The dynamical interaction of material bodies does not consist in their gravitational attraction alone. Electric and magnetic forces between them have been known for a very long time and have by Faraday and Maxwell been reduced to the notion of the electromagnetic field. In ordinary circumstances electromagnetic forces are, whenever they are observed at all, very much stronger than the gravitational pull, which is exceedingly weak unless at least one of the interacting pieces of matter is very large, of the size of a celestial body. Of late, one has been induced to admit that between the elementary particles (nucleons) which go to build up the nucleus of an atom there is a force (called the nuclear force) which is perceptible only at very small distances, but outweighs there even the strong electric repulsion between some of those particles. The field of this force is usually referred to as the meson field, for reasons on which we will not enter at the moment.

Ever since Finstein discovered his theory of the gravitational field in 1915, there have been unceasing attempts to generalize it so as to account in the same natural way for the electromagnetic field as well. Since the latter is in empty space described by an antisymmetric tensor of the second rank, the idea suggests itself at once that one should take the fundamental tensor gik to be non-symmetric, hoping that its skew part ½(gik − gki) should have something to do with electromagnetism. But this plan meets with a certain difficulty. We had established Einstein's field equations in two steps.