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  • richardmitnick 11:26 am on December 6, 2017 Permalink | Reply
    Tags: , , George Uhlenbeck and Samuel Goudsmit came up with the idea of quantum spin in the mid-1920s, How a quantum number that made no physical sense turned out to be real… and irreplaceable, , Spin (physics)   

    From Ethan Siegel: “Spin: The Quantum Property That Should Have Been Impossible” 

    Ethan Siegel

    Dec 5, 2017
    Paul Halpern

    1
    George Uhlenbeck (L) and Samuel Goudsmit (R) came up with the idea of quantum spin in the mid-1920s. This photo was taken with Hendrik Kramers (center) in 1928 (Public Domain)

    How a quantum number that made no physical sense turned out to be real… and irreplaceable.

    In the early 1920s, physicists were first working out the mysteries of the quantum Universe. Particles sometimes behaved as waves, with indeterminate positions, momenta, energies, and other properties. There was an inherent uncertainty to a great many properties that we could measure, and physicists raced to work out the rules.

    Amidst this frenzy, a young Dutch researcher named George Uhlenbeck implored Paul Ehrenfest, his research supervisor at the University of Leiden, not to submit the paper he wrote with Samuel “Sam” Goudsmit about a new quantum number called spin. It was not correct, Uhlenbeck told him in a frenzy. Let’s just drop it and start over, he implored.

    Uhlenbeck and Goudsmit, both then in their mid-20s, had just showed their joint result to the great Dutch physicist Hendrik Lorentz who had found what seemed like a major error. Electrons, he pointed out, couldn’t possibly rotate fast enough to generate the magnetic moment (interaction strength between a particle and an external magnetic field) that the duo had predicted. The particles would need to whirl faster than the sacred speed limit of light. How could they? The spin paper is unphysical, Uhlenbeck told Ehrenfest, and should not be published.

    1
    Electrons, like all spin-1/2 fermions, have two possible spin orientations when placed in a magnetic field (CK-12 Foundation / Wikimedia Commons).

    Ehrenfest’s reply was curt. “It is too late,” he told Uhlenbeck. “I have already submitted the paper. It will be published in two weeks.” Then he added, “Both of you are young and can afford to do something stupid.”

    Ehrenfest’s words certainly weren’t comforting. Surely, Uhlenbeck didn’t want to start off his career with a foolish error. Luckily, however, the spin quantum number, interpreted abstractly and having nothing whatsoever to do with rotation despite its name, has become an essential feature of modern physics. Electrons somehow acted in a magnetic field as if they were whirling, even thought they really couldn’t be. Uhlenbeck and Goudsmit’s roulette wheel bet on a weird new concept had paid off handsomely.

    3
    Thomas precession demonstrated with a gyroscope in space, as in the Gravity Probe B experiment (NASA).

    One of the harshest critics of spin was the acerbic physicist Wolfgang Pauli. Pauli, like Ehrenfest was born in Vienna, and moved elsewhere for his career. Like Lorentz, Pauli believed at first that spin was unphysical. (In January 1925, German American researcher Ralph Kronig had made a similar suggestion to Pauli, which he had immediately rejected and was never published.) He changed his mind only after Llewellyn Thomas demonstrated a phenomenon called “Thomas precession” that examined spin using special relativity.

    4
    Wolfgang Pauli (L) and Paul Ehrenfest (R), only a few years before Ehrenfest would tragically commit suicide (CERN photo archives)

    Pauli and Ehrenfest shared a blunt demeanor and willingness to criticize others in matters of science. They had first met in 1922 at the “Bohrfestspiele” (celebration of Niels Bohr’s work around the time of his Nobel Prize ) in Göttingen, Germany. Pauli, then in his early 20s, was already famous as a “wunderkind” for an excellent article about general relativity that appeared in a scientific encyclopedia edited by German physicist Arnold Sommerfeld. Ehrenfest and his wife had contributed a piece on statistical mechanics for the same volume. Pauli and Ehrenfest’s initial conversation centered on those respective works.

    As physicist Oskar Klein reported: “On that occasion Ehrenfest stood a little away from Pauli, looked at him mockingly and said: ‘Herr Pauli, I like your article better than I like you! To which Pauli very calmly replied: ‘That is funny, with me it is just the opposite!’”

    5
    In an atom, each s orbital (red), each of the p orbitals (yellow), the d orbitals (blue) and the f orbitals (green) can contain only two electrons apiece: one spin up and one spin down in each one (Libretexts Library / NSF / UC Davis).

    It was ironic that Pauli was initially opposed to spin, given that one of his key proposals — the exclusion principle — was one of the main motivators for its development. Introduced in early 1925, it stated that no two electrons (later extended to an entire class of particles called fermions) could occupy exactly the same quantum state. (Other types of particles, such as photons, that don’t obey that law are called bosons.)

    Quantum states in atoms (such as hydrogen) can be characterized by quantum numbers denoting the properties of an electron occupying such a state. The principal quantum number, introduced by Bohr, described the energy of an electron due to its electric interaction with the nucleus. The second and third quantum numbers, introduced by Sommerfeld, pertained to aspects of an electron’s angular momentum (a measure of the shape and configuration of its orbit). Traditionally, each of those quantum numbers were integers — counting numbers denoting a finite set of possibilities, such as the seat and row numbers in an arena. In tandem, those three quantum numbers determine how the probability clouds representing the electrons position themselves in the “stadium” surrounding the nucleus. That intricate pattern, well known by chemists, helps explain the periodic table.

    6
    Periodic Table 2017. Wikipedia

    7
    Hydrogen density plots for an electron in a variety of quantum states. While the three quantum numbers of charge and angular momentum in two different dimensions could explain a great deal, ‘spin’ must be added to explain the periodic table and the number of electrons in orbitals for each atom (PoorLeno / Wikimedia Commons).

    However, as Goudsmit realized in May 1925, there was a problem with using pure integers to characterize the quantum states. If you did, the exclusion principle couldn’t be maintained. Two electrons in the ground state (lowest energy level) of an atom would have identical set of those three quantum numbers. Goudsmit found that by introducing a fourth quantum number, representing a kind of intrinsic or extra angular momentum, that could take on only one of two possible values — either +½ or -½ — he could preserve the Pauli exclusion principle. The ground state could still have two electrons, but their fourth quantum numbers would be opposite: if one was +½, the other would be -½.

    8
    In the absence of a magnetic field, the energy levels of various states within an atomic orbital are identical (L). If a magnetic field is applied, however (R), the states split according to the Zeeman effect. Here we see the Zeeman splitting of a P-S doublet transition (Evgeny at English Wikipedia).

    Introducing a half-integer quantum number without physical justification was a rather audacious move. In a stadium concert, if an agency issued two tickets for the same seat A11 by labeling them A10½ & A11½ that would seem like chicanery. In hindsight, Goudsmit freely admitted that his physical understanding was not developed enough to justify such a move. He was working part time with Pieter Zeeman on atomic spectral lines, but had yet to see the connection. Zeeman had found extra spectral lines when an atom was placed in a magnetic field for which there was no explanation. Luckily Ehrenfest paired Goudsmit with Uhlenbeck, who knew a greater deal of foundational physics.

    9
    Graph showing the Zeeman splitting in Rb-87, the energy levels of the 5s orbitals, including fine structure and hyperfine structure (Danski14 / Wikimedia Commons).

    As Goudsmit recalled, “Ehrenfest said: ‘You should work together with him for a while, then he may learn something about the new atomic structure and all that spectral business.’ What he clearly thought, of course, was: ‘Perhaps I might learn a little bit of real physics from Uhlenbeck.’”

    Uhlenbeck learned from Goudsmit about the anomalous spectral lines as well as his theory of a half-integer quantum number and brilliantly connected the two ideas. The fourth quantum number, Uhlenbeck pointed out, made sense if the electron generated its own magnetic field like a spinning ball of charge. If it was a mini-magnet that could spin either clockwise or counterclockwise, it would have two different energy states in the presence of an external magnet — either aligned or anti-aligned — which would explain the split in spectral lines. Goudsmit was convinced. They wrote up their results and gave them to Ehrenfest, who promptly submitted them to a journal.

    10
    The visualization of an electron’s spin on the exterior wall of a building in Leiden (Vysotsky: Wikimedia)

    The young physicists were lucky that Ehrenfest could be impulsive. If he had discussed the spin idea with others, probably few in the physics community (except, potentially, for Werner Heisenberg, who was also thinking about half-integer quantum numbers) would have supported it. But once it was published, and the spin idea was re-interpreted as an abstract quantum number, it seemed the perfect way of understanding Pauli’s exclusion principle. Integer “stadium seating” for electrons was out, half-integer was in.

    When they left Leiden, Uhlenbeck and Goudsmit conducted a different kind of experiment, dubbed the “Michigan experiment,” when they both took on roles as Assistant Professors at the University of Michigan at the same time. They even collaborated on training graduate students, including Dutch physicist Max Dresden (who would become the research supervisor of this author and carry on the pedagogical tradition handed down by Ehrenfest, Uhlenbeck, and Goudsmit.) Open-minded inquiry was the hallmark of that school of thought — which splendidly led to the important concept of spin.

    See the full article here .

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    “Starts With A Bang! is a blog/video blog about cosmology, physics, astronomy, and anything else I find interesting enough to write about. I am a firm believer that the highest good in life is learning, and the greatest evil is willful ignorance. The goal of everything on this site is to help inform you about our world, how we came to be here, and to understand how it all works. As I write these pages for you, I hope to not only explain to you what we know, think, and believe, but how we know it, and why we draw the conclusions we do. It is my hope that you find this interesting, informative, and accessible,” says Ethan

     
  • richardmitnick 9:31 am on March 14, 2016 Permalink | Reply
    Tags: , , Spin (physics)   

    From AAAS: “‘Shocking’ unification reduces a lot of tough physics problems to just one” 

    AAAS

    AAAS

    Mar. 10, 2016
    Adrian Cho

    2D Ising model Spin model, shown schematically on the left, can be made equivalent to any other more complicated spin model, such as those on the right. Christian Hackenberg
    2D Ising model Spin model, shown schematically on the left, can be made equivalent to any other more complicated spin model, such as those on the right

    It’s the sort of physics advance that Sauron might appreciate. The villain in J. R. R. Tolkien’s fantasy trilogy, The Lord of the Rings, gives the kings of men, elves, and dwarves magic rings, but then forges a single ring that controls all the others. In a similar way, a duo of theoretical physicists has come up with a way to transform all the disparate members of a vast family of complex systems known as spin models into different shades of a single simple model, which now serves as the one to rule them all.

    That Ising model is the simplest spin model and already has a legendary history. The advance could have implications well beyond physics, as spin models have been used to simulate everything from stock markets to protein folding. “I find it pretty shocking,” says David Perez, a mathematician at the Complutense University of Madrid (UCM), who was not involved with the work. “What is surprising is not that there is a universal model, but that it is so simple.”

    Spin models were invented to explain magnetic materials, such as iron and nickel. Those metals can be magnetized because each of their atoms acts like a tiny bar magnet. At high temperatures, the jiggling atoms point in random directions and their magnetic fields cancel one another. However, below the so-called Curie temperature, the material undergoes a “phase transition” much like water freezing into ice, and all the atoms suddenly point in the same direction. That alignment reduces the atoms’ total energy and makes their magnetic fields add together. Because each atom’s magnetism originates from the spin of an unpaired electron within it, models of how magnetism arises are known as spin models.

    The Ising model was the first spin model, invented in 1920 by German physicist Wilhelm Lenz, who gave it to his student Ernst Ising to analyze. In it, each atom is a simple object that can point either up or down. Each spin flips randomly with thermal energy, but it interacts with its neighbors so that each pair of spins can lower its energy by pointing in the same direction. Each spin can also lower its energy by aligning with an externally applied magnetic field. The coupling between each pair of spins can be different, as can be the external field applied to each spin.

    Ising hoped to show that below a certain temperature the spins would undergo a magnetic phase transition. However, he could “solve” only the 1D Ising model—a single string of spins—and found it had no phase transition. Ising speculated that the 2- and 3D cases wouldn’t, either. Then in 1944 the enigmatic Norwegian-American chemist Lars Onsager solved the Ising model with uniform couplings and no external fields on a 2D square pattern of spin. The famously incomprehensible Onsager, who won the 1968 Nobel Prize in Chemistry for earlier work but also lost two faculty jobs, showed that the 2D Ising model does have a phase transition—the first seen in a theoretical model. Onsager’s tour de force calculation is now legendary, although he published it only 2 years after the fact. The 3D Ising model is still unsolved.

    Meanwhile, spurred in part by Ising’s difficulties, physicists invented plenty of other spin models. Instead of up and down, the spins can have, say, five possible settings, or like compass needles can point in any direction. The spins might also interact in groups larger than pairs and with spins far beyond their neighbors. Spin models have found use outside physics. For example, the spread of an epidemic might be simulated on a spin model with spins having three states corresponding to well, sick, and recovered. “Spin model is a really bad name for something that’s a lot more general,” says Gemma De las Cuevas, a theoretical physicist at the Max Planck Institute of Quantum Optics in Garching, Germany.

    But all those disparate spin models can be transformed into the good old 2D Ising model, De las Cuevas and Toby Cubitt, a theorist of University College London, report online today in Science. Crudely their proof works as follows. First, the two scientists note that the up-or-down Ising spin resembles the true-or-false character of a logical statement such as “the car is white.” They then prove that any particular 2D Ising model—i.e., with a particular set of coupling and external fields — is equivalent to an instance of a logical problem called the satisfiability, or SAT, problem, in which the goal is to come up with a set of logical statements, A,B,C, … that satisfy a long logical formula such as “A and not (B or C) …” The theorists present a way to map the SAT problem onto the 2D Ising model.

    Next, they show how any other spin model can also be translated into a SAT problem. That SAT problem can then be translated onto the 2D Ising model, thus making the two spin models equivalent. There is a price to pay, however. The 2D Ising model must have more spins than the original spin model. But De las Cuevas says that the computational demands of the Ising model are only modestly bigger than those of the original model. “If you could explain all of the parameter regions of the 2D Ising model with fields, that would be equivalent to probing all possible spin models,” she says.

    That’s a big “if.” Although Onsager solved the 2D Ising model with uniform couplings and no external fields, the general problem with nonuniform couplings and external fields remains unsolved and is among the most computationally demanding problems there is—with the number of computational steps exploding exponentially with the number of spins. “It’s surprising that you can map any model onto this simple model,” says Miguel Angel Martin-Delgado, a theoretical physicist at UCM. “But you can take the other side, which is that this simple-seeming model is as complex as any other.”

    De las Cuevas agrees and says that the value of the advance may come in practical computations. It provides a recipe for translating any spin model, no matter how baroque, into a 2D Ising model, with the complexity of the original model encoded in the couplings between the Ising spins and the magnetic fields. If that recipe can be optimized, then it may be easier to simulate on a computer the Ising model instead of the original model, De las Cuevas says. “I think there’s a lot of room for thinking, ‘Hey, now I can study this model that I couldn’t before, using this universal model.'”

    The advance might also make into the textbooks. The Ising model is introduced in statistical mechanics courses as the simplest spin model. Future texts might also note that in spite of its simplicity, it can reproduce all other spin models. In a sense, it’s all you need to know.

    See the full article here .

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  • richardmitnick 4:10 pm on February 5, 2016 Permalink | Reply
    Tags: , , , Spin (physics)   

    From Quantum Diaries: “Spun out of proportion: The Proton Spin Crisis” 

    2.4.16
    Ricky Nathvani

    We’ve known about the proton’s existence for nearly a hundred years, so you’d be forgiven for thinking that we knew all there was to know about it. For many of us, our last exposure to the word “proton” was in high school chemistry, where they were described as a little sphere of positive charge that clumps with neutrons to make atomic nuclei, around which negatively charged electrons orbit to create all the atoms, which make up Life, the Universe and Everything (1).

    Like many ideas in science, this is a simplified model that serves as a good introduction to a topic, but skips over the gory details and the bizarre, underlying reality of nature. In this article, we’ll focus on one particular aspect, the quantum mechanical spin of the proton. The quest to measure its origin has sparked discovery, controversy and speculation that has lasted 30 years, the answer to which is currently being sought at a unique particle collider in New York.

    The first thing to note is that protons, unlike electrons (2), are composite particles, made up from lots of other particles. The usual description is that the proton is made up of three smaller quarks which, as far as we know, can’t be broken down any further. This picture works remarkably well at low energies but it turns out at very high energies, like those being reached at the at the LHC, this description turns out to be inadequate.

    CERN LHC Map
    CERN LHC Grand Tunnel
    CERN LHC particles
    LHC at CERN

    At that point, we have to get into the nitty-gritty and consider things like quark-antiquark pairs that live inside the proton interacting dynamically with other quarks without changing its the overall charge. Furthermore, there are particles called gluons that are exchanged between quarks, making them “stick” together in the proton and playing a crucial role in providing an accurate description for particle physics experiments.

    So on closer inspection, our little sphere of positive charge turns out to be a buzzing hive of activity, with quarks and gluons all shuffling about, conspiring to create what we call the proton. It is by inferring the nature of these particles within the proton that a successful model of the strong nuclear force, known as Quantum Chromodynamics (QCD), was developed. The gluons were predicted and verfied to be the carriers of this force between quarks. More on them later.

    That’s the proton, but what exactly is spin? It’s often compared to angular momentum, like the objects in our everyday experience might have. Everyone who’s ever messed around on an office chair knows that once you get spun around in one, it often takes you a bit of effort to stop because the angular momentum you’ve built up keeps you going. If you did this a lot, you might have noticed that if you started spinning with your legs/arms outstretched and brought them inwards while you were spinning, you’d begin to spin faster! This is because angular momentum (L) is proportional to the radial (r) distribution of matter (i.e. how far out things are from the axis of rotation) multiplied by the speed of rotation (3) (v). To put it mathematically L = m × v × r where m is just your constant mass. Since L is constant, as you decrease r (by bringing your arms/legs inwards), v (the speed at which you’re spinning) increases to compensate. All fairly simple stuff.

    So clearly, for something to have angular momentum it needs to be distributed radially. Surely r has to be greater than 0 for L to be greater than 0. This is true, but it turns out that’s not all there is to the story. A full description of angular momentum at the quantum (atomic) level is given by something we denote as “J”. I’ll skip the details, but it turns out J = L + S, where L is orbital angular momentum, in a fashion similar to what we’ve discussed, and S? S is a slightly different beast.

    Both L and S can only take on discrete values at the microscopic level, that is, they have quantised values. But whereas a point-like particle cannot have L>0 in its rest frame (since if it isn’t moving around and v = 0, then L = 0), S will have a non-zero value even when the particle isn’t moving. S is what we call Spin. For the electron and quarks, it takes on the value of ½ in natural units.

    Spin has a lot of very strange properties. You can think of it like a little arrow pointing in a direction in space but it’s not something we can truly visualise. One is tempted to think of the electron like the Earth, a sphere spinning about some kind of axis, but the electron is not a sphere, it’s a point-like particle with no “structure” in space. While an electron can have many different values of L depending on its energy (and atomic structure depends on these values), it only has one intrinsic magnitude of spin: ½. However, since spin can be thought of as an arrow, we have some flexibility. Loosely speaking, spin can point in many different directions but we’ll consider it as pointing “up” (+½) or “down” (- ½). If we try to measure it along a particular axis, we’re bound to find it in one of these states relative to our direction of measurement.

    One of the peculiar things about spin-½ is that it causes the wave-function of the electron to exhibit some mind bending properties. For example, you’d think rotating any object by 360 degrees would put it back into exactly the same state as it was, but it turns out that doesn’t hold true for electrons. For electrons, rotating them by 360 degrees introduces a negative sign into their wave-function! You have to spin it another 360 degrees to get it back into the same state! There are ways to visualise systems with similar behaviour (see right) but that’s just a sort of “metaphor” for what really happens to the electron. This links into the famous conclusion of Pauli’s that no two identical particles with spin-½ (or any other half-integer spin) can share the same quantum mechanical state.

    ——

    Spin is an important property of matter that only really manifests on the quantum scale, and while we can’t visualise it, it ends up being important for the structure of atoms and how all solid objects obtain the properties they do. The other important property it has is that the spin of a free particle likes to align with magnetic fields (4) (and the bigger the spin, the greater the magnetic coupling to the field). By using this property, it was discovered that the proton also had angular momentum J = ½. Since the proton is a stable particle, it was modelled to be in a low energy state with L = 0 and hence J = S = ½ (that is to say, the orbital angular momentum is assumed to be zero and hence we may simply call J, the “spin”). The fact the proton has spin and that spin aligns with magnetic fields, is a crucial element to what makes MRI machines work.

    Once we got a firm handle on quarks in the late 1960s, the spin structure of the proton was thought to be fairly simple. The proton has spin-½. Quarks, from scattering experiments and symmetry considerations, were also inferred to have spin-½. Therefore, if the three quarks that make up the proton were in an “up-down-up” configuration, the spin of the proton naturally comes out as ½ – ½ + ½ = ½. Not only does this add up to the measured spin, but it also gives a pleasant symmetry to the quantum description of the proton, consistent with the Pauli exclusion principle (it doesn’t matter which of the three quarks is the “down” quark). But hang on, didn’t I say that the three-quarks story was incomplete? At high energies, there should be a lot more quark-antiquark pairs (sea quarks) involved, messing everything up! Even so, theorists predicted that these quark-antiquark pairs would tend not to be polarised, that is, have a preferred direction, and hence would not contribute to the total spin of the proton.

    If you can get the entirety of the proton spinning in a particular direction (i.e. polarising it), it turns out the scattering of an electron against its constituent quarks should be sensitive to their spin! Thus, by scattering electrons at high energy, one could check the predictions of theorists about how the quarks’ spin contributes to the proton.

    In a series of perfectly conducted experiments, the theory was found to be absolutely spot on with no discrepancy whatsoever. Several Nobel prizes were handed out and the entire incident was considered resolved, now just a footnote in history. OK, not really.

    In truth, the total opposite happened. Although the experiments had a reasonable amount of uncertainty due to the inherent difficulty of polarising protons, a landmark paper by the European Muon Collaboration found results consistent with the quarks contributing absolutely no overall spin to the proton whatsoever! The measurements could be interpreted with the overall spin from the quarks being zero (5). This was a complete shock to most physicists who were expecting verification from what was supposed to be a fairly straightforward measurement. Credit where it is due, there were theorists who had predicted that the assumption about orbital angular momentum (L = 0) had been rather ad-hoc and that L>0 could account for some of the missing spin. Scarcely anyone would have expected, however, that the quarks would carry so little of the spin. Although the nuclear strong force, which governs how quarks and gluons combine to form the proton, has been tested to remarkable accuracy, the nature of its self-interaction makes it incredibly difficult to draw predictions from.

    Future experiments (led by father and son rivals, Vernon and Emlyn Hughes (6) of CERN and SLAC respectively) managed to bring this to a marginally less shocking proposal.

    SLAC Campus
    SLAC

    The greater accuracy of the measurements from these collaborations had found that the total spin contributions from the quarks was actually closer to ~30%. An important discovery was that the sea quarks, thought not to be important, were actually found to have measurable polarisation. Although it cleared up some of the discrepancy, it still left 60-70% of spin unaccounted for. Today, following much more experimental activity in Deep Inelastic Scattering and precision low-energy elastic scattering, the situation has not changed in terms of the raw numbers. The best estimates still peg the quarks’ spin as constituting only about 30% of the total.

    Remarkably, there are theoretical proposals to resolve the problem that were hinted at long before experiments were even conducted. As mentioned previously, although currently impossible to test experimentally, the quarks may carry orbital angular momentum (L) that could compensate for some of the missing spin. Furthermore, we have failed to mention the contribution of gluons to the proton spin. Gluons are spin-1 particles, and were thought to arrange themselves such that their total contribution to the proton spin was nearly non-existent.

    The Relativistic Heavy Ion Collider (RHIC) in New York is currently the only spin-polarised proton collider in the world.

    BNL RHIC Campus
    BNL RHIC
    RHIC at Brookhaven National Lab, New York, USA

    This gives it a unique sensitivity to the spin structure of the proton. In 2014, an analysis of the data collected at RHIC indicated that the gluons (whose spin contribution can be inferred from polarised proton-proton collisions) could potentially account for up to 30 of the missing 70% of proton spin! About the same as the quarks. This would bring the “missing” amount down to about 40%, which could be accounted for by the unmeasurable orbital angular momentum of both quarks and gluons.

    As 2016 kicks into gear, RHIC will be collecting data at a much faster rate than ever after a recent technical upgrade that should double it’s luminosity (loosely speaking, the rate at which proton collisions occur). With the increased statistics, we should be able to get an even greater handle on the exact origin of proton spin.

    The astute reader, provided they have not already wandered off, dizzy from all this talk of spinning protons, may be tempted to ask “Why on earth does it matter where the total spin comes from? Isn’t this just abstract accountancy?” This is a fair question and I think the answer is a good one. Protons, like all other hadrons (similar, composite particles made of quarks and gluons) are not very well understood at all. A peculiar feature of QCD called confinement binds individual quarks together so that they are never observed in isolation, only bound up in particles such as the proton. Understanding the spin structure of the proton can inform our theoretical models for understanding this phenomenon.

    This has important implications, one being that 98% of the mass of all visible matter does not come from the Higgs Boson. It comes from the binding energy of protons! And the exact nature of confinement and precise properties of QCD have implications for the cosmology of the early universe. Finally, scattering experiments with protons have already revealed so much to fundamental physics, such as the comprehension of one of the fundamental forces of nature. As one of our most reliable probes of nature, currently in use at the LHC, understanding them better will almost certainly aid our attempts to unearth future discoveries.

    Kind regards to Sebastian Bending (UCL) for several suggestions (all mistakes are unreservedly my own).

    [1] …excluding dark matter and dark energy which constitute the dark ~95% of the universe.

    [2] To the best of our knowledge.

    [3] Strictly speaking the component of velocity perpendicular to the radial direction.

    [4] Sometimes, spins in a medium like water like to align against magnetic fields, causing an opposite magnetic moment (known as diamagnetism). Since frogs are mostly water, this effect can and has been used to levitate frogs.

    [5] A lot of the information here has been summarised from this excellent article by Robert Jaffe, whose collaboration with John Ellis on the Ellis-Jaffe rule led to many of the predictions discussed here.

    [6] Emlyn was actually the spokesperson for SLAC, though he is listed as one of the primary authors on the SLAC papers regarding the spin structure of the proton.

    See the full article here .

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  • richardmitnick 7:54 pm on January 6, 2016 Permalink | Reply
    Tags: , , Spin (physics)   

    From BNL: “Beam-Beam Compensation Scheme Doubles Proton-Proton Collision Rates at RHIC” 

    Brookhaven Lab

    January 4, 2016
    Karen McNulty Walsh, (631) 344-8350
    Peter Genzer, (631) 344-3174

    Temp 1
    Wolfram Fischer stands next to the electron lensing apparatus at the Relativistic Heavy Ion Collider (RHIC). A schematic diagram showing the components appears below.

    Accelerator physicists at the U.S. Department of Energy’s (DOE) Brookhaven National Laboratory have successfully implemented an innovative scheme for increasing proton collision rates at the Relativistic Heavy Ion Collider (RHIC).

    BNL RHIC Campus
    BNL RHIC
    RHIC map and Collider

    More proton collisions at this DOE Office of Science User Facility produce more data for scientists to sift through to answer important nuclear physics questions, including the search for the source of proton spin.

    “So far we have doubled the peak and average luminosity—measures that are directly related to the collision rates,” said Wolfram Fischer, Associate Chair for Accelerators of Brookhaven’s Collider-Accelerator Department and lead author on a paper describing the success just published in Physical Review Letters. And, he says, there’s potential for further gains by increasing the number protons from the injectors even more.

    Colliding polarized protons

    RHIC is the world’s only polarized proton collider, capable of sending beams of protons around its 2.4-mile-circumference racetrack with their internal magnetic axes (also known as spins) aligned in a chosen direction. Colliding beams of such “spin polarized” protons and manipulating the spin directions gives scientists a way to explore how their internal building blocks, quarks and gluons, contribute to this intrinsic particle property.

    Data at RHIC have revealed that both quarks and gluons make substantial contributions to spin, but still not enough to explain the total spin value. More data will help resolve this spin mystery by reducing uncertainties and allowing nuclear physicists to tease out other unaccounted for contributions.

    But getting more protons to collide is an ongoing challenge because, as one beam of these positively charged particles passes through the other, the particles’ like charges make them want to move away from one another.

    “The strongest disturbance a proton experiences when it travels around the RHIC ring is when it flies through the other proton beam,” Fischer said. “The result of the positive charges repelling is that the protons get deflecting kicks every time they fly through the oncoming beam.”

    Opposite charge produces opposite push

    The size of the repulsive kick depends on where the proton flies through the beam, with protons about halfway from dead center to the outside edge of the beam’s cross-section experiencing the largest outward push. Particles closer to the center or the outer edge of the cross-section experience less repulsion.

    Because of the variable shape of this effect—increasing to a peak and then decreasing with distance from the beam’s center—it’s impossible to correct using magnets. “The magnetic field strength in magnets increases steadily from the center out,” Fischer said.

    So instead, the scientists turned to using oppositely charged particles to produce a compensating push in the opposite direction.

    “We’ve implemented electron lensing technology to compensate for these head-on beam-beam effects,” Fischer said.

    Temp 2
    Schematic layout of electron lens components. An electron gun creates a low-energy electron beam that is transported into a superconducting magnet where the magnetic field keeps the electrons from being deflected by the more energetic protons circulating in RHIC. As the protons pass through the negatively charged electron beam, they experience a kick that compensates for the repulsive positive charge of the oncoming proton beam. These kicks nudge the protons toward the center of the beam to maximize proton collision rates. No image credit found

    Essentially, they use an electron gun to introduce a low-energy electron beam into a short stretch of the RHIC accelerator. Within that stretch, the electrons are guided by a magnetic field that keeps them from being deflected by the more energetic protons. As the protons pass through the negatively charged electron beam, they experience a kick in the opposite direction from the repulsive positive charge, which nudges the protons back toward the center of the beam.

    “It’s not a glass lens like you’d find in a camera,” Fischer said, “but we call the technique ‘electron lensing’ because, like a lens that focuses light, the electron beam changes the trajectory of the protons flying through it.”
    Riding the optical wave

    The scientists also take advantage of certain “optical” properties of RHIC’s particle beams to ensure the method’s efficacy.

    “Ideally you would like to produce these compensating pushes right where the collisions happen, within the STAR and PHENIX detectors,” Fischer said. “But then the experiments wouldn’t work anymore.

    BNL Star Detector II
    BNL/STAR detector

    BNL Phenix
    BNL/PHENIX detector

    So we placed the electron lenses, one on each beam, at a certain distance from the detectors—called the optical distance—where they have an effect at the same point in the ‘phase’ of the particle beam that’s inside the detectors.”

    Temp 3
    The electron lensing team (front row, left to right): Xiaofeng Gu, Peter Thieberger, Wolfram Fischer, Zeynep Altinbas, Yun Luo, (back, l to r) Chuyu Liu, Alexander Pikin, Al Marusic, Jon Hock, Mike Costanzo. Additional co-authors on the electron lensing paper not shown: Rob Michnoff, Toby Miller, Vincent Schoefer, and Simon White.

    Like a wave of light or sound that oscillates up and down in amplitude at a given frequency, the particles that travel around RHIC also oscillate a tiny bit. As long as the nuclear physicists know the frequency of the oscillations and give their electron-lensing kicks at the same point in that oscillation that the particles reach within the detector, the effect will compensate for the proton repulsion the particles experience at that distant location.

    So far, the scientists have doubled the proton-proton collision rates at RHIC. They could potentially get even higher gains by increasing the number of protons injected into the machine.

    “The key challenge will be to maintain the high degree of polarization the experiments need to explore the question of proton spin,” Fischer said. But he insists there is clear potential for even higher proton-proton luminosity.

    This work was performed by many people in the Collider-Accelerator Department and the Superconducting Magnet Division at Brookhaven National Laboratory, and was funded by the DOE Office of Science (NP). The scientists also acknowledge the U.S. LHC Accelerator Research Program (LARP) for support of beam-beam simulations, and researchers around the world especially the electron lens experts at Fermi National Accelerator Laboratory.

    See the full article here .

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    One of ten national laboratories overseen and primarily funded by the Office of Science of the U.S. Department of Energy (DOE), Brookhaven National Laboratory conducts research in the physical, biomedical, and environmental sciences, as well as in energy technologies and national security. Brookhaven Lab also builds and operates major scientific facilities available to university, industry and government researchers. The Laboratory’s almost 3,000 scientists, engineers, and support staff are joined each year by more than 5,000 visiting researchers from around the world.Brookhaven is operated and managed for DOE’s Office of Science by Brookhaven Science Associates, a limited-liability company founded by Stony Brook University, the largest academic user of Laboratory facilities, and Battelle, a nonprofit, applied science and technology organization.
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