continuous field. With this application, one could see that the continuous ripples actually had a discrete character; the ripples communicating the attraction could be viewed as particles zipping back and forth between electrons and protons. In addition to making spectacularly accurate, empirically verified predictions, this “quantum field” theory showed that any field that permeated space would have at least one particle associated with it— a minuscule ripple in the field. In the case of the electric field, the discrete ripples were none other than the already known photons. In the parlance of quantum field theory, physicists say that photons are “force carriers” mediating the interaction of charged particles. At the time, the mathematical mechanism of applying quantum mechanics to a continuous field in order to explain the origin of particles was very inviting: perhaps other forces, such as the attraction of protons and neutrons that binds them together in a nucleus, could be explained through a mediating particle; perhaps all particles are manifestations of ripples in space-pervading fields. However, hopes to explain other forces using quantum field theory ran into a serious technical impediment. One could write down equations for other possible fields, but whenever the rules of quantum mechanics were applied, the particles associated with these fields had zero mass. This result had been fine for the photon, which was
between current-carrying electrons flowing through the material and the protons and neutrons frozen in place inside it. While this theory was a triumph of low-energy physics, it contained an insight that would aid the high-energy community. A few individuals who started examining the theory and mulling over its structure and consequences noticed a peculiar feature. From the theoretical equations it appeared that the quantum particles associated with the electric field took on a very different character inside superconductors. Massless photons that can zip along at the speed of light as they travel through empty space slow down and stop upon entering a superconductor. According to the equations, photons are massless outside of a superconductor, but photons have mass inside of a superconductor. The mechanism by which photons acquire mass involves the interplay of the electric field and another field that arises in a superconductor due to the dynamics of its constituent electrons, protons, and neutrons. With the electric field alone, the photons would be massless, but the additional field inside a superconductor combines with the electric field to give photons mass. The mathematics of how this interplay of two fields works quickly migrated from low-energy theorists to high-energy theorists, and by the early 1960s a number of high-energy theorists were using this interplay to explain how par-
physicists on the low-energy end are hot on the trail of a particle thought to inhabit the interface between a superconductor and a new class of materials called topological insulators.
known to have no mass, but the photon was unique; all other known particles had mass, including the electrons, protons, and neutrons that comprise ordinary matter. By the middle of the 1950s, highenergy quantum field theorists were stuck. It seemed that there was no way to write down equations that predicted particles with mass.
the origin of the origin of mass During the same decade many members of the low-energy community were exploring an apparently unrelated problem. In 1911 scientists discovered that when certain elements, such as aluminum, lead, zinc, or tin, are cooled to temperatures within a degree or so of absolute zero, electric current, which usually flows through these metals with little resistance, can suddenly start flowing with no resistance at all. The mystery of this “superconductivity” remained for a generation, until technological advances allowed new experiments that probed details of what was going on inside these materials. Guided by the results of these experiments, low-energy theorists in the 1950s constructed a microscopic theory of superconductivity that explained how a zero-resistance current could arise from complex interactions
10 frontiers of physics
ticles traveling in the vacuum of empty space could have mass. Perhaps, they posited, there was a new field (later termed the “Higgs field”) that permeates all of space, combining with other fields and giving mass to their quantized ripples. Perhaps the entire universe is analogous to the interior of a superconductor. It took a few years for all the details of the mathematics to be ironed out and incorporated into the Standard Model, and a few decades for experiments to corroborate many of its predictions. One principal prediction that has eluded confirmation stems from the structure of quantum field theory: if a field exists there must be at least one corresponding particle, a ripple in the fabric of the field. For the Higgs field that gives particles mass, the corresponding ripple is the Higgs boson, the particle that appears to have finally emerged at the Large Hadron Collider.
worlds without measure In addition to showing how the study of low-energy phenomena can aid in understanding the nature of matter itself, this history illustrates that particles existing inside a material can be different from particles that exist in the empty space outside a material. In empty space,