It is believed that many other vector fields exist. Perhaps the most important of these are the X-fields, which may convert protons and neutrons into energy. The observed fact that ordinary matter is essentially stable indicates that if these X vector fields exist, the associated particles must be very massive, with masses greater than 1014 or 1015 proton masses. This means that it will probably not be possible to experimentally create and detect them using accelerators for at least a century. They are therefore considered to be outside the domain of particle physics which we have proclaimed to be "well-established". (4) But there is another hypothetical direction of importance to cosmology: the really deep question is, Do other types of fields - non-vector fields - exist? We know for sure that the gravitational field exists. In the old Newtonian version, the gravitational field was characterized by one quantity which depended on the coordinates and time - it seemed to be analogous to the Coulomb electrostatic field. The question of the behavior of the gravitational field in the moving frame under the Lorentz transformation did not arise, since this was two centuries before the birth of Lorentz, Einstein and Poincaré. There was already one hint that the gravitational and electromagnetic fields were different: in gravitation, all masses attract one another, while in electrostatics, positive and negative charges attract one another and like charges repel one another.
We shall make the following statement without proof: we now understand that this one fact means that the gravitational field is not a vector field. It could be either a scalar or a tensor field. General relativity (which is the relativistic theory of gravitation) shows that it is a tensor field. Experiment confirms this brilliantly. A detailed description of what a tensor field is would take us too far from the ultimate goal of this paper. There are many good books at every level on gravitation (see Misner et al. 1973). We shall describe scalar fields (of which gravitation is not an example) later on.
4 This is the end of our discussion of
vector fields. Back.
4 This is the end of our discussion of vector fields. Back.