Abstract Assuming a six-dimensional world with a singular metric, a unitary theory of gravitation and electromagnetic field is formulated. Electric charge is interpreted as angular momentum in the fifth and sixth dimensions. Sommerfeld's constant is closely connected with the degree of singularity of the metric tensor. Isobaric spin and its connection with the electric charge as well as the pseudo-scalar character of pions are easily interpretable. The hypothesis of a six-dimensional world enables a systematization of elementary particles. In particular, it is shown that the baryon family fits quite naturally into the six-dimensional framework.