However, these symmetries lead to an astonishing-and obviously wrong prediction: All of the elementary particles should be massless. To reconcile this puzzle, the symmetries must be "broken," which implies that there must be new forces that have not yet been discovered. In the Standard Model, these new forces are related to a hypothetical particle called the Higgs boson. Interaction of the Higgs boson with other particles generates particle masses but does not provide real understanding of the observed pattern of masses. Also, one might expect such a theory to generate particle masses that are much heavier than observed. The masses of elementary particles are a crucial clue in deciphering the ultimate theory of nature, and much detective work lies ahead.

With all of its successes in giving order to the wealth of data from high-energy particle collisions, the Standard Model brings a whole new set of questions into sharp focus. What determines the particles, symmetries, and mass scales of this theory? Could they have been very different, completely changing the nature of the world in which we live? Physicists are able to describe the physical universe with astonishing simplicity and precision but have very little understanding as to why it is this way. Several theoretical proposals are discussed later that extend the Standard Model to address, particularly, the question of particle masses. There are other issues that even these theories do not begin to address, such as the role of gravity. Superstring theory, which offers the hope of a complete, all-encompassing theory of the origin of particles-together with all of their symmetries and interactions-is discussed at the end of this chapter.

Symmetry arguments have a long and honorable history in physics, but only in recent times have they come to dominate our understanding of fundamental physics. The power and beauty of such arguments became fully apparent only when expressed in mathematical form. The committee hopes, however, to convey the spirit of this subject by discussing some of its central physical concepts.

What precisely do we mean when we say that physical laws display symmetry? A square is symmetric when rotated through 90 degrees around its center. This operation produces an orientation identical to the initial one-we say that a symmetry operation leaves an object invariant. A circle is left unchanged (invariant) by a rotation through any angle. Since it allows more symmetry operations, it possesses a larger symmetry. More generally, an object is said to be symmetrical when there are operations on the object that could have changed its appearance but in fact do not.

Similarly, physical laws also have symmetry. One of the basic principles of physics is that the laws of physics at one location are the same as at another, and at one time, the same as at another. This principle is equivalent to a symmetry: The laws of physics are invariant when we change our viewpoint-either from one location to another or from one time to another.