?” etc).

In short, the “Selling Points” section is about demonstrating “importance”, and the “Potential Weaknesses” section is about assessing “feasibility” and “efficiency”.

After you’ve got an initial list, you have to step back, evaluate, and edit.

• Go through the selling points and prioritize. Decide what the “main message” of your proposal is, based on which bullet points speak most effectively to the larger importance of what you’re proposing. If your ideas are strong, you’ll usually find that several of the most compelling bullet points will group together and can be ordered to tell a single story. You’ll also find that some of the bullet points will not naturally fit within that narrative. Identify this subset of arguments that are “nice, but not compelling”. You’ll want to be sure to minimize these in the proposal, to avoid their distracting from a more central idea. I speak from experience when I say that you really do not want to confuse the reviewers about what your proposal is about (i.e. It’s better to have something like “Dark Matter! Dark Matter! Dark Matter! and by the way it also tells you something about planets, frogs, and quark stars” rather than “Dark Matter! Planets! Frogs! Quark Stars!”, since the latter leads to complaints from the reviewers that while they believed your dark matter ideas, you had not fully fleshed out a compelling case for the frog science.) 
• For each entry in the “Potential Weakness” section, write down any brief ideas about addressing those concerns (something like “Make figure showing evolution of models with time” “Check number of stars expected and compare to sizes of Galactic samples”, etc). You don’t have to come up with definitive answers, but you should lay out a road map for what you need to do to make your experiment look feasible and efficient.

At this point, I sometimes make a third section and list a few figures that seem like they support the key scientific ideas, or that shore up some of the obvious weaknesses.

Now that you have this silly little ASCII file (which you shouldn’t spend more than a day on, if that), send it to your collaborators. Get their feedback about what they think the strongest selling points are, what their additional concerns are, and what arguments they would use to shore up weaknesses. Expand the file accordingly, so you have a record of everything that you think needs to go into the proposal. You’ll probably find that it’s a huge time savings to get this to your collaborators in this form, before you have a 10 page latex file with embedded figures. If you do the latter, your collaborator will likely come back and say “You know, I think the reviewers are going to be way more interested in frogs”, at which point you have to chuck out weeks of work. With this method, you get feedback quickly (since they have to skim a very short list of bullet points), and you don’t have a lot of sunk costs if you decide to overhaul the arguement.

At this point you’ll have a document that summarizes your rhetorical argument. Your case will be laid out so that you can easily evaluate it on its scientific merits. So, before you dive into writing, you need to step back and decide if you’ve actually constructed a strong case. Sometimes, it will become obvious that there are too many weaknesses to address, and that it’s going to be an uphill battle to convince anyone that this needs to be done. If that’s the case DON’T WRITE THE PROPOSAL! I have probably a half dozen of these ASCII files where I spent half a day deciding that I didn’t, in fact, have a compelling project, and I’d be better off investing my time elsewhere. That’s OK! The exercise of structuring your argument first is designed to be fast, so you don’t sink much time in before you decide whether to continue or not.

Once you (and your collaborators) are convinced that you do in fact have a strong case, you need to start building the actual text. I frequently will estimate the number of paragraphs I expect to have for my scientific justification (usually 2.5-3 per page), and then make an enumerated list showing how the argument will flow through the paragraphs. This exercise helps to keep the text following the structure of the argument, so that it builds to make the main points. It also helps me to figure out when I’m trying to cram too much information in.

If you’ve gone through all of the above, you’ll find that the proposal will almost write itself. You will have cleanly separated “generating text” from “generating a compelling project”, such that you know exactly what you want to convey, and what the text needs to accomplish. Generating lovely English sentences at this point is much easier.

The perfect secrecy offered by quantum mechanics appears to have been scuppered by a previously unknown practical problem, say physicists.

The problem of sending messages securely has troubled humankind since the dawn of civilisation and probably before. 

In recent years, however, physicists have raised expectations that this problem has been solved by the invention of quantum key distribution. This exploits the strange quantum property of entanglement to guarantee the secrecy of a message.

Entanglement is so fragile that any eavesdropper cannot help but break it, revealing the ruse. So cryptographers can use it to send a secure key called a one time pad that can then be used to encrypt a message. If the key is intercepted, the sender simply sends another and repeats this until one gets through.

So-called quantum key distribution is unconditionally secure--it offers perfect secrecy guaranteed by the laws of physics.

Or at least that's what everyone thought. More recently, various groups have begun to focus on a fly in the ointment: the practical implementation of this process. While quantum key distribution offers perfect security in practice, the devices used to send quantum messages are inevitably imperfect.

For example, lasers that are supposed to send one photon at a time can sometimes send several and this allows information to leak to an eavesdropper. 

Last year, we discussed another trick used by a group of quantum hackers to eavesdrop on a commercial quantum cryptography system. This system, although theoretically secure, turned out to be embarrassingly vulnerable in practice. 

That led quantum theorists to begin the search for a device-independent protocol that would be free of the practical imperfections of everyday equipment. Such a system would offer guaranteed security regardless of any weaknesses in the equipment it relies on.  

Today, however, Jonathan Barrett at the Royal Holloway, University of London, and a few pals reveal a problem that looks to scupper this work. The worrying implication of their discovery is that there is no known way to guarantee the security of data sent on any quantum cryptographic system including those that are commercially available today. 

Here's the problem. Some groups claim to have made progress in developing  device-independent protocols but Barrett and co have found an issue that all others appear to have overlooked. These protocols all treat quantum cryptography as a single-shot process, as if the equipment is used only once. 

The question that Barrett and co consider is what tricks could a malicious manufacturer exploit in a device that is likely to be used more than ince. The answer is obvious: such a manufacturer could build in a memory that stores information before it is transmitted. This information would then be released when the device is reused.  

"In short, the problem is that an adversary can program devices to store data in one protocol and leak it in subsequent protocols, in ways that are hard or impossible to counter if the devices are reused," say Barrett and co.   

This is a particular worry, they say, because there is no general technique for identifying security loopholes in standard cryptography devices.

Of course, there are a couple of simple ways round this new problem. The most obvious is to discard a quantum cryptography device after it has been used; to actually make the equipment single-use like a disposable camera. 

But Barrett and friends think this impractical: "While these attacks can be countered by not reusing devices, this solution is so costly that we query whether it is generally practical."

Another is based on the fact that the security of message is guaranteed until the device is re-used. So quantum cryptography could still be used only for secrets that need to be kept only for a short period of time, until the equipment is re-used.

Neither of these is going to stop blood pressures rising at the various government and military organisations that have bet the farm on the guarantees that quantum cryptography was thought to provide. That's not to mention the commercial organisations offering quantum cryptography such as ID Quantique.

There may be other ways round this problem that have yet to emerge. Indeed, Barrett and co's ideas will be an important driver of future work. 

In the meantime, they conclude: "In our view, the attacks are generic and problematic enough to merit a serious reappraisal of the scope for device-independent quantum cryptography as a practical technology."

That'll mean more than few a few sleepless nights over this.

Ref: arxiv.org/abs/1201.4407: Prisoners Of Their Own Device: Trojan Attacks On Device-Independent Quantum Cryptography

The Alice experiment completes during shutdown the electromagnetic calorimeter on the outer arc: Alice researcher Peter Jacobs explains the installation on youtube.

CERN: EMCal supermodule is guided into ALICE.

You might also be interested in the Alice 2011-2012 shutdown summary report detailing the various ongoing work.

Since we’re now approaching the time when the preliminary results from December on the search for the Higgs particle at the Large Hadron Collider (LHC) will be presented in final form, possibly with small but important adjustments, and since there will be additional results based on the fall’s data in the next few weeks, it would be good to do a little review of where things stand and where they’re going.  I won’t do this all in one post but let’s get started.

Of course there is a lot of material on this website already and I’ll point you to it.  Perhaps my most concise and least technical discussion of the search for the Higgs appeared as a guest post on Cosmic Variance (thank you to Sean Carroll for the invitation.)  In that post I emphasized that the LHC’s Higgs program has two phases (broadly speaking.)  The first phase is to search for and either find or exclude the simplest possible form of Higgs particle, known as the Standard Model Higgs particle (or SM Higgs for short).  This is a finite task, so at a certain point (presumably this year) this phase comes to an end.  The second phase, which will take a better part of a decade, and (as I’ll describe over time) begins this year, depends on whether a particle that resembles an SM Higgs is discovered or not.  To explain the basic logic, I presented a figure in the Cosmic Variance post, which I am reproducing here:

Fig. 1: From my guest post in Cosmic Variance: The basic logic of the Higgs search, showing Phase 1 in which the simplest form of Higgs particle (the Standard Model Higgs) is found or excluded, and the logical questions that will follow in Phase 2. See Figure 3 for a more complete version.

If you’ve been noticing how slowly the discovery of the Higgs takes place — first there are hints, and only months later can one know whether those hints are real or not — then it will not surprise you to learn that the line between Phase 1 and Phase 2 isn’t sharp. The scientists at the LHC experiments ATLAS and CMS will be doing both of them this year, because they can, and because they should.

• The search for the SM Higgs in 2011 was so successful that only a few possibilities remain (see Figure 2): a Higgs between about 115 and 128 GeV/c² or above 600 GeV/c² (though the latter is disfavored by precision measurements.)
• We’ve got clear-enough hints for a Higgs particle with a mass of about 125 GeV/c² (where c is the speed of light and GeV is defined here) to take seriously the possibility that it’s been found.
• If it’s been found, it resembles (only roughly so far, but that’s perhaps because there’s not enough data yet) an SM Higgs particle.
• All that remains to be done in Phase 1 is to close the window between 115 and 127 GeV/c² , to confirm or refute the hints around 125, and push up the limits at 600 up as far as they can go, perhaps 800 and beyond.

Fig. 2: Phase 1 of the Higgs search now leaves only a tiny window at small masses and a window at large masses that is disfavored by two decades of precision measurements. Notice how much progress was made in 2011 alone!

So we can start looking ahead to Phase 2 — indeed we must.    In particular, if there is indeed a new particle with a mass of 125 GeV/c² that resembles an SM Higgs, then (from Figure 1) we now have to verify whether it is or isn’t exactly what the Standard Model predicts.  Any deviation whatsoever from the precise predictions of the Standard Model would be a historic, game-changing, and Nobel Prize-deserving discovery!  So the stakes are very high.

Now, Figure 1 was actually a simplified version of the game plan for the Higgs search.  A more complete version, which was too elaborate for the short and sweet Cosmic Variance article, is shown in Figure 3.  I’ll go through this figure carefully (which itself isn’t entirely complete) over the coming days and weeks.  But suffice it to say that 2012 will involve a lot of work on the three research programs located at the far right of the figure:

• Keep doing what we’ve been doing in the SM Higgs search (as described in the three articles here) but with more data.  Specifically, if there is a new particle at 125  GeV/c² we want to make sure that it is produced and that it decays as expected of an SM Higgs particle.
• Focus especially on production of the Higgs in the process (the second of five production processes described here) known as q q –> q q H, which involves the scattering of W and Z virtual particles (which aren’t really particles at all, but rather are more general disturbances in the W and Z fields.)  This process is a very powerful test of whether any newly found particle is an SM Higgs particle or not.
• Look for something that shouldn’t be there if there is only an SM Higgs particle: exotic modes of production, or exotic decays, or a second Higgs particle. As I’ve not previously described the large class of searches required, I will write one or more articles about this soon.

Fig. 3: As Phase 1 of the Higgs search comes to a close, Phase 2 begins, with a series of logical questions and corresponding measurements. Even while the hints of a Higgs particle at 125 GeV are being checked with more data, studies of whether this might or might not be a Standard Model Higgs particle will be underway.

As you can see from the figure, these very large research programs needs to be carried out whether or not the current hints of a Higgs turn out to be ephemeral.  In other words, the experimenters can be working already on Phase 2 no matter what the outcome of Phase 1 turns out to be!  Very convenient, of course…  but it means we need to do some planning for Phase 2 now!  [And not of all of the most urgent issues have been addressed yet, which is why I've been very busy... more on that later...]

So, back when How to Teach Physics to Your Dog was coming out, I did a few "dramatic readings" of bits of the book, such as this one on the Quantum Zeno Effect:

This was made with Windows Movie Maker, because it was free (came with the computer) and dead simple. However, Movie Maker on my new computers is hopelessly broken-- I've made a couple of attempts to do the same sort of thing with my laptop, but I've never managed to get more than a couple of steps in before it crashes. (To be fair, this is one of only two things that are worse under Windows 7 than Vista, and the only one that's Microsoft's fault...)

For that reason, I'm looking for an alternative: I need some non-Movie Maker software package that will let me do the same sort of thing I did in that video: record an audio track of me reading a bit of the book, and put together video to go with it out of still photos and maybe short video clips. I could, of course, simply Google this, but I value the opinions of my wise and worldly readers more than random reviewers on some other site, so if you know of a good (and preferably cheap) program that will let me do this, leave a recommendation in the comments.

On 13 February 2012, I will give a talk at Google in the form of a robot. I will look like this:

My talk will be about “Energy, the Environment and What We Can Do.” Since I think we should cut unnecessary travel, I decided to stay here in Singapore and use a telepresence robot instead of flying to California.

I thank Mike Stay for arranging this at Google, and I especially thank Trevor Blackwell and everyone else at Anybots for letting me use one of their robots!

I believe Google will film this event and make a video available. But I hope reporters attend, because it should be fun, and I plan to describe some ways we can slash carbon emissions.

More detail: I will give this talk at 4 pm Monday, February 13, 2012 in the Paramaribo Room on the Google campus (Building 42, Floor 2). Visitors and reporters are invited, but they need to check in at the main visitor’s lounge in Building 43, and they’ll need to be escorted to and from the talk, so someone will pick them up 10 or 15 minutes before the talk starts.

Energy, the Environment and What We Can Do

Abstract: Our heavy reliance on fossil fuels is causing two serious problems: global warming, and the decline of cheaply available oil reserves. Unfortunately the second problem will not cancel out the first. Each one individually seems extremely hard to solve, and taken
together they demand a major worldwide effort starting now. After an overview of these problems, we turn to the question: what can we do about them?

I also need help from all of you reading this! I want to talk about solutions, not just problems—and given my audience, and the political deadlock in the US, I especially want to talk about innovative solutions that come from individuals and companies, not governments.

Can changing whole systems produce massive cuts in carbon emissions, in a way that spreads virally rather than being imposed through top-down directives? It’s possible. Curtis Faith has some inspiring thoughts on this:

I’ve been looking on various transportation and energy and environment issues for more than 5 years, and almost no one gets the idea that we can radically reduce consumption if we look at the complete systems. In economic terms, we currently have a suboptimal Nash Equilibrium with a diminishing pie when an optimal expanding pie equilibrium is possible. Just tossing around ideas a a very high level with back of the envelope estimates we can get orders of magnitude improvements with systemic changes that will make people’s lives better if we can loosen up the grip of the big corporations and government.

To borrow a physics analogy, the Nash Equilibrium is a bit like a multi-dimensional metastable state where the system is locked into a high energy configuration and any local attempts to make the change revert to the higher energy configuration locally, so it would require sufficient energy or energy in exactly the right form to move all the different metastable states off their equilibrium either simultaneously or in a cascade.

Ideally, we find the right set of systemic economic changes that can have a cascade effect, so that they are locally systemically optimal and can compete more effectively within the larger system where the Nash Equilibrium dominates. I hope I haven’t mixed up too many terms from too many fields and confused things. These terms all have overlapping and sometimes very different meaning in the different contexts as I’m sure is true even within math and science.

One great example is transportation. We assume we need electric cars or biofuel or some such thing. But the very assumption that a car is necessary is flawed. Why do people want cars? Give them a better alternative and they’ll stop wanting cars. Now, what that might be? Public transportation? No. All the money spent building a 2,000 kg vehicle to accelerate and decelerate a few hundred kg and then to replace that vehicle on a regular basis can be saved if we eliminate the need for cars.

The best alternative to cars is walking, or walking on inclined pathways up and down so we get exercise. Why don’t people walk? Not because they don’t want to but because our cities and towns have optimized for cars. Create walkable neighborhoods and give people jobs near their home and you eliminate the need for cars. I live in Savannah, GA in a very tiny place. I never use the car. Perhaps 5 miles a week. And even that wouldn’t be necessary with the right supplemental business structures to provide services more efficiently.

Or electricity for A/C. Everyone lives isolated in structures that are very inefficient to heat. Large community structures could be air conditioned naturally using various techniques and that could cut electricity demand by 50% for neighborhoods. Shade trees are better than insulation.

Or how about moving virtually entire cities to cooler climates during the hot months? That is what people used to do. Take a train North for the summer. If the destinations are low-resource destinations, this can be a huge reduction for the city. Again, getting to this state is hard without changing a lot of parts together.

These problems are not technical, or political, they are economic. We need the economic systems that support these alternatives. People want them. We’ll all be happier and use far less resources (and money). The economic system needs to be changed, and that isn’t going to happen with politics, it will happen with economic innovation. We tend to think of our current models as the way things are, but they aren’t. Most of the status quo is comprised of human inventions, money, fractional reserve banking, corporations, etc. They all brought specific improvements that made them more effective at the time they were introduce because of the conditions during those times. Our times too are different. Some new models will work much better for solving our current problems.

Your idea really starts to address the reason why people fly unnecessarily. This change in perspective is important. What if we went back to sailing ships? And instead of flying we took long leisurely educational seminar cruises on modern versions of sail yachts? What if we improved our trains? But we need to start from scratch and design new systems so they work together effectively. Why are we stuck with models of cities based on the 19th-century norms?

We aren’t, but too many people think we are because the scope of their job or academic career is just the piece of a system, not the system itself.

System level design thinking is the key to making the difference we need. Changes to the complete systems can have order of magnitude improvements. Changes to the parts will have us fighting for tens of percentages.

Do you know good references on ideas like this—preferably with actual numbers? I’ve done some research, but I feel I must be missing a lot of things.

This book, for example, is interesting:

• Michael Peters, Shane Fudge and Tim Jackson, editors, Low Carbon Communities: Imaginative Approaches to Combating Climate Change Locally, Edward Elgar Publishing Group, Cheltenham, UK, 2010.

but I wish it had more numbers on how much carbon emissions were cut by some of the projects they describe: Energy Conscious Households in Action, the HadLOW CARBON Community, the Transition Network, and so on.

A non-destructive method for imaging single proteins could help solve one of the biggest challenges in biology

The behaviour and function of proteins is largely determined by their shape.  So one of the great ongoing quests in biology is to understand and model the structure of proteins. 

That's a tricky task. Biologists currently do it using techniques such as X-ray crystallography, which requires millions of protein chains to form into a crystal.  The trouble is that most proteins don't form crystals. And even when they do, not all the molecules will be in the same conformation and so the diffraction pattern can end up being a kind of average of several different shapes.

That's why biologists know the shape of less than 2 per cent of the proteins in humans.

What's needed, of course, is a way of imaging individual proteins. One idea is to us x-rays or electron beams to do the trick and indeed some groups have had some success with this technique. But the disadvantage is that beams with an energy of a few KeV tend to destroy biomolecules so it's not clear how accurate these images can be. Nether is it possible to view the molecules over time.

Today, Jean Nicholas Longchamp and pals at the University of Zurich in Switzerland have found a way round this. These guys make the entirely sensible suggestion of imaging proteins using low energy electron beams that don't destroy biomolecules. 

At this energy, electron beams have a wavelength of a nanometre or so, making them perfect not just for imaging with atomic resolution, but for holography. 

And that's exactly what these guys have done. They've created an electron hologram of a protein molecule called ferritin--that's the football-shaped protein that stores and releases iron and is found in almost all living things.

The technique is fairly straightforward. They mix ferritin and carbon nanotubes in water which they then allow to evaporate. This leaves carbon nanotubes with single ferritin proteins bonded to them.

The evaporation takes place in a sieve-like container and leaves some of the ferritin-carrying nanotubes suspended across the holes in the sieve. That allows Longchamp and co to send the low energy electron beam from one side of the hole and then record the interference pattern on the other. 

The result is the first atomic resolution electron hologram of ferritin ever made in a non-destructive way. "We have reported the very first non-destructive investigation of an individual protein by means of  low-energy electron holography," they say.

They've even compared their images to ones of ferritin imaged with high energy electrons and are able to show the damage that the high energy bombardment causes.

That's exciting news. The problem of accurately determining the structure, and therefore the function, of proteins is a major headache for biologists and one that low energy electron holography could help to solve quickly. "The sample preparation method can be applied to a broad class of molecules," say Longchamp and friends.

They now want to improve the resolution of their technique and have a number of tricks up their sleeves that they are no doubt investigating.

Given that the techniques is relatively straightforward and inexpensive, expect to see an explosion of interest in single molecule structural biology at atomic resolution.

Ref: arxiv.org/abs/1201.4300: Non-Destructive Imaging Of An Individual Protein

I'm fairly certain somebody has already done this, because it's such an obvious idea. It's a little beyond my cargo-cult VPython skills right at the moment, though (I can probably learn to do it, but not right now), and I none of the applets I Googled up seemed to be doing this, so I'm posting this sketchy description because I've spent some time thinking about it, and might as well get a blog post out of the deal.

So, as we said back in the holiday season, one of the most fundamental concepts in the modern understanding of thermodynamics and statistical physics is the notion of entropy. You can also argue that entropy is in some sense responsible for our perception of time-- that is, the reason we see time marching forward into the future, not backwards into the past is that entropy increases as we move forward, and it's the increase in entropy that determines the arrow of time.

We can define entropy using Boltzmann's formula:

which says that the entropy of a given arrangement of microscopic objects (atoms or molecules in a gas, say) is related to the number of possible ways that you can arrange those objects to produce states that are macroscopically indistinguishable. The more states that look the same on a coarse scale, the higher the entropy. This makes the arrow of time a sort of statistical property: entropy tends to increase because it's easy for a collection of stuff to randomly move toward a high-entropy state (which you can do lots of ways) but unlikely that a random motion will take you to a low-entropy state (which can only be made a few ways).

Boltzmann's idea is simple and powerful, but it can be a little hard to do anything more than qualitative hand-waving with it at the intro level. It's kind of hard to explain how you "count" microstates of things that are (classically) continuous variables, like the velocities of atoms in a gas, without getting infinite results.

So, here's my rough idea, that I might still try to code into a model for my timekeeping class this term: Rather than thinking about continuous variables, let's think about a lattice of points that may or may not contain an atom. It's easiest to picture in 1-d, where a low-entropy starting state might look something like this:

1 1 1 1 1 0 0 0 0 0

This represents all of the "atoms" being on one side of the lattice representing space.. Then you just allow each "atom" some probability of moving either left or right to an unoccupied space. So, for example, a few time steps later, the state might look like this:

After last year decision that the Royal society opens journal archive. It has now been decided: Royal Society journal archive made permanently free to access.

Professor Uta Frith FRS, Chair of the Royal Society library committee, said: 'I'm delighted that the Royal Society is continuing to increase access to its wonderful resources by opening up its publishing archives.'

We are in the process of finalizing a little article:

Domenico Fiorenza, Hisham Sati, Urs Schreiber,
Multiple M5-branes, String 2-connections, and 7d nonabelian Chern-Simons theory

Below is the abstract, and, below the fold, the beginning of the introduction. A pdf with the current version is behind the above link.

We would be grateful for comments.

The article is written in a non-formal style with an audience of certain physicists in mind, but ample pointers are given to places where all the ingredients are spelled out in detail and precisely.

Abstract

The worldvolume theory of coincident M5-branes is expected to contain a nonabelian 2-form/nonabelian gerbe gauge theory that is a higher analog of self-dual Yang-Mills theory. But the precise details – in particular the global moduli / instanton / magnetic charge structure – have remained elusive.

Here we argue that the holographic dual of this nonabelian 2-form field, under ${\mathrm{AdS}}_7/{\mathrm{CFT}}_6$ duality, can be deduced from anomaly cancellation.

We find this way a 7-dimensional nonabelian Chern-Simons theory of twisted String 2-connection fields, which, in a certain higher gauge, are given locally by non-abelian 2-forms with values in a Kac-Moody loop Lie algebra. We construct the corresponding action functional on the entire smooth moduli 2-stack of field configurations, thereby defining the theory globally, at all levels and with the full instanton structure, which is nontrivial due to the twists imposed by the quantum corrections. Along the way we explain some general phenomena of higher nonabelian gauge theory that we need.

Introduction

The quantum field theory (QFT) on the worldvolume of M5-branes is known to be a 6-dimensional (2,0)-superconformal theory that contains a 2-form potential field $B_2$, whose 3-form field strength $H_3$ is self-dual. Whatever it is precisely and in generality, this QFT has been argued to be the source of deep physical and mathematical phenomena, such as Montonen-Olive S-duality, geometric Langlands duality, and Khovanov homology. Yet, and despite this interest, a complete description of the precise details of this QFT is still lacking.

In particular, as soon as one considers the worldvolume theory of several coincident M5-branes, the 2-form appearing locally in this 6d QFT is expected to be nonabelian (to take values in a nonabelian Lie algebra). But a description of this nonabelian gerbe theory has been elusive. Here we present a consistent formulation of nonabelian 2-form fields and propose dynamics for them under holography.

On the other hand, for a single M5-brane the Lagrangian of the theory has been formulated. Furthermore, in this abelian case there is a holographic dual description of the 6d theory by 7-dimensional abelian Chern-Simons theory, as part of ${\mathrm{AdS}}_7/{\mathrm{CFT}}_6$-duality.

We give here an argument, following Witten96, Witten98 but taking the quantum anomaly cancellation of the M5-brane in 11-dimensional supergravity into account, that in the general case the ${\mathrm{AdS}}_7$/${\mathrm{CFT}}_6$-duality involves a 7-dimensional nonabelian Chern-Simons action that is evaluated on higher nonabelian gauge fields which we identify as _twisted 2-connections over the String-2-group.

Then we give a precise description of a certain canonically existing 7-dimensional nonabelian gerbe-theory on boundary values of quantum-corrected supergravity field configurations in terms of nonabelian differential cohomology. We show that this has the properties expected from the quantum anomaly structure of 11-dimensional supergravity. In particular, we discuss that there is a higher gauge in which these field configurations locally involve non-abelian 2-forms with values in the Kac-Moody central extension of the loop Lie algebra of the special orthogonal Lie algebra $\mathrm{𝔰𝔬}$ and of the exceptional Lie algebra of E8. We also describe the global structure of the smooth moduli 2-stack of field configurations, which is more subtle.

I showed you last time that in many branches of physics—including classical mechanics and thermodynamics—we can see our task as minimizing or maximizing some function. Today I want to show how we get from that task to symplectic geometry.

So, suppose we have a smooth function

where is some manifold. A minimum or maximum of can only occur at a point where

Here the differential which is a 1-form on If we pick local coordinates in some open set of then we have

and these derivatives are very interesting. Let’s see why:

Example 1. In classical mechanics, consider a particle on a manifold Suppose the particle starts at some fixed position at some fixed time. Suppose that it ends up at the position at time Then the particle will seek to follow a path that minimizes the action given these conditions. Assume this path exists and is unique. The action of this path is then called Hamilton’s principal function, Let

and assume Hamilton’s principal function is a smooth function

We then have

where are local coordinates on

is called the momentum in the ith direction, and

is called the energy. The minus signs here are basically just a mild nuisance. Time is different from space, and in special relativity the difference comes from a minus sign, but I don’t think that’s the explanation here. We could get rid of the minus signs by working with negative energy, but it’s not such a big deal.

Example 2. In thermodynamics, consider a system with the internal energy and volume Then the system will choose a state that maximizes the entropy given these constraints. Assume this state exists and is unique. Call the entropy of this state Let

and assume the entropy is a smooth function

We then have

where is the temperature of the system, and is the pressure. The slight awkwardness of this formula makes people favor other setups.

Example 3. In thermodynamics there are many setups for studying the same system using different minimum or maximum principles. One of the most popular is called the energy scheme. If internal energy increases with increasing entropy, as usually the case, this scheme is equivalent to the one we just saw.

In the energy scheme we fix the entropy and volume Then the system will choose a state that minimizes the internal energy given these constraints. Assume this state exists and is unique. Call the internal energy of this state Let

and assume the entropy is a smooth function

We then have

where

is the temperature, and

is the pressure. You’ll note the formulas here closely resemble those in Example 1!

Example 4. Here are the four most popular schemes for thermodynamics:

• If we fix the entropy and volume the system will choose a state that minimizes the internal energy

• If we fix the entropy and pressure the system will choose a state that minimizes the enthalpy

• If we fix the temperature and volume the system will choose a state that minimizes the Helmholtz free energy

• If we fix the temperature and pressure the system will choose a state that minimizes the Gibbs free energy

These quantities are related by a pack of similar-looking formulas, from which we may derive a mind-numbing little labyrinth of Maxwell relations. But for now, all we need to know is that all these approaches to thermodynamics are equivalent given some reasonable assumptions, and all the formulas and relations can be derived using the Legendre transformation trick I explained last time. So, I won’t repeat what we did in Example 3 for all these other cases!

Example 5. In classical statics, consider a particle on a manifold This particle will seek to minimize its potential energy which we’ll assume is some smooth function of its position We then have

where are local coordinates on and

is called the force in the ith direction.

Conjugate variables

So, the partial derivatives of the quantity we’re trying
to minimize or maximize are very important! As a result, we often want to give them more of an equal status as independent quantities in their own right. Then we call them ‘conjugate variables’.

To make this precise, consider the cotangent bundle which has local coordinates (coming from the coordinates on ) and (the corresponding coordinates on each cotangent space). We then call the conjugate variable of the coordinate

Given a smooth function

the 1-form can be seen as a section of the cotangent bundle. The graph of this section is defined by the equation

and this equation ties together two intuitions about ‘conjugate variables’: as coordinates on the cotangent bundle, and as partial derivatives of the quantity we’re trying to minimize or maximize.

The tautological 1-form

There is a lot to say here, especially about Legendre transformations, but I want to hasten on to a bit of symplectic geometry. And for this we need the ‘tautological 1-form’ on

We can think of as a map

sending each point to the point where is defined by the equation we just saw:

Using this map, we can pull back any 1-form on to get a 1-form on

What 1-form on might we like to get? Why, of course!

Amazingly, there’s a 1-form on such that when we pull it back using the map we get the 1-form —no matter what smooth function we started with!

Thanks to this wonderfully tautological property, is called the tautological 1-form on You should check that it’s given by the formula

If you get stuck, try this.

So, if we want to see how much changes as we move along a path in we can do this in three equivalent ways:

• Evaluate at the endpoint of the path and subtract off at the starting-point.

• Integrate the 1-form along the path.

• Use to map the path over to and then integrate over this path in

The last method is equivalent thanks to the ‘tautological’ property of It may seem overly convoluted, but it shows that if we work in where the conjugate variables are accorded equal status, everything we want to know about the change in is contained in the 1-form no matter which function we decide to use!

So, in this sense, knows everything there is to know about the change in Hamilton’s principal function in classical mechanics, or the change in entropy in thermodynamics… and so on!

But this means it must know about things like Hamilton’s equations, and the Maxwell relations.

The symplectic structure

We saw last time that the fundamental equations of classical mechanics and thermodynamics—Hamilton’s equations and the Maxwell relations—are mathematically just the same. They both say simply that partial derivatives commute:

where is the function we’re trying to minimize or maximize.

I also mentioned that this fact—the commuting of partial derivatives—can be stated in an elegant coordinate-free way:

Perhaps I should remind you of the proof:

but

changes sign when we switch and while

does not, so It’s just a wee bit more work to show that conversely, starting from it follows that the mixed partials must commute.

How can we state this fact using the tautological 1-form ? I said that using the map

we can pull back to and get . But pulling back commutes with the operator! So, if we pull back we get But So, has the magical property that when we pull it back to we always get zero, no matter what we choose!

This magical property captures Hamilton’s equations, the Maxwell relations and so on—for all choices of at once. So it shouldn’t be surprising that the 2-form

is colossally important: it’s the famous symplectic structure on the so-called phase space

Well, actually, most people prefer to work with

It seems this whole subject is a monument of austere beauty… covered with minus signs, like bird droppings.

Example 6. In classical mechanics, let

as in Example 1. If has local coordinates then has these along with the conjugate variables as coordinates. As we explained, it causes little trouble to call these conjugate variables by the same names we used for the partial derivatives of namely, and So, we have

and thus

Example 7. In thermodynamics, let

as in Example 3. If has coordinates then the conjugate variables deserve to be called So, we have

and

You’ll see that in these formulas for variables get paired with their conjugate variables. That’s nice.

But let me expand on what we just saw, since it’s important. And let me talk about without tossing in that extra sign.

What we saw is that the 2-form is a ‘measure of noncommutativity’. When we pull back to we get zero. This says that partial derivatives commute—and this gives Hamilton’s equations, the Maxwell relations, and all that. But up in is not zero. And this suggests that there’s some built-in noncommutativity hiding in phase space!

Indeed, we can make this very precise. Consider a little parallelogram up in :

Suppose we integrate the 1-form up the left edge and across the top. Do we get the same answer if integrate it across the bottom edge and then up the right?

No, not necessarily! The difference is the same as the integral of all the way around the parallelogram. By Stokes’ theorem, this is the same as integrating over the parallelogram. And there’s no reason that should give zero.

However, suppose we got our parallelogram in by taking a parallelogram in and applying the map

Then the integral of around our parallelogram would be zero, since it would equal the integral of around a parallelogram in … and that’s the change in as we go around a loop from some point to… itself!

And indeed, the fact that a function doesn’t change when we go around a parallelogram is precisely what makes

So the story all fits together quite nicely.

The big picture

I’ve tried to show you that the symplectic structure on the phase spaces of classical mechanics, and the lesser-known but utterly analogous one on the phase spaces of thermodynamics, is a natural outgrowth of utterly trivial reflections on the process of minimizing or maximizing a function on a manifold .

The first derivative test tells us to look for points with

while the commutativity of partial derivatives says that

everywhere—and this gives Hamilton’s equations and the Maxwell relations. The 1-form is the pullback of the tautologous 1-form on and similarly is the pullback of the symplectic structure The fact that

says that holds noncommutative delights, almost like a world where partial derivatives no longer commute! But of course we still have

everywhere, and this becomes part of the official definition of a symplectic structure.

All very simple. I hope, however, the experts note that to see this unified picture, we had to avoid the most common approaches to classical mechanics, which start with either a ‘Hamiltonian’

or a ‘Lagrangian’

Instead, we started with Hamilton’s principal function

where is not the usual configuration space describing possible positions for a particle, but the ‘extended’ configuration space, which also includes time. Only this way do Hamilton’s equations, like the Maxwell relations, become a trivial consequence of the fact that partial derivatives commute.

But what about those ‘noncommutative delights’? First, there’s a noncommutative Poisson bracket operation on functions on . This makes the functions into a so-called Poisson algebra. In classical mechanics of a point particle on the line, for example, it’s well-known that we have

In thermodynamics, the analogous relations

seem sadly little-known. But you can see them here, for example:

• M. J. Peterson, Analogy between thermodynamics and mechanics, American Journal of Physics 47 (1979), 488–490.

at least up to one of those pesky minus signs! We can use these Poisson brackets to study how one thermodynamic variable changes as we slowly change another, staying close to equilibrium all along.

Second, we can go further and ‘quantize’ the functions on . This means coming up with an associative but noncommutative product of these function that mimics the Poisson bracket to some extent. In the case of a particle on a line, we’d get commutation relations like

where is Planck’s constant. Now we can represent these quantities as operators on a Hilbert space, the uncertainty principle kicks in, and life gets really interesting.

In thermodynamics, the analogous relations would be

The math works just the same, but what does it mean physically? Are we now thinking of temperature, entropy and the like as ‘quantum observables’—for example, operators on a Hilbert space? Are we just quantizing thermodynamics?

That’s one possible interpretation, but I’ve never heard anyone discuss it. Here’s one good reason: as Blake Stacey pointed out below, these equations don’t pass the test of dimensional analysis! The quantities at left have units of energy, while Plank’s constant has units of action. So maybe we need to introduce a quantity with units of time at right, or maybe there’s some other interpretation, where we don’t interpret the parameter as the good old-fashioned Planck’s constant, but something else instead.

And if you’ve really been paying attention, you may wonder how quantropy fits into this game! I showed that at least in a toy model, the path integral formulation of quantum mechanics arises, not exactly from maximizing or minimizing something, but from finding its critical points: that is, points where its first derivative vanishes. This something is a complex-valued quantity analogous to entropy, which I called ‘quantropy’.

Now, while I keep throwing around words like ‘minimize’ and ‘maximize’, most everything I’m doing works just fine for critical points. So, it seems that the apparatus of symplectic geometry may apply to the path-integral formulation of quantum mechanics.

But that would be weirdly interesting! In particular, what would happen when we go ahead and quantize the path-integral formulation of quantum mechanics?

If you’re a physicist, there’s a guess that will come tripping off your tongue at this point, without you even needing to think. Me too. But I don’t know if that guess is right.

Less mind-blowingly, there is also the question of how symplectic geometry enters into classical statics via the idea of Example 4.

But there’s a lot of fun to be had in this game already with thermodynamics.

Appendix

I should admit, just so you don’t think I failed to notice, that only rather esoteric physicists study the approach to quantum mechanics where time is an operator that doesn’t commute with the Hamiltonian In this approach commutes with the momentum and position operators. I didn’t write down those commutation equations, for fear you’d think I was a crackpot and stop reading! It is however a perfectly respectable approach, which can be reconciled with the usual one. And this issue is not only quantum-mechanical: it’s also important in classical mechanics.

Namely, there’s a way to start with the so-called extended phase space for a point particle on a manifold :

with coordinates and and get back to the usual phase space:

with just and as coordinates. The idea is to impose a constraint of the form

to knock off one degree of freedom, and use a standard trick called ‘symplectic reduction’ to knock off another.

Similarly, in quantum mechanics we can start with a big Hilbert space

on which and are all operators, then impose a constraint expressing in terms of and and then use that constraint to pick out states lying in a smaller Hilbert space. This smaller Hilbert space is naturally identified with the usual Hilbert space for a point particle:

Here is called the configuration space for our particle; its cotangent bundle is the usual phase space. We call the extended configuration space for a particle on the line; its cotangent bundle is the extended phase space.

I’m having some trouble remembering where I first learned about these ideas, but here are some good places to start:

• Toby Bartels, Abstract Hamiltonian mechanics.

• Nikola Buric and Slobodan Prvanovic, Space of events and the time observable.

• Piret Kuusk and Madis Koiv, Measurement of time in nonrelativistic quantum and classical mechanics, Proceedings of the Estonian Academy of Sciences, Physics and Mathematics 50 (2001), 195–213.

The leap from our universe to another is theoretically possible, say physicists. And the technology to test the idea is available today

The idea that our universe is embedded in a broader multidimensional space has captured the imagination of scientists and the general population alike. 

This notion is not entirely science fiction. According to some theories, our cosmos may exist in parallel with other universes in other sets of dimensions. Cosmologists call these universes braneworlds. And among that many prospects that this raises is the idea that things from our Universe might somehow end up in another.

A couple of years ago, Michael Sarrazin at the University of Namur in Belgium and a few others showed how matter might make the leap in the presence of large magnetic potentials. That provided a theoretical basis for real matter swapping. 

Today, Sarrazin and a few pals say that our galaxy might produce a magnetic potential large enough to make this happen for real. If so, we ought to be able to observe matter leaping back and forth between universes in the lab. In fact, such observations might already have been made in certain experiments.

The experiments in question involve trapping ultracold neutrons in bottles at places like the Institut Laue Langevin in Grenoble, France, and the Saint Petersburg Institute of Nuclear Physics. Ultracold neutrons move so slowly that it is possible to trap them using 'bottles' made of magnetic fields, ordinary matter and even gravity.

One reason to do this is  to measure how quickly the neutrons decay by beta emission. So physicists measure the rate at which the neutrons hit the bottle walls and how quickly this drops.   

There are two processes at work here: the rate of neutron decay and the rate at which neutrons escape from the bottle. So in the case of an ideal bottle, the rate of decay should be equal to the beta decay rate. But the bottles are not ideal so the rate of decay is always faster. 

That leaves open the possibility that there might be a third process at work: that some of the extra decay might be the result of neutrons jumping from our universe to another. 

So Sarrazin and co have used the measured decay rates to place an upper limit on how often this can happen. 

Their conclusion is that the probability of a neutron jumping ship is smaller than about one in a million.

That doesn't really say anything about whether matter swapping actually takes place. Only that if it does, it doesn't happen very often.  

However, Sarrazzin and co also say it should be straightforward to take better data that places stricter limits.

According to their theoretical work, a change in the gravitational potential should also influence the rate of matter swapping. So one idea is to carry out a neutron trapping experiment that lasts for a year or more, allowing the Earth to complete at least one orbit of the Sun.

In that time, the gravitational potential changes in a way that should influence the rate of matter swapping. Indeed, there ought to be an annual cycle. “If one can detect such a modulation it would be a strong indication that matter swapping really occurs,” they say.

That would be one of the biggest and most controversial discoveries in modern physics and one that is possible with technologies available today. 

Anyone got an old neutron bottle lying around and a bit of spare time on their hands?

Ref: arxiv.org/abs/1201.3949: Experimental Limits On Neutron Disappearance Into Another Braneworld

1. You collapse the wavefunction of the quantum particle and measure its position to a precision determined by the short wavelength of the gravitational wave yet without transferring a large momentum. It is then possible to violate Heisenberg's uncertainty principle, thus the quantum part of the theory doesn't survive.
2. You collapse the wavefunction of the quantum particle without violating Heisenberg's uncertainty principle, then you will violate energy conservation because your wave can't provide the necessary spread in momentum.
3. You don't collapse the wavefunction, in which case you can use your measurement for superluminal communication. You then had two types of measurements, one that does and one that doesn't collapse the wavefunction. By spatially separating an entangled state and monitoring one part of it without collapsing it, you can find out, instantaneously, when a collapse was induced in the other part.

An Auction Market for Journal Articles
By Jens Prufer and David Zetland
Public Choice (2010) 145: 379-403

"The [auction market for journal articles] quantifies academic output through A$ income, and academics need an accurate measure now more than ever. Long ago, decisions on professional advancement depended on subjective factors. These were replaced over time by "objective" factors such a publication or citation counts. As publication has grown more important, the number of submitted papers has increased... [T]he multiplication of titles has made measurement (and professional decisions) more difficult. Neither tenure candidates nor committees are happy with current evaluation methods; they need a simple indicator."

"It is a simple step to sum an individual's A$ income... to get an accurate signal of academic productivity. This signal could facilitate decisions on tenure, promotion, grants, and so on."