## Archive for September, 2011

### Angular Momentum in Quantum Mechanics: Spin Indepth

Monday, September 26th, 2011

﻿Last week we began a journey through quantum wonderland with our discussion on Angular Momentum in Quantum Mechanics. We learned that for quantum angular momentum you can only ever know the total and one of its components (i.e. x, y or z) at any time t. We learned that this was strange result was due to the what the Generalized Uncertainty Principle has to say about the observables for operators that do not commute with one and other. Additionally we saw that angular momentum in quantum mechanics was a discrete variable that could only take certain quantized values, unlike its continuous counterpart in Classical Mechanics (CM).

For this week, as promised, we shall follow Alice’s footsteps deeper into wonderland and try to catch a glimpse of the probabilistic nature of Quantum Mechanics (QM). And for this journey we will further explore the nature of Spin Angular Momentum in QM. But before we begin, let’s arm ourselves with the notion of what physicists like to call an ensemble of identically prepared systems.

# An Ensemble Romance

Let’s imagine we have some brave young female physicist, who happens to be single, let’s call her Juliet (we always need more women in science anyway, even fictitious Shakespearian women). Now Juliet has some dark-haired, “handsome,” physicist come to call upon her, his name is Romeo.

Juliet, being a scientist, wants to see if she and Romeo will make a good long-term couple. However, Juliet is rather impatient and doesn’t want to spend the months/years that it would take to learn this knowledge (she doesn’t have long to live after all, only three Acts!). She hatches a plan to assess whether or not the two of them will be a good couple. She’s discovered how to make a perfect clone of a person (not just genetically, she can also clone their consciousness, personality, memories, etc…).

So she asks our dear Romeo for a lock of his hair, a swab of the inside of his cheek, and an MRI of his brain. Romeo finding this all rather odd, but eager to please Juliet, agrees to all of the above. Juliet then takes these back to her laboratory, deep underground, and makes a countless number of identical Romeo Clones.

She places each Romeo Clone in an identically prepared, but separate room. In each room she walks in and performs a single action and records the Romeo Clone’s response. The actions she performs are, what she would consider, half the time pleasant and half the time unpleasant (see examples below). During this process Juliet ensures that each Romeo Clone has no knowledge of the other clones, rooms, or actions. All the Clones are blank slates with respect to Juliet’s actions (though all the clones, like the original Romeo, are romantically interested in Juliet at the start). When Juliet repeats this process on enough Romeo Clones she will learn if she and the original Romeo are compatible.

After her experiment, she decides to not to date him; thinking he will probably be the death of her anyway.

# The Statistical Interpretation

While this story in the preceding section is absurd in numerous ways, it highlights several facts key ideas.

As I’ve said, Quantum Mechanics is a probabilistic theory. Physicists work within this theory much in the same way Juliet does for her love life. We prepare an ensemble of identically prepared systems (i.e. each identical Romeo Clone in an identical, but separate, room). With each system we make a single measurement (i.e. Juliet’s single action toward each Romeo Clone). And then from the results of the experiment on each single system we build a distribution which has an expectation value.

The expectation value is the average of all the independent measurements performed on each independent identically prepared system (i.e. Juliet’s decision not to date Romeo after she finished her experiment). You should not confuse the expectation value with the most probable value. For almost all but some very special cases, they are two different numbers.

Additionally, in Quantum Mechanics you could never say exactly what the outcome of a single experiment will be (just like Juliet did not know if she was compatible with a single Romeo Clone). However, as I outlined above, Quantum Mechanics is able to say what the average outcome for a series of measurements on a series of identically prepared systems will be.

This idea has no analog in Classical Mechanics (for those of you who know what a partition sum function is, you know more than what’s good for you; let’s just leave Statistical Mechanics out of this discussion [1]).

But what in Feynman’s name does all this have to do with Spin Angular Momentum!? Stay with me and you shall find out, I’ll bring this all together at the very end.

# Spin Angular Momentum Revisited

﻿Last week I mentioned that spin angular momentum exists in the abstract world of linear algebra (specifically something known as a 2×2 Hilbert Space).  Let’s learn a little more about that here.  We know from last week that the total spin angular momentum for a particle can have the value:

For particles known as fermions, s is a half-integer, with the lowest possible value being ½. We also know from last week that the component of the spin angular momentum along a given direction (let’s say, the z-direction) can be written as:

It should not shock you to learn that there is a relation between a particle’s spin s, and the component of spin in a given direction, ms (keep in mind we are measuring this component in units of ).  This relation can be described as:

so that there are 2s+1 values of ms for every value of s (hence the reason there are  two values for ms for spin ½ particles). This can be written very tidily if we use Dirac Notation:

Spin State = |s ms>

Where this term above is known as a “ket,” and shows the spin, s, and z-component of the spin, ms , for the state.  Then we have what is termed as “spin up” and “spin down:”

{Spin Up}z = |½ ½>z and {Spin Down}z = |½ -½>z

These two states form what is known as a “basis set,” any arbitrary spin state, |ψ> can be describe by a sum of these two states (called a linear combination):

|ψ> = α |½ ½>z + β |½ -½>z

For two constants α and β.

Let’s expand a little bit on the what this idea of a basis set entails. In the above expression we have a set of objects (spin states), that are unique; meaning we can’t use one to make the other (i.e. you can’t mathematically make spin up from spin down). Mathematicians and physicists call such objects/states linearly independent. Furthermore, using these two unique spin states, I was able to form any arbitrary spin state. Mathematicians and physicists would then say these objects span the space (here the space in question is the space of all possible spin states).

So then a basis set is any set of objects that are all linearly independent of one and other and span the space those objects exist in.  Just to drive this idea of a basis home let’s take an example. If we look at the two points in the xy plane, (1,0) and (0,1), they are obviously linearly independent. There is no way to make (1,0) from a constant multiple of (0,1). Also, any arbitrary point, (x,y), in the plane can be made by adding the correct multiples of these two points, (1,0) and (0,1), together. Then these two points span the space and are linearly independent! Hence they form a basis set, and each of the points are known as basis elements. An important point which I must stress is that the set {(1,0), (0,1)} isn’t the only basis set that exists for the xy-plane! The points (1,1) and (1,-1) are also linearly independent and span the space, so they too form a basis set!

Returning to quantum mechanics, recall how last week we learned that any physical observable has a corresponding operator. Then if the total and one component of spin angular momentum take values according to the two equations I started this section with, there must be some operator that is responsible for these observed values! To see these operators in action we have:

S2 |s ms> = s (s + 1) ℏ﻿2 |s ms>

Sj |s ms> = ms ℏ ﻿|s ms>      for j = x, y, or z

Then for a spin up electron (s = ½) it’s total spin angular momentum would be √(3/4) and its component in the z-direction is then +½ .

Now, this begs the question, what is the component of spin for this state (spin up along the z-direction) in the x-direction!?

For this we must express our spin up z-state in terms of the basis elements for spin in the x-direction. So we must make a change of basis!

Visualization of a fermion's spin angular momentum in the "spin-up" and "spin-down" orientations along the z-axis. Notice how the vector sweeps out a circle in the xy-plane. This causes the x & y components of the spin-angular momentum to be smeared all along this circle. Ref 2.

Our spin up z-state can be expressed as:

|½ ½>z = √(2)/2 |½ ½>x + √(2)/2 |½ -½>x

Where the states on the right hand side are now with respect to spin up and down along the x-axis  (so the subscripts are denoting which basis I’m using). Notice how a purely spin up z-state breaks into a combination of spin up and spin down x-states!! This is precisely what I spoke of last week, for a spin up z-state, the spin is exactly defined in the z-direction. But now, when we switch to expressing the state with respect to x-state basis elements we get a state that is smeared, i.e. it is made of both spin up and spin down x-components (as it must be according to the Generalized Uncertainty Principle!).

So for our spin up z-state, which has an amount of it’s spin, ½ , along the z-direction we get spin components along the x-direction that are + ½ and – ½ ! This result is seen from using the operator equation above, involving Sj, on our state expressed in terms of the x-spin basis states.

This is all well and good, but does this happen in nature? And how does this relate to an ensemble of identically prepared systems?

# Bringing It All Together:  The Stern-Gerlach Experiment

In 1922, Germany was the center of the new dazzling theory of Quantum Mechanics. Otto Stern and Walther Gerlach decided to join the club with a brand new experiment. They decided to investigate the radical new theory of Erwin Schrödinger, by experimenting with a beam of silver atoms in a non-uniform magnetic field.  A sketch of their experimental apparatus can be seen here:

Experimental setup used by Walther Gerlach & Otto Stern. A furnace vaporized silver atoms and created a beam which was passed through a non-uniform magnetic field (oriented along the z-direction) toward a screen. Ref 3.

Classical Physics, states that this beam should be turned into a smeared line in the presence of the magnetic field due to the magnetic moment of the silver atom interacting with the field (as we can see in the above image).  Schrödinger’s wave theory (Quantum Physics) predicted that the beam would be split into 2l+1 pieces for a given orbital angular momentum l. Now for l=0, this gives one piece, l=1 gives three, l=2 gives five, etc… So for any orbital angular momentum the beam is predicted to split into an odd number of pieces.

Now silver is a “hydrogen like” atom, it has 47 electrons, but the first 46 are all paired up in their respective orbitals. If the silver atom is in its ground state, this lone 47th electron is in the 5s orbital (l=0), and has no partner (the fact that silver has one electron all by its lonesome in the outer shell makes it hydrogen like).  Now if you were to place a silver atom in a magnetic field, it’s magnetic moment is solely due to the 47th electron (because to a very good approximation, the magnetic moment of the other 46 electrons cancel each other out).

So Stern & Gerlach prepared an ensemble of identical systems.  Where one individual system is a single silver atom (and thankfully due to nature, all silver atoms are identical!).  Then the beam of silver atoms is an ensemble of systems! Stern & Gerlach, as I mentioned, sent this beam of silver through a non-uniform magnetic field that was aligned along the, you guessed it, z-direction.

What they observed however was utterly baffling, the beam split into exactly two pieces! As you can see in the figure from their original publication almost a century ago:

Stern & Gerlach's beam of silver atoms impacting a screen with no magnetic field (left) and with magnetic field (right), Ref 4.

This didn’t match either of the predictions of Classical Physics or Schrödinger’s wave theory (but keep in mind Schrödinger’s wave theory is correct, the silver atoms are just in their ground state.  If spin didn’t exist, the beam wouldn’t have split at all!).

So here is experimental proof for spin-angular momentum if you ever saw it (don’t let your physical chemistry professor tell you spin is not a valid quantum number, I certainly didn’t)!

What would later become the theory of spin in quantum mechanics gave rise to the prediction that the beam should split into 2s+1 pieces. The spin of the first 46 electrons in the silver atom cancel with each other; the lone 47th electron has spin s = ½, hence the theoretical prediction is that the beam will split into exactly two pieces. Which is confirmed by the experiment!

Let’s get philisophical for a moment to tie more of our discussion together.  The act of passing the silver beam through the field causes a single measurement to be performed on each of these atoms.  So the non-uniform magnetic field is applying the spin-angular momentum operator for the z-direction.  And from the application of this operator, we got a measurement, i.e. the deflected beams.

# Probability At Its Finest

The Stern-Gerlach experiment is then capable of creating “spin-polarized” beams of atoms.  By putting a screen in front of part of the split beam you can select a beam of atoms that are all either spin up in the z-direction or spin down in the z-direction.

Here’s a question…what happens if we then pass a spin up z beam through a non-uniform magnetic field aligned along the x-direction?  Well we’d be applying the spin angular momentum operator for the x-direction.  But these operators do not commute!  So our single beam spin up z-beam, will be smeared into two beams, one spin up in x, the other spin down in x.  Nothing major right?  We knew that a spin up z-beam should have uncertainty in the spin along the x-direction.

So let’s just pass one of these spin up x and spin down x beams back through a non-uniform magnetic field aligned in the z-direction.  We’ll take the spin up x piece for simplicity, and then the non-uniform magnetic field aligned in the z-direction will apply the spin angular momentum operator for that direction.  Since this beam was originally pure spin up z, applying this operator should then return this beam back to how it was before the beam encountered the x-magnet, namely, pure spin up-z…..

But this cannot be done!

You will never recover your pure spin up z beam from the above procedure.  You will only ever get a smeared beam that is spin up z and spin down z.

By placing the non-uniform magnetic field in the x-direction.  You made a measurement, you learned some information about the spin along the x-direction.  In doing so you forever modified the silver atom’s wave function.  As a result you placed an amount of uncertainty into the spin along the z-direction.

But you were really really really careful right? Wrong!

The Generalized Uncertainty Principle forbids you from predicting a determinate outcome for such an experiment.  These two operators, Sx and Sz , do not commute; as such you will always have an irreducible uncertainty in your theoretical prediction/experimental measurement.  You can certainly measure this final spin in the z-direction, and you could certainly say, I predict it to be spin up z.  However, you would be wrong half the time.

What you can say, is that the expectation value for the final spin along the z-direction is half the time spin up, and half the time spin down.

To help you visualize this very confusing (and complicated arrangement) feel free to take a look at this image below:

Three Stern-Gerlach magnets in a row. The first & third magnets are aligned along the z-axis, the second magnet is aligned along the x-axis. Notice how the pure spin up-z beam was forever altered by the second magnet. We are left with two beams, a spin down z and spin up z beam. Ref 5

Finally I will leave you with this Java applet [6] so that you can get a “hands-on” feel for the experiment, and help yourself understand the consequences of the Generalized Uncertainty Principle:

Until Next Time,

-Brian

(Special thanks to fellow physics graduate students Samaneh Sadighi and her husband Shahab “Sean” Arabshahi for playing Juliet & Romeo for this week)!

# References

1. Adapted from footnote on page 81 of David J. Griffiths, “Introduction to Elementary Particles,” 2nd ed., John Wiley & Sons, Inc., 1987.

2. Theresa Knott, “Quantum projection of S onto z for spin half particles.PNG,” Wikipedia, The Free Encyclopedia, http://en.wikipedia.org/wiki/File:Quantum_projection_of_S_onto_z_for_spin_half_particles.PNG, Sept. 27th 2011.

3. Theresa Knott, “Stern-Gerlach experiment.PNG,” Wikipedia, The Free Encyclopedia, http://en.wikipedia.org/wiki/File:Stern-Gerlach_experiment.PNG, Sept 27th 2011.

4. Walther Gerlach, Otto Stern, “Der experimentelle Nachweis der Richtungsquantelung im Magnetfeld,” Zeitschrift fur Physik A Hadrons and Nuclei, Vol 9, No. 1, 349-352, 1922.

5. Techne, “Quantum Physics vs The Principle of Casuality,” Telic Thoughts, http://telicthoughts.com/quantum-physics-vs-the-principle-of-causality/, Sept. 27th 2011.

6. Doug Mounce, Chris Mounce, Michael Dubson, Sam McKagan, and Carl Wieman, “Stern-Gerlach Experiment,” http://phet.colorado.edu/en/simulation/stern-gerlach, Sept. 27th 2011.

### Science is Happening!

Monday, September 26th, 2011

I’ve been following the discussion over the CNGS neutrino velocity measurement from the OPERA collaboration with great interest.  A lot of excellent stuff has already been written on this blog on the subject.  A couple of my favorite posts are this early take by Kathy Copic, and Michael Schmitt’s post, which has some interesting links.  I’m not going to even attempt to duplicate their efforts.  Instead, I just want to share a few of my impressions from the last several days.

The very short version is that the OPERA collaboration has measured the travel time (a little under 2.5 milliseconds) of neutrinos from CERN, where they are produced, to their detector in the Gran Sasso laboratory in Italy, with an uncertainty of 5 parts per million. They also measure the distance traveled (730 km) with better than a part per million accuracy. They divide and find a that the neutrinos seem to arrive 60 ns faster than expected, corresponding to a velocity greater than the speed of light by a part in 10,000.

Yeah, exactly.

It’s a startling result. The collaboration was right to submit their work (http://arxiv.org/abs/1109.4897) for public review at this point, I think, and they’ve done a good job of not overstating their claims. There has been a huge response from the particle physics community and the tone is skeptical but collegial. I tried to go to the seminar here at CERN on Friday but it was already standing room only, so I fled back to my office to watch the webcast (see Aidan’s liveblog of the seminar). There was nearly an hour of questions afterwards, many of which were quite good.

The questions at first centered on the distance measurement, which may seem at first blush to be the weak link in the measurement, until you realize that the distance is measured rather more precisely than the time of flight (see the numbers in my first paragraph). The speaker explained that the distance measurement is based on well-established geodesy techniques and confirmed that the precision of the velocity measurement is really determined by the precision of the time-of-flight measurement.

The rest of the questions that I thought were good revolved around one key fact: when OPERA measures the time of flight of the neutrinos, they don’t measure the time of flight of an individual neutrino. Rather, a batch of neutrinos are produced in some short window of time (10.5 μs) by a bunch of protons hitting a target. Then, the time-of-flight measurement is based off of fitting the recorded times of the events with a template based off of the measured time structure of the proton bunch created at CERN.

One question asked at the talk is whether the time structure of the neutrino bunch is somehow modified between departure and arrival, possibly by correlations between the position in time within the bunch and the way that the beam spreads out as it travels to Grand Sasso.  It’s an open question, as far as I can tell, and it strikes me as a potentially important one.

The majority of the community’s attention right now seems to be on the statistical analysis of the data as a possible source of unaccounted-for systematic uncertainty in the determination of the travel time. Because they are measuring the travel time of a bunch of neutrinos, they are essentially measuring the timing of the leading and trailing edge of the bunch at CERN and then again at Gran Sasso. But there’s a lot packed into that “essentially”, which people are now unpacking. Related to the above concern, the seminar speaker said in response to a question that the bunch length — the distance between the leading edge and trailing edge — is fixed in the analysis so that it’s not possible to account for the bunch somehow stretching or shrinking between CERN and Gran Sasso. The speaker at the seminar pointed to the good chisquared (chisquared is a standard measure of goodness of fit) as evidence for the quality of the fit (i.e. how well the model matches the shape of the data). It was pointed out by a questioner that the chisquared is not a useful measure of goodness of fit in this case, since the information it contains is diluted by the good fit to the points in the middle which don’t actually contribute that much information on where the edges are.   My variation on this theme is to wonder if you get a different answer by only fitting the leading half or only fitting the trailing half of the distribution.

It’s going to be interesting to see how this shakes out over time. In the meanwhile, I think that so far it’s a pretty great example of science working the way it’s supposed to.

### Neutrinos are in a year of wonders

Sunday, September 25th, 2011

After the T2K’s indication of non-zero theta13, neutrinos from LNGS throw out another bomb: the neutrino speed > c. The non-zero theta13 might only attract the eyes of particle physicists, but ‘the neutrino speed > c’ is really an earthquake to the fundamentals of whole modern physics and causes worldwide discussions.

Most people regard the T2K’s non-zero theta13 result is an ‘indication’, not a ‘discovery’, because the significance is only 2.5 sigma. Though the significance from OPERA is 6 sigma (http://static.arxiv.org/pdf/1109.4897.pdf), they are very cautious about the anomaly they observed. Almost every number in their paper has been cross-checked independently. Perhaps the neutrinos have some other properties that we never thought before, otherwise some systematic effects are in the dark. After all, the accurate metrology techniques used by OPERA, like GPS and geodesy, are common and mature. We also use them in our Daya Bay experiment to synchronize different experimental sites and measure the reactor baseline, of cause, with relative low precision requirements. So it is very important that other experiment can repeat this measurement with different experimental systematics.

Looking at OPERA’s results, I recall one thing. In this year’s ISSP11, students were asking Prof. Ting about when they will release the first results of AMS. He said it is not about time, it’s about right or wrong. “Likely the human will never send a detector like AMS into space again in next a few decades, so we have to tell people the right thing”, says Prof. Ting when ended his lecture.

Now it seems neutrinos become in a year of wonders. What is the next? I would prefer zero theta13, ^_^.

### Is science objective or influenced by culture?

Friday, September 23rd, 2011

– By Byron Jennings, Theorist and Project Coordinator

Franz Boas (1858 – 1942) was another scientist trained as a physicist who made a name for himself in another field, in this case, anthropology. He was the founder of modern anthropology and brought to the field the methodology of the natural sciences; the idea one should formulate theories and conclusions only after thorough and rigorous collection and examination of hard evidence.  In cultural anthropology, he established the contextualist approach to culture, cultural relativism. Culture can be thought of as the paradigm that gives context and meaning to social interactions. Cultural relativism recognizes that comparing cultures has the same incommensurability problems as comparing other paradigms. The same words (actions) have different meanings depending on the paradigm (culture).

To see how this different meaning works in practice, consider headgear. The rules on what is acceptable head covering is cultural and religious and varies over time and place. What one group considers good and proper, another considers inappropriate. At one time, the English considered the Irish uncouth because they doffed their hats to people they met on the street. The horror of it. At another time, no self-respecting woman would appear in church without a hat (following Paul’s instructions), but they now condemn Muslim women for covering their heads. The Canadian Legion considered it an insult to the Queen not to remove head covering in Legion halls. At least in the case of Sikhs, the Queen did not agree.  What one culture praises, another condemns.

Cultural relativism had two main tenets: 1) all people are civilized and 2) there are no higher and lower cultures. This gave a much-needed antidote to the evolutionist idea that preceded it; the idea of the innate and absolute superiority of the western culture, since it was considered more evolved than other cultures. Western culture was then used as the hallmark against which other cultures were judged. In England, it was the White Man’s Burden (now mostly dead) and in the USA, American Exceptionalism (not mostly dead). To understand exceptionalism, think of Raskolnikov—he thought himself exceptional so he did not have to follow normal behaviour—in Crime and Punishment, or Dostoyevsky’s statement to the effect that most people are not sufficiently intelligent to realize they are not exceptional. Be that as it may, the only truly exceptional people are Nova Scotia born physicists [1]. Hmm, perhaps I should not have juxtopositioned that next to Dostoyevsky’s statement. However, it seems all people like to think that their own particular group, culture or religion is exceptional, so why not Nova Scotian physicists?  Cultural relativism is a direct attack on this common idea that one’s own group is exceptional or superior. It instead says that all cultures should be evaluated and judged on their own merits, not against the standards of another culture.

Unfortunately, the idea of cultures being self contained and statements being valid only within a given culture has been extended too far, to exclude all cross-cultural statements. But in the context of science, what does it mean? In some cultures, does the sun rise in the west and sets in the east? Or is “the sun rises in the east,” a cross-culturally valid statement? Can we solve the energy crisis by finding a culture where the second law of thermodynamics does not hold—“Build your perpetual motion machines in Lower Slobbovia!”—or is the second law cross-cultural?  I mean, in Australia the swans are black, the sun is in the north and they play Aussie rules football. But as far as I know, all the models of science are equally valid there (except perhaps on the football pitch). It is only in Douglas Adams’ imagination that we have bistro mathematics.  Whether the Higgs boson or another particle will found at CERN or Fermilab depends on the nature of the accelerators and detectors, not the culture at the two labs. Trying to change by the culture by bringing in mystics or other counter culture people will not result in finding different types of particles.  It has never been observed to work that way.

Now, the supporters of relativism (or its double cousin post-modernism) will complain that the examples I have given are too simple. But a general rule must apply to simple cases, as well as the complex ones where the very complexity makes it hard to see what is happening.  If you want me to believe the model of germs causing disease is only cultural, you must first explain why the model that the sun raises in the east is also only cultural. They both arise from the same method.  In the cold fusion debate, I heard the statement, “if it wasn’t for those damn physicists we would have an infinite supply of energy.” If the physicists had not debunked cold fusion, it would still be happening and we would have cold fusion powered Hondas (why not if all statements are relative, perhaps science is different in Japan). Unfortunately, scientists do not make the laws, only discover them. Culture could not make Lysenkoism [2] valid, even in Stalinist Russia.  In the same way that raw observations are valid across scientific paradigms, scientific models are valid (or, as in the case of Lysenkoism, invalid) across cultures or cultural paradigms.

And yet—to balance this argument out—culture and context does play a role in how the results of science are expressed and in who discovers them.  A pessimist would be more apt to discover the second law of thermodynamics than an optimist. In England in the 17th century they discovered laws—Hooke’s Law, Boyle’s Law—but now such regularities are just rules–the OZI rule [3] for example.  Thus, how things are expressed changes with the fashion, but the ideas behind them stay the same. If there is an enduring cultural influence in science, it is the culture of mathematics. As Poincare said, “But what we call objective reality…can only be the harmony expressed by mathematical laws. It is this harmony then which is the sole objective reality, the only truth we can obtain.”

[1] It is entirely coincidental that this describes the author.

[2] The biological inheritance principle which Trofim Lysenko subscribed to and which derive from theories of the heritability of acquired characteristics. It contributed to the collapse of Soviet agriculture.

[3] The Okubo, Zweig, Iizuka rule on the decay of excited nucleons and other hadrons. It contributed to acceptance of the quark model.

### Élémentaire, mon cher neutrino…

Friday, September 23rd, 2011

Parfois, l’on fait des découvertes scientifiques là où on les cherche, un peu comme lorsqu’on trouve un trésor près d’une épave. Mais il arrive aussi qu’on fasse des découvertes par hasard, comme un cadeau du ciel. En physique des particules, les deux cas de figure se produisent très souvent, mais, quelle que soit la découverte, le processus est le même. Dès que l’on trouve quelque chose de nouveau – que ce soit attendu ou que cela arrive par hasard –, tout est passé au peigne fin, en s’assurant que rien n’a été négligé. Un détail nous aurait-il échappé ? Avons-nous omis un aspect qui pourrait simuler quelque chose de nouveau ?

C’est à ce stade que l’on fait connaître ses résultats à un jury composé de pairs – d’autres scientifiques du domaine qui évaluent les travaux en vérifiant qu’aucun détail n’a été omis. Ensuite, pour citer l’un des détectives de fiction les plus célèbres, Sherlock Holmes, « lorsque vous avez éliminé l’impossible, ce qui reste, aussi improbable que cela paraisse, doit être la vérité ».

C’est particulièrement le cas lorsqu’un résultat est complètement inattendu. Dans un sens, cela revient à un travail de détective : les expérimentateurs doivent s’assurer qu’ils interprètent correctement toutes les preuves avant d’identifier le suspect.

Le curieux cas des neutrinos en excès de vitesse – qui ont semble-t-il dépassé la vitesse de la lumière, la vitesse limite de la nature, lors de leur voyage entre le CERN et le Gran Sasso, au centre de l’Italie – est désormais entre les mains du jury. La collaboration OPERA n’a pas pu expliquer cet effet par un artefact dans son dispositif expérimental. Les chercheurs ont donc révélé à leurs pairs ce qu’ils ont observé par le biais d’un article posté sur le site arXiv.org, qui détaille toutes les étapes – de la collecte de données à l’analyse finale – et d’un séminaire organisé au CERN. Les expériences sur les neutrinos sont connues pour être difficiles du fait que les interactions de neutrinos sont extrêmement rares, mais d’ici des mois – voire des années – d’autres équipes travaillant sur des expériences comparables passeront leurs données au crible pour voir si elles trouvent le même effet.

La science a toujours fonctionné ainsi, et pas seulement lorsqu’un effet inattendu fait son apparition comme un invité surprise. Les résultats sont vérifiés par d’autres : des questions peuvent être posées, et des réponses apportées, et lorsque tout le monde est convaincu que rien n’a été omis, ces résultats sont alors publiés. Évidemment, il arrive que des résultats erronés passent entre les mailles du filet et que de surprenants effets s’évanouissent quand les autres expériences sont incapables de confirmer les résultats. Là encore, cela fait partie du processus scientifique, qui ressemble bien plus à une rivière changeant de direction en fonction du paysage qu’elle traverse qu’à une voie romaine, bien droite, qui relierait entre elles les grandes découvertes.

Les résultats de l’expérience OPERA vont donc maintenant être examinés de près par la communauté des physiciens des particules, et on est impatient de savoir s’ils résisteront à l’épreuve du temps. Après, et seulement après, lorsque les résultats auront été confirmés, suivant la devise de Sherlock Holmes, les neutrinos super-rapides seront alors considérés non plus comme de la science fiction, mais comme un fait scientifique. Pour l’instant, « wait and see ».

Christine Sutton

### Nothing travels faster than light but gossip!

Friday, September 23rd, 2011

This is what one of my professors told us way back then at the end of a very serious lecture on relativity. And rumors have certainly been going fast and wild at CERN this past week. The news of the possible spotting of particles travelling faster than the speed of light is just as exciting as it is unexpected. This could be the most earth-shattering discovery we’ve had in decades.  Hard to get any wilder than this! The whole question now is to determine if this is really the case.

I remember being a teenager and hearing about tachyons, these hypothetical particles that could travel faster than the speed of light. They were supposed to have a speed at rest not of zero, but equal to the speed of light. Not only that, but they would lose mass (that is energy) as their speed increased! I remember the shiver I got then. I got it again when I heard about this measurement earlier this week. So here are more details.

The OPERA experiment is located in an underground laboratory under the Gran Sasso mountain in central Italy 730 km away from CERN. Neutrinos produced at CERN travel through the Earth’s crust to reach the OPERA detector. That’s what so great and so hard with neutrinos: they can zip through matter nearly unaffected, making them also terribly difficult to detect.

OPERA was built mostly to detect the appearance of tau neutrinos from a beam of muon neutrinos, a phenomenon called “oscillation” that enables one type of neutrinos to mutate into a completely different type when travelling over a large distance. This is something that had never been observed directly before but OPERA spotted one such event last year. To do so, they need to correlate the appearance of tau neutrinos in their detector with the arrival of muon neutrinos sent from CERN. Obviously, getting the timing right was essential, hence their careful checks on the arrival time of the muon neutrinos in Gran Sasso.

And there, surprise! The neutrinos reached the Gran Sasso laboratory 60 nanoseconds (i.e. 60 billionth of a second) faster than light travelling over the same distance, even though neutrinos are expected to travel slightly below the speed of light.

Both CERN and OPERA upgraded their equipment to use the most sophisticated timing devices and the same GPS satellite to synchronize their atomic clocks to within one nanosecond. The timing equipment was calibrated by the Swiss Metrology Institute and independently verified by the German Metrology Institute PTB (Physikalisch-Technische Bundesanstalt).

The distance between the point of emission at CERN and the point of detection in Gran Sasso was determined by CERN surveyors to be 731278.0 ± 0.2 meters, that is a 20 cm uncertainty over a distance of 731 km! All experimental errors amount to ten nanoseconds, six times smaller than the effect observed, a clear evidence if (and only if…) nothing has been omitted. This is precisely what further scrutiny from the scientific community at large and other experiments will try to determine in the near future.

So after months of very thorough crosschecks, the OPERA collaboration is finally going public with it. They are looking for independent measurements to refute or confirm what they observe. Anything is possible given the complexity of the measurement: a technical flaw, a small calibration problem, an experimental bias. Nothing can be neglected.

But if it turns out to be real, much work will remain to get the proper theoretical interpretation and its implications on relativity. We will still have to figure out if these particles are travelling faster than light or if they are just sneaky little neutrinos taking a shortcut through some extra dimension…

Pauline Gagnon

### Rien ne voyage plus vite que la lumière, sauf les rumeurs !

Friday, September 23rd, 2011

C’est ce que nous avait affirmé mon professeur de relativité à la fin d’une longue et aride leçon! Et les rumeurs allaient certainement bon train cette semaine au CERN sur l’imminence de l’annonce de l’observation de particules voyageant plus vite que la lumière. Cette nouvelle était tout aussi excitante qu’inattendue! Qui aurait pu prédire un truc aussi étrange et surprenant? Ce serait la découverte la plus ahurissante des dernières décennies. Difficile d’en imaginer les conséquences et implications mais il faudra d’abord l’établir avec certitude.

Je me souviens encore du frisson qui m’avait parcouru quand,  adolescente, j’avais entendu parlé des tachyons, des particules hautement hypothétiques possédant l’étrange propriété de voyager plus vite que la vitesse de la lumière, défiant un des fondements de la théorie de la relativité. Ces particules, au repos, se déplaceraient à la vitesse de la lumière et perdraient de la masse (et donc de l’énergie) lorsqu’on les accélère… Le même frisson m’est revenu lorsque j’ai entendu parler de ce résultat. Voici donc de quoi il en retourne.

L’expérience OPERA se trouve dans un laboratoire souterrain localisé dans un tunnel sous la montagne du Gran Sasso au centre de l’Italie, à 730 km du CERN. Des neutrinos produits au CERN traversent la couche terrestre pour aboutir au détecteur OPERA. C’est ce qui est à la fois incroyable et déplorable avec les neutrinos: ils peuvent traverser des quantités de matière phénoménales sans être affectés, ce qui rend aussi leur détection bien difficile.

OPERA a été construit principalement pour tenter de détecter l’apparition de neutrinos tau à partir d’un faisceau de neutrinos de muon, un phénomène appelé «oscillations» de neutrinos. Cela permet à des neutrinos d’un type donné de se muter en neutrinos d’un autre type lorsqu’ils voyagent sur une longue distance. Cela n’avait jamais été observé auparavant entre neutrinos de muons et taus mais OPERA en a capté un l’an dernier. Pour ce faire, il faut associer l’apparition d’un neutrino tau dans le détecteur avec l’arrivée de neutrinos de muons envoyés depuis le CERN. Bien évidemment, cela requiert une parfaite synchronisation, d’où la nécessité de bien vérifier le temps d’arrivée des neutrinos de smuons au Gran Sasso.

Et là, surprise. Les neutrinos auraient atteint le Gran Sasso 60 nanosecondes (i.e. 60 milliardièmes de seconde) plus vite que ne l’aurait fait la lumière alors qu’ils devraient normalement voyager juste un peu en dessous de la vitesse de la lumière.

CERN et OPERA se sont récemment rééquipé avec la fine pointe de la technologie pour obtenir une synchronisation d’une précision d’une nanoseconde entre leurs horloges. Leur équipement fut calibré par l’Institut Suisse de Métrologie, et vérifié indépendamment par son équivalent allemand, le Physikalisch-Technische Bundesanstalt.

La distance entre le point d’émission au CERN et le point de détection au Gran Sasso a été établie par des géomètres du CERN à 731278.0 ± 0.2 mètres, soit 20 cm d’erreur sur 731 km!

L’imprécision totale, en tenant compte de toutes les sources, s’élève à moins de dix nanomètres, soit six fois moins que les 60 nanosecondes d’avance mesurées pour les neutrinos. C’est donc un résultat solide si et seulement si tout a bien été pris en compte.

Après de longs mois passés à tout vérifier, la collaboration OPERA a présenté ses résultats en public au CERN cet après-midi devant une salle bondée en espérant maintenant que d’autres équipes tenteront de reproduire ce résultat et en invitant la communauté scientifique à passer tout ça au peigne fin. Une mesure indépendante pourrait réfuter ou valider leurs résultats. Tout est possible: il pourrait s’agir d’une erreur expérimentale, d’un problème de calibration, d’une technique biaisée. Rien ne doit être négligé.

Et si cela s’avère véridique, il restera encore beaucoup de travail pour déterminer quel cadre théorique peut expliquer ce phénomène et son implication sur la théorie de la relativité. Reste à voir si ces neutrinos voyagent vraiment plus vite que la lumière ou si on a affaire à de petits tricheurs (des snoros de neutrinos) qui se seraient taillé un raccourci en passant par une autre dimension…

Pauline Gagnon

Pour être averti-e lors de la parution de nouveaux blogs, suivez-moi sur Twitter: @GagnonPauline

### Live blog: neutrinos!

Friday, September 23rd, 2011

This is a live blog for the CERN EP Seminar “New results from OPERA on neutrino properties“, presented by Dario Autiero. Live webcast is available. The paper is available on the arXiv.

The crowd in the auditorium (Thanks to Kathryn Grim)

15:39: So here I am at CERN, impatiently waiting for the Colloquium to start on the OPERA result. The room is already filling up and the chatter is quite loud. I’m here with my flatmate Sudan, and we have a copy of the paper on the desk in front of us. I just bumped into a friend, Brian, and wished him look finding a chair! (He just ran to get me a coffee. Cheers Brian!)

15:53: Wow, the room is really crowded now! People are sitting on the steps, in the aisles, and more are coming in. The title slide is already up on the projector, and some AV equipment is being brought in. I was just chatting to Sudan and Brian, and we commenting that this is probably the biggest presentation that the world’s biggest physics lab has seen in a long time! As Sudan says, “The whole world is going to be watching this man.”

15:55: Burton and Pauline are here too, getting some photos before the talk begins. Expect to see more (less hastily written) blog posts about this talk!

15:59: We’re not allowed to take photos of the talk itself, but there will be a video feed that you can watch. See this link for details about the live webcast.

16:03: The talk begins. A fairly straightforward start so far. As usual, the speaker introduces the OPERA Collaboration, and gives a bit of background. Nothing ground breaking so far!

16:06: The analysis was performed blind, which means that the physicists checked and double checked their systematic uncertainties before looking at the data. This is a common best practice in these kinds of experiments and it is a good way to eliminate a lot of experimenter bias. The speaker is now discussing past results, some of which show no faster than light speed, and one of which (from MINOS) that shows a small effect which is less than 2σ.

16:16: Autiero is currently discussing the hardware of the experiment. It looks like a standard neutrino observatory setup- large amounts of dense matter (Pb), scintillation plates and tracking hardware for the muons which get produced when the neutrinos interact. By the time the beam reaches Gran Sasso it is about 2km wide! At CERN the neutrinos are produced by accelerating protons at a target, producing pions and kaons, which are then allowed to decay to muons and muon neutrinos. The hadrons are stopped with large amounts of Carbon and Iron, so that only the neutrinos and some muons survive. By the time the neutrino beam reaches Gran Sasso the muons have long since interacted and are no longer present in the beam. The neutrinos have 17GeV of energy when they leave CERN, so they are very energetic!

16:29: The discussion has moved onto the timing system, probably the most controversial aspect of the experiment. The timing challenge is probably the most difficult part of the whole analysis, and the part that particle physicists are least familiar with. Autiero points out that the same methods of timing are commonly used in metrology experiments. For OPERA, the location of each end of the experiment in space and time is determined using GPS satellites in the normal way, and then a “common view” is defined, leading to 1ns accuracy in synchronization. It looks like variations in the local clocks are corrected using the common view method. The time difference between CERN and Gran Sasso was found to be 2.3 ± 0.9 ns, consistent with the corrections.

16:36: Things are made trickier by identifying where in the “spill” of protons a neutrino came from. For a given neutrino it’s pretty much impossible to get ns precision timing, so probability density functions are used and the time interval for a given proton spill is folded into the distribution. We also don’t know where each neutrino is produced within the decay tube. The average uncertainty in this time is about 1.4ns. Autiero is now talking about the time of flight measurement in more detail, showing the proton spills and neutrino measurements overlaid.

16:39: Geodesy is important to this analysis. OPERA need to know the distance between CERN and Gran Sasso to good precision (they need to know the distances underground, which makes things more complicated.) They get a precision of 20cm in 730km. Not bad! Autiero is now showing the position information, showing evidence of continental drift and even an earthquake. This is very cool!

16:47: Two techniques are used to verify timing, using Caesium clocks and optical fibers. These agree to ns precision. The overall timing system is rather complicated, and I’m having trouble following it all!

16:48: I just got a message from a friend who saw this blog via Twitter. Hello Angela! Welcome to all the readers from Twitter!

16:52: Currently discussing event selection at Gran Sasso. Events must have a highly relativistic muon associated with them. (The speed of the muon and slight difference in direction of flight can only increase the measured time of flight.)

16:54: Autiero is telling us about how the analysis is blinded. They used very old calibrations, intentionally giving meaningless results. A novel approach to blinding!

16:56: No evidence of variation with respect to time of day or time of year. So that’s the “Earth moved!” theory sunk.

17:01: Unblinding: Δt = -987.8ns correction to time of flight after applying corrections (ie using up to date calibration.) Total systematic uncertainty is 7.4ns. Time of flight obtained using maximum likelihood. Measured difference in time of flight between speed of light and speed of neutrinos is

$\delta t (c-\nu) = (60.7 \pm 6.9(stat) \pm 7.40 (syst)) ns$

$\frac{c-v_{\nu}}{c} = -(2.4 \pm 0.28 \pm 0.30)\times 10^{-5}$

17:03: ~16,000 events observed. OPERA has spent six months checking and rechecking systematic uncertainties. Cannot account for discrepancy in terms of systematic uncertainties.

17:04: “Thank you”. Huge ripple of applause fills the auditorium.

### Questions

(These questions and answers are happening fast. I probably make an error or omission here and there. Apologies. Consult the webcast for a more accurate account or for any clarifications.)

17:05: Questions are to be organized. Questions about the distance interval, then the time interval, then the experiment itself. There will be plenty of questions!

17:08: Question: How can you be sure that the timing calibrations were not subject to the same systematic uncertainties whenever they were made? Answer: Several checks made. One suggestion is to drill a direct hole. This was considered, but has an uncertainty associated of the order of 5%, too large for this experiment.

17:12: Question: Geodesy measurements were taken at one time. There are tidal effects (for example, measured at LEP.) How can you be sure that there are no further deviations in the geodesy? Answer: Many checks made and many measurements checked.

17:14: Question: Looking for an effect of 1 part in 105. Two measurements not sufficient. Movement of the Moon could affect measurements, for example. Answer: Several measurements made. Data taken over three years, tidal forces should average out.

17:15: Question: Is the 20cm uncertainty in 730km common? Answer: Similar measurements performed elsewhere. Close to state of the art. Even had to stop traffic on half the highway to get the measurement of geodesy!

17:16: Question: Do you take into account the rotation of the Earth? Answer: Yes, it’s a sub ns effect.

17:23: Question: Uncertainty at CERN is of the order of 10μs. How do you get uncertainty of 60ns at Gran Sasso? Answer: We perform a maximum likelihood analysis averaging over the (known shape) of the proton spill and use probability density functions.

(Long discussion about beam timings and maximum likelihood measurement etc.)

17:31: Large uncertainty from internal timers at each site (antenna gives large uncertainty.) Measurements of timing don’t all agree. How can you be sure of the calibration? Answer: There are advanced ways to calibrate measurements. Perform inclusive measurement using optic fibers. Comment from timing friends in the audience? Audience member: Your answer is fine. Good to get opportunity to work on timing at CERN.

17:33 Question: What about variation with respect to time of day/year? Answer: Results show no variation in day/night or Summer vs Spring+Fall.

17:35: Question: How can you be sure of geodesy measurements if they do not agree? Answer: The measurements shown are for four different points, not the same point measured four times. Clocks are also continually resynchronized.

17:37: Question: Do temperature variations affect GPS signals? Answer: Local temperature does not affect GPS measurements. Two frequencies are used to get the position in ionosphere. 1ps precision possible, but not needed for OPERA.

17:41: Question: Can you show the tails of the timing distributions with and without the correction? Is selection biasing the shapes of the fitted distributions? Answer: Not much dependence on spatial position from BCT at CERN. (Colleague from audience): The fit is performed globally. More variation present than is shown in the slides, with more features to which the fit is sensitive.

17:43: Question: Two factors in the fit: delay and normalization. Do you take normalization into account? Answer: Normalization is fixed to number of events observed. (Not normalized to the cross section.)

17:45: Question: Do you take beam stretching/squeezing into account? Answer: Timing is measured on BCT. No correlation between position in Gran Sasso and at CERN.

17:47: Question: Don’t know where muons were generated (could be in rock.) How is that taken in to account? Answer: We look at events with and without selections on muons.

17:49: Question: Do you get a better fit if you fit to the whole range and different regions? What is the χ2/n for the fits? Answer: We perform the fit on the whole range and have the values of χ2/n, but I can’t remember what they are, and they are not on the slides.

17:50: Question: What about any energy dependence of the result? Answer: We don’t claim energy dependence or rule it out with our level of precision and accuracy.

17:52: Question: Is a near experiment possible? Answer: This is a side analysis. The main aim is to search for τ appearance. (Laughter and applause from audience.) We cannot compromise our main physics focus. E-mail questions welcome!

17:53: End, and lots of applause. Time for discussion over coffee! Thanks for reading!

The start of the neutrinos journey, taken from the OPERA paper. (http://arxiv.org/abs/1109.4897)

### Elementary, my dear neutrino…

Friday, September 23rd, 2011

Sometimes discoveries in science turn up where you are looking for them, like finding treasure near a shipwreck. At other times they seem to appear from nowhere, as if they’ve fallen from the sky. In particle physics there are plenty of examples of both kinds, but all discoveries have one thing in common. As soon you find something new – whether it’s expected or completely out of the blue – you go back through the analysis with a fine tooth comb, making sure that you’ve missed nothing. Is there a detail you’ve forgotten? Have you overlooked some aspect that could mimic the effect of something new?

It’s at this stage that you make your results known to the jury of your peers – other scientists working in the same area who look at what you’ve done and see if they can find anything you might have missed. Then, to quote one of the famous fictional detectives, Sherlock Holmes, “when you have eliminated the impossible, whatever remains, however improbable, must be the truth”.

This is particularly the case when a result is completely unexpected. In a sense, it’s all down to detective work, and the experimenters must make sure that they are interpreting all the evidence correctly before identifying the suspect.

The curious case of the speeding neutrinos – apparently breaking nature’s speed limit of the velocity of light as they fly from CERN to the OPERA experiment in central Italy – is now open to the jury. The OPERA collaboration has been able to find no explanation in terms of the experimental set up for this effect. So the researchers have revealed what they observe to their peers through a paper posted on arXiv.org that explains all the steps from data collection to the final analysis, and through a talk at CERN. Neutrino experiments are notoriously difficult because neutrino interactions are so rare, but over the coming months – and indeed years – the teams working on similar experiments elsewhere will scrutinise their data to see if they see the same effect.

This is the way that science works all the time, not just when a surprise effect appears like an unexpected guest at a party. Results are checked by others, questions can be asked – and answered – and when everyone is satisfied that nothing has been overlooked, then the results are published. Of course, wrong results do get published and surprising effects can fade away as further experiments fail to find fresh evidence. Again, this is all part of the scientific process; far from being a straight line like a Roman road linking major discoveries, it wanders more like river that changes direction in response to the landscape it crosses,

So the OPERA results are now coming under close scrutiny in the particle physics community, and it will be fascinating to see whether they do eventually stand the test of time. Then, and only then, if the results remain, fulfilling Sherlock Holmes’s requirement, would super-fast neutrinos become established, not as science fiction, but as science fact. For now, however, we have to wait and see.

Christine Sutton

### Measurement of the neutrino velocity with the OPERA detector in the CNGS beam

Thursday, September 22nd, 2011

Here is the article on the anomaly being reported for the speed of neutrinos from CERN to the OPERA detector in Italy

http://arxiv.org/pdf/1109.4897v1