A New Theory to Explain the Higgs Mass

Jun8

THREE PHYSICISTS WHO have been collaborating in the San Francisco Bay Area over the past year have devised a new solution to a mystery that has beleaguered their field for more than 30 years. This profound puzzle, which has driven experiments at increasingly powerful particle colliders and given rise to the controversial multiverse hypothesis, amounts to something a bright fourth-grader might ask: How can a magnet lift a paperclip against the gravitational pull of the entire planet?

Despite its sway over the motion of stars and galaxies, the force of gravity is hundreds of millions of trillions of trillions of times weaker than magnetism and the other microscopic forces of nature. This disparity shows up in physics equations as a similarly absurd difference between the mass of the Higgs boson, a particle discovered in 2012 that controls the masses and forces associated with the other known particles, and the expected mass range of as-yet-undiscovered gravitational states of matter.

In the absence of evidence from Europe’s Large Hadron Collider (LHC) supporting any of the theories previously proposed to explain this preposterous mass hierarchy—including the seductively elegant “supersymmetry”—many physicists have come to doubt the very logic of nature’s laws. Increasingly, they worry that our universe might just be a random, rather bizarre permutation among uncountable other possible universes—an effective dead end in the quest for acoherent theory of nature.

This month, the LHC launched its eagerly anticipated second run at nearly double its previous operating energy, continuing its pursuit of new particles or phenomena that would solve the hierarchy problem. But the very real possibility that no new particles lie around the corner has left theoretical physicists facing their “nightmare scenario.” It has also gotten them thinking.

“It is in moments of crisis that new ideas develop,” saidGian Giudice, a theoretical particle physicist at the CERN laboratory near Geneva, which houses the LHC.

The new proposal offers a possible way forward. The trio is “super excited,” said David Kaplan, 46, a theoretical particle physicist from Johns Hopkins University in Baltimore, Md., who developed the model during a West Coast sabbatical with Peter Graham, 35, of Stanford University and Surjeet Rajendran, 32, of the University of California, Berkeley.

Their solution traces the hierarchy between gravity and the other fundamental forces back to the explosive birth of the cosmos, when, their model suggests, two variables that were evolving in tandem suddenly deadlocked. At that instant, a hypothetical particle called the “axion” locked the Higgs boson into its present-day mass, far below the scale of gravity. The axion has appeared in theoretical equations since 1977 and is deemed likely to exist. Yet no one, until now, noticed that axions could be what the trio calls “relaxions,” solving the hierarchy problem by “relaxing” the value of the Higgs mass.

“It’s a very, very clever idea,” said Raman Sundrum, a theoretical particle physicist at the University of Maryland in College Park who was not involved in developing it. “Possibly some version of that is the way the world works.”

In the weeks since the trio’s paper appeared online, it has opened up “a new playground” populated with researchers eager to revise its weaknesses and take its basic premise in different directions, said Nathaniel Craig, a theoretical physicist at the University of California, Santa Barbara.

“This just seems like a pretty simple possibility,” Rajendran said. “We’re not standing on our heads to do something crazy here. It just wants to work.”

However, as several experts noted, in its current form the idea has shortcomings that will need to be carefully considered. And even if it survives this scrutiny, it could take more than a decade to test experimentally. For the time being, experts said, the relaxion is shaking up longheld views and encouraging some physicists to see the hierarchy problem in a new light. The lesson, saidMichael Dine, a physicist at the University of California, Santa Cruz, and a veteran of the hierarchy problem, is “not to just give up and assume that we won’t be able to figure it out.”

An Unnatural Balance

For all the revelry surrounding the 2012 discovery of the Higgs boson, which completed the “Standard Model” of particle physics and earned Peter Higgs and François Englert the 2013 Nobel Prize in physics, it came as little surprise; the particle’s existence and measured mass of 125 giga-electron volts (GeV) agreed with years of indirect evidence. It’s what wasn’t found at the LHC that left experts baffled. Nothing showed up that could reconcile the Higgs mass with the predicted mass scale associated with gravity, which lies beyond experimental reach at 10,000,000,000,000,000,000 GeV.

The mass-energy scale associated with gravity (right) lies 17 orders of magnitude beyond the scale of the known particles (left), where 1 GeV = 1,000 MeV. The tendency of particle masses to equalize in calculations makes this a puzzling hierarchy. NELSON HSU/QUANTA MAGAZINE

“The issue is that in quantum mechanics, everything influences everything else,” Giudice explained. The super-heavy gravitational states should mingle quantum mechanically with the Higgs boson, contributing huge factors to the value of its mass. Yet somehow, the Higgs boson ends up lightweight. It’s as if all the gargantuan factors affecting its mass—some positive, others negative, but all dozens of digits long—have magically canceled out, leaving an extraordinarily tiny value behind. The improbably fine-tuned cancellation of these factors seems “suspicious,” Giudice said. “You think, well, there must be something else behind it.”

Experts often compare the finely tuned Higgs mass to a pencil standing on its lead tip, nudged this way and that by powerful forces like air currents and table vibrations that have somehow struck a perfect balance. “It is not a state of impossibility; it is a state of extremely small likelihood,” said Savas Dimopoulos of Stanford. If you came across such a pencil, he said, “you would first move your hand over the pencil to see if there was any string holding it from the ceiling. [Next] you would look at the tip to see if there is chewing gum.”

Physicists have similarly sought a natural explanation for the hierarchy problem since the 1970s, confident that the search would lead them toward a more complete theory of nature, perhaps even turning up the particles behind “dark matter,” the invisible substance that permeates galaxies. “Naturalness has really been the leitmotif of that research,” Giudice said.

Since the 1980s, the most popular proposal has been supersymmetry. It solves the hierarchy problem by postulating a yet-to-be-discovered twin for each elementary particle: for the electron, a hypothetical “selectron,” for each quark, a “squark,” and so on. Twins contribute opposite terms to the mass of the Higgs boson, rendering it immune to the effects of super-heavy gravity particles (since they are nullified by the effects of their twins).

But no evidence for supersymmetry or for any competing ideas—such as “technicolor” and “warped extra dimensions”—turned up during the first run of the LHC from 2010 to 2013. When the collider shut down for upgrades in early 2013 without having found a single “sparticle” or any other sign of physics beyond the Standard Model, many experts felt they could no longer avoid contemplating a stark alternative. What if the Higgs mass, and by implication the laws of nature, are unnatural? Calculations show that if the mass of the Higgs boson were just a few times heavier and everything else stayed the same, protons could no longer assemble into atoms, and there would be no complex structures—no stars or living beings. So, what if our universe really is as accidentally fine-tuned as a pencil balanced on its tip, singled out as our cosmic address from an inconceivably vast array of bubble universes inside an eternally frothing “multiverse” sea simply because life requires such an outrageous accident to exist?

This multiverse hypothesis, which has loomed over discussions of the hierarchy problem since the late 1990s, is seen as a bleak prospect by most physicists. “I just don’t know what to do with it,” Craig said. “We don’t know what the rules are.” Other bubbles of the multiverse, if they exist, lie beyond the boundaries of light communication, forever limiting theories about the multiverse to what we can observe from within our lonely bubble. With no way to tell where our data point lies on the vast spectrum of possibilities in a multiverse, it becomes difficult or impossible to construct multiverse-based arguments about why our universe is the way it is. “I don’t know at what point we would ever be convinced,” Dine said. “How would you settle it? How would you know?”

The Higgs and the Relaxion

Kaplan visited the Bay Area last summer to collaborate with Graham and Rajendran, whom he knew because all three had worked at various times under Dimopoulos, who was one of the key developers of supersymmetry. Over the past year the trio split their time between Berkeley and Stanford—and the various coffee shops, lunch spots and ice cream parlors bordering both campuses—exchanging “embryonic bits of the idea,” Graham said, and gradually developing a new origin story for the laws of particle physics.

Inspired by a 1984 attempt by Larry Abbott to address a different naturalness problem in physics, they sought to recast the Higgs mass as an evolving parameter, one that could dynamically “relax” to its tiny value during the birth of the cosmos rather than starting out as a fixed, seemingly improbable constant. “Though it took six months of dead ends and really stupid models and very baroque, complicated things, we ended up landing on this very simple picture,” Kaplan said.

In their model, the Higgs mass depends on the numerical value of a hypothetical field that permeates space and time: an axion field. To picture it, “we think of the totality of space as being this 3-D mattress,” Dimopoulos said. The value at each point in the field corresponds to how compressed the mattress springs are there. It has long been recognized that the existence of this mattress—and its vibrations in the form of axions—could solve two deep mysteries: First, the axion field would explain why most interactions between protons and neutrons run both forward and backward, solving what’s known as the “strong CP” problem. And axions could make up dark matter. Solving the hierarchy problem would be a third impressive achievement.

The story of the new model begins when the cosmos was an energy-infused dot. The axion mattress was extremely compressed, which made the Higgs mass enormous. As the universe expanded, the springs relaxed, as if their energy were spreading through the springs of the newly created space. As the energy dissipated, so did the Higgs mass. When the mass fell to its present value, it caused a related variable to plunge past zero, switching on the Higgs field, a molasseslike entity that gives mass to the particles that move through it, such as electrons and quarks. Massive quarks in turn interacted with the axion field, creating ridges in the metaphoric hill that its energy had been rolling down. The axion field got stuck. And so did the Higgs mass.

In what Sundrum called a radical break from past models, the new one shows how the modern-day mass hierarchy might have been sculpted by the birth of the cosmos. “The fact that they’ve put equations to this in a realistic sense is really remarkable,” he said.

Dimopoulos remarked on the striking minimalism of the model, which employs mostly pre-established ideas. “People like myself who have invested quite a bit on these other approaches to the hierarchy problem were very happily surprised that you don’t have to look very far,” he said. “In the backyard of the Standard Model, the solution was there. It took very clever young people to realize that.

“This elevates the stock price of the axion,” he added. Recently, the Axion Dark Matter eXperiment at the University of Washington in Seattle began looking for the rare conversions of dark matter axions into light inside strong magnetic fields. Now, Dimopoulos said, “We should look even harder to find it.”

However, like many experts, Nima Arkani-Hamed of the Institute for Advanced Study in Princeton, N.J., noted that it’s early days for this proposal. While “it’s definitely clever,” he said, its current implementation is far-fetched. For example, in order for the axion field to have gotten stuck on the ridges created by the quarks rather than rolling past them, cosmic inflation must have progressed much more slowly than most cosmologists have assumed. “You add 10 billion years of inflation,” he said. “You have to wonder why all of cosmology arranges itself just to make this happen.”

And even if the axion is discovered, that alone wouldn’t prove it is the “relaxion”—that it relaxes the value of the Higgs mass. As Kaplan’s stay in the Bay Area winds down, he, Graham and Rajendran are beginning to develop ideas for how to test that aspect of their model. It might eventually be possible to oscillate an axion field, for example, to see whether this affects the masses of nearby elementary particles, by way of the Higgs mass. “You would see the electron mass wiggling,” Graham said.

These tests of the proposal will not happen for many years. (The model doesn’t predict any new phenomena that the LHC would detect.) And realistically, several experts said, it faces long odds. So many clever proposals have failed over the years that many physicists are reflexively skeptical. Still, the intriguing new model is delivering a timely dose of optimism.

“We thought we had thought of everything and there was nothing new under the sun,” Sundrum said. “What this shows is that humans are pretty smart and there’s still room for new breakthroughs.”

Editor’s Note: David Kaplan hosts Quanta Magazine’sIn Theory video series.

Original story reprinted with permission from Quanta Magazine, an editorially independent publication of theSimons Foundation whose mission is to enhance public understanding of science by covering research developments and trends in mathematics and the physical and life sciences.

Source: http://www.wired.com/2015/06/new-theory-explain-higgs-mass/

The female mathematician who changed the course of physics—but couldn’t get a job

May27

(Emmy) Noether’s Theorem may be the most important theoretical result in modern physics.

By 1915, any list of the world’s greatest living mathematicians included the name David Hilbert. And though Hilbert previously devoted his career to logic and pure mathematics, he, like many other critical thinkers at the time, eventually became obsessed with a bit of theoretical physics.

With World War I raging on throughout Europe, Hilbert could be found sitting in his office at the great university at Göttingen trying and trying again to understand one idea—Einstein’s new theory of gravity.

Göttingen served as the center of mathematics for the Western world by this point, and Hilbert stood as one of its most notorious thinkers. He was a prominent leader for the minority of mathematicians who preferred a symbolic, axiomatic development in contrast to a more concrete style that emphasized the construction of particular solutions. Many of his peers recoiled from these modern methods, one even calling them “theology.” But Hilbert eventually won over most critics through the power and fruitfulness of his research.

For Hilbert, his rigorous approach to mathematics stood out quite a bit from the common practice of scientists, causing him some consternation. “Physics is much too hard for physicists,” hefamously quipped. So wanting to know more, he invited Einstein to Göttingen to lecture about gravity for a week.

Before the year ended, both men would submit papers deriving the complete equations of general relativity. But naturally, the papers differed entirelywhen it came to their methods. When it came to Einstein’s theory, Hilbert and his Göttingen colleagues simply couldn’t wrap their minds around a peculiarity having to do with energy. All other physical theories—including electromagnetism, hydrodynamics, and the classical theory of gravity—obeyed local energy conservation. With Einstein’s theory, one of the many paradoxical consequences of this failure of energy conservation was that an object could speed up as it lost energy by emitting gravity waves, whereas clearly it should slow down.

Unable to make progress, Hilbert turned to the only person he believed might have the specialized knowledge and insight to help. This would-be-savior wasn’t even allowed to be a student at Göttingen once upon a time, but Hilbert had long become a fan of this mathematician’s highly “abstract” approach (which Hilbert considered similar to his own style). He managed to recruit this soon-to-be partner to Göttingen about the same time Einstein showed up.

And that’s when a woman—one Emmy Noether—created what may be the most important single theoretical result in modern physics.

Emmy who?

Emmy (officially Amalie Emmy) Noether, born 1882, did not stand out in any particular way as a child, although she did, on occasion, attract some notice for her astonishing quickness in providing accurate answers to puzzles or problems in logic or mathematics. Her father, Max, was a fairly prominent mathematician, and one of her brothers eventually attained a doctorate in math. In retrospect, perhaps the Noethers may be another historical example of a family with a math gene.

Germany in the early years of the 20th century was not a convenient place for a woman who wanted to pursue mathematics, or for that matter, any academic field outside of a few considered appropriate for the sex. Luckily for Noether, she had a facility with languages and was allowed to become certified as a language teacher. But Noether recognized her passion was in mathematics, and she decided to chase her dream and find a way to study the subject at the university level.

While women were not permitted to be official students at most German universities then, they were able to audit courses with the permission of the professor. Noether started this way, sitting in on classes at the University of Erlangen. But she also spent a semester in 1903−1904 auditing courses at Göttingen, where she first encountered Hilbert. Rules surrounding enrollment eventually relaxed, and Noether later matriculated at Erlangen to earn her doctorate in mathematics (summa cum laude) in 1907.

However, women were still not accepted as teachers in German universities at the time. Emmy took her fresh doctorate and became an unofficial assistant to her ailing and increasingly frail father, a professor at Erlangen. She also vigorously attacked her own research, forging a personal and original path through abstract algebra. Just a year after her doctorate, Noether’s papers and the doctoral research that she was unofficially supervising gained her election to several academic societies, which prompted invitations to speak around Europe. Among those wanting her around, Hilbert reached out to bring Noether to Göttingen in order to tackle Einstein’s theory.

The problem with Einstein’s theory

No one denied it—Einstein’s Theory of General Relativity was undoubtedly beautiful. It was unlike any theory of nature yet imagined by humankind, more surprising and radical even than the special theory of relativity that Einstein had laid out in his revolutionary paper ten years before.

Newton described gravity simply as a force acting over a distance attracting any two masses, whether planets or apples, to each other. The force was proportional to the product of the two masses and inversely proportional to the square of the distance between them. That’s the entire story, and it worked well for over two hundred years.

But there was a mystery embedded in this description of gravity that physicists lived with for those two centuries. This coincidence was impossible to ignore, yet seemingly impossible to explain. The mass that determined the strength of the gravitational force was the same mass that appeared in Newton’s second law of motion, F = ma; gravitational mass was the same as the “inertial mass.” There was no apparent reason this had to be true, it simply was.

Einstein didn’t think this was mere coincidence. He formulated a “principle of equivalence” that can be described in several ways. One way is to insist that the two types of mass are identical because of a fundamental symmetry in nature; that the laws of physics must take the same form whether one is in a gravitational field or in a region of space with no gravity (say, in a spaceship undergoing an equivalent acceleration). Carrying this principle to its logical conclusions eventually led to the equations of general relativity, the theory considered by many (including the great theoretical physicist Lev Landau) to be “probably the most beautiful of all existing physical theories.”

Although Hilbert recognized that general relativity was a tremendous accomplishment, the energy conservation conundrum struck him as unacceptable. To illustrate this idea, let’s draw a circle around a region of space, as in the diagram here.

The circle might contain electric and magnetic fields, water in motion, or something else. If we keep track of the energy flowing out of (and into) the perimeter of the circle (E_f) during a certain interval of time, then that total transfer of energy is equal to the amount that the total energy inside the circle (E_v) has changed. This is local energy conservation. In simple terms, energy is not created or destroyed, just moved around.

Listing image by Flickr user: Eli Brody

Noether’s Theorem

During Noether’s stay at Göttingen, Hilbert contrived a way to allow her to lecture unofficially. He repeatedly attempted to get her hired as a Privatdozent, or an officially recognized lecturer. The science and mathematics faculty was generally in favor of this, but Hilbert could not overcome the resistance of the humanities professors, who simply could not stomach the idea of a female teacher. At one meeting of the faculty senate, frustrated again in his attempts to get Noether a job, he famously remarked, “I do not see that the sex of a candidate is an argument against her admission as Privatdozent. After all, we are a university, not a bathing establishment.”

Social barriers aside, Noether immediately grasped the problem with Einstein’s theory. Over the course of three years, she not only solved it, but in doing so she proved a theorem that simultaneously reached back to the dawn of physics and pushed forward to the physics of today. Noether’s Theorem, as it is now called, lies at the heart of modern physics, unifying everything from the orbits of planets to the theories of elementary particles.

The full statement of Noether’s Theorem involves a good amount of advanced mathematics, far beyond the scope of this article. But it has a clear and intuitive physical meaning: the theorem uncovers a hidden relationship between symmetry and conservation, and that relationship is what came to unify all of physics.

To start, symmetry in a physics sense refers to whether you can change something about an object or a system and have everything look and behave the same. A sphere has a lot of symmetry, because you can change its orientation by rotating it around any axis by any angle, and it makes no difference. A cylinder has symmetry, but not as much as the sphere: it doesn’t change if you rotate it around its axis of symmetry, but if you rotate it around any other axis, it looks different. These are examples of continuous symmetries, because the angle can be as large or small as you like. A perfectly mirror-symmetrical butterfly is an example of a symmetry that is not continuous: you can reflect it around its midsection without changing its appearance, but there is no way to reflect it through different amounts.

A physics experiment gives the same result at different times. When something is immune to change in physics, it’s sometimes called invariant. The really important invariants in physics are transformations that leave the laws of physics themselves unchanged: so now we are talking about, instead of spheres and cylinders, whole systems of equations that describe how nature works. Time is an example. If the equations that describe the universe changed as time passed, we could never make sense of anything. We could do an experiment today and get one result, then try to repeat it in an hour and get something entirely different—even if nothing changed except the time that we made the measurements.At a bare minimum, therefore, we require any theory in physics to be time invariant: we should be able to add a constant to the time variable wherever it appears in the equations and get the same equations back. Spatial invariance is another example. Physics should be the same no matter where in space we are, if nothing else changes. The equations of motion need to be the same in New York or Göttingen.

Spatial invariance in physics

These are also examples of continuous invariants, because we can shift time and space by an arbitrary amount. There are also discontinuous invariants, such as time-reversal, or mirror reflection. These also hold, at least in classical mechanics.

Enlarge / Spatial invariance in physics.

Noether’s Theorem relates continuous invariants to conservation laws. A conservation law is a rule that says that some quantity remains numerically constant as the system evolves in time. Conservation of energy, momentum, and angular momentum from classical physics are famous examples. Once you know a conservation law, you can often use it as a shortcut to solve problems. In the diagrams here, if the ball starts at rest at the top of the ramp and is allowed to roll down a certain distance under gravity, we can calculate its energy of motion (including its rotation) without having to figure out the force acting on it by using the law of conservation of energy.In order to appreciate the astonishing power of the theorem discovered by Noether in 1918, we must fully understand the differences between conservation laws and invariants. Most of the elementary invariants are intuitively obvious, corresponding to our instincts about the structure of space and time. They reflect the fundamental symmetries of nature. (It would be strange if the very laws of physics altered themselves as we moved from place to place.) Conservation laws are not typically as obvious, often needing to be derived or discovered empirically. It may be hard to believe now, but conservation of energy was not discovered for almost 200 years after Newton published his laws of motion.

Noether’s Theorem proves that for every invariant, there is a corresponding conservation law. She also proved the converse, meaning that for every conservation law there must be an invariant behind it. (In this article we refer to “Noether’s Theorem” as physicists usually do and as is common in elementary discussions of the result. In fact, however, Noether proved four related theorems in the same paper: two theorems for invariants with different types of symmetry and their converses.)

The theorem shows that conservation of energy is equivalent to time invariance in classical physics. This hard-won yet essential conservation law is directly implied by, and implies, a fundamental symmetry of nature. It shows that momentum conservation is equivalent to spatial invariance. It establishes the equivalence of other symmetries, more mathematical in flavor, with other conservation laws. For example, the conservation of charge is related to a gauge symmetry, a complex mathematical symmetry in the equations of electrodynamics.

It is the theorem’s power to derive new conservation laws from abstract symmetries that has guided physical theory up to the present day. Noether’s result is an important tool in contemporary areas like particle physics, and it’s likely to remain so. But how did it solve the problem of energy conservation in general relativity?

Refer back to the diagram above, showing energy being carried out of a circular region, leaving a smaller amount of energy behind. In all the known theories of physics, including electromagnetism and Newtonian gravity, this energy could be carried by a body in motion, and the electric or gravitational field inside the circle could be considered part of an unchanging background, perhaps exerting a force on the body. Noether’s work helped shed light on the fact that Einstein’s gravity behaves as no theory devised before, in that the energy of matter moving in a gravitational field can not be considered separately from the energy of the field itself. There is a conservation law, but it involves taking all of matter and gravity in a region of space as a unified whole (the hairy mathematical details are laid out in §102 of this textbook).

In essence, Noether showed that Hilbert was correct—normal local energy conservation did not hold in Einstein’s work. However, she discovered that this was because of the peculiar kind of symmetry in general relativity. In this radically new model of the universe, gravity altered the very geometry of space and time. In a Euclidean world, the ratio of the circumference of a circle to its diameter equals π. But in Einstein’s universe, this ratio depends on where in space you happen to be.

Originally, Hilbert and his colleagues thought they had a problem: either general relativity was faulty or they had made a mistake. Noether showed them a new outcome. The Göttingen team did not make a mistake; energy conservation in general relativity just could not take the form that it had in allprevious physics theories.

This Doodle from March may be familiar to physicists in the know.

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Untouched by it all

Long after she had earned it, Noether finally received the opportunity she wanted. Once the war ended and German politics and social attitudes underwent a rapid liberalization, Professor Noetherlectured under Göttingen’s official auspices. While accounts seem to indicate classroom teaching wasn’t her strength, Noether proved to be a superb leader of small research groups. Her advanced students were devoted to her.

Sadly, this period would come to an end in 1933. The Nazis came to power, and Noether was not only female but Jewish. The Nazis’ purge of Jewish faculty in German universities had a particularly dramatic effect on the mathematical world. One-third of the mathematics professors, and three-fourths of the heads of Göttingen’s mathematics and physics institutes, were Jewish despite less than one percent of the German population identifying that way at the time.

With the help of other illustrious refugees who settled in the United States (such as Einstein), Noether ended up across the Atlantic in 1933. She soon settled into a visiting professor’s role at the venerable women’s college, Bryn Mawr, and had a very happy two years there. In 1935, however, Noether underwent an operation for an ovarian cyst and died of an infection within days at the age of 53.

Einstein, rather concerned that little notice of her death had been taken in the newspapers, wrote an obituary in the form of a letter that was published in The New York Times.

Emmy Noether, who, in spite of the efforts of the great Göttingen mathematician, Hilbert, never reached the academic standing due her in her own country, none the less surrounded herself with a group of students and investigators at Göttingen, who have already become distinguished as teachers and investigators.

But even if the public wasn’t aware of Noether’s greatness and passing, the mathematics community certainly was. Fellow Göttingen mathematics great Hermann Weyl delivered a moving eulogy at Noether’s funeral.

You did not believe in evil, indeed it never occurred to you that it could play a role in the affairs of man. […] in a sea of hate and violence, of fear and desperation and dejection — you went your own way, pondering the challenges of mathematics […] When you were not allowed to use the institute’s lecture halls you gathered your students in your own home. Even those in their brown shirts were welcome […] Many of us believed that an enmity had been unleashed in which there could be no pardon; but you remained untouched by it all.

In retrospect, Noether’s work seemed to unify the most abstract mathematics with the most basic physical intuition, unifying the earliest successful systems of physics with science yet unborn. The circumstances of her life provide a powerful example of the humanizing influence of science and mathematics. It was the exponents of these fields who were eager to welcome her into their fellowship without regard for her sex or ancestry; the men of philosophy, history, politics, and government sought to exclude her for these very reasons.

This year marks the 100th anniversary of the theory of general relativity, but Emmy Noether remains the tale’s best kept secret. Little by little, however, history seems to rediscover her brilliance. A street and school in her home town have been named after her, as well as a crater on the moon. And for her birthday on March 23, Google dedicated its coveted Doodle real estate to one of history’s most under-appreciated minds.

Lee Phillips is a repeat features writer at Ars Technica. On a personal note regarding Noether’s work, he wrote: “I know I am not alone in my wonderment upon encountering the result while studying advanced classical mechanics as an undergraduate. Noether’s Theorem reveals the power of physics to provide a harmonious picture of nature at a more profound level than is possible without it. For me, this sealed the deal, dooming me to graduate school.”

Source: http://arstechnica.com/science/2015/05/the-female-mathematician-who-changed-the-course-of-physics-but-couldnt-get-a-job/

Σταγόνες νερού… αιωρούνται στον αέρα!

Mar14

Εμπνευσμένοι, ίσως, από τον μαγικό κόσμο του Χάρι Πότερ, ερευνητές της NASA και του Πανεπιστημίου του Ιλινόις με επικεφαλής τον φυσικό κ. Chris Benmore κατόρθωσαν να “κρατήσουν” στον αέρα μια σταγόνα νερού! Όχι δεν πρόκειται για κάποιο τρικ, είναι απλά… επιστήμη! Συγκεκριμένα, οι ερευνητές κατασκεύασαν δύο μηχανές παραγωγής κυμάτων, τις οποίες τοποθέτησαν αντικριστά.

Σύμφωνα λοιπόν με την κυματική, τα δύο παραγόμενα κύματα είναι ικανά να δομήσουν ένα σταθερό σύστημα, ή, όπως λέγεται, μια στάσιμη κατάσταση. Έτσι, όταν η σταγόνα τοποθετηθεί στο κατάλληλο σημείο, λόγω της συχνότητας των κυμάτων, περίπου 20 kHz (λίγο πάνω από τη συχνότητα που μπορούμε να ακούσουμε), αυτή μπορεί να αιωρείται σαν να βρισκόταν στο απόλυτο κενό! Τρομερό… Παρακολουθήστε την επίδειξη τής καινοτομίας και νιώστε ότι βρίσκεστε σε έναν πραγματικά μαγικό κόσμο…

perierga.gr - Σταγόνες νερού αιωρούνται στο κενό!

πηγή: http://perierga.gr/2013/03/%CF%83%CF%84%CE%B1%CE%B3%CF%8C%CE%BD%CE%B5%CF%82-%CE%BD%CE%B5%CF%81%CE%BF%CF%8D-%CE%B1%CE%B9%CF%89%CF%81%CE%BF%CF%8D%CE%BD%CF%84%CE%B1%CE%B9-%CF%83%CF%84%CE%BF%CE%BD-%CE%B1%CE%AD%CF%81%CE%B1/

«Αγάπη μου, συρρίκνωσα το πρωτόνιο»…

Jan26

Η πιο ακριβής μέτρηση που έχει γίνει μέχρι σήμερα για την ακτίνα του πρωτονίου, του θεμελιώδους υποατομικού σωματιδίου, από μια διεθνή επιστημονική ομάδα, δείχνει ότι είναι μικρότερο από ό,τι προβλέπει η καθιερωμένη θεωρία της Φυσικής.

Εδώ και δύο χρόνια υπήρχαν ενδείξεις γι’ αυτό και ο νέος υπολογισμός έρχεται να τις επιβεβαιώσει – και να δημιουργήσει νέους πονοκεφάλους στους φυσικούς, που πρέπει να εξηγήσουν γιατί αυτό συμβαίνει (αν όντως συμβαίνει).Οι ερευνητές, που έκαναν τη σχετική δημοσίευση στο περιοδικό «Science», σύμφωνα με το «New Scientist» και το «Nature», υπολόγισαν την ακτίνα του πρωτονίου σε 0,84087 femtometres (δισεκατομμυριοστά του δισεκατομμυριοστού του μέτρου). Η νέα μέτρηση, που έγινε στο ελβετικό Ινστιτούτο Πάουλ Σέρερ, επιβεβαιώνει ότι η ακτίνα του πρωτονίου είναι περίπου 4% (ή 0,03 femtometres) μικρότερη από την έως τώρα αποδεκτή ακτίνα των 0,8768 femtometres (ένα femtometre ισούται με 0,000000000001 χιλιοστά ή ένα τρισεκατομμυριοστό του χιλιοστού ή ένα δισεκατομμυριοστό του δισεκατομμυριοστού του μέτρου).

Η μέτρηση αφορά το άτομο του υδρογόνου, το οποίο περιέχει ένα θετικά φορτισμένο πρωτόνιο και ένα αρνητικά φορτισμένο ηλεκτρόνιο. Το υδρογόνο είναι το πιο κοινό στοιχείο στο σύμπαν και η νέα εκτίμηση για το πρωτόνιό του έχει μπερδέψει τους επιστήμονες, καθώς άλλες μετρήσεις, με διαφορετικές τεχνικές, συνεχίζουν να δίνουν το παλιό αποτέλεσμα, που ισχύει μέχρι σήμερα.

Τα προβλήματα ξεκίνησαν το 2010, όταν για πρώτη φορά η ίδια ερευνητική ομάδα, με άρθρο της στο «Nature», ισχυρίστηκε ότι το πρωτόνιο είναι κατά 4% μικρότερο. H νέα μέτρηση επιβεβαιώνει αυτή την απόκλιση από τη γενικώς παραδεκτή ακτίνα του σωματιδίου. Φυσικοί σε διάφορα σημεία του κόσμου προσπαθούν να καταλάβουν τι ακριβώς συμβαίνει, αλλά προς το παρόν επικρατεί σύγχυση.

Μερικοί υποστηρίζουν ότι ίσως είναι λανθασμένη η κυρίαρχη θεωρία της κβαντικής ηλεκτροδυναμικής (πράγμα όχι πολύ πιθανό), ορισμένοι ότι ίσως ανοίγει ένα «παράθυρο» σε μια νέα «εξωτική» φυσική, αλλά άλλοι, πιο επιφυλακτικοί, ψάχνουν να βρουν που ακριβώς βρίσκεται το λάθος.

πηγή: http://newpost.gr/post/186235/agapi-moy-syrriknosa-to-protonio/

Ρομπότ – κολυμβητής ταξίδεψε τον Ειρηνικό συλλέγοντας στοιχεία

Jan8

Διένυσε 16.668 χιλιόμετρα -σχεδόν 9.000 ναυτικά μίλια- από τη μια άκρη του Ειρηνικού στην άλλη. Χρειάστηκε κάτι περισσότερο από ένα έτος για να ολοκληρώσει το ταξίδι του. Το ρομπότ – κολυμβητής της Liquid Robotics συνέλεξε πολύτιμα στοιχεία για τη θερμοκρασία, την αλμυρότητα και το οικοσύστημα του Ειρηνικού ωκεανού.

Το μοντέλο PacX Wave Glider με την ονομασία Πάπα Μάου -από τον θαλασσοπόρο Πίους «Μάου» Πιαϊλούνγκ από την Μικρονησία- «ξεπέρασε θυελλώδεις καταιγίδες, απέκρουσε επιθέσεις καρχαριών, παρέμεινε περισσότερες από 365 ημέρες στη θάλασσα, περιπλανήθηκε γύρω από το Μεγάλο Κοραλλιογενή Ύφαλο και τελικώς έφτασε στον προορισμό του, στο Κουίνσλαντ της Αυστραλίας» ανακοίνωσε η κατασκευάστρια εταιρεία.

Εκτός από το Πάπα Μάου, η Liquid Robotics διαθέτει ακόμη τρία ρομπότ – κολυμβητές. Το ένα αναμένεται να φτάσει στην Αυστραλία στις αρχές του 2013, το δεύτερο κατευθύνεται στην Ιαπωνία ενώ το τρίτο αντιμετώπισε μηχανικό πρόβλημα και σταμάτησε στη Χαβάη για επισκευή.

Πηγή: http://www.ert.gr/erevna-nea/item/27960-Rompot-%E2%80%93-kolymbhths-taxidepse-ton-Eirhniko-syllegontas-stoicheia

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