The Zero-Body Problem

Before I depart from quantum field theory, let me point out a rather amusing consequence of being able to create almost anything you like out of nothing, provided you only do it for a very short time: As you may have heard, no one has ever found a completely satisfactory general solution for the three-body problem in classical mechanics - the detailed behaviour of 3 particles all mutually interacting; however, the two-body problem (2 particles orbiting or scattering off one another) was "solved." Relativistic quantum field theory makes the 2-body problem into a many-body problem by virtue of all those virtual quanta being exchanged. Worse yet, the one-body problem (a single particle hanging around lonely in empty space) is similarly complicated by its tendancy to emit and reabsorb a "cloud" of virtual quanta - not a trivial matter, since most "bare" particles are thought to acquire many of their "dressed" properties (such as mass) by virtue of such "renormalization."

Worst of all, the zero-body problem (the vacuum) is now poorly understood, since there is truly no such thing as "empty space" - it is constantly filled with virtual electron-positron pairs (for example) popping into and out of existence, and these short-lived virtual quanta have the capacity to interact with each other and external particles! For example, there is a measurable effect on the H atom energy levels due to "vacuum polarization," in which the virtual pairs actually notice the presence of passing "real" electrons and interact with them before disappearing again.

Simple, eh?