Forces and Interactions

In the macroscopic world two forces are part of our daily life: the electromagnetic and gravitational forces. The reason that these are the only forces that we know by direct experience is because these are long range forces, where long means long compared to the size of a nucleus. Other forces have much shorter ranges. For example, the forces that hold protons and nucleons together in the nucleus are forces with a small range, in practice about 13 10- cm. These are basically the same forces that bind the quarks in a proton or a neutron. The weak forces, manifesting themselves in neutron decay, now also observed in many other reactions, notably in neutrino experiments, have a very small range. At low energies (below 20 GeV) they are quite weak, hence the name weak interactions. At higher energies they are about as strong as the electromagnetic interactions.

The concept of a force has grown, historically, from the study of electromagnetic and gravitational interactions. That was a long process, and it evolved from the idea of objects exerting force upon each other into the concept of a field. The latter, due to Faraday, was a major change. The field has an independent existence. It contains energy. To create a field (for example a magnetic field by sending a current through a wire) requires energy. In Newton’s time no field was associated with gravitation, no one thought of there existing something in the space between earth and sun. But with electromagnetism it became very difficult not to introduce the concept, given the energy contained in the field. This then led to the idea of an electromagnetic field that could exist and propagate all by itself, as a wave. That in turn led to the idea that light was such a propagating electromagnetic field. It is Maxwell who took that step.

Quantum mechanics made this process even more explicit. Electromagnetic waves consist of photons. So the field idea was replaced by particles. For light that is not that hard to imagine, but what about an electric field around a charged object, for example the electric field around the proton in a hydrogen atom? Is this field also to be seen as a collection of photons?

Indeed, even static fields are seen as collections of photons, although these photons are subtly different from the photons of light. One imagines that the charged source, the proton, continuously emits photons that then move out and later return. This is a very quantum mechanical situation; in the conventional view a photon moving out would be unstoppable and normally not return. In quantum mechanics strange processes like this can happen for short times, longer as the energy of the associated photon is less. An electron passing by the proton might intercept such a photon, absorbing its momentum and energy and thus changing course. This is how we understand scattering of an electron in the electric field of a proton.

In this view the concept of a force does not make any sense. Instead we have interactions, protons or electrons emitting or absorbing photons. What we thought of as a force has become the exchange of a particle.