Beautiful Losers: Plato's Geometry of Elements

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 This essay is part of the series
 <a href="http://www.pbs.org/wgbh/nova/blogs/physics/2011/12/beautiful-losers/">
 Beautiful Losers
 </a>

 .
 

 Plato believed that he could describe the Universe using five simple shapes. These shapes, called the Platonic solids, did not originate with Plato. In fact, they go back thousands of years before Plato; you can find stone models (perhaps dice?) of each of the Platonic solids in the Ashmolean Museum at Oxford dating to around 2000 BC, as pictured below. But Plato made these solids central to a vision of the physical world that links ideal to real, and microcosm to macrocosm in an original, and truly remarkable, style.
 
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 AN1927.2727-31 Neolithic Carved Sandstone Balls, Copyright Ashmolean Museum, University of Oxford.
 
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 Let me explain, first, what the Platonic solids are. To begin, consider something simpler: regular polygons. Regular polygons, by definition, are two-dimensional shapes bounded by sides of equal length, each making the same angles with its neighbors. Equilateral triangles, squares, regular pentagons, and so on are all regular polygons. Platonic solids are the three-dimensional analog of regular polygons, and prove to be far more interesting. Platonic solids are bounded by regular polygons, all of the same size and shape. One can prove mathematically that there are exactly five Platonic solids. Here they are:
 


 The tetrahedron has four triangular faces, the cube six square faces, the octahedron eight triangular faces, the dodecahedron twelve pentagonal faces, and the icosahedron twenty triangular faces. Plato proposed that four of these solids built the Four Elements: sharp-pointed tetrahedra give the sting of Fire, smooth-sliding octahedra give easily-parted Air, droplety icosahedra give Water, and lumpish, packable cubes give Earth. The dodecahedron, at last, is the shape of the Universe as a whole. Later Aristotle emended Plato’s system, suggesting that dodecahedra provide a fifth essence—the space-filling Ether.
 

 Plato’s ideas lent dignity and grandeur to the study of geometry, and greatly stimulated its development. The thirteen and final book of Euclid’s
 
 Elements
 
 , the grand synthesis of Greek geometry that is the founding text of axiomatic mathematics, culminates with the construction of the five Platonic solids, and a proof that they exhaust the possibilities. Scholars speculate that Euclid planned the
 
 Elements
 
 with that climax in mind from the start.
 

 From a modern scientific perspective, of course, Plato’s mapping from mathematical ideals to physical reality looks hopelessly wrong. The four (or five) ancient “elements” are not simple substances, nor are they usable building blocks for constructing the material world. Today’s rich and successful analysis of matter involves entirely different concepts. And yet…
 

 In its general approach, and its ambition, Plato’s utterly mistaken theory anticipated the spirit of modern theoretical physics. His program of describing the material world by analyzing (“reducing”) it to a few atomic substances, each with simple properties, existing in great numbers of identical copies, coincides with modern understanding.
 

 Deeper still penetrates his insight that
 
 symmetry defines structure
 
 . Plato sensed enormous potential in the fact that asking for perfect symmetry leads one to discover a small number of possible structures. Based on that foundation, and a few clues from experience, the outlandish synthesis that his philosophy suggested should be possible, to realize the World as Ideas, might be achievable. And clues were there to be found: Near-coincidence between the number of perfect solids (five) and the number of suspected elements (four); suggestions of how observed qualities might reflect underlying shapes (e.g., the sting of fire from the sharp points of tetrahedra). One must also admire the boldness of genius in seeing an apparent defect in the theory—five solids for four elements—as an opportunity for crowning creation, either with the Universe as a whole (Plato) or with space itself (Aristotle).
 

 Modern physicists, when seeking equations to describe the unfamiliar laws of the microcosm, must make guesses based on fragmentary information. Optimistically—and lacking constructive alternatives—they have turned, as Plato did, to symmetry as their guide. Symmetry of equations is perhaps a less familiar idea than symmetry of shapes, but there is nothing obscure or mystical about it. We say an equation, like a shape, displays symmetry when it allows
 
 changes that make no change
 
 . So for instance the equation
 


 X = Y
 


 has a nice symmetry to it, because exchanging
 
 X
 
 for
 
 Y
 
 changes it into this:
 


 Y = X
 


 and this transformed equation expresses exactly the same content as the original. On the other hand
 
 X = Y + 2
 
 , say, turns into
 
 Y = X + 2
 
 , which expresses something else entirely. As this baby example demonstrates, symmetric equations can be rare and special, even when the symmetry involves quite simple transformations.
 

 The equations of interest for physics are considerably richer, of course, and the “changes that make no change” we hope they allow are much more extensive and elaborate. But the central idea inspiration remains, as it was for Plato, the hope that symmetry defines a few interesting structures, and that Nature chooses one (or all!) of those most beautiful possibilities.
 

 Plato’s Beautiful Loser was, in hindsight, a product of premature, and immature, ambition. He tried to leap directly from beautiful mathematics, some imaginative numerology, and primitive, cherry-picked observations to a Theory of Everything. In this his ambition was premature. Also, Plato failed to draw out specific consequences from his ideas, or to test them critically. He sketched an inspiring world-model, but was content to “declare victory” without engaging any serious battles. The mature and challenging form of scientific ambition, which aspires to understand specific features of the world in detail and with precision, emerged only centuries later.
 
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Beautiful Losers: Kelvin's Vortex Atoms

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 This essay is part of the series
 <a href="http://www.pbs.org/wgbh/nova/blogs/physics/2011/12/beautiful-losers/">
 Beautiful Losers
 </a>

 .
 

 A tornado is just air in motion, but its ominous funnel gives an impression of autonomous existence. A tornado seems to be an object; its pattern of flux possesses an impressive degree of permanence. The Great Red Spot of Jupiter is a tornado writ large, and it has retained its size and shape for at least three hundred years. The powerful notion of vortices in fluids abstracts the mathematical essence of such objects, and led William Thomson, the 19th century physicist whose work earned him the title Lord Kelvin, to ask: Could atoms themselves be vortices in an ether that pervades space?
 

 Kelvin’s idea was inspired by the work of Hermann Helmholtz, who first realized that the core of a vortex—analogous to the eye of a hurricane—is a line-like filament that can become tangled up with other filaments in a knotted loop that cannot come undone. Helmoltz also demonstrated that vortices exert forces on one another, and those forces take a form reminiscent of the magnetic forces between wires carrying electric currents.
 

 To Thomson, these results seemed wonderfully suggestive. At the time, evidence from chemistry and the theory of gases had persuaded most physicists that matter was indeed composed of atoms. But there was no physical model indicating how a few types of atoms, each existing in very large numbers of identical copies—as required by chemistry—could possibly arise.
 

 In seemingly unrelated work, physicists were discovering that space-filling entities are an essential tool in Nature’s workshop. Today we accept those entities—known as electric and magnetic fields—on their own terms, as fundamental; but Thomson and his contemporaries believed them to be manifestations of an underlying fluid: an updated version of Aristotle’s Aether.
 

 Thomson’s bold ambition, and instinct for unity, led him to a propose a synthesis: The theory of vortex atoms. The Ethereal fluid, being so fundamental, should be capable of supporting stable vortices, he reasoned. Those vortices, according to Helmholtz’ theorems, would fall into distinct species corresponding to different types of knots. Multiple knots might aggregate into a variety of quasi-stable “molecules.” All this remarkably fits the heart’s desire, in a theory of atoms: Naturally stable building-blocks, whose possibilities for combination seem sufficiently rich to do justice to chemistry.
 

 Thomson himself, a restless intellect, moved on to gush other ideas, but his friend and colleague Peter Guthrie Tait, enthralled by the vortex atom theory, set to work. Thus inspired, he did pioneering work on the theory of knots, producing a systematic classification of knots with up to 10 crossings.
 
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 A table of knots. The ‘Unknot’ was thought to represent hydrogen; to its right, the knot thought to represent carbon. By Jkasd (Own work, Public domain), via Wikimedia Commons
 
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 Alas this beautiful and mathematically fruitful synthesis is, as a physical theory of atoms, a Beautiful Loser. Its failure was not so much due to internal contradictions—it was too vague and flexible for that!—but by a certain sterility. Above all, it was put out of business by more successful competitors. Eventually the mechanical Ether was discredited by Einstein’s relativity, and the triumphant Maxwell equations for electric and magnetic fields do not support vortices. The modern, successful quantum theory of atoms is based on entirely different ideas. And yet…
 

 It’s easy to understand the appeal of vortex atoms, not only as fascinating mathematics, but as potential elements for world-building. When we turn from
 
 understanding
 
 the natural world to
 
 designing
 
 micro-worlds on our own, we might come to treasure their virtues. Vortices can have an impressive degree of stability; they can be knotted into topologically distinct forms, which are also quasi-stable; and their interactions are complex and intricate, yet reproducible.
 

 Those attractive features can be embodied in artificial “atoms” specifically designed to be building blocks for quantum engineering. For quantum theory, though it made the vortex theory of natural atoms obsolete, provides us with a variety of far more reliable, and far more perfect, aethers than the old Aetherial fantasies. Classical fluids, whether they are real liquids or speculative substrates, are inherently imperfect. Any motion in them will stir up little waves that carry away energy, and eventually dissipate the flow. Quantum fluids, such as superfluid helium and a variety of superconductors, on the contrary, support flows that, in theory, will persist unchanged forever. And in practice, too—that’s why we call them “super”! The deep point is that in quantum mechanics energy comes packaged in discrete lumps (quanta). If you operate at low temperatures, where there’s very little energy available, it can become impossible to stir up those little waves that bedevil classical fluids at all. In quantum fluids, vortices really are forever.
 

 There is lots of room for creativity in designing and constructing artificial aethers. Many materials become perfect (quantum) fluids at low temperature.
 

 By choosing the right media, we can tailor our fluids to have useful properties. Physicists and engineers have become quite adept at designing useful fluids, such as the liquid crystals that enable computer monitors and LCD displays. In those examples the fluids have internal structure, which can be manipulated electrically to change their appearance. So far most of the effort has gone into classical fluids, but physicists are beginning to awaken to some promising new possibilities offered by quantum fluids. Though the details can be quite different—as I said, there’s lots of room for creativity here—the basic inspiration, to make fluids that we can manipulate externally to make them do something useful, is the same.
 

 Designer quantum fluids can offer us a variety of vortex atoms, and the opportunity to design new chemistries that accomplish something we want done. Perhaps the most intriguing possibility is to embody, in real materials, the so-far theoretical concept of anyons. Anyons are particles that interact in a special, peculiarly quantum-mechanical way. Anyons don’t exert any forces upon one another, but when you wind one anyon around another, you make interesting, predictable changes in the wave function that describes your system. Quantum computers are, in principle, nothing but machines that process wave functions. (Since wave functions can simulate a tape, or more generally a collection of tapes, that encode data, operations on wave functions can be massively parallel operations on data.) On paper, at least, theorists have proposed ways whereby one might orchestrate the motion of anyons to construct a general-purpose quantum computer. The future will tell whether this beautiful idea blossoms into reality, or proves another seductive Beautiful Loser.
 
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Hail and Farewell, Grand Colliders

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 Physicists, to their credit, are notoriously unsentimental and future-oriented. “Today’s sensation is tomorrow’s calibration” describes their
 
 modus operandi
 
 .
 

 Nevertheless! Today America’s ﬂagship collider, the
 <a href="http://www.fnal.gov/pub/tevatron/">
 Tevatron
 </a>
 at Fermilab in Illinois, will cease operation, and Europe’s
 <a href="http://www.pbs.org/wgbh/nova/sciencenow/3410/02-bigdeal.html">
 Large Hadron Collider
 </a>
 (LHC) at CERN, near Geneva, will lead the exploration of the deep microcosmos. That changing of the guard inspires reﬂection, and merits celebration too.
 

 Some historical perspective will highlight the special role of colliders in fundamental physics. The goal of experimental work in fundamental physics, crudely speaking, is to ﬁnd out what the smallest, most basic building-blocks of the material world are, and how they behave (which, if you think about it, effectively
 
 deﬁnes
 
 what they are). In the early days of science, optical microscopes revealed the existence of tiny creatures and the cellular structure of life in general. But light cannot resolve structures much smaller than its wavelength, and the wavelength of ordinary light is tens of thousands of times larger than the size of atoms.
 

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After a Golden Age

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 Are physicists victims of their own success? They have strived to find the fundamental laws of matter, and in recent years they’ve done it. The so-called standard model of physics provides us with a thorough census of the subatomic particles that combine to make everything we see, and its equations define a complete mathematical explanation of how they behave. The golden age, it seems, has come and gone.
 

 Or has it?
 

 A millennium from today, historians will look back at the twentieth century primarily as the age of a rich flowering of science. Within a few decades molecular biology unveiled the body and soul of the genetic code, cosmology reconstructed the history of the universe, and geophysics disclosed a home planet more dynamic than ever previously imagined. Yet the biggest revolution of all, from which all those others drew, was ironically the smallest: the conquest of microphysics.
 
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 Three icons of twentieth century science. Clockwise: The double helix structure of DNA, revealed by analysis of its x-ray diffraction pattern (credit: Richard Wheeler via Wikimedia); anisotropies in the microwave background radiation, providing a picture of the very early universe (credit: WMAP Science Team, NASA); motion of the continents, proved and then mapped by analysis of magnetic field reversals at mid-ocean ridges. In each case, the enabling sensitive instruments and technologies depend upon profound understanding of the properties of matter, based on microphysics (credit: EMAG2)
 
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 History does not come with time-stamps affixed, but two epochal experiments roughly bracket the High Golden Age of microphysics. In 1912, Ernest Rutherford decoded atoms experimentally, revealing that each has a tiny nucleus containing all its positive charge and almost all its mass. That nucleus is surrounded by electrons, which are bound to it by electric forces. Just a year later, Niels Bohr introduced strange new ideas about the laws of motion in the microworld. His breakthrough matured into quantum mechanics.
 

 Quantum mechanics broke the code of the microworld, but it took decades to master its text. Finally, in the “November Revolution” of 1974, two separate experimental groups announced the discovery of a striking set of new particles, the charmonium system. Their discoveries provided a brilliant confirmation of, and a fertile proving ground for, the collection of theoretical ideas we now call the Standard Model. The charm quarks (and their antiquarks) that make the charmonium particles rounded out the theory of the weak interaction, and the forces that bind them were just right for the theory of the strong interaction. Those theories tamed nuclear physics, and together with electromagnetism and gravity they complete the description of matter.
 

 The Standard Model provides, we believe (after very thorough, rigorous, quantitative testing!), a complete mathematical explanation of how subatomic particles combine to make atoms, atoms to make molecules, and molecules to make materials, and how all this stuff interacts with light and radiation. Its equations are comprehensive yet economical, symmetrical but spiced with interesting detail, austere yet strangely beautiful. The Standard Model provides a complete, secure foundation for astrophysics, materials science, chemistry, and physical biology. Good stuff!
 

 The Standard Model marks the ultimate triumph of reductionism. As Isaac Newton put it, we
 
 analyze
 
 matter by finding complete and simple laws governing the behavior of its elementary components, and then use those laws to
 
 synthesize
 
 the properties of macroscopic objects.
 

 Triumph on that scale has a dark side: It’s a tough act to follow. By the late 1980s, articles and books with titles like “The End of Physics” began to appear. At the same time, “Theory of Everything” hyperbole erupted.
 

 Neither reaction, however unseemly, was entirely baseless. The achievements of this golden age did mark the end of a certain special—and especially wonderful—kind of physics. After plumbing the bottom of ordinary matter (that is, physical material that’s reasonably accessible and usefully stable), where do you go? As physicists deciphered the atom, they revolutionized chemistry and enabled microelectronics; as they deciphered the nucleus, they revolutionized not only astrophysics and physical cosmology, but also bomb technology and medicine. There is no realistic prospect that the sort of frontier physics explored at the Large Hadron Collider, as esoteric and expensive as it is marvelous, will yield practical fruit. (This is not to say that the
 
 indirect
 
 value of this work, which serves as “
 <a href="http://www.constitution.org/wj/meow.htm">
 the moral equivalent of war
 </a>
 ” for many talented, enthusiastic, creative young seekers, will not repay the money invested in it. It will, handsomely.) Its application in the natural world is likely to be restricted to the extremely early universe, and (maybe) a few super-extreme astrophysical situations, like Hawking’s black hole explosions.
 

 But lamenting the passing of a golden age, or professing to reanimate it, are exercises in nostalgia. A healthier attitude, and an attitude that is truer to the unselfconscious exploratory spirit of the golden age itself, is to engage with its legacy of unanswered challenges and new opportunities. What a legacy it is, and what opportunities there are!
 

 For the Standard Model, despite its practical success in describing ordinary matter, leaves many loose ends and unanswered questions. One of its ingredients, the Higgs particle, has not yet been observed directly. That embarrassment may soon be remedied, but other flaws run deeper. Its equations remain lopsided in peculiar ways. They beg to be embedded in a larger, still more symmetric theory. There are, in fact, excellent ideas for advancing toward such unification. Those ideas suggest new lines of experimental investigation, notably the search for proton decay and for supersymmetric particles. The other interactions, and indeed quantum mechanics itself, have not yet been organically united with gravity. String theory might help with those problems, but it’s clear that crucial ideas still await discovery.
 

 We’d also like to understand why the laws of microphysics appear so nearly unchanged if we run time backwards. The only known explanation predicts the existence of a remarkable new class of particles called axions. These wraithlike cousins of photons, more elusive even than neutrinos, plausibly provide the astronomical dark matter. And if axions don’t—what does?
 

 These and other unanswered challenges amply refute the notion that physicists are, in any
 
 meaningful
 
 sense, close to having a “Theory of Everything” (or that we’ve reached “The End of Physics”).
 

 Yet the biggest challenges, I think, are of a different kind. The art of using our comprehension of microphysics is an open-ended invitation to creativity. Music-making doesn’t end when you’ve learned how your instrument works—it begins.
 

 Can we engineer quantum computers, and through them fashion truly alien forms of intelligence? Can we tune in to the messages the universe itself broadcasts in gravity waves, in neutrinos, and in axions? Can we understand the human mind, molecule by molecule, and systematically improve it? To ask these questions is to discover, in the ripeness of one golden age, the seeds of new ones.
 
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Ten Lessons from the Standard Model

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 The most recent Nobel Prize in physics,
 <a href="http://www.pbs.org/wgbh/nova/blogs/physics/2013/10/higgs-and-englert-win-physics-nobel-prize/">
 awarded to Francois Englert and Peter Higgs
 </a>
 for the prediction of the Higgs boson, marks the apotheosis of the Standard Model in two ways. First, the Higgs particle is a milestone in itself: It is the last ingredient required to complete the Standard Model. But second, and more profoundly, the discovery
 
 process
 
 bore witness to the extraordinary power of the Standard Model. Higgs particles are rare and fleeting visitors to our world. Even at the Large Hadron Collider (LHC), where the discovery was made, they are produced in less than a billionth of all collisions. When they are produced, they quickly decay, leaving behind just a few extra tracks among hundreds of others from more conventional sources. It is only because physicists can so reliably predict such “backgrounds,” as well as the rate of Higgs particle production and the modes of its decay, that the discovery experiments could be planned and their results interpreted.
 

 After this crowning triumph it seems appropriate to reflect on the big picture. What does the Standard Model teach us? What does it mean?
 

 To answer that, I’ve adopted the List of Ten format pioneered by God and copied by Letterman and the “For Dummies” series. Here follow ten big lessons from the Standard Model organized into four categories: epistemology, natural philosophy, emergent simplicity, and unfinished business.
 
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 1. Reductionism Works
 
 : The premise of reductionism is that you can understand how things work by breaking them down into constituent parts with simple properties and interactions and then building back up. As a strategy for understanding the physical world, it’s been brilliantly successful! Matter as we know it, in all its richness, can be represented as vast numbers of identical copies of a few ingredients whose properties and interactions we can describe quite fully and accurately. It appears that we
 
 have
 
 achieved, following the reductionist program, a foundation in fundamental physical law for all applications of physics to chemistry, biology, materials science, engineering in general, astrophysics, and major aspects of cosmology.
 


 2. The Surface Appearance of the Physical World is Quite Different from its Deep Structure
 
 : In general, quantum theory presents a picture of the world that appears quite different from the everyday world of experience. There is still considerable work to be done, I think, to show convincingly how observed macroscopic “classical” behavior follows from the underlying quantum equations, with their indeterminacy and discreteness, even at the level of mundane low-energy physics. The specifics of the Standard Model make this strangeness even stranger. We find that the familiar, effective building blocks of low-energy physics, i.e. protons, neutrons, electrons, and photons, are themselves complicated objects when expressed in terms of more truly fundamental entities. Protons and neutrons are complex bound states of quarks, antiquarks, and gluons. Quarks, antiquarks, and gluons obey simple mathematical equations, while protons and neutrons don’t—but protons and neutrons are what we get to see. Even “structureless” electrons arise, in the basic equations, from mixtures of massless particles. It is those more basic entities, not the emergent electron, whose properties are ideally simple.
 


 Natural Philosophy
 



 3. Relativity (Poincare Symmetry), Quantum Mechanics, and Local (Gauge) Symmetry Rule
 
 : It might have been the case that the basic recipe for nature would be like the basic recipe for a human being (i.e., the human genome) or the software that runs a complex program like Word—a long list of instructions, containing many logically independent modules and accidental details. That is
 
 not
 
 what we find. Instead, there are three powerful principles that can serve as axioms, allowing us to formulate the Standard Model deductively. Two of these guiding principles, special relativity and quantum mechanics, date from the early twentieth century. The third, gauge symmetry, only came to full fruition in the 1970s, though its roots go back decades further. Gauge symmetry is (even) more abstract and mathematical than relativity and quantum mechanics, and perhaps for that reason it is less well known to the general public. I will not be able to remedy that situation here, though I’ll be attempting it in a forthcoming book (“The Beautiful Question”). Let me just advertise, as an illustration of its power, that gauge symmetry is what allowed
 <a href="http://www.kitp.ucsb.edu/gross">
 David Gross
 </a>
 and me to predict the existence of gluons and their detailed properties prior to their observation.
 

 The Standard Model is best understood not as a list of particles, but as a realization of principles. That nature’s basic operating system can be so understood, in detail, marks a profound revolution in natural philosophy.
 


 4. The Distinction between “Matter” and “Light” is Superficial
 
 : Like light, the building-blocks of matter are essentially massless, and they can be created and destroyed. Conversely, as its wavelength shortens, “light” as we ordinarily sense it is on a continuum with the sorts of gamma rays that leave tracks at the LHC, which are manifestly particles.
 


 5. “Empty Space” is a Substance
 
 : What we perceive to be “empty space” is actually filled with pervasive
 <a href="http://www.pbs.org/wgbh/nova/blogs/physics/2012/06/the-higgs-boson-explained/">
 condensates
 </a>
 and also exhibits spontaneous activity. Both the condensates, and the fluctuating activity (“virtual particles,” vacuum polarization) radically alter the qualitative properties of particles moving through space.
 


 6. Nature Loves Transformations
 
 : Superficially, the Standard Model seems to contain dozens of independent ingredients—for instance, quarks with different colors and flavors and gluons galore. But many of these particles are related to one another by
 <a href="http://www.pbs.org/wgbh/nova/blogs/physics/2013/04/symmetry-how-beautiful-math-makes-elegant-physics/">
 symmetry
 </a>
 and can physically transform into one another. Thus the unwieldy account using dozens of degrees of freedom becomes the story of a much smaller number of underlying ur-substances and their transformations.
 


 Emergent Simplicity
 



 7. The Behavior of Matter at High Energy Simplifies and Reveals Its Deep Structure
 
 : Flows of particles we can observe at accelerators follow patterns we can calculate using fundamental equations directly. The observed flows are found to be organized into narrow jets: If we turn down the resolution and lump observed particles moving in the same direction into units, adding their energy and momenta, then those units obey the equations of quarks and gluons. In that very strong sense, they
 
 are
 
 quarks and gluons.
 

 It is like an impressionist painting where you have to blur the resolution to see the shapes.
 

 Because the fundamental equations themselves are much easier to work with than the complicated “solutions” we find embodied in everyday (low-energy) matter, it is profoundly correct to say that the behavior we see at the Large Hadron Collider is simpler than the behavior we study in an undergraduate chemistry laboratory.
 


 8. The Early Universe is Open to Rational Reconstruction
 
 : At the extremely high energy density of the Big Bang, the equations for matter simplify dramatically, as we just discussed. This allows us to make serious, scientifically grounded models for what happened in the very early Universe and to draw observable conclusions from them. Moreover, by reproducing those extreme conditions on a small scale at accelerators, we can check our equation.
 


 Unfinished Business
 



 9. We’ve Got Vexing Family Problems
 
 : When the muon—a more massive, unstable version of the electron—was discovered in 1934, I.I. Rabi famously asked, “Who ordered that?” Since then, the discovery of the tau lepton (1973) has given the electron a yet heavier, more unstable brother and the up and down quarks have also sprouted triplets. When we expand the Standard Model to describe the properties of these unexpected kin, its elegant core grows an oversized appendix, uncomfortably like the “long list of instructions” we were happy to avoid. This is where the Standard Model, otherwise remarkably beautiful and tight, gets sloppy.
 

 There is one bright spot. An adequate account of it would require a separate post, but to make a long story short, we can fix the worst of our family problems by postulating the existence of a new particle, the
 
 axion
 
 . Axions are predicted to be Higgs-like particles, but much lighter and much more weakly interacting. If they exist at all, they will contribute a large fraction of the astronomical “dark matter.” Difficult but promising experiments to search for axions are in progress.
 


 10. Unification Looks Good, and Suggests Supersymmetry
 
 : The standard model contains three (mathematically) similar but distinct forces and neatly accommodates a fourth—gravity, in the form of general relativity. It also contains, even after we count particles that transform into another by symmetry as the same and ignore the family triplication, five distinct ur-particles. We would like to build a more economical description, without so many independent parts. And in fact we can transcend the standard model, by pushing its ideas further. If the gauge symmetries that lead to the different forces are all part of a larger, better hidden but more encompassing symmetry, then the different forces are not truly independent, but instead are merely different aspects of a single basic force. Remarkably, then, the different ur-particles turn out to be different aspects of a single basic particle, too.
 

 Unification dynamics can work as a quantitative idea and explain the relative strength of the different forces (including gravity). But for this to work in detail, we need to augment the standard model. The most convincing idea in that direction is
 <a href="http://www.pbs.org/wgbh/nova/blogs/physics/2012/07/supersymmetry-looking-in-natures-mirror/">
 supersymmetry
 </a>
 . Supersymmetry, too, deserves a post of its own, and here I will only mention its most immediate, testable consequence—namely that for every particle we currently known there must be a heavier superpartner with different spin (and of course mass) from its conventional mate, but sharing other properties like electric and strong color charges. Hopes are high that the next round of LHC experiments, at higher energy, will uncover some of the new particles supersymmetry requires.
 


 Bonus Item, for our baker’s list of 10:
 


 The standard model, as we currently understand it, does not account for the astronomical dark matter. On the other hand, that dark matter appears to be composed of some kind of relic gas of particles, surviving from the earliest moments of the Big Bang. Axions are a good candidate to be that particle, as are possible stable superpartners.
 


 Go Deeper
 
 

 Editor’s picks for further reading
 


 CERN:
 <a href="http://home.web.cern.ch/about/physics/standard-model">
 The Standard Model
 </a>
 
 Discover the Standard Model in this brief primer from CERN.
 

 Science:
 <a href="http://news.sciencemag.org/physics/2013/11/live-chat-does-dark-matter-consist-weird-particles-called-axions">
 Does Dark Matter Consist of Weird Particles Called Axions?
 </a>
 
 In this video archived from a 2013 live chat, Frank Wilczek and Gianpaolo Carosi, spokesperson for the Axion Dark Matter Experiment team, discuss axions and how physicists hope to detect them.
 
</section>

Nobel Prize-winning physicist Frank Wilczek reflects on what the successes of the standard model of physics teach us.

Maybe Higgs: What the LHC Might or Might Not Have Seen

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 Tuesday’s
 <a href="http://press.web.cern.ch/press/PressReleases/Releases2011/PR25.11E.html">
 big announcement
 </a>
 from CERN was that something important might or might not have been discovered at the Large Hadron Collider (LHC). That something, if it’s anything, could well be the long-awaited Higgs particle, also called the God particle.
 

 “Higgs” is Peter Higgs, a professor at Edinburgh, who made some interesting suggestions along the lines I’ll discuss below in 1964. The name “Higgs particle,” though standard, is not entirely fair, for several reasons: the basic idea has a significant pre-history; what’s original with Higgs has co-claimants; and the modern, mature version of the theory involves many ideas that were not anticipated in 1964. I’ll leave those issues for historians of science and the Swedish Academy to sort out.
 

 God on the other hand deserves full credit, or blame.
 

 Herewith a brief introduction, in question and answer format, for the buzz-curious.
 


 What’s the basic idea?
 


 Suppose that a species of fish evolved to the point that some of them became physicists, and began to ponder how things move. At first the fish-physicists would, by observation and measurement, derive very complicated laws. But eventually a fish-genius would imagine a different, ideal world ruled by much simpler laws of motion–the laws we humans call Newton’s laws. The great new idea would be that motion looks complicated, in the everyday fish-world, because there’s an all-pervasive medium–water!–that complicates how things move.
 

 Modern physics proposes something very similar for our world. We can use much nicer equations if we’re ready to assume that the “space” of our everyday perception is actually a medium whose influence complicates how matter is observed to move.
 

 
 Are there precedents for such an outrageous dodge?
 


 Yes. In fact it’s a time-honored, successful strategy.
 

 For example: In its basic equations, Newtonian mechanics postulates complete symmetry among the three dimensions of space. Yet in everyday experience there’s a big difference between motion in vertical, as opposed to horizontal, directions. The difference is ascribed to a medium: a pervasive gravitational field.
 

 A much more modern example occurs in quantum chromodynamics (QCD), our fundamental theory of the strong force between quarks and gluons. There we discover that the universe is filled with a medium, the sigma (σ) field, that forms a sort of cosmic molasses for protons and neutrons. The σ field slows protons and neutrons down. Allowing a bit of poetic license, we can say that the σ field gives protons and neutrons mass. Many consequences of the σ field have been calculated and successfully observed, so that to modern physicists it is now every bit as real as Earth’s gravity field. But the σ field exists everywhere and everywhen; it is not tied to Earth.
 


 What’s the new idea, then?
 


 In the theory of the weak force, we need to do a similar trick for less familiar particles, the W and Z bosons. We could have beautiful equations for those particles if their masses were zero; but their masses are observed not to be zero. So we postulate the existence of a new all-pervasive field, the so-called Higgs condensate, which slows them down. This proposal, which here I’ve described only loosely and in words, comes embodied in specific equations and leads to many testable predictions. This proposal has been resoundingly successful.
 


 What is the Higgs particle, conceptually?
 


 Trouble is, no known form of matter has the right properties to make the Higgs condensate. In order to build that medium, we need to add to our inventory of world-ingredients. The simplest, “minimal” implementation introduces exactly one new elementary particle: the Higgs particle.
 


 What is the Higgs particle, specifically?
 


 There’s a quotation I love from Heinrich Hertz, about Maxwell’s equations, that’s relevant here.
 
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 To the question: “What is Maxwell’s theory?” I know of no shorter or more definite answer than the following: “Maxwell’s theory is Maxwell’s system of equations.”
 

</blockquote>

 Similarly, Higgs particles are the entities that obey the equations of Higgs particle theory. Those equations prescribe everything about how Higgs particles move, interact with other particles, and decay—with just one, albeit glaring, exception: The equations do not determine the mass of the Higgs particle. The theory can accommodate a wide range of values for that mass.
 


 What is a Higgs particle, operationally?
 


 A Higgs particle is a highly unstable particle, visible only through its decay products. It has zero electric charge, and—unlike all other known elementary particles—no intrinsic rotation, or “spin.” These null properties reflect the fact that many Higgs particles, uniformly distributed through space, build up the Higgs condensate, which we sense as emptiness or pure vacuum. (Although individual Higgs particles are highly unstable, a uniform distribution of them is stabilized through their mutual interactions. Visible Higgs particles are disturbances above that uniform background.)
 

 As mentioned before, theory does not predict what mass a Higgs particle should have. Masses anywhere from 10 Giga-electron Volts (GeV) to 800 GeV might be accommodated, though problems start to emerge near either extreme. (Physicists commonly use GeV as the unit of mass for elementary particles. One GeV is close to, but slightly more than, the mass of one proton.)
 

 Because Higgs particles are unstable, to study them one must produce them. That requires concentrating lots of energy into a very small space to create enormous energy density. The required concentration of energy is achieved at particle colliders. At the LHC, two counter-rotating beams of high energy protons are made to pass through one another, or cross, at a few points. At each crossing some fraction of the protons, which are moving in opposite directions at very close to the speed of light, collide. The collisions produce fireballs that explode into tens or hundreds of stable or near-stable particles including electrons and positrons, pi mesons, photons, protons and antiprotons, and several other possibilities.
 

 Known physical processes account for the vast majority of this debris. Production and decay of Higgs particles, if they exist, will produce some additional debris. To get evidence for the existence of Higgs particles, therefore, one must identify some distinctive patterns in the observed debris that could result from Higgs particle decays but which are difficult to produce with conventional processes.
 

 Putting it another way: If you’re looking for needles in a haystack, you’d better have a really good grip on what hay can look like—and it helps to look for needles that are hard to mistake!
 

 Several patterns play an important role in the analysis, but I’ll discuss just one—a crucial one—to give a flavor of what’s involved. One process of Higgs particle production and decay is depicted in this sketch:
 
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 The sequence of events in the sketch above unfolds reading upwards. Gluons inside the fast-moving protons convert, by quantum fluctuations, into a “virtual” top quark and its antiparticle. The virtual top quark and antiquark swiftly recombine into a Higgs particle. Then the Higgs particle decays by a similar mechanism: quantum fluctuations convert it into a particle-antiparticle pair, which recombine into two photons. At the end of the day, it is those two photons that are observed. (I’m particularly fond of this exotically beautiful quantum process, which I discovered theoretically in 1977.) The point is that more conventional processes, i.e. processes that don’t involve Higgs particles, but which produce two energetic photons are fairly rare. Thus the calculated contribution from Higgs particles, should they exist, can be discerned above the background.
 


 So, does it exist?
 


 Short answer: We still don’t know for sure. There’s been dramatic progress on the question, however.
 

 A very large range of potential mass-values has been ruled out. Only a small window in the range between 115 and 127 GeV remains viable.
 

 On the other hand, an excess of events, above expectations from known processes, has been observed in the two-photon channel mentioned above and (less clearly) in several others. The excesses are compatible with, and could be explained by, the existence of Higgs particles with mass close to 125 GeV.
 

 The observed excess might also be compatible with a statistical fluctuation in the background processes—e.g., an improbable run of normal processes leading to photon pairs, comparable to rolling four consecutive sixes at dice. With more data a true signal will grow more rapidly than any plausible fluctuation, so the ambiguity in interpretation will disappear. If the LHC continues to function brilliantly, as it has so far, we should have a definitive answer within the next few months.
 


 What will it mean, if the hints pan out?
 


 First of all, it will be a dazzling triumph for theoretical physics. Physicists will have used intricate equations and difficult calculations to predict not only the mere existence of the Higgs particle, but also (given its mass) its rate of production in the complex, extreme conditions of ultra high energy proton-proton collisions. Those equations will also have accurately rendered the relative rates at which the Higgs particle decays in different ways. Yet the most challenging task of all may be computing the much larger, competing background “noise” from known processes, in order to successfully contrast the Higgs’ “signal.” Virtually every aspect of our current understanding of fundamental physics comes into play, and gets a stringent workout, in crafting these predictions.
 

 The animating spirit of research in fundamental physics, captured in the maxim “Today’s sensation is tomorrow’s calibration,” will not rest in that triumph, however. A Higgs particle at mass 125 GeV would portend a new level of fundamental understanding and discovery. Let me explain why.
 

 Within our current theories of the fundamental interactions, embodied in the so-called
 <a href="http://www.pbs.org/wgbh/nova/elegant/part-flash.html">
 Standard Model
 </a>
 , the Higgs particle mass might, as previously mentioned, have any value within a wide range. Yet there are good reasons to suspect that despite its many virtues, the Standard Model is incomplete. Notably, its equations postulate four different forces (strong, weak, electromagnetic and gravitational) and six different materials they act on. It would be prettier to have a more coherent, unified theory. And in fact there are beautiful, concrete proposals for unified field theories, within which we have just one force and just one kind of material. But to make the unified theory work quantitatively, in detail, we need to expand the equations of the Standard Model so that they integrate a concept called supersymmetry.
 

 Supersymmetry has many aspects and ramifications, but two are most relevant here. First, supersymmetry (for experts: more specifically, focus point supersymmetry) predicts that the Higgs particle mass should lie in the range 120-130 GeV. Finding Higgs particles with mass in that range would give strong circumstantial evidence both for supersymmetry and for the unification that supersymmetry enables.
 

 Second, supersymmetry predicts the existence of many additional new fundamental particles, besides the Higgs particle, that should be accessible to the LHC. So if supersymmetry is right, the LHC will have many more years of brilliant discovery in front of it.
 


 And if not?
 


 I’ll be heartbroken. Mother Nature will have shown that Her taste is very different from mine. I don’t doubt that it’s superior, but I’ll have to struggle to understand it.
 
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Thanks, Mom! Finding the Quantum of Ubiquitous Resistance

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 CERN’s July 4 declaration of victory in the quest to find the Higgs particle (or something very much like it) is a many-splendored triumph. It confirms, as it completes, the Standard Model of fundamental physics. It hints at the splendid new prospect of supersymmetry while debunking rival speculations. Most fundamentally, it reaffirms our scientific faith that nature works according to precise yet humanly comprehensible laws—and, importantly, rewards our moral commitment to testing that faith rigorously.
 

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 Inside the tunnel of the Large Hadron Collider, particles speed through a 27-kilometer ring of superconducting magnets. Credit: David Parker/Photo Researchers, Inc.
 
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 A few months ago, when the evidence was suggestive but not yet conclusive, I discussed
 <a href="http://www.pbs.org/wgbh/nova/blogs/physics/2012/06/the-higgs-boson-explained/">
 here
 </a>
 the nature of the Higgs particle, and what its discovery would mean for the enterprise of physics. Now I will supplement that discussion, focusing on
 
 what it took
 
 to win the victory.
 

 Physicists had to overcome three challenges to discover the Higgs particle: producing it, detecting it, and proving that they really had produced and detected it.
 

 To put these challenges in context, let me introduce another perspective on what the Higgs particle is: The Higgs particle is
 
 The Quantum of Ubiquitous Resistance
 
 . I’m referring here to a universe-filling medium that offers resistance to the motion of many elementary particles, thus producing what we commonly think of as their mass.
 

 The Standard Model of physics—our best-yet model of the matter and forces that make our universe—requires, for consistency of its equations, that many of its ingredients are particles with zero mass. These particles should travel at the speed of light in empty space, but in reality, some of them—like quarks, leptons, and W and Z bosons—travel more slowly. What is slowing them down?
 

 Our Standard Model comes equipped with a Standard Reconciliation: Space is never empty! Space is filled with a material that resists the motion of those particles. Over the past decades, physicists have deduced many of the properties of the Ubiquitous Resistance by observing its effects on the forms of matter we can see. They even gave it a name: the Higgs field. But none of the known particles had the right properties to build up the Ubiquitous Resistance. So theorists drew up the specifications for a particle that would do the job. They called it the Higgs particle.
 

 But wishing doesn’t make it so. Only experiments can grant (or deny) theorists’ wishes. With that in mind, let us consider the three challenges facing experimental observation of the Higgs particle.
 


 Producing it
 


 Any physical material, hit hard enough, is bound to break. The smallest possible shard reveals the most basic unit of the material: its “quantum.” For the Ubiquitous Resistance, that quantum is the Higgs particle.
 

 To break off a piece of the Ubiquitous Resistance, though, requires producing disturbances of unprecedented intensity, albeit confined to tiny volumes of space for tiny intervals of time. That is what the Large Hadron Collider (LHC) is all about. By accelerating beams of protons to extremely high energy, and bringing them into collision, the LHC creates “Little Bangs” systematically.
 


 Detecting it
 


 Once you’ve produced a Higgs particle, the next challenge is to detect it. This isn’t as easy as it sounds, as the Higgs rapidly decays into other particles. We can look for those secondary particles, but most of them are useless for detection because they are produced more abundantly by other processes. The Higgs’ tiny signal competes with a cacophony of noise. The most likely mode of Higgs decay, into a bottom quarks and its antiparticle, in particular, is diluted by garden-variety strong interaction processes which produce those particles in droves.
 

 So detection requires cunning.
 

 Some decay processes that we might be able to detect are sketched below. Each has its own advantages and limitations, and each adds information, so experimenters have pursued them all. (For more information on the characters you’ll encounter below—W bosons, Z bosons, and the rest of the particle zoo,
 <a href="http://en.wikipedia.org/wiki/Standard_Model">
 this
 </a>
 is a good starting point.)
 

 #1: Photon pairs
 
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 After a Higgs particle is created, quantum fluctuations convert it into a particle-antiparticle pair, which
 <a href="http://www.pbs.org/wgbh/nova/blogs/physics/2012/06/the-higgs-boson-explained/">
 recombines into two photons
 </a>
 .
 

 The observable signal, in this case, is the pair of photons emerging from the decay. From the energy and momentum of the two photons, one can reconstruct the mass of the Higgs particle. This is significant because there are many other ways to make photons in collisions at the LHC that don’t require the production and decay of Higgs particles. The Higgs signal would be swamped, if not for the redeeming feature that randomly produced photons will “add up” to indicate random masses for their hypothetical progenitors, and only by rare accident land on the Higgs particle mass, whatever it happens to be. The signature of the Higgs, then, is an excess of photon pairs in a very narrow mass range. The mass where there’s an excess is fingered as the Higgs particle mass. Since the energy and momentum of photons can be measured accurately, this method gives an excellent measurement of the Higgs particle mass.
 

 The main limitation of this technique, besides the unavoidable background “noise,” is the fact that this decay process is quite rare compared to other possibilities.
 

 #2: W boson+ (Higgs -&gt; bottom-antibottom)
 
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 Here is one of those other possibilities: In this case, the Higgs particle is produced as a byproduct of the creation of a W boson. The W boson itself decays, but in ways that experimentalists are thoroughly familiar with, and can often identify with confidence. The presence of the W boson, itself a relatively rare occurrence, helps this class of event to stand out above the strong interaction background. Thus the most common Higgs decay, into bottom-antibottom pairs, becomes discernable when you demand an accompanying W.
 

 There are two more possibilities:
 

 #3: Higgs -&gt; WW -&gt; lepton + antilepton + neutrino + antineutrino
 
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 #4: H -&gt; ZZ -&gt; 2 leptons + 2 antileptons
 
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 In Processes 3 and 4, the observed particles are leptons (l), which is just another way of saying that they might be either electrons or muons, and their antiparticles; the ghostly neutrinos escape detection. The Higgs boson barely interacts with those light particles, but it can communicate with them indirectly, through fluctuations in the W and Z boson fields (a.k.a. “virtual particles”). Process 4 is special, in that it is the only case where the background is so small that individual events, as opposed to enhanced probabilities, can be ascribed with confidence to Higgs particles.
 

 By measuring the rates of all of these processes, one can determine how powerfully the Higgs communicates with many different things: two gluons, two photons, two Z bosons, two W bosons, and bottom-antibottom pairs. Their different rates are logically independent, of course, but theory connects them.
 


 Proving it
 


 This is the final challenge. Finding the Higgs boson depends on assuming that the Standard Model is reliable, so we can work around the “background noise”. Here years of hard bread-and-butter work at earlier accelerators—especially the Large Electron-Positron Collider (LEP), which previously occupied the same CERN tunnel in which the LHC resides today, and the Tevatron at Fermilab, as well as at the LHC itself—pays off big. Over the years, many thousands of quantitative predictions of the Standard Model have been tested and verified. Its record is impeccable; it has earned our trust.
 

 The next step is to search for data that the Standard Model can’t explain, like excesses of the decay products discussed earlier, and compare them against our predictions for yields from a hypothetical Higgs boson. Insofar as these quantitative predictions match the observations, which they do, one can speak of proof.
 

 Future observations may reveal new effects, or small quantitative discrepancies in the effects already observed. (I’ll be surprised if they don’t!) But the original, simplest sketch of what The Quantum of Ubiquitous Resistance could possibly be resembles reality enough to pass muster, at least as its first draft.
 

 Finally, I’d like to reprise the conclusion of my
 <a href="http://www.pbs.org/wgbh/nova/blogs/physics/2012/06/the-higgs-boson-explained/">
 earlier piece
 </a>
 , in which I considered what might happen if the hints of the Higgs did
 
 not
 
 pan out:
 
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 And if not?
 


 I’ll be heartbroken. Mother Nature will have shown that Her taste is very different from mine. I don’t doubt that it’s superior, but I’ll have to struggle to understand it.
 
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 Thanks, Mom!
 
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Theoretical physicist Frank Wilczek explains what it took to find the Higgs boson. 


Frank Wilczek

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