What Is a Particle Quanta Magazine.Pdf

SE R IES H I D D E N S T R U C T U R E What Is a Particle? By N A T A L I E W O L C H O V E R November 12, 2020 It has been thought of as many things: a pointlike object, an excitation of a eld, a speck of pure math that has cut into reality. But never has physicists’ conception of a particle changed more than it is changing now. 50 Elementary particles are the basic stu of the universe. They are also deeply strange. Illustrations by Ashley Mackenzie for Quanta Magazine iven that everything in the universe reduces to particles, a question presents itself: What are G particles? The easy answer quickly shows itself to be unsatisfying. Namely, electrons, photons, quarks and other “fundamental” particles supposedly lack substructure or physical extent. “We basically think of a particle as a pointlike object,” said Mary Gaillard, a particle theorist at the University of California, Berkeley who predicted the masses of two types of quarks in the 1970s. And yet particles have distinct traits, such as charge and mass. How can a dimensionless point bear weight? “We say they are ‘fundamental,’” said Xiao-Gang Wen, a theoretical physicist at the Massachusetts Institute of Technology. “But that’s just a [way to say] to students, ‘Don’t ask! I don’t know the answer. It’s fundamental; don’t ask anymore.’” With any other object, the object’s properties depend on its physical makeup — ultimately, its constituent particles. But those particles’ properties derive not from constituents of their own but from mathematical patterns. As points of contact between mathematics and reality, particles straddle both worlds with an uncertain footing. When I recently asked a dozen particle physicists what a particle is, they gave remarkably diverse descriptions. They emphasized that their answers don’t conict so much as capture dierent facets of the truth. They also described two major research thrusts in fundamental physics today that are pursuing a more satisfying, all-encompassing picture of particles. “‘What is a particle?’ indeed is a very interesting question,” said Wen. “Nowadays there is progress in this direction. I should not say there’s a unied point of view, but there’s several dierent points of view, and all look interesting.” 1 A Particle Is a ‘Collapsed Wave Function’ The quest to understand nature’s fundamental building blocks began with the ancient Greek philosopher Democritus’s assertion that such things exist. Two millennia later, Isaac Newton and Christiaan Huygens debated whether light is made of particles or waves. The discovery of quantum mechanics some 250 years after that proved both luminaries right: Light comes in individual packets of energy known as photons, which behave as both particles and waves. Wave-particle duality turned out to be a symptom of a deep strangeness. Quantum mechanics revealed to its discoverers in the 1920s that photons and other quantum objects are best described not as particles or waves but by abstract “wave functions” — evolving mathematical functions that indicate a particle’s probability of having various properties. The wave function representing an electron, say, is spatially spread out, so that the electron has possible locations rather than a denite one. But somehow, strangely, when you stick a detector in the scene and measure the electron’s location, its wave function suddenly “collapses” to a point, and the particle clicks at that position in the detector. Samuel Velasco/Quanta Magazine A particle is thus a collapsed wave function. But what in the world does that mean? Why does observation cause a distended mathematical function to collapse and a concrete particle to appear? And what decides the measurement’s outcome? Nearly a century later, physicists have no idea. 2 A Particle Is a ‘Quantum Excitation of a Field’ The picture soon got even stranger. In the 1930s, physicists realized that the wave functions of many individual photons collectively behave like a single wave propagating through conjoined electric and magnetic elds — exactly the classical picture of light discovered in the 19th century by James Clerk Maxwell. These researchers found that they could “quantize” classical eld theory, restricting elds so that they could only oscillate in discrete amounts known as the “quanta” of the elds. In addition to photons — the quanta of light — Paul Dirac and others discovered that the idea could be extrapolated to electrons and everything else: According to quantum eld theory, particles are excitations of quantum elds that ll all of space. In positing the existence of these more fundamental elds, quantum eld theory stripped particles of status, characterizing them as mere bits of energy that set elds sloshing. Yet despite the ontological baggage of omnipresent elds, quantum eld theory became the lingua franca of particle physics because it allows researchers to calculate with extreme precision what happens when particles interact — particle interactions being, at base level, the way the world is put together. Helen Quinn proposed the still-hypothetical “axion eld” in the 1970s. Nicholas Bock/SLAC National Accelerator Laboratory As physicists discovered more of nature’s particles and their associated elds, a parallel perspective developed. The properties of these particles and elds appeared to follow numerical patterns. By extending these patterns, physicists were able to predict the existence of more particles. “Once you encode the patterns you observe into the mathematics, the mathematics is predictive; it tells you more things you might observe,” explained Helen Quinn, an emeritus particle physicist at Stanford University. The patterns also suggested a more abstract and potentially deeper perspective on what particles actually are. A Particle Is an ‘Irreducible Representation of a Group’3 Mark Van Raamsdonk remembers the beginning of the rst class he took on quantum eld theory as a Princeton University graduate student. The professor came in, looked out at the students, and asked, “What is a particle?” “An irreducible representation of the Poincaré group,” a precocious classmate answered. Taking the apparently correct denition to be general knowledge, the professor skipped any explanation and launched into an inscrutable series of lectures. “That entire semester I didn’t learn a single thing from the course,” said Van Raamsdonk, who’s now a respected theoretical physicist at the University of British Columbia. It’s the standard deep answer of people in the know: Particles are “representations” of “symmetry groups,” which are sets of transformations that can be done to objects. Take, for example, an equilateral triangle. Rotating it by 120 or 240 degrees, or reecting it across the line from each corner to the midpoint of the opposite side, or doing nothing, all leave the triangle looking the same as before. These six symmetries form a group. The group can be expressed as a set of mathematical matrices — arrays of numbers that, when multiplied by coordinates of an equilateral triangle, return the same coordinates. Such a set of matrices is a “representation” of the symmetry group. Samuel Velasco/Quanta Magazine Similarly, electrons, photons and other fundamental particles are objects that essentially stay the same when acted on by a certain group. Namely, particles are representations of the Poincaré group: the group of 10 ways of moving around in the space-time continuum. Objects can shift in three spatial directions or shift in time; they can also rotate in three directions or receive a boost in any of those directions. In 1939, the mathematical physicist Eugene Wigner identied particles as the simplest possible objects that can be shifted, rotated and boosted. For an object to transform nicely under these 10 Poincaré transformations, he realized, it must have a certain minimal set of properties, and particles have these properties. One is energy. Deep down, energy is simply the property that stays the same when the object shifts in time. Momentum is the property that stays the same as the object moves through space. A third property is needed to specify how particles change under combinations of spatial rotations and boosts (which, together, are rotations in space-time). This key property is “spin.” At the time of Wigner’s work, physicists already knew particles have spin, a kind of intrinsic angular momentum that determines many aspects of particle behavior, including whether they act like matter (as electrons do) or as a force (like photons). Wigner showed that, deep down, “spin is just a label that particles have because the world has rotations,” said Nima Arkani-Hamed, a particle physicist at the Institute for Advanced Study in Princeton, New Jersey. Dierent representations of the Poincaré group are particles with dierent numbers of spin labels, or degrees of freedom that are aected by rotations. There are, for example, particles with three spin degrees of freedom. These particles rotate in the same way as familiar 3D objects. All matter particles, meanwhile, have two spin degrees of freedom, nicknamed “spin-up” and “spin-down,” which rotate dierently. If you rotate an electron by 360 degrees, its state will be inverted, just as an arrow, when moved around a 2D Möbius strip, comes back around pointing the opposite way. Samuel Velasco/Quanta Magazine Elementary particles with one and ve spin labels also appear in nature. Only a representation of the Poincaré group with four spin labels seems to be missing. The correspondence between elementary particles and representations is so neat that some physicists — like Van Raamsdonk’s professor — equate them. Others see this as a conation. “The representation is not the particle; the representation is a way of describing certain properties of the particle,” said Sheldon Glashow, a Nobel Prize-winning particle theorist and professor emeritus at Harvard University and Boston University.

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