A Quantum Diaries Survivor

Peter, over at Not Even Wrong, facetiously directs people willing to discuss the physical appearance of Lisa Randall to my blog. [A long thread and a followup discussion developed six months ago here after I included a description of Lisa in a writeup of a very interesting seminar she gave on black holes at the LHC].

He does it in a discreet manner, without a direct link - and I appreciate the subtlety. Funny how with the internet you directly experience how knowledge is power: from the stats page of my blog I get a “signal” of people looking for “Tommaso Dorigo Lisa Randall”, and with some investigation I am able to figure out it is coming from people reading the comment thread in Peter’s blog.

Anyway, Scarlett and Natalie. As I retorted in the thread at NEW, I am not good at gossip. My wife says I am not interested in the people who surround me: I loathe discussing their life - I find it a rather vacuous way to spend one’s time. But I have my own weaknesses - I am interested in young, attractive girls. I feel no shame in admitting it: at 42, I have not lost interest in young female bodies yet. Got sex in my mind. How’s that for a coming out, JoAnne ?

So, really, Scarlett Johansson and Natalie Portman. They are walking the walks of the Berlin festival, where is presented among others the movie they  acted in, “The Other Boleyn girl“. They are enemies in the movie, but close friends in real life. A rare instance in the world of acting, where beautiful women are accustomed to be prima donnas and the presence of a competitor wreaks havoc. Anyway, a picture with both smiling and looking gorgeous is too beautiful to resist the temptation of pasting it here…

For fourteen years Silvio Berlusconi and Pierferdinando Casini, respectively the leader of Forza Italia and the leader of “UDC” (the christian union of centrists) were allies in the “Polo delle Libertà”, a center-right coalition which included the ex-fascist Fini and the separationist Bossi. They governed Italy together for seven years, and when they didn’t they joined their forces to oppose the center-left together.  Not a glitch, no arguments - journalists had a hard time finding anything of the kind to report.

All that is over now. Italians will vote on April 13th, when they will have to choose a new government after Prodi’s coalition was defeated in the Senate by the defection of Clemente Mastella, indicted for bribery and other frauds. And today, after a few days of contradictory news, the formal announcement: UDC will run alone, with the indication of Casini as candidate for premiership. A blow to Berlusconi, who can only lose these elections, after two years of center-left government which many italians perceived as a failure. Polls credit the right with a 7.5% lead over the democratic party and the left - but these two months will be very interesting from a political point of view.

Why did Casini decided to go alone ? His party is credited with 5-6% of the votes - not much, objectively. But I have a pretty good idea of why he did so. Had Casini’s UDC  joined forces with Berlusconi, the center-right coalition would have won hands down: a large margin of seats in the parliament, which would have allowed Berlusconi to ignore his allies and decide everything by himself. Casini much prefers a weaker Berlusconi, and the added visibility of UDC being instrumental in keeping the future government going. A cold-blooded political calculus. I am happy to see it happening, however: Veltroni, the leader of the newborn Democratic Party, can still hope for a successful comeback in the next two months.

“Rather than assuming quantum behavior as a nuisance to shield from, we have to accept it as an intrinsic and powerful element of reality, and learn to exploit it in our designs. Once we do that, everything in engineering is going to change radically: from design, to construction, to building, to project management.”

David Orban

The LHC will start running towards the end of this year, at the design energy and with a bunch crossing time of 25 ns. That means 40 million intersections per second between two proton packets in the core of CMS and ATLAS [things are a bit more complicated -some bunches are empty- but this has no relevance for my point].

We expect that the beams will contain few protons in this initial phase: low luminosity, that is. That’s because a high energy beam requires a lot of tuning before it can accommodate a large number of particles. Charged particles, in fact, have the nasty tendency to repel each other, and squeezing them into a narrow corner of phase space -knee to knee, all together as a single man- is a tremendously hard task, requiring successive approximations. Moreover, as the beams travel through the LHC tunnel, each making over ten thousand turns a second, they generate strong induced currents on the machine’s hardware. This electromagnetic interplay is impossible to compute beforehand, and a trial and error procedure by the machinists is unavoidable.

Luminosity is a function of the number of protons spinning in the two directions. Basically one can compute it from the number of particles circulating in the two directions by taking their product and dividing it by the revolution frequency and the transverse section of the beam. One obtains a number whose units are inverse area (the beam size) times inverse time in seconds (the frequency). The LHC will start at , but we expect it to reach the design value of in a couple of years.

Luminosity is not just a number with which machinists boast about their gadget. With it, you can compute the rate of production of any given process, if you know its cross section.

Cross section, a number labeled with the greek letter carrying units of area, basically tells you the effective area a proton must hit in another in order to give rise to a given reaction. The total cross section for proton-proton collisions at the LHC energy is : more or less like a circle with a radius of 1.6 millionths of a billionth of a meter - the “size” of a proton seen by another colliding with it head-on. But the total pp cross section is huge! Compare it with the cross section for producing a top quark pair: , or a hundred million times smaller. It is like if the incoming proton had to hit the other one “just right there”, to produce a top pair.

With a knowledge of what a cross section is we can answer questions. What is the total rate of proton collisions at the LHC if the luminosity is - the one we will have in the “low luminosity” phase ? Simply,

.

With  as quoted above, we get a rate of proton collisions: eighty million collisions per second! How many per bunch crossing ? Well, if all proton bunches contain the same number of particles, we get on average two interactions per bunch crossing, since the crossing rate is . Easy, huh ?

Well, things in reality are just a bit more complicated. The probability of events that may come incoherently in integer numbers follows the rules of Poisson statistics. Poisson statistics allows us to compute the probability that a bunch crossing will contain no collisions, or one, or two, or N, given the average as computed above. The formula looks awful, but it is quite benign:

( the exclamation mark indicates taking the factorial of N).

We need a pocket calculator, but other than that there is nothing that should scare you out of this post. Keep reading if you want to use what you just learned to get some insight in the inner workings of the LHC experiments!

With the formula for the probability of N collisions, we have gained power - knowledge, they say, is just that. The power to make wonderful calculations. If I tell you that the cross section for producing an event with two energetic jets (say, energy above 30 GeV each) is , or  (we prefer to use microbarns -labeled - for the area of , a quite convenient unit),  how many such events will be produced in a single bunch crossing at the full LHC luminosity of , on average ?

Easy. Use the formula , and you get a rate , that is,  2 MHz. Then, by dividing by 40 million bunch crossings per second, you get the rate per bunch crossing, 0.05: one in twenty. If instead we had taken the cross section for producing four energetic jets, , we would have obtained a rate of 30 kHz, and a bunch crossing frequency of 7.5 in ten thousand. Mind you, the cross sections I quote are approximate - I estimated them with some back-of-the-envelope calculation. But let’s not be distracted by details and let me get to the point.

Those computed above are average rates. What happens if I ask you what is the chance that two, or more, separate proton collisions each producing two jets like the ones above in the same bunch crossing?

Now, that might sound like a weird question, devoid of any practical importance. Quite the contrary. Let me compute it for you before making my point. We use the Poisson probability formula, with and . Instead of computing P(2), P(3), P(4)… and then adding them together, we use the fact that the sum of all P(N) is one: a nice property of probability, indeed! Here is the computation:

,

, and so

.

Interesting! The chance of two distinct dijet events in a single bunch crossing is not that negligible… If we cannot distinguish where the jets come from (i.e., if the two proton collisions happen too close to each other), we will interpret the event as one with four energetic jets!

Now compare this 0.00121 with the number computed above with , the rate of collisions producing four jets in the final state from a single proton-proton interaction: we discover that at the LHC, there are instances when two separate collisions may conspire to mimic rarer processes! If I am looking for four-jet events, I will find 1.21 every thousand bunch crossings coming from two 2-jet “multiple interaction” events, while only an additional 0.75 every thousand will be genuine 4-jet events. I have a background to consider which lower luminosity machines would never have to care about!

The exercise is over. It is not an academic one: in the study of the very rare production of top pairs with higgs-strahlung, , one gets to consider the collection of exceedingly rare events with up to eight energetic jets in the final state. The background from multiple interactions conjuring a multijet final state by adding different contributions is to be removed! We can do that by actually tracking the jets down to the space point where they were originated: we only keep events where all eight jets originated from the same spot, and we are ok. We can do it, since we have such a wonderful silicon tracker (see picture)…

Two weeks ago I visited a high school in Bassano del Grappa, Liceo Brocchi, to give a lecture in the context of the Masterclasses 2008. The lecture discussed the history of 20th century nuclear and subnuclear physics, and I covered some of the main issues up to the November revolution of 1974, when the charm quark was discovered and quarks were recognized as physical entities.

Today I gave the second part of the lecture. Two more hours spent discussing the discoveries that led to the verification of the Standard Model, and the hunt for the Higgs boson. I was surprised by the attention and interest of the students, who did their best to understand my garbled babble and messy scribblings on the blackboard. Definitely an afternoon well spent, considering that among these youngsters are probably hiding one or two successful particle physicists of tomorrow. The slides (in Italian, sorry - although I think a good part of them are plots, pictures and charts) can be downloaded from this link. Let me translate only the last one here: 

I just finished reading an enlightening paper by Michelangelo Mangano, a theorist at CERN and longtime colleague in the CDF experiment. Michelangelo is one of the few theorists who have consistently helped CDF from the inside, falling just short of pulling cables during Run II commissioning but other than that doing his share of dirty work as a full collaborator.

Michelangelo’s insight in the problems and the pitfalls of extracting a signal of new physics in hadron collider data is well known to me, since the time when we were both members of the oversight committee charged with assessing the soundness of Paolo Giromini’s analyses of the “superjets” - 13 weird events isolated in a sample of b-tagged W+jet events collected by CDF during Run I (I described the saga of the superjets and the following signal of a scalar quark in a series of posts about a year ago). Working with him in that committee did teach me one thing or two back then.

The paper (titled “Understanding the Standard Model, as a bridge to the discovery of new phenomena at the LHC“) contains no formulas -everybody can read it and understand it. It is a refreshing read, which tries to put in perspective what it will mean to “discover new physics” with CMS and ATLAS.

Michelangelo in fact focuses on the very incremental process whereby data is analyzed, gradually better understood as the combination of known effects, to the point when discrepancies with the models arise, and an interpretation is required.

Hic sunt leones: a discrepancy is not a sign of new physics, regardless of whether there are indications that this or that model, cunningly tailored around the effect or unsuspectingly formulated years before, explains the discrepancy perfectly. Not until every possible mundane explanation has been ruled out. Michelangelo makes the point quite clearly:

“As we move away from the default Higgs scenarios, into the territory of new physics beyond the SM, life becomes more difficult. One should think of two phases for a discovery: establishing the deviation from the SM, and understanding what this deviation corresponds to. It is crucial to maintain these two phases separate. The fact that a given anomaly is consistent with one possible interpretation does not increase its significance as an indication of new physics. If we see something odd in a given final state, it is not by appealing to, or freshly concocting, a new physics model that gives rise to precisely this anomaly that makes the signal more likely or more credible. The process of discovery, namely the detection of a deviation from the SM by more than, say, 5 standard deviations of combined statistical and systematic uncertainties, should be based solely on the careful examination of whether indeed the signal violates the SM expectation. Assigning this discrepancy to a slot in the space of possible BSM scenarios is a subsequent step.”

In the paper Mangano considers different examples of where a discrepancy might build up. Mass peaks are of course one of the clearest indications of the creation of a new particle or final state, but anomalous shapes of kinematical distributions are no less intriguing to the hunting physicist. Indeed, one of the very first things that many will look in LHC data will be the distribution of missing transverse energy - a possible “smoking gun” for the production of supersymmetric particles. Here is a sobering cautionary remark:

“There is no question, therefore, that unless each of the background components can be separately tested and validated, it will not be possible to draw conclusions from the mere comparison of data against the theory predictions.

I am not saying this because I do not believe in the goodness of our predictions. But because claiming that supersymmetry exists is far too important a conclusion to make it follow from the straight comparison against a Monte Carlo. One should not forget relevant examples from the colliders’ history [...]“.

Then a third “clear” signature of new physics is considered. The murkiest: counting experiments. In a counting experiment one relies solely on the numerical excess of the data in a given region of phase space, and in that, they are similar to searches for shape anomalies. Here a positive example is given, only for the purpose of showing just how complex it is to use with confidence a numerical excess as an indication of a discovery: the case of the top quark discovery. Here, a number of checks were necessary in order to make the excess rise from the status of a mere anomaly to that of a genuine new signal. But here too lies a caveat. Michelangelo compares the observation of the particle, which was based on just one, very striking, event, with an anomalous event collected by CDF in Run I, the infamous - one which has a probability of fractions of one part in a million to be due to known processes.

“In terms of pure statistics, the is (still today, after 30 times more luminosity has been collected by CDF and D0) even more significant as a deviation from the background (whether caused by physics or instrumental) than the first W obsertvations at UA1 and UA2. Why do we not consider it as evidence of new physics ? Because consensus built up in the community that, in spite of the ““, the evidence is not so compelling. On one side plausible BSM [Beyond the Standard Model] interpretations have been ruled out by the LEP experiments [...]. On the other, doubts will always remain that some freaky and irreproducible detector effect may be at the origin of this event.”

Michelangelo is optimistic on the way the review process works and prevents incorrect claims from being accepted by the physics community in large experiments:

“All apparent instances of deviations from the SM emerged so far in hadronic or leptonic high-energy collisions have eventually been sorted out, thanks to intense tests, checks, and reevaluations of the experimental and theoretical systematics. This shows that the control mechanisms set in place by the commonly established practice are very robust.”

I agree with him… But if I think of the effort it took eight years ago to our oversight committee to perform those intense tests, checks, and reevaluations, in the case of the superjet affair… Well, I hope it will be somebody else’s job this time around. I believe Michelangelo concurs!

It was sky transparency. We had suspected that Casera Razzo, the site I occasionally visit with a few amateur astronomer buddies in our deep-sky observing sessions, had the potential to offer a very dark, almost perfect sky; but only once in our dozen visits we had experienced it, while in all other cases the sky had been dark but had left something wanting.

We suspected that the factor that had been adverse in most cases was the transparency of the sky, but we needed some confirmation - after all, there are indeed many possible causes for a light-polluted atmosphere, some of them due to human activity and some others due to atmospheric conditions. Yesterday we reached the same level of quality of our formerly best night at the site - April 14th, 2007-, and we convinced ourselves that light scattered by particles and humidity in the atmosphere is a major factor affecting the darkness of the night in the eastern Alps. Light from towns 50 km away is masked well by the mountains surrounding the site, but the atmosphere needs to be transparent above your head if you want to avoid the photons from those far-away sodium lamps to bounce back  there and hit you.

Mauro’s sky quality meter -a calibrated exposimeter yielding a reading of the sky’s visual magnitude per squared arcsecond - started off at 21.42 at 10.50PM, and as lights in nearby towns were turned off it consistently grew to reach a 21.58 reading at 2AM yesterday night. The latter reading corresponds to a “Bortle-2″ sky - just one notch below the best possible sky, which corresponds to readings of 21.9 or 22.0. Of course, those 0.4 mags of difference mean a whole lot when one observes faint galaxies visually, but 21.6 is probably the best one can hope for on italian territory. Better values can probably be found only far, far away from northern Italy; even professional sites do not often go above 21.6: for instance,  it is a typical reading at sites such as the Roque de los Muchachos, at La Palma - where several observatories are located. See for instance the following plot, taken from the site of the observatorio:

In the plot you see that the V-band magnitude (y axis) reaches 21.5 at zenith on a typical night. The x axis shows the azimuthal direction where the measurement is made, and the different curves refer to different altitudes in degrees. 

So, what did we see yesterday night ? Well, a lot indeed. The temperature went from minus 5 to minus 11 degrees during the four hours of observation, and the wind was almost absent -I had feared it a lot before arriving there. However, the fact that the temperature did not stay constant prevented the mirror of the telescope to reach thermal equilibrium, and this affected the resolution quite a bit, and with it our possibility to push the magnification. For that reason, we mainly observed extended objects at 120x or 200x. Indeed, we were naturally led to spending most of our time on the real showpieces of the winter sky, which -when observed under truly dark skies- show picture-like detail with a 16″ scope. So, little time was spent on the faintest objects, which are usually small and require magnifications in excess of 400x.

A list of observed objects is a rather dry way for a description of the night. Rather, I only mention what really impressed me. Messier 51, the whirlpool galaxy, was one object on which we spent several minutes. It showed filamentary detail inside the main spiral arms, and was a really glorious sight - you felt you could pick it up by one arm, peeling it off the eyepiece lens as you would remove a dead insect from your windshield. And Messier 101, another face-on spiral galaxy in Ursa Major, did not pale in comparison: it showed several H-II regions in the arms, and the details in its structure were the best I ever saw on this object.

M101 is an extended object - covering almost a fourth of a squared degree of sky - and light pollution can make it utterly invisible even with large instruments! In fact, one often sees threads on popular amateur astronomy forums where it is discussed whether M101 is visually observable at all… Quite ironic: under dark skies this galaxy is a true beauty. The picture below (taken by italian amateurs from Verona) represents a good approximation of what was visible through the eyepiece. It is sights like these that keep me wanting for more nights out, hands and feet freezing and nothing else around but snow and silence.

In a few minutes I will be leaving to Casera Razzo with two buddies, a large dobson telescope, and lots of warm clothes. The weather is clear, and we expect a rich observing session, with UMA and LEO starting to show their bounty of galaxies high in the night sky.

The temperature should not dip below minus ten Celsius - or so I gather from the local forecasts. Instead, wind might turn out to be a problem - despite my dobson has a robust mount, a 10 mph breeze is enough to make high-power observations painful, and leave alone the wind chill effect during the night at 1700 meters above sea level, with only snow around. The gradient in pressure between balcans and alps could make things hard for us.

Nonetheless, I have already put together a list of objects I wish to watch with some detail. Among them, several galaxies of course. M51 (aka the whirlpool), the most photogenic interacting pair of the whole sky; M101, a wonderful spiral which usually cannot be observed well - it requires very dark skies to see its spiral arms; and then M106, M65-M66, … the list is very long and thick with showpieces, but also with less-known galaxies. If wind is a problem for chill and stability of the scope, it will indeed help the sky transparency, and I expect we will have a fair chance of exceeding previous records as far as dim details on deep-sky objects are concerned. Wish us good luck… A night of observations during winter time is not too different from a sport performance: you drive two hours, unload the material, mount everything, observe for four-five hours, and then put back things in the car and leave. Not for the faint hearted. 

I just finished browsing a paper by Gabor Orosz and Gabor Stepan, researchers respectively in nonlinear mathematics and applied mechanics. The pdf file had rest on the virtual desktop of my laptop computer for a while now, begging to be read like a hundred more, but advantaged by having not been thrown to the darkness of my “papers to read” folder with all the others. And today, with some time to spend before the arrival of the next train to Venice, I just ventured to read it. 

After my quick read I am left with mixed feelings. The paper is not the kind of science that fits George Bernard Shaw’s definition, which I learned from Jeff a week ago: “Science is always wrong! It never solves a problem without creating ten more“. In fact, it does answer the question of how traffic jams are created from a uniform flow. The problem in this case is that the answer was already rather well known. Nonetheless, just thinking at the elegant math which is the ultimate cause of your anguish at the wheel when stuck on a highway makes it easier to accept the situation, and this is enough justification for the article. But the study is indeed some breakthrough in modeling traffic jams.

Orosz and Stepan consider an idealized highway such as the one pictured on the right: vehicles are the points at coordinates along a circumference, all moving in the same direction. They then analyze the nonlinearities that arise in a model of traffic flow in their toy highway when one introduces a realistic time delay in the response of drivers to the detection of an impact threat with the car preceding them. They find that the time delay is crucial in allowing to model, with quite complicated formulas, the onset of backward-traveling “stop-and-go” waves, which interrupt the unstable solution of a well-behaved uniform flow of vehicles.

Apparently, the duality between uniform flow and “stop-and-go” waves has a name: it is an instance of a Hopf bifurcation. Now, since I had never heard of Hopf bifurcations before (or maybe I have, and have forgotten about them – oblivion is the privilege of a cultured man), I am not the best person to explain it here.
So you can read about it on wikipedia if you can not stand your own ignorance (I have accepted mine long ago). If you have lost your mouse and cannot click above, here is a quote:

In bifurcation theory a Hopf or Andronov-Hopf bifurcation is a local bifurcation in which a fixed point of a dynamical system loses stability as a pair of complex conjugate eigenvalues of the linearization around the fixed point cross the imaginary axis of the complex plane.

Everything is clear now, huh ? Well, the math is really not for everybody, not even in the simplest case. And it turns out that the time delay introduced by Orosz and Stepan changes the description of the system from one with ordinary differential equations in a finite-dimensional dynamical space to one modeled by delay differential equations and infinite-dimensional phase spaces. Hugh.

In any case, however complex the main body of the paper is, its conclusions are quite readable. Basically, the model of Orosz and Stepan demonstrates the onset of backward-traveling waves of traffic jams, and shows how a highway is basically a bistable system, with the linear flow easily affected by large enough “perturbations” -.such as a truck changing lane – which cause the onset of stop-and-go waves. All things we knew, but the formulas in the model do allow some planning: just a little decrease in the speed of cars approaching a backward-moving wave could significantly dampen it. Something we knew qualitatively, but we can now compute. A step in the right direction, towards the fulfilment of my highway dream.

I dream of highways where you enter with your car, and then leave the wheel and the gas pedal and read a book. An electronic wireless system controls the speed of your car and its steering, and you get to destination in the smallest possible time available given the number of vehicles on the road. This is not science fiction: we have owned the technology to do this since maybe ten years ago. Just imagine the amount of time saved to human beings, the decrease in pollution, and in the amount of stress… I know these systems are being studied, and I am rooting for those guys.

“One reason we like supersymmetry is that we haven’t seen any of the particles“

Michael Weinberger (interviewed here). What can I say… “So far so good”