The story takes place in 2048, 51 years after scientists at Lawrence Livermore National Laboratory develop "the ultimate weapon", a force field generating device they term a Bobbler. The bureaucracy running the Laboratory use it to enforce an end to conventional warfare (triggering a brief war in the process), calling themselves the Peace Authority. The Bobbler creates a perfectly spherical, impenetrable, and persistent shield around or through anything, and is used to contain nuclear weapons, people, and occasionally entire cities or governments, separating them from the rest of the world (and presumably killing everyone inside by eventual suffocation and lack of sunlight).
In an effort to retain their monopoly on this weapon, they make technological progress illegal, and their power and fear of rebellion corrupts them. In this world, governments are weak, where they are permitted at all; the Peace Authority is the true bearer of power and becomes a worldwide government. A group of rebels, the Tinkers, develop technology clandestinely far beyond what the Authority has (while limited to riding horseback and other Authority-mandated anachronisms), but still has no defense against the bobble. One of the original inventors of the bobble is part of the resistance, and he develops a more advanced version of the bobbler which does not require the huge electrical power sources available only to the Peace Authority.
It is discovered by the Tinkers (and much later by the Peace Authority) that the bobbles are actually not force fields, but stasis fields; within which time has stopped. So not only are the contents perfectly preserved, but they open spontaneously after a certain time period. The Tinkers use their knowledge and the Peacers' ignorance of this effect to their advantage (bobbling themselves for short time periods, for instance), and with the help of a young thief (and mathematical genius), they lead a rebellion to try to bobble the power generators of the Peace Authority and thus neutralize its primary weapon.