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in the 17th century dominates physics at the largest distances of our universe. The electromagnetic force, synthesized triumphantly in the 19th century in the form of Maxwell's equations, determines the behavior of atoms, molecules, and materials. Investigation of the subatomic world has so far revealed two further forces that operate only at the most minute distances: the strong force, responsible for the structure of nuclei, and the weak force, first revealed in nuclear decay. The constituents of matter together with these four forces constitute the underlying structure of contemporary physics, the so-called standard model.

HIDDEN SYMMETRIES AND THE STANDARD MODEL

One of the deep ideas embodied in the standard model is the notion that symmetries may be hidden—what we observe in nature may not directly reflect the underlying symmetries of the laws of physics. The spherically symmetric laws of electricity and magnetism, which determine most of the phenomena of our everyday experience, are equally responsible for the highly irregular snowflake and the round raindrop. In the first case the spherical symmetry of electricity and magnetism is hidden, while in the second it is manifest. Materials that do not exhibit the symmetry, like the ice in the snowflake, are in a different “phase” from materials like liquid water, in which the symmetry is evident. Frequently, changes in the environment with which the material interacts—the air temperature, the pressure, or other factors—determine whether the symmetry is hidden or revealed. Thus by heating the snowflake (hidden symmetry) we obtain the raindrop (manifest symmetry). This change of a substance from a hidden-symmetry phase to another where it is manifest, a phase transition, plays a role in nearly all branches of physics.

The idea of hidden symmetry is central to understanding the pattern of elementary particles and their interactions. One celebrated example, the relationship between radioactive decays and electromagnetic phenomena, was originally introduced as an analogy: Enrico Fermi suggested that the force responsible for certain radioactive decays, now known as the weak interaction, might be described in terms of weak charges and weak currents, just as electromagnetism involves ordinary charges and currents. The analogy was not precise—the analogue of the electromagnetic radiation was absent from Fermi's theory. Although Fermi's idea did partially explain the weak interaction, it was unable to encompass all of the phenomena observed in radioactive decay or those observed in the properties of “hadrons,” bound states of quarks

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