virtual particles

When two electrons repel each other, what actually pushes them apart? In quantum field theory the answer is that they exchange something — a photon passed between them, like two skaters tossing a ball back and forth and recoiling. But this exchanged photon is not an ordinary one you could ever catch; it exists only fleetingly, in the middle of the interaction, and it does not obey the usual rule connecting a particle's energy, momentum, and mass. Physicists call such transient go-betweens virtual particles.

A virtual particle is best understood as a bookkeeping device inside a calculation, not a tiny object you could photograph. In a Feynman diagram, the internal lines that connect the visible incoming and outgoing particles are the virtual ones. They are allowed to be off-shell, meaning their energy and momentum do not satisfy the relation E^2 = (pc)^2 + (mc^2)^2 that real particles must obey, which is permitted because the energy-time uncertainty principle lets a fleeting state borrow energy as long as it is paid back quickly. The shorter the interaction, the larger the energy that can be borrowed. Forces between particles are described as the exchange of such virtual carriers, which also explains why a heavy force carrier gives a short-range force: a heavy virtual particle can only be borrowed for a brief moment, so it cannot reach far.

It is important to be honest about what virtual particles are and are not. They are real and indispensable as terms in the calculation, and the calculations they enable match experiment to extraordinary precision (for example the electron's magnetic moment). But you never detect a virtual particle directly; only real, on-shell particles register in detectors. Calling them particles is a vivid shorthand for mathematical contributions to a quantum amplitude, and it is a mistake to picture them as a swarm of tiny balls literally flitting in and out of existence between two electrons.