On Degenerate Metrics and Electromagnetism

A theory of degenerate metrics is developed and applied to the problem of unifying gravitation with electromagnetism. The approach is similar to the Kaluza-Klein approach with a fifth dimension, however no ad hoc conditions are needed to explain why the extra dimension is not directly observable under everyday conditions. Maxwell's theory is recovered with differences only at very small length scales, and a new formula is found for the Coulomb potential that is regular everywhere.